http://2009.igem.org/wiki/index.php?title=Special:Contributions&feed=atom&limit=500&target=FR&year=&month=2009.igem.org - User contributions [en]2024-03-29T08:14:51ZFrom 2009.igem.orgMediaWiki 1.16.5http://2009.igem.org/Team:TorontoMaRSDiscovery/TeamTeam:TorontoMaRSDiscovery/Team2010-11-02T19:10:51Z<p>FR: /* Farhan Raja */</p>
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<div>[[image:To_igem_wiki_banner.jpg|965px]]<br />
{| style="color:white;background-color:#99CCFF;" height:100px cellpadding="2" cellspacing="0" border="0" width="100%" align="center" class="menu"<br />
!align="center"|[[Team:TorontoMaRSDiscovery|Home]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Team|The Team]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Project|The Project]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Parts|BioBricks]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Modeling|Modelling]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Bioinformatics|Bioinformatics]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Safety|Safety]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Notebook|Notebook]]<br />
|}<br />
<br><br />
<br />
=The Team=<br />
<br />
[[Image:TMDT_Team2.jpg|900px|center|thumb|Left to right: Farhan, James, Graham, John, Yen, Kenny, Meah, Stacy]]<br />
<br />
<br clear="all" /><br />
<br />
=Advisors=<br />
<br />
<table><br />
<tr><br />
<th width=50%></th><br />
<th width=50%></th><br />
</tr><br />
<br />
<tr><br />
<td style="padding: 10px; vertical-align: top"><br />
==Dr. John Parkinson==<br />
[[Image:JohnParkinson.jpg|x200px|left|thumb|Dr. John Parkinson aka The Dragon in the Dragon's Den]]<br />
Graduated from the University of Bath with a bachelor of science in Applied Biology in 1990. After receiving a PhD in Biochemistry from the University of Manchester in 1995, I completed a NATO fellowship at the University of Manitoba. From 1997 to 2000, I was awarded a fellowship at the Edinburgh Centre for Protein Technology, University of Edinburgh and from 2000 to 2003 completed another fellowship at the University of Edinburgh on Nematode genomics. I am currently a scientist at The Hospital for Sick Children Research Institute. The research in our laboratory is aimed at understanding how molecular information can give rise to complex biological behaviour. Using computational methods, we study the organization and dynamics of cellular components within the context of integrated biological systems. Comparative genomics methods are also being applied to provide insights into how these systems may have evolved from the remote origins of life.<br />
</td><br />
<td style="padding: 10px; vertical-align: top"><br />
==Graham Cromar==<br />
[[Image:graham.jpg|x200px|left|thumb|Graham Cromar aka The Wizard of Id]]<br />
I am a 4th year Ph.D. student in the Department of Molecular Structure and Function at the Hospital for Sick Children in Toronto. At various times in the past I have studied cell and molecular biology (B.Sc. Toronto), molecular biology and genetics (M.Sc. Guelph), computer programming and systems analysis (dip. Inst. Computer Studies, Toronto), bioinformatics (cert. Canadian Genetic Disease Network) and, systems and matrix biology (present). I have worked as a lab technician, teaching assistant, computer programmer/systems analyst and IS manager. But, what I would most like to do is what I wrote in my high school yearbook about 20 years ago... Design organisms for export to far away galaxies. Thanks to iGEM I'm 1/4 of the way there...<br />
</td><br />
</tr><br />
<br />
<tr><br />
<td style="padding: 10px; vertical-align: top"><br />
<br />
==Stacy Hung==<br />
[[Image:team_Stacy.jpg|x200px|left|thumb|Stacy Hung aka Mini Wheats]]<br />
With a B.Sc. Honours Biology and Bioinformatics from the University of Waterloo, Stacy is currently a 3rd year Ph.D. student at the University of Toronto. Her main focus is to identify novel enzyme drug targets against malaria by studying the metabolic networks of these parasites. She is inspired by anything that is new, exciting, and can have a long-term impact for making the world a better place -- besides her research, iGEM is certainly one of these things!<br />
</td><br />
<td style="padding: 10px; vertical-align: top"><br />
<br />
==Daniel Wong==<br />
[[Image:tmdt_dan.png|x200px|left|thumb|Daniel Wong aka The Architect]]<br />
Daniel Wong received his BASc in Engineering Science biomedical option at the University of Toronto. He is currently with the Institute of Biomaterials and Biomedical Engineering, working toward his PhD. He works in the Cochlear Implant Laboratory at the Hospital for Sick Children, developing neuroimaging algorithms for the analysis of multichannel EEG data. As design team lead for this year's iGEM team, he guided the design team in developing the protocols for creating the team's biobrick parts. His academic interests include neuroimaging and systems modelling. To relax, he enjoys a good round of golf or social salsa dancing.<br />
</td><br />
</tr><br />
<br />
<tr><br />
<td style="padding: 10px; vertical-align: top"><br />
==Natalie Yeung==<br />
[[Image:tmdt_natalie.png|x200px|left|thumb|Natalie Yeung aka The Strategist]]<br />
I'm a graduate student at the University of Toronto's iSchool (sometimes known as the Faculty of Information). Having been involved in iGEM previously, it's been my privilege to see other people catch the synthetic biology bug each year. This team is a great example of the creativity of multidisciplinary groups, as well as iGEM's potential to be a catalyst for innovation (and some great stories!).<br />
</td><br />
<td style="padding: 10px; vertical-align: top"><br />
==Conrad Lochovsky==<br />
[[Image:tmdt_conrad.png|x200px|left|thumb|Conrad Lochovsky aka The Invisible Man]]<br />
Conrad Lochovsky completed his BASc in Biomedical Engineering in Toronto and is currently pursuing his MASc in the exciting area of microfluidics. With a minor in Economics, Conrad played a very important role as our treasurer. He has also been involved with past Toronto iGEM teams: 2006(design/lab), 2007(design/lab/finance) and is active on the executive of several other campus clubs.<br />
</td><br />
</tr><br />
</table><br />
<br />
<br clear="all" /><br />
<br />
=Students=<br />
<br />
<table><br />
<tr><br />
<th width=50%></th><br />
<th width=50%></th><br />
</tr><br />
<br />
<tr><br />
<td style="padding: 10px; vertical-align: top"><br />
==Yen Leung==<br />
[[Image:team_Yen.JPG|x200px|left|thumb|Yen Leung aka Elastigirl]]<br />
Yen Leung has been an invaluable member of the iGem Wet lab team. She has always been around the lab helping out, doing experiments and keeping my (Kenny) craziness (when I come up with crazy ideas) and messiness in check. Currently Yen is pursuing a specialist degree in Nutrition and Neuroscience at the University of Toronto and in September '09 she will be entering her third year.<br />
</td><br />
<td style="padding: 10px; vertical-align: top"><br />
<br />
==Kenny Zhan==<br />
[[Image:team_Ken2.JPG|x200px|left|thumb|Kenny Zhan aka Mad Scientist]]<br />
Hi everyone my name is Kenny Zhan and I am a third year undergraduate student. I am currently pursuing a specialization in biochemistry at the University of Toronto. This year I have been part of the iGEM design team at UofT and during the summer I have been fortunate enough to be part of the roster team that works in the lab to bring the design into reality. I find synthetic biology fascinating as I have an interest in developing new techniques and procedures to support the rapidly expanding field of biological sciences. In my free time I enjoy activities such as hiking, biking, ultimate and geocaching. Also you will see me from time to time updating our lab wiki. Hope to see you all down at the jamboree in Boston come October.<br />
</td><br />
</tr><br />
<br />
<tr><br />
<td style="padding: 10px; vertical-align: top"><br />
<br />
==Meah Gao==<br />
[[Image:team_Meah.png|x200px|left|thumb|Meah Gao aka The Bionic Woman]]<br />
Hi everyone! I am currently a 3rd-year undergraduate student at the University of Toronto specializing in Pathobiology and majoring in Cell and Systems biology. This year as part of the Toronto Mars Discovery iGEM team, my job is to apply bioinformatics methods to identify potential protein candidates for enzymatic channeling and explore alternative microcompartment platforms. Previously, I have also been involved in projects in Neurophysiology and Cellular & Molecular Biology. My current research interest lies in genomics studies using bioinformatics tools. <br />
</td><br />
<td style="padding: 10px; vertical-align: top"><br />
<br />
==James Juras==<br />
[[Image:TmdtJames.png|x200px|left|thumb|James Juras aka The Sporatic Action Man]]<br />
Hey there, I'm a virgo and enjoy long snowboarding adventures in the mountains. Also in my spare time I'm a 4th year undergraduate specializing in Neuroscience at the University of Toronto. This summer I've been doing lots of work all over the place, but mainly my job has been to design the wiki you're presently navigating.<br />
</td><br />
</tr><br />
<br />
<tr><br />
<td style="padding: 10px; vertical-align: top"><br />
<br />
==Farhan Raja==<br />
[[Image:TmdtFR.jpg|x200px|left|thumb|Farhan Raja aka Dr. Zoidberg]]<br />
I am a graduate student in Biochemistry and my research involves applying computational techniques (eg. FBA) towards the reconstruction and analysis of pathogenic metabolism. I helped with the modeling portion of this year's iGEM team.<br />
</td><br />
</tr><br />
<br />
</table></div>FRhttp://2009.igem.org/File:TmdtFR.jpgFile:TmdtFR.jpg2010-11-02T19:10:02Z<p>FR: </p>
<hr />
<div></div>FRhttp://2009.igem.org/File:TmdtFarhan.jpgFile:TmdtFarhan.jpg2010-11-02T18:47:10Z<p>FR: uploaded a new version of "Image:TmdtFarhan.jpg"</p>
<hr />
<div></div>FRhttp://2009.igem.org/Team:TorontoMaRSDiscovery/TeamTeam:TorontoMaRSDiscovery/Team2010-11-02T18:20:45Z<p>FR: /* Farhan Raja */</p>
<hr />
<div>[[image:To_igem_wiki_banner.jpg|965px]]<br />
{| style="color:white;background-color:#99CCFF;" height:100px cellpadding="2" cellspacing="0" border="0" width="100%" align="center" class="menu"<br />
!align="center"|[[Team:TorontoMaRSDiscovery|Home]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Team|The Team]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Project|The Project]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Parts|BioBricks]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Modeling|Modelling]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Bioinformatics|Bioinformatics]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Safety|Safety]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Notebook|Notebook]]<br />
|}<br />
<br><br />
<br />
=The Team=<br />
<br />
[[Image:TMDT_Team2.jpg|900px|center|thumb|Left to right: Farhan, James, Graham, John, Yen, Kenny, Meah, Stacy]]<br />
<br />
<br clear="all" /><br />
<br />
=Advisors=<br />
<br />
<table><br />
<tr><br />
<th width=50%></th><br />
<th width=50%></th><br />
</tr><br />
<br />
<tr><br />
<td style="padding: 10px; vertical-align: top"><br />
==Dr. John Parkinson==<br />
[[Image:JohnParkinson.jpg|x200px|left|thumb|Dr. John Parkinson aka The Dragon in the Dragon's Den]]<br />
Graduated from the University of Bath with a bachelor of science in Applied Biology in 1990. After receiving a PhD in Biochemistry from the University of Manchester in 1995, I completed a NATO fellowship at the University of Manitoba. From 1997 to 2000, I was awarded a fellowship at the Edinburgh Centre for Protein Technology, University of Edinburgh and from 2000 to 2003 completed another fellowship at the University of Edinburgh on Nematode genomics. I am currently a scientist at The Hospital for Sick Children Research Institute. The research in our laboratory is aimed at understanding how molecular information can give rise to complex biological behaviour. Using computational methods, we study the organization and dynamics of cellular components within the context of integrated biological systems. Comparative genomics methods are also being applied to provide insights into how these systems may have evolved from the remote origins of life.<br />
</td><br />
<td style="padding: 10px; vertical-align: top"><br />
==Graham Cromar==<br />
[[Image:graham.jpg|x200px|left|thumb|Graham Cromar aka The Wizard of Id]]<br />
I am a 4th year Ph.D. student in the Department of Molecular Structure and Function at the Hospital for Sick Children in Toronto. At various times in the past I have studied cell and molecular biology (B.Sc. Toronto), molecular biology and genetics (M.Sc. Guelph), computer programming and systems analysis (dip. Inst. Computer Studies, Toronto), bioinformatics (cert. Canadian Genetic Disease Network) and, systems and matrix biology (present). I have worked as a lab technician, teaching assistant, computer programmer/systems analyst and IS manager. But, what I would most like to do is what I wrote in my high school yearbook about 20 years ago... Design organisms for export to far away galaxies. Thanks to iGEM I'm 1/4 of the way there...<br />
</td><br />
</tr><br />
<br />
<tr><br />
<td style="padding: 10px; vertical-align: top"><br />
<br />
==Stacy Hung==<br />
[[Image:team_Stacy.jpg|x200px|left|thumb|Stacy Hung aka Mini Wheats]]<br />
With a B.Sc. Honours Biology and Bioinformatics from the University of Waterloo, Stacy is currently a 3rd year Ph.D. student at the University of Toronto. Her main focus is to identify novel enzyme drug targets against malaria by studying the metabolic networks of these parasites. She is inspired by anything that is new, exciting, and can have a long-term impact for making the world a better place -- besides her research, iGEM is certainly one of these things!<br />
</td><br />
<td style="padding: 10px; vertical-align: top"><br />
<br />
==Daniel Wong==<br />
[[Image:tmdt_dan.png|x200px|left|thumb|Daniel Wong aka The Architect]]<br />
Daniel Wong received his BASc in Engineering Science biomedical option at the University of Toronto. He is currently with the Institute of Biomaterials and Biomedical Engineering, working toward his PhD. He works in the Cochlear Implant Laboratory at the Hospital for Sick Children, developing neuroimaging algorithms for the analysis of multichannel EEG data. As design team lead for this year's iGEM team, he guided the design team in developing the protocols for creating the team's biobrick parts. His academic interests include neuroimaging and systems modelling. To relax, he enjoys a good round of golf or social salsa dancing.<br />
</td><br />
</tr><br />
<br />
<tr><br />
<td style="padding: 10px; vertical-align: top"><br />
==Natalie Yeung==<br />
[[Image:tmdt_natalie.png|x200px|left|thumb|Natalie Yeung aka The Strategist]]<br />
I'm a graduate student at the University of Toronto's iSchool (sometimes known as the Faculty of Information). Having been involved in iGEM previously, it's been my privilege to see other people catch the synthetic biology bug each year. This team is a great example of the creativity of multidisciplinary groups, as well as iGEM's potential to be a catalyst for innovation (and some great stories!).<br />
</td><br />
<td style="padding: 10px; vertical-align: top"><br />
==Conrad Lochovsky==<br />
[[Image:tmdt_conrad.png|x200px|left|thumb|Conrad Lochovsky aka The Invisible Man]]<br />
Conrad Lochovsky completed his BASc in Biomedical Engineering in Toronto and is currently pursuing his MASc in the exciting area of microfluidics. With a minor in Economics, Conrad played a very important role as our treasurer. He has also been involved with past Toronto iGEM teams: 2006(design/lab), 2007(design/lab/finance) and is active on the executive of several other campus clubs.<br />
</td><br />
</tr><br />
</table><br />
<br />
<br clear="all" /><br />
<br />
=Students=<br />
<br />
<table><br />
<tr><br />
<th width=50%></th><br />
<th width=50%></th><br />
</tr><br />
<br />
<tr><br />
<td style="padding: 10px; vertical-align: top"><br />
==Yen Leung==<br />
[[Image:team_Yen.JPG|x200px|left|thumb|Yen Leung aka Elastigirl]]<br />
Yen Leung has been an invaluable member of the iGem Wet lab team. She has always been around the lab helping out, doing experiments and keeping my (Kenny) craziness (when I come up with crazy ideas) and messiness in check. Currently Yen is pursuing a specialist degree in Nutrition and Neuroscience at the University of Toronto and in September '09 she will be entering her third year.<br />
</td><br />
<td style="padding: 10px; vertical-align: top"><br />
<br />
==Kenny Zhan==<br />
[[Image:team_Ken2.JPG|x200px|left|thumb|Kenny Zhan aka Mad Scientist]]<br />
Hi everyone my name is Kenny Zhan and I am a third year undergraduate student. I am currently pursuing a specialization in biochemistry at the University of Toronto. This year I have been part of the iGEM design team at UofT and during the summer I have been fortunate enough to be part of the roster team that works in the lab to bring the design into reality. I find synthetic biology fascinating as I have an interest in developing new techniques and procedures to support the rapidly expanding field of biological sciences. In my free time I enjoy activities such as hiking, biking, ultimate and geocaching. Also you will see me from time to time updating our lab wiki. Hope to see you all down at the jamboree in Boston come October.<br />
</td><br />
</tr><br />
<br />
<tr><br />
<td style="padding: 10px; vertical-align: top"><br />
<br />
==Meah Gao==<br />
[[Image:team_Meah.png|x200px|left|thumb|Meah Gao aka The Bionic Woman]]<br />
Hi everyone! I am currently a 3rd-year undergraduate student at the University of Toronto specializing in Pathobiology and majoring in Cell and Systems biology. This year as part of the Toronto Mars Discovery iGEM team, my job is to apply bioinformatics methods to identify potential protein candidates for enzymatic channeling and explore alternative microcompartment platforms. Previously, I have also been involved in projects in Neurophysiology and Cellular & Molecular Biology. My current research interest lies in genomics studies using bioinformatics tools. <br />
</td><br />
<td style="padding: 10px; vertical-align: top"><br />
<br />
==James Juras==<br />
[[Image:TmdtJames.png|x200px|left|thumb|James Juras aka The Sporatic Action Man]]<br />
Hey there, I'm a virgo and enjoy long snowboarding adventures in the mountains. Also in my spare time I'm a 4th year undergraduate specializing in Neuroscience at the University of Toronto. This summer I've been doing lots of work all over the place, but mainly my job has been to design the wiki you're presently navigating.<br />
</td><br />
</tr><br />
<br />
<tr><br />
<td style="padding: 10px; vertical-align: top"><br />
<br />
==Farhan Raja==<br />
[[Image:tmdtFarhan.jpg|x200px|left|thumb|Farhan Raja aka Dr. Zoidberg]]<br />
I am a graduate student in Biochemistry and my research involves applying computational techniques (eg. FBA) towards the reconstruction and analysis of pathogenic metabolism. I helped with the modeling portion of this year's iGEM team.<br />
</td><br />
</tr><br />
<br />
</table></div>FRhttp://2009.igem.org/Team:TorontoMaRSDiscovery/TeamTeam:TorontoMaRSDiscovery/Team2010-11-02T18:16:23Z<p>FR: /* Farhan Raja */</p>
<hr />
<div>[[image:To_igem_wiki_banner.jpg|965px]]<br />
{| style="color:white;background-color:#99CCFF;" height:100px cellpadding="2" cellspacing="0" border="0" width="100%" align="center" class="menu"<br />
!align="center"|[[Team:TorontoMaRSDiscovery|Home]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Team|The Team]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Project|The Project]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Parts|BioBricks]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Modeling|Modelling]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Bioinformatics|Bioinformatics]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Safety|Safety]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Notebook|Notebook]]<br />
|}<br />
<br><br />
<br />
=The Team=<br />
<br />
[[Image:TMDT_Team2.jpg|900px|center|thumb|Left to right: Farhan, James, Graham, John, Yen, Kenny, Meah, Stacy]]<br />
<br />
<br clear="all" /><br />
<br />
=Advisors=<br />
<br />
<table><br />
<tr><br />
<th width=50%></th><br />
<th width=50%></th><br />
</tr><br />
<br />
<tr><br />
<td style="padding: 10px; vertical-align: top"><br />
==Dr. John Parkinson==<br />
[[Image:JohnParkinson.jpg|x200px|left|thumb|Dr. John Parkinson aka The Dragon in the Dragon's Den]]<br />
Graduated from the University of Bath with a bachelor of science in Applied Biology in 1990. After receiving a PhD in Biochemistry from the University of Manchester in 1995, I completed a NATO fellowship at the University of Manitoba. From 1997 to 2000, I was awarded a fellowship at the Edinburgh Centre for Protein Technology, University of Edinburgh and from 2000 to 2003 completed another fellowship at the University of Edinburgh on Nematode genomics. I am currently a scientist at The Hospital for Sick Children Research Institute. The research in our laboratory is aimed at understanding how molecular information can give rise to complex biological behaviour. Using computational methods, we study the organization and dynamics of cellular components within the context of integrated biological systems. Comparative genomics methods are also being applied to provide insights into how these systems may have evolved from the remote origins of life.<br />
</td><br />
<td style="padding: 10px; vertical-align: top"><br />
==Graham Cromar==<br />
[[Image:graham.jpg|x200px|left|thumb|Graham Cromar aka The Wizard of Id]]<br />
I am a 4th year Ph.D. student in the Department of Molecular Structure and Function at the Hospital for Sick Children in Toronto. At various times in the past I have studied cell and molecular biology (B.Sc. Toronto), molecular biology and genetics (M.Sc. Guelph), computer programming and systems analysis (dip. Inst. Computer Studies, Toronto), bioinformatics (cert. Canadian Genetic Disease Network) and, systems and matrix biology (present). I have worked as a lab technician, teaching assistant, computer programmer/systems analyst and IS manager. But, what I would most like to do is what I wrote in my high school yearbook about 20 years ago... Design organisms for export to far away galaxies. Thanks to iGEM I'm 1/4 of the way there...<br />
</td><br />
</tr><br />
<br />
<tr><br />
<td style="padding: 10px; vertical-align: top"><br />
<br />
==Stacy Hung==<br />
[[Image:team_Stacy.jpg|x200px|left|thumb|Stacy Hung aka Mini Wheats]]<br />
With a B.Sc. Honours Biology and Bioinformatics from the University of Waterloo, Stacy is currently a 3rd year Ph.D. student at the University of Toronto. Her main focus is to identify novel enzyme drug targets against malaria by studying the metabolic networks of these parasites. She is inspired by anything that is new, exciting, and can have a long-term impact for making the world a better place -- besides her research, iGEM is certainly one of these things!<br />
</td><br />
<td style="padding: 10px; vertical-align: top"><br />
<br />
==Daniel Wong==<br />
[[Image:tmdt_dan.png|x200px|left|thumb|Daniel Wong aka The Architect]]<br />
Daniel Wong received his BASc in Engineering Science biomedical option at the University of Toronto. He is currently with the Institute of Biomaterials and Biomedical Engineering, working toward his PhD. He works in the Cochlear Implant Laboratory at the Hospital for Sick Children, developing neuroimaging algorithms for the analysis of multichannel EEG data. As design team lead for this year's iGEM team, he guided the design team in developing the protocols for creating the team's biobrick parts. His academic interests include neuroimaging and systems modelling. To relax, he enjoys a good round of golf or social salsa dancing.<br />
</td><br />
</tr><br />
<br />
<tr><br />
<td style="padding: 10px; vertical-align: top"><br />
==Natalie Yeung==<br />
[[Image:tmdt_natalie.png|x200px|left|thumb|Natalie Yeung aka The Strategist]]<br />
I'm a graduate student at the University of Toronto's iSchool (sometimes known as the Faculty of Information). Having been involved in iGEM previously, it's been my privilege to see other people catch the synthetic biology bug each year. This team is a great example of the creativity of multidisciplinary groups, as well as iGEM's potential to be a catalyst for innovation (and some great stories!).<br />
</td><br />
<td style="padding: 10px; vertical-align: top"><br />
==Conrad Lochovsky==<br />
[[Image:tmdt_conrad.png|x200px|left|thumb|Conrad Lochovsky aka The Invisible Man]]<br />
Conrad Lochovsky completed his BASc in Biomedical Engineering in Toronto and is currently pursuing his MASc in the exciting area of microfluidics. With a minor in Economics, Conrad played a very important role as our treasurer. He has also been involved with past Toronto iGEM teams: 2006(design/lab), 2007(design/lab/finance) and is active on the executive of several other campus clubs.<br />
</td><br />
</tr><br />
</table><br />
<br />
<br clear="all" /><br />
<br />
=Students=<br />
<br />
<table><br />
<tr><br />
<th width=50%></th><br />
<th width=50%></th><br />
</tr><br />
<br />
<tr><br />
<td style="padding: 10px; vertical-align: top"><br />
==Yen Leung==<br />
[[Image:team_Yen.JPG|x200px|left|thumb|Yen Leung aka Elastigirl]]<br />
Yen Leung has been an invaluable member of the iGem Wet lab team. She has always been around the lab helping out, doing experiments and keeping my (Kenny) craziness (when I come up with crazy ideas) and messiness in check. Currently Yen is pursuing a specialist degree in Nutrition and Neuroscience at the University of Toronto and in September '09 she will be entering her third year.<br />
</td><br />
<td style="padding: 10px; vertical-align: top"><br />
<br />
==Kenny Zhan==<br />
[[Image:team_Ken2.JPG|x200px|left|thumb|Kenny Zhan aka Mad Scientist]]<br />
Hi everyone my name is Kenny Zhan and I am a third year undergraduate student. I am currently pursuing a specialization in biochemistry at the University of Toronto. This year I have been part of the iGEM design team at UofT and during the summer I have been fortunate enough to be part of the roster team that works in the lab to bring the design into reality. I find synthetic biology fascinating as I have an interest in developing new techniques and procedures to support the rapidly expanding field of biological sciences. In my free time I enjoy activities such as hiking, biking, ultimate and geocaching. Also you will see me from time to time updating our lab wiki. Hope to see you all down at the jamboree in Boston come October.<br />
</td><br />
</tr><br />
<br />
<tr><br />
<td style="padding: 10px; vertical-align: top"><br />
<br />
==Meah Gao==<br />
[[Image:team_Meah.png|x200px|left|thumb|Meah Gao aka The Bionic Woman]]<br />
Hi everyone! I am currently a 3rd-year undergraduate student at the University of Toronto specializing in Pathobiology and majoring in Cell and Systems biology. This year as part of the Toronto Mars Discovery iGEM team, my job is to apply bioinformatics methods to identify potential protein candidates for enzymatic channeling and explore alternative microcompartment platforms. Previously, I have also been involved in projects in Neurophysiology and Cellular & Molecular Biology. My current research interest lies in genomics studies using bioinformatics tools. <br />
</td><br />
<td style="padding: 10px; vertical-align: top"><br />
<br />
==James Juras==<br />
[[Image:TmdtJames.png|x200px|left|thumb|James Juras aka The Sporatic Action Man]]<br />
Hey there, I'm a virgo and enjoy long snowboarding adventures in the mountains. Also in my spare time I'm a 4th year undergraduate specializing in Neuroscience at the University of Toronto. This summer I've been doing lots of work all over the place, but mainly my job has been to design the wiki you're presently navigating.<br />
</td><br />
</tr><br />
<br />
<tr><br />
<td style="padding: 10px; vertical-align: top"><br />
<br />
==Farhan Raja==<br />
I am a graduate student in Biochemistry and my research involves applying computational techniques (eg. FBA) towards the reconstruction and analysis of pathogenic metabolism. I helped with the modeling portion of this year's iGEM team.<br />
</td><br />
</tr><br />
<br />
</table></div>FRhttp://2009.igem.org/Team:TorontoMaRSDiscovery/TeamTeam:TorontoMaRSDiscovery/Team2010-11-02T18:05:57Z<p>FR: /* Farhan Raja */</p>
<hr />
<div>[[image:To_igem_wiki_banner.jpg|965px]]<br />
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!align="center"|[[Team:TorontoMaRSDiscovery/Team|The Team]]<br />
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!align="center"|[[Team:TorontoMaRSDiscovery/Bioinformatics|Bioinformatics]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Safety|Safety]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Notebook|Notebook]]<br />
|}<br />
<br><br />
<br />
=The Team=<br />
<br />
[[Image:TMDT_Team2.jpg|900px|center|thumb|Left to right: Farhan, James, Graham, John, Yen, Kenny, Meah, Stacy]]<br />
<br />
<br clear="all" /><br />
<br />
=Advisors=<br />
<br />
<table><br />
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<th width=50%></th><br />
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</tr><br />
<br />
<tr><br />
<td style="padding: 10px; vertical-align: top"><br />
==Dr. John Parkinson==<br />
[[Image:JohnParkinson.jpg|x200px|left|thumb|Dr. John Parkinson aka The Dragon in the Dragon's Den]]<br />
Graduated from the University of Bath with a bachelor of science in Applied Biology in 1990. After receiving a PhD in Biochemistry from the University of Manchester in 1995, I completed a NATO fellowship at the University of Manitoba. From 1997 to 2000, I was awarded a fellowship at the Edinburgh Centre for Protein Technology, University of Edinburgh and from 2000 to 2003 completed another fellowship at the University of Edinburgh on Nematode genomics. I am currently a scientist at The Hospital for Sick Children Research Institute. The research in our laboratory is aimed at understanding how molecular information can give rise to complex biological behaviour. Using computational methods, we study the organization and dynamics of cellular components within the context of integrated biological systems. Comparative genomics methods are also being applied to provide insights into how these systems may have evolved from the remote origins of life.<br />
</td><br />
<td style="padding: 10px; vertical-align: top"><br />
==Graham Cromar==<br />
[[Image:graham.jpg|x200px|left|thumb|Graham Cromar aka The Wizard of Id]]<br />
I am a 4th year Ph.D. student in the Department of Molecular Structure and Function at the Hospital for Sick Children in Toronto. At various times in the past I have studied cell and molecular biology (B.Sc. Toronto), molecular biology and genetics (M.Sc. Guelph), computer programming and systems analysis (dip. Inst. Computer Studies, Toronto), bioinformatics (cert. Canadian Genetic Disease Network) and, systems and matrix biology (present). I have worked as a lab technician, teaching assistant, computer programmer/systems analyst and IS manager. But, what I would most like to do is what I wrote in my high school yearbook about 20 years ago... Design organisms for export to far away galaxies. Thanks to iGEM I'm 1/4 of the way there...<br />
</td><br />
</tr><br />
<br />
<tr><br />
<td style="padding: 10px; vertical-align: top"><br />
<br />
==Stacy Hung==<br />
[[Image:team_Stacy.jpg|x200px|left|thumb|Stacy Hung aka Mini Wheats]]<br />
With a B.Sc. Honours Biology and Bioinformatics from the University of Waterloo, Stacy is currently a 3rd year Ph.D. student at the University of Toronto. Her main focus is to identify novel enzyme drug targets against malaria by studying the metabolic networks of these parasites. She is inspired by anything that is new, exciting, and can have a long-term impact for making the world a better place -- besides her research, iGEM is certainly one of these things!<br />
</td><br />
<td style="padding: 10px; vertical-align: top"><br />
<br />
==Daniel Wong==<br />
[[Image:tmdt_dan.png|x200px|left|thumb|Daniel Wong aka The Architect]]<br />
Daniel Wong received his BASc in Engineering Science biomedical option at the University of Toronto. He is currently with the Institute of Biomaterials and Biomedical Engineering, working toward his PhD. He works in the Cochlear Implant Laboratory at the Hospital for Sick Children, developing neuroimaging algorithms for the analysis of multichannel EEG data. As design team lead for this year's iGEM team, he guided the design team in developing the protocols for creating the team's biobrick parts. His academic interests include neuroimaging and systems modelling. To relax, he enjoys a good round of golf or social salsa dancing.<br />
</td><br />
</tr><br />
<br />
<tr><br />
<td style="padding: 10px; vertical-align: top"><br />
==Natalie Yeung==<br />
[[Image:tmdt_natalie.png|x200px|left|thumb|Natalie Yeung aka The Strategist]]<br />
I'm a graduate student at the University of Toronto's iSchool (sometimes known as the Faculty of Information). Having been involved in iGEM previously, it's been my privilege to see other people catch the synthetic biology bug each year. This team is a great example of the creativity of multidisciplinary groups, as well as iGEM's potential to be a catalyst for innovation (and some great stories!).<br />
</td><br />
<td style="padding: 10px; vertical-align: top"><br />
==Conrad Lochovsky==<br />
[[Image:tmdt_conrad.png|x200px|left|thumb|Conrad Lochovsky aka The Invisible Man]]<br />
Conrad Lochovsky completed his BASc in Biomedical Engineering in Toronto and is currently pursuing his MASc in the exciting area of microfluidics. With a minor in Economics, Conrad played a very important role as our treasurer. He has also been involved with past Toronto iGEM teams: 2006(design/lab), 2007(design/lab/finance) and is active on the executive of several other campus clubs.<br />
</td><br />
</tr><br />
</table><br />
<br />
<br clear="all" /><br />
<br />
=Students=<br />
<br />
<table><br />
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<td style="padding: 10px; vertical-align: top"><br />
==Yen Leung==<br />
[[Image:team_Yen.JPG|x200px|left|thumb|Yen Leung aka Elastigirl]]<br />
Yen Leung has been an invaluable member of the iGem Wet lab team. She has always been around the lab helping out, doing experiments and keeping my (Kenny) craziness (when I come up with crazy ideas) and messiness in check. Currently Yen is pursuing a specialist degree in Nutrition and Neuroscience at the University of Toronto and in September '09 she will be entering her third year.<br />
</td><br />
<td style="padding: 10px; vertical-align: top"><br />
<br />
==Kenny Zhan==<br />
[[Image:team_Ken2.JPG|x200px|left|thumb|Kenny Zhan aka Mad Scientist]]<br />
Hi everyone my name is Kenny Zhan and I am a third year undergraduate student. I am currently pursuing a specialization in biochemistry at the University of Toronto. This year I have been part of the iGEM design team at UofT and during the summer I have been fortunate enough to be part of the roster team that works in the lab to bring the design into reality. I find synthetic biology fascinating as I have an interest in developing new techniques and procedures to support the rapidly expanding field of biological sciences. In my free time I enjoy activities such as hiking, biking, ultimate and geocaching. Also you will see me from time to time updating our lab wiki. Hope to see you all down at the jamboree in Boston come October.<br />
</td><br />
</tr><br />
<br />
<tr><br />
<td style="padding: 10px; vertical-align: top"><br />
<br />
==Meah Gao==<br />
[[Image:team_Meah.png|x200px|left|thumb|Meah Gao aka The Bionic Woman]]<br />
Hi everyone! I am currently a 3rd-year undergraduate student at the University of Toronto specializing in Pathobiology and majoring in Cell and Systems biology. This year as part of the Toronto Mars Discovery iGEM team, my job is to apply bioinformatics methods to identify potential protein candidates for enzymatic channeling and explore alternative microcompartment platforms. Previously, I have also been involved in projects in Neurophysiology and Cellular & Molecular Biology. My current research interest lies in genomics studies using bioinformatics tools. <br />
</td><br />
<td style="padding: 10px; vertical-align: top"><br />
<br />
==James Juras==<br />
[[Image:TmdtJames.png|x200px|left|thumb|James Juras aka The Sporatic Action Man]]<br />
Hey there, I'm a virgo and enjoy long snowboarding adventures in the mountains. Also in my spare time I'm a 4th year undergraduate specializing in Neuroscience at the University of Toronto. This summer I've been doing lots of work all over the place, but mainly my job has been to design the wiki you're presently navigating.<br />
</td><br />
</tr><br />
<br />
<tr><br />
<td style="padding: 10px; vertical-align: top"><br />
<br />
==Farhan Raja==<br />
[[Image:tmdtFarhan.jpg|x200px|left|thumb|Farhan Raja aka Dr. Zoidberg]]<br />
I am a graduate student in Biochemistry and my research involves applying computational techniques (eg. FBA) towards the reconstruction and analysis of pathogenic metabolism. I helped with the modeling portion of this year's iGEM team.<br />
</td><br />
</tr><br />
<br />
</table></div>FRhttp://2009.igem.org/File:Tmdt_biobrick.pngFile:Tmdt biobrick.png2009-10-21T21:37:00Z<p>FR: uploaded a new version of "Image:Tmdt biobrick.png"</p>
<hr />
<div></div>FRhttp://2009.igem.org/Team:TorontoMaRSDiscovery/ModelingTeam:TorontoMaRSDiscovery/Modeling2009-10-21T21:27:18Z<p>FR: </p>
<hr />
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!align="center"|[[Team:TorontoMaRSDiscovery/Team|The Team]]<br />
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!align="center"|[[Team:TorontoMaRSDiscovery/Parts|BioBricks]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Modeling|Modeling]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Bioinformatics|Bioinformatics]]<br />
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<br><br />
<br />
<p style="font-size:18pt;">Modelling the production of eCFP, Encapsulin, and Encapsulin microcompartments</p><br />
=Summary=<br />
<br />
A kinetic model of our system has been constructed. Approximate parameter values were gathered from online resources to represent all processes up to the production of the eCFP and Encapsulin proteins. Current simulations predict the production of these two proteins at various initial concentrations of IPTG and aTc effector molecules. A sensitivity analysis reveals that the rate of constitutive expression of lacI and tetR has the greatest effect on eCFP and Encapsulin concentrations. Furthermore, we have outlined approaches for the detailed modelling of the eCFP degredation/maturation and Encapsulin assembly pathways.<br />
<br />
<br />
The initial simulations will be used to identify a critical concentration of Encapsulin mononomer required for microcompartment assembly. To strengthen the model, the constitutive expression rate of BBa_J23100 (our most sensitive parameter) will be experimentally determined. Subsequently, a detailed model of Encapsulin assembly will be integrated into the current model, and its parameters filled-in using parameter-scanning methods and experiments outlined in the relevant references. By comparing experimental measures of microcompartment formation with that predicted by the kinetic model, we aim to gain insight on the mechanisms of Encapsulin assembly.<br />
<br />
=Model=<br />
Our model is based on the following design (See [https://2009.igem.org/Team:TorontoMaRSDiscovery/Project Project Page] for a full description of this system).<br />
<br />
[[image:tmdt_biobrick.png|center|600px|The Encapsulator]]<br />
<br />
The reaction framework was mainly generated using the [http://synbioss.sourceforge.net/ SynBioSS Designer (a really useful modeling tool for iGEM teams)], which also provides default parameter values. These parameter values have been gathered from various literature [http://neptune.cems.umn.edu/designer/designer_defaults.pdf sources], and should be taken as approximations. All units were taken to be (1 / molarity^n-1 * s), where n is the order of the reaction. For example, for the reaction 2 lacI --> lacI2, n = 2, thus the rate constant has the units 1/molarity*s. <br />
<br />
The pathways for the expressed proteins, eCFPt and Encapsulin, need to be modeled in more detail. For example, in this basic model eCFPt is degraded via a first order reaction and Encapsulin makes a dimer complex. However, in reality fluorescent proteins have been shown to degreade via Micheales-menton kinetics and Encapsulin is thought to make a complex of about 60 monomers. These issues will be addressed in future work.<br />
<br />
'''The reactions can be accessed here:'''<br />
<br />
[[The Encapsulator Model]] (opens new page)<br />
<br />
[[Media:Uft_mod_Rxns2.xls|Download Encapsulator Model ]] (download Excel file)<br />
<br />
=Simulations=<br />
<br />
All simulations were carried out using the [https://2009.igem.org/Partner_Offers SimBiology Matlab Toolbox], which was freely available to iGEM teams. <br />
<br />
===Accumulation of eCFP at Different Initial Concentrations of IPTG===<br />
<br />
[[Image:uft_mod_cfp-iptg.png | 900px]]<br />
<br />
The IPTG effector eventually loses effect, and the eCFP concentration approaches a maximum. This happens because the IPTG proteins eventually ''tie up'' all available LacI4 proteins, leaving the transcription and translation of eCFP to operate at its maxiumum rate. <br />
<br />
===Accumulation of Encapsulin monomer at Different Initial Concentrations of aTc===<br />
<br />
[[Image:uft_mod_enc-atc.png | 900px]]<br />
<br />
(NOTE: in order to observe Encapsulin monomer levels, the above simulations were carried out without any Encapsulin assembly reactions in place)<br />
<br />
The production of Encapsulin occurs at a slower rate than eCFP because the BBa_R0040 promoter has two tetR binding sites, resulting in more repression and more off-pathway scenarios. Thus, the Encapsulin concentration also seems assymptotic but at higher concentrations of aTc (relative to IPTG). <br />
<br />
It seems beneficial to have the Encapsulin protein under control of the BBa_R0040-tetR-aTc construct because at zero levels of aTc we can have essentially zero levels of Encapsulin (whereas even at zero levels of IPTG, there is still significantly more eCFP). This will enable us to probe extremely low concentrations of Encapsulin monomer when testing for optimal Encapsulin assembly conditions. The disadvantage is that if Encapsulin assembly requires a very high initial concentration of Encapsulin monomer, we would have to wait a long time to see microcompartments. If this later scenario is observed, it may be better to switch the eCFP and Encapsulin expression systems.<br />
<br />
===Sensitivity Analysis===<br />
<br />
Since all of our parameters are approximations from literature sources, those which have the greatest affect on system dynamics (ie. the most ''sensitive'' parameters) would be leading candidates to be experimentally determined. Currently we are interested in the parameters that have the greatest effect on the production of eCFP and Encapsulin. Ideally, it would be best to tighten-up the model by experimentally determining these, before incorporating the largely unexplored Encapsulin assembly pathways. <br />
<br />
<br />
'''1) Sensitivity of eCFP Production'''<br />
<br />
[[Image:uft_mod_SAecfp.png | centre | 600px]]<br />
<br />
<br />
<br />
'''2) Sensitivity of Encapsulin Production'''<br />
<br />
[[Image:uft_mod_SAenc.png | centre | 600px]]<br />
<br />
Parameters 1 and 2 correspond to the rates of constitutive expression of the repressors lacI and tetR respectively. Thus, it is predicted that eCFP and Encapsulin production is largely sensitive to the expression rates of lacI and tetR. <br />
<br />
The specific constitutive promoter used in our construct is BBa_J23100. In our model, this was given the generic rate of 1E-10 molarity\s by SynBioSS based on a variety of empirically-fitted protein expression rates found in literature. This generic approach to assigning parameter values is a suitable fist-step, but our sensitivity results suggest that experimentally determining the expression rate of BBa_J23100 should significantly improve our model's predictive capability.<br />
<br />
=Future Work=<br />
<br />
Improvements to the basic model presented above can be separated into three areas; 1) performing experiments to determine parameter values that are specific to our system, 2) more detailed modeling of eCFPt behavior, 3) more detailed modeling of Encapsulin assembly. <br />
<br />
The experiments required to determine general transcription and translation parameters need to be further researched, so this will be skipped over for now. Here we will discuss the more interesting areas – the detailed modeling of eCFP and Encapsulin pathways. This will be accomplished by incorporating previous modeling efforts that are applicable to the eCFP and Encapsulin proteins. <br />
<br />
===Maturation and Degredation of eCFP===<br />
<br />
The expression and degradation of [http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=95514&blobtype=pdf Green Fluorescent Protein (GFP) was modeled previously]. This paper noted that GFP must mature before going into fluorescent phase, and GFP degradation was shown to follow M-M kinetics, as depicted below. This paper also outlined how the degradation parameters could be derived for any expression system using only simple fluorescence and optical density measurements.<br />
<br />
[[Image:uft_mod_ecfp1.png | centre | thumb | Degredation and maturation pathways for eCFP. (Leveau and Lindow 2001)]]<br />
<br />
<br />
The GFP maturation and degradation parameters found in this paper were:<br />
<br />
<html><br />
<centre><br />
<table><br />
<tr><td> m = 0.0004279 1/s </td></tr><br />
<tr><td> Vmax = 2E-10 molality/s </td></tr><br />
<tr><td> Km = 9E-13 molality/s </td></tr><br />
<tr><td> </td></tr><br />
</table><br />
</centre><br />
</html><br />
<br />
<br />
Assuming eCFP would behave similarly to eGFP, the following additional reactions would be included in the model:<br />
<br />
<html><br />
<table><br />
<tr> <td><b> Maturation </b></td> <td> </td> </tr><br />
<tr> <td> eCFPt --> F_eCFPT </td> <td> 0.0004279 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Degradation </b></td> <td> </td> </tr><br />
<tr> <td> eCFPt --> </td> <td> Vmax = 2E-10 </td> </tr><br />
<tr> <td> </td> <td> Km = 9E-13 </td> </tr><br />
<tr> <td> F_eCFPt --> </td> <td> Vmax = 2E-10 </td> </tr><br />
<tr> <td> </td> <td> Km = 9E-13 </td> </tr><br />
</table><br />
</html><br />
<br />
===Assembly of Encapsulin Microcompartments===<br />
<br />
Though Encapsulin microcompartment assembly is not well-studied, it has been theorized to resemble the assembly of viral capsids. Thus, we could look to this relatively well-studied phenomenon as a representation of Encapsulin microcompartment assembly.<br />
<br />
Adam Zlotnick has published models of viral capsid assembly using different approaches. An early paper described an equilibrium model of assembly for a 12-unit polyhedral capsid head, and a more recent paper used a kinetic model that could be applied to many examples of spherical polymerization. We will consider how each approach could be incorporated as a representation of Encapsulin assembly.<br />
<br />
<br />
'''1) Equilibrim Approach to Encapsulin Assembly'''<br />
<br />
Zlotnick's [[Media:Uft_mod_to_build_a_virus_capsid.pdf|equilibrium-based model]] consists of reactions from an initial monomer subunit leading to a final capsid product. The sequential reactions take into account DeltaG for contact (Kn'), and parameters describing path degeneracy (varies for different intermediates).<br />
[[image:uft_mod_encap1.png|centre|thumb|Kn for assembly subunits based on path degeneracy. (Zlotnick 1994)]]<br />
<br />
<br />
'''2) Kinetic Model of Spherical Polymerization'''<br />
<br />
A [http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1302223/pdf/12124301.pdf general kinetic model for the spherical polyermization] process is shown below. In our case, the initial monomer subunit concentration (''u'') would represent our expressed Encapsulin BioBrick, and the number of monomers in the final assembly (''N'') is thought to be 60. All of the included parameters can be calculated from the four basic parameters; the microscopic, per-contact equilibrium constant (KAcon), the nucleus size (nuc), the nucleation on-rate (f_nuc), and the elongation on-rate (f_elong). The referenced paper describes methods to aquire these parameters from kinetic experiments, and provides examples for N = 12 and 30 unit viral capsid assemblies.<br />
[[image:uft_mod_encap2.png| centre | thumb |System of ODEs to represent spherical polymerization, where ''u'' is the initial subunit concentration, ''m'' is the "mth" intermediate species, and ''N'' is the number of monomers in the final assembly. (Endres and Zlotnick 2002)]]<br />
<br />
<br />
<br />
Zlotnick's models also describe two important features of spherical polymerization that we should also expect to observe in Encapsulin assembly: kinetic trapping and nucleation. A kinetic trap occurs when the initial monomer subunit concentration or the release of Gibbs free energy (deltaG) of the first assembly reaction is too high. This results in over-initiation of assembly and the reactions quickly become starved for subunits. Kinetic trapping is prevented by nucleation, where the initial reactions occur at a slower rate because the first few intermediates in a series of reactions are less stable than downstream products. Essentially, nucleation serves as a “slow first step” that regulates the assembly pathway. <br />
<br />
It will be interesting to note how the translational dynamics of Encapsulin interplay with its assembly dynamics. Since our system does not start with any initial concentration of Encapsulin, there will be an optimum rate of production that essentially serves the role of nucleation – avoiding kinetic traps while still maintaining a maximum production of full Encapsulin assemblies.<br />
<br />
=References=<br />
<br />
1. Hill AD, Tomshine JR, Weeding EM, Sotiropoulos V, Kaznessis YN. ''SynBioSS: the synthetic biology modeling suite.'' Bioinformatics. 2008 Nov 1;24(21):2551-3. Epub 2008 Aug 30.<br />
[http://neptune.cems.umn.edu/designer/interface1.php SynBioSS Web Designer]<br />
<br />
2. Leveau JH, Lindow SE. ''Predictive and interpretive simulation of green fluorescent protein expression in<br />
reporter bacteria.'' J Bacteriol. 2001 Dec;183(23):6752-62.<br />
<br />
3. Endres D, Zlotnick A. ''Model-based analysis of assembly kinetics for virus capsids or other spherical<br />
polymers.'' Biophys J. 2002 Aug;83(2):1217-30.</div>FRhttp://2009.igem.org/File:TmdtFarhan.jpgFile:TmdtFarhan.jpg2009-10-21T17:26:31Z<p>FR: </p>
<hr />
<div></div>FRhttp://2009.igem.org/Team:TorontoMaRSDiscovery/TeamTeam:TorontoMaRSDiscovery/Team2009-10-21T17:24:25Z<p>FR: /* Who we are */</p>
<hr />
<div>[[image:To_igem_wiki_banner.jpg|965px]]<br />
{| style="color:white;background-color:#99CCFF;" height:100px cellpadding="2" cellspacing="0" border="0" width="100%" align="center" class="menu"<br />
!align="center"|[[Team:TorontoMaRSDiscovery|Home]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Team|The Team]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Project|The Project]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Parts|BioBricks]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Modeling|Modeling]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Bioinformatics|Bioinformatics]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Safety|Safety]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Notebook|Notebook]]<br />
|}<br />
<br><br />
<br />
== '''Who we are''' ==<br />
{|border = "0"<br />
|-<br />
|rowspan="3"|<br />
<br />
'''Masterminds:'''<br />
<br />
*'''Graham Cromar''': The Wizard of Id<br />
*'''Stacy Hung''': Mini Wheats<br />
*'''Daniel Wong''': The Architect <br />
*'''Conrad Lochovsky''': The Invisible Man<br />
*'''Natalie Yeung''': The Strategist <br />
*'''Farhan Raja''': Dr. Zoidberg<br />
<br />
<br />
'''Lowly Minions:'''<br />
<br />
*'''Kenny Zhan''': Mad Scientist<br />
*'''Yen Leung''': Elastigirl<br />
*'''Meah Gao''': The Bionic Woman<br />
*'''James Juras''': The Sporatic Action Man<br />
<br />
|<br />
<gallery><br />
Image:JohnParkinson.jpg|Dr. John Parkinson<br />
Image:graham.jpg|Graham Cromar<br />
Image:Stacy_igem.jpg| Stacy Hung<br />
Image:tmdtDaniel.JPG|Daniel Wong<br />
Image:tmdtConrad.JPG| Conrad Lochovsky<br />
Image:tmdtNatalie.JPG| Natalie Yeung<br />
Image:tmdtFarhan.jpg| Farhan Raja<br />
<br />
Image:Ken_igem.JPG| Kenny Zhan<br />
Image:Yen_igem.JPG| Yen Leung<br />
Image:insert.JPG| Meah Gao<br />
Image:Jamescuba.jpg|James Juras<br />
</gallery><br />
|}<br />
<br />
== '''Where we're from''' ==<br />
<br />
'''Dr. John Parkinson''': a.k.a. The Dragon in the Dragon's Den<br />
<br />
Graduated from the University of Bath with a bachelor of science in Applied Biology in 1990. After receiving a PhD in Biochemistry from the University of Manchester in 1995, I completed a NATO fellowship at the University of Manitoba. From 1997 to 2000, I was awarded a fellowship at the Edinburgh Centre for Protein Technology, University of Edinburgh and from 2000 to 2003 completed another fellowship at the University of Edinburgh on Nematode genomics. I am currently a scientist at The Hospital for Sick Children Research Institute. The research in our laboratory is aimed at understanding how molecular information can give rise to complex biological behaviour. Using computational methods, we study the organization and dynamics of cellular components within the context of integrated biological systems. Comparative genomics methods are also being applied to provide insights into how these systems may have evolved from the remote origins of life.<br />
<br />
<br />
'''Graham Cromar''': a.k.a. The Wizard of Id<br />
<br />
I am a 4th year Ph.D. student in the Department of Molecular Structure and Function at the Hospital for Sick Children in Toronto. At various times in the past I have studied cell and molecular biology (B.Sc. Toronto), molecular biology and genetics (M.Sc. Guelph), computer programming and systems analysis (dip. Inst. Computer Studies, Toronto), bioinformatics (cert. Canadian Genetic Disease Network) and, systems and matrix biology (present). I have worked as a lab technician, teaching assistant, computer programmer/systems analyst and IS manager. But, what I would most like to do is what I wrote in my high school yearbook about 20 years ago... Design organisms for export to far away galaxies. Thanks to iGEM I'm 1/4 of the way there...<br />
<br />
<br />
'''Stacy Hung''': a.k.a. Mini Wheats<br />
<br />
With a B.Sc. Honours Biology and Bioinformatics from the University of Waterloo, Stacy is currently a 3rd year Ph.D. student at the University of Toronto. Her main focus is to identify novel enzyme drug targets against malaria by studying the metabolic networks of these parasites. She is inspired by anything that is new, exciting, and can have a long-term impact for making the world a better place -- iGEM is certainly one of these things.<br />
<br />
<br />
'''Daniel Wong''': a.k.a. The Architect<br />
<br />
Daniel Wong received his BASc in Engineering Science biomedical option at the University of Toronto. He is currently with the Institute of Biomaterials and Biomedical Engineering, working toward his PhD. He works in the Cochlear Implant Laboratory at the Hospital for Sick Children, developing neuroimaging algorithms for the analysis of multichannel EEG data. As design team lead for this year's iGEM team, he guided the design team in developing the protocols for creating the team's biobrick parts. His academic interests include neuroimaging and systems modelling. To relax, he enjoys a good round of golf or social salsa dancing.<br />
<br />
<br />
'''Conrad Lochovsky''': a.k.a. The Invisible Man<br />
<br />
Conrad Lochovsky completed his BASc in Biomedical Engineering in Toronto and is currently pursuing his MASc in the exciting area of microfluidics. With a minor in Economics, Conrad played a very important role as our treasurer. He has also been involved with past Toronto iGEM teams: 2006(design/lab), 2007(design/lab/finance) and is active on the executive of several other campus clubs.<br />
<br />
<br />
'''Natalie Yeung''': a.k.a. The Strategist <br />
<br />
I'm a graduate student at the University of Toronto's iSchool (sometimes known as the Faculty of Information). Having been involved in iGEM previously, it's been my privilege to see other people catch the synthetic biology bug each year. This team is a great example of the creativity of multidisciplinary groups, as well as iGEM's potential to be a catalyst for innovation (and some great stories!).<br />
<br />
<br />
'''Farhan Raja''': a.k.a. Dr. Zoidberg<br />
<br />
I did my undergrad in chemical engineering, and now I'm doing a Masters in Biochemistry. My grad work has to do with applying computational techniques (eg. FBA) towards the reconstruction and analysis of pathogenic metabolism. I am considering of a few different options for the future, but I think it will somehow involve synthetic biology because I find it very interesting. <br />
<br />
<br />
'''Kenny Zhan''': a.k.a. The Mad Scientist<br />
<br />
Hi everyone my name is Kenny Zhan and I am a third year undergraduate student. I am currently pursuing a specialization in biochemistry at the University of Toronto. This year I have been part of the iGEM design team at UofT and during the summer I have been fortunate enough to be part of the roster team that works in the lab to bring the design into reality. I find synthetic biology fascinating as I have an interest in developing new techniques and procedures to support the rapidly expanding field of biological sciences. In my free time I enjoy activities such as hiking, biking, ultimate and geocaching. Also you will see me from time to time updating our lab wiki. Hope to see you all down at the jamboree in Boston come October.<br />
<br />
<br />
'''Yen Leung''': a.k.a ElastiGirl<br />
<br />
Yen Leung has been an invaluable member of the iGem Wet lab team. She has always been around the lab helping out, doing experiments and keeping my (Kenny) craziness (when I come up with crazy ideas) and messiness in check. Currently Yen is pursuing a specialist degree in Nutrition and Neuroscience at the University of Toronto and in September '09 she will be entering her third year.<br />
<br />
<br />
'''Meah Gao''': a.k.a. The Bionic Woman<br />
<br />
Hi everyone! I am currently a 3rd-year undergraduate student at the University of Toronto specializing in Pathobiology and majoring in Cell and Systems biology. This year as part of the Toronto Mars Discovery iGEM team, my job is to apply bioinformatics methods to identify potential protein candidates for enzymatic channeling and explore alternative microcompartment platforms. Previously, I have also been involved in projects in Neurophysiology and Cellular & Molecular Biology. My current research interest lies in genomics studies using bioinformatics tools. <br />
<br />
<br />
'''James Juras''': a.k.a. The Sporadic Action Man<br />
<br />
Hey there, I'm a virgo and enjoy long snowboarding adventures in the mountains. Also in my spare time I'm a 4th year undergraduate specializing in Neuroscience at the University of Toronto. This summer I've been doing lots of work all over the place, but mainly my job has been to design the wiki you're presently navigating.</div>FRhttp://2009.igem.org/Team:TorontoMaRSDiscovery/TeamTeam:TorontoMaRSDiscovery/Team2009-10-21T14:20:41Z<p>FR: /* Where we're from */</p>
<hr />
<div>[[image:To_igem_wiki_banner.jpg|965px]]<br />
{| style="color:white;background-color:#99CCFF;" height:100px cellpadding="2" cellspacing="0" border="0" width="100%" align="center" class="menu"<br />
!align="center"|[[Team:TorontoMaRSDiscovery|Home]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Team|The Team]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Project|The Project]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Parts|BioBricks]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Modeling|Modeling]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Bioinformatics|Bioinformatics]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Safety|Safety]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Notebook|Notebook]]<br />
|}<br />
<br><br />
<br />
== '''Who we are''' ==<br />
{|border = "0"<br />
|-<br />
|rowspan="3"|<br />
<br />
'''Masterminds:'''<br />
<br />
*'''Graham Cromar''': The Wizard of Id<br />
*'''Stacy Hung''': Mini Wheats<br />
*'''Daniel Wong''': The Architect <br />
*'''Conrad Lochovsky''': The Invisible Man<br />
*'''Natalie Yeung''': The Strategist <br />
*'''Farhan Raja''': Dr. Zoidberg<br />
<br />
<br />
'''Lowly Minions:'''<br />
<br />
*'''Kenny Zhan''': Mad Scientist<br />
*'''Yen Leung''': Elastigirl<br />
*'''Meah Gao''': The Bionic Woman<br />
*'''James Juras''': The Sporatic Action Man<br />
<br />
|<br />
<gallery><br />
Image:JohnParkinson.jpg|Dr. John Parkinson<br />
Image:graham.jpg|Graham Cromar<br />
Image:Stacy_igem.jpg| Stacy Hung<br />
Image:tmdtDaniel.JPG|Daniel Wong<br />
Image:tmdtConrad.JPG| Conrad Lochovsky<br />
Image:tmdtNatalie.JPG| Natalie Yeung<br />
Image:Insert.jpg| Farhan Raja<br />
<br />
Image:Ken_igem.JPG| Kenny Zhan<br />
Image:Yen_igem.JPG| Yen Leung<br />
Image:insert.JPG| Meah Gao<br />
Image:Jamescuba.jpg|James Juras<br />
</gallery><br />
|}<br />
<br />
== '''Where we're from''' ==<br />
<br />
'''Dr. John Parkinson''': a.k.a. The Dragon in the Dragon's Den<br />
<br />
Graduated from the University of Bath with a bachelor of science in Applied Biology in 1990. After receiving a PhD in Biochemistry from the University of Manchester in 1995, I completed a NATO fellowship at the University of Manitoba. From 1997 to 2000, I was awarded a fellowship at the Edinburgh Centre for Protein Technology, University of Edinburgh and from 2000 to 2003 completed another fellowship at the University of Edinburgh on Nematode genomics. I am currently a scientist at The Hospital for Sick Children Research Institute. The research in our laboratory is aimed at understanding how molecular information can give rise to complex biological behaviour. Using computational methods, we study the organization and dynamics of cellular components within the context of integrated biological systems. Comparative genomics methods are also being applied to provide insights into how these systems may have evolved from the remote origins of life.<br />
<br />
<br />
'''Graham Cromar''': a.k.a. The Wizard of Id<br />
<br />
I am a 4th year Ph.D. student in the Department of Molecular Structure and Function at the Hospital for Sick Children in Toronto. At various times in the past I have studied cell and molecular biology (B.Sc. Toronto), molecular biology and genetics (M.Sc. Guelph), computer programming and systems analysis (dip. Inst. Computer Studies, Toronto), bioinformatics (cert. Canadian Genetic Disease Network) and, systems and matrix biology (present). I have worked as a lab technician, teaching assistant, computer programmer/systems analyst and IS manager. But, what I would most like to do is what I wrote in my high school yearbook about 20 years ago... Design organisms for export to far away galaxies. Thanks to iGEM I'm 1/4 of the way there...<br />
<br />
<br />
'''Stacy Hung''': a.k.a. Mini Wheats<br />
<br />
With a B.Sc. Honours Biology and Bioinformatics from the University of Waterloo, Stacy is currently a 3rd year Ph.D. student at the University of Toronto. Her main focus is to identify novel enzyme drug targets against malaria by studying the metabolic networks of these parasites. She is inspired by anything that is new, exciting, and can have a long-term impact for making the world a better place -- iGEM is certainly one of these things.<br />
<br />
<br />
'''Daniel Wong''': a.k.a. The Architect<br />
<br />
Daniel Wong received his BASc in Engineering Science biomedical option at the University of Toronto. He is currently with the Institute of Biomaterials and Biomedical Engineering, working toward his PhD. He works in the Cochlear Implant Laboratory at the Hospital for Sick Children, developing neuroimaging algorithms for the analysis of multichannel EEG data. As design team lead for this year's iGEM team, he guided the design team in developing the protocols for creating the team's biobrick parts. His academic interests include neuroimaging and systems modelling. To relax, he enjoys a good round of golf or social salsa dancing.<br />
<br />
<br />
'''Conrad Lochovsky''': a.k.a. The Invisible Man<br />
<br />
Conrad Lochovsky completed his BASc in Biomedical Engineering in Toronto and is currently pursuing his MASc in the exciting area of microfluidics. With a minor in Economics, Conrad played a very important role as our treasurer. He has also been involved with past Toronto iGEM teams: 2006(design/lab), 2007(design/lab/finance) and is active on the executive of several other campus clubs.<br />
<br />
<br />
'''Natalie Yeung''': a.k.a. The Strategist <br />
<br />
I'm a graduate student at the University of Toronto's iSchool (sometimes known as the Faculty of Information). Having been involved in iGEM previously, it's been my privilege to see other people catch the synthetic biology bug each year. This team is a great example of the creativity of multidisciplinary groups, as well as iGEM's potential to be a catalyst for innovation (and some great stories!).<br />
<br />
<br />
'''Farhan Raja''': a.k.a. Dr. Zoidberg<br />
<br />
I did my undergrad in chemical engineering, and now I'm doing a Masters in Biochemistry. My grad work has to do with applying computational techniques (eg. FBA) towards the reconstruction and analysis of pathogenic metabolism. I am considering of a few different options for the future, but I think it will somehow involve synthetic biology because I find it very interesting. <br />
<br />
<br />
'''Kenny Zhan''': a.k.a. The Mad Scientist<br />
<br />
Hi everyone my name is Kenny Zhan and I am a third year undergraduate student. I am currently pursuing a specialization in biochemistry at the University of Toronto. This year I have been part of the iGEM design team at UofT and during the summer I have been fortunate enough to be part of the roster team that works in the lab to bring the design into reality. I find synthetic biology fascinating as I have an interest in developing new techniques and procedures to support the rapidly expanding field of biological sciences. In my free time I enjoy activities such as hiking, biking, ultimate and geocaching. Also you will see me from time to time updating our lab wiki. Hope to see you all down at the jamboree in Boston come October.<br />
<br />
<br />
'''Yen Leung''': a.k.a ElastiGirl<br />
<br />
Yen Leung has been an invaluable member of the iGem Wet lab team. She has always been around the lab helping out, doing experiments and keeping my (Kenny) craziness (when I come up with crazy ideas) and messiness in check. Currently Yen is pursuing a specialist degree in Nutrition and Neuroscience at the University of Toronto and in September '09 she will be entering her third year.<br />
<br />
<br />
'''Meah Gao''': a.k.a. The Bionic Woman<br />
<br />
Hi everyone! I am currently a 3rd-year undergraduate student at the University of Toronto specializing in Pathobiology and majoring in Cell and Systems biology. This year as part of the Toronto Mars Discovery iGEM team, my job is to apply bioinformatics methods to identify potential protein candidates for enzymatic channeling and explore alternative microcompartment platforms. Previously, I have also been involved in projects in Neurophysiology and Cellular & Molecular Biology. My current research interest lies in genomics studies using bioinformatics tools. <br />
<br />
<br />
'''James Juras''': a.k.a. The Sporadic Action Man<br />
<br />
Hey there, I'm a virgo and enjoy long snowboarding adventures in the mountains. Also in my spare time I'm a 4th year undergraduate specializing in Neuroscience at the University of Toronto. This summer I've been doing lots of work all over the place, but mainly my job has been to design the wiki you're presently navigating.</div>FRhttp://2009.igem.org/Team:TorontoMaRSDiscovery/TeamTeam:TorontoMaRSDiscovery/Team2009-10-21T14:20:12Z<p>FR: /* Where we're from */</p>
<hr />
<div>[[image:To_igem_wiki_banner.jpg|965px]]<br />
{| style="color:white;background-color:#99CCFF;" height:100px cellpadding="2" cellspacing="0" border="0" width="100%" align="center" class="menu"<br />
!align="center"|[[Team:TorontoMaRSDiscovery|Home]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Team|The Team]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Project|The Project]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Parts|BioBricks]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Modeling|Modeling]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Bioinformatics|Bioinformatics]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Safety|Safety]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Notebook|Notebook]]<br />
|}<br />
<br><br />
<br />
== '''Who we are''' ==<br />
{|border = "0"<br />
|-<br />
|rowspan="3"|<br />
<br />
'''Masterminds:'''<br />
<br />
*'''Graham Cromar''': The Wizard of Id<br />
*'''Stacy Hung''': Mini Wheats<br />
*'''Daniel Wong''': The Architect <br />
*'''Conrad Lochovsky''': The Invisible Man<br />
*'''Natalie Yeung''': The Strategist <br />
*'''Farhan Raja''': Dr. Zoidberg<br />
<br />
<br />
'''Lowly Minions:'''<br />
<br />
*'''Kenny Zhan''': Mad Scientist<br />
*'''Yen Leung''': Elastigirl<br />
*'''Meah Gao''': The Bionic Woman<br />
*'''James Juras''': The Sporatic Action Man<br />
<br />
|<br />
<gallery><br />
Image:JohnParkinson.jpg|Dr. John Parkinson<br />
Image:graham.jpg|Graham Cromar<br />
Image:Stacy_igem.jpg| Stacy Hung<br />
Image:tmdtDaniel.JPG|Daniel Wong<br />
Image:tmdtConrad.JPG| Conrad Lochovsky<br />
Image:tmdtNatalie.JPG| Natalie Yeung<br />
Image:Insert.jpg| Farhan Raja<br />
<br />
Image:Ken_igem.JPG| Kenny Zhan<br />
Image:Yen_igem.JPG| Yen Leung<br />
Image:insert.JPG| Meah Gao<br />
Image:Jamescuba.jpg|James Juras<br />
</gallery><br />
|}<br />
<br />
== '''Where we're from''' ==<br />
<br />
'''Dr. John Parkinson''': a.k.a. The Dragon in the Dragon's Den<br />
<br />
Graduated from the University of Bath with a bachelor of science in Applied Biology in 1990. After receiving a PhD in Biochemistry from the University of Manchester in 1995, I completed a NATO fellowship at the University of Manitoba. From 1997 to 2000, I was awarded a fellowship at the Edinburgh Centre for Protein Technology, University of Edinburgh and from 2000 to 2003 completed another fellowship at the University of Edinburgh on Nematode genomics. I am currently a scientist at The Hospital for Sick Children Research Institute. The research in our laboratory is aimed at understanding how molecular information can give rise to complex biological behaviour. Using computational methods, we study the organization and dynamics of cellular components within the context of integrated biological systems. Comparative genomics methods are also being applied to provide insights into how these systems may have evolved from the remote origins of life.<br />
<br />
<br />
'''Graham Cromar''': a.k.a. The Wizard of Id<br />
<br />
I am a 4th year Ph.D. student in the Department of Molecular Structure and Function at the Hospital for Sick Children in Toronto. At various times in the past I have studied cell and molecular biology (B.Sc. Toronto), molecular biology and genetics (M.Sc. Guelph), computer programming and systems analysis (dip. Inst. Computer Studies, Toronto), bioinformatics (cert. Canadian Genetic Disease Network) and, systems and matrix biology (present). I have worked as a lab technician, teaching assistant, computer programmer/systems analyst and IS manager. But, what I would most like to do is what I wrote in my high school yearbook about 20 years ago... Design organisms for export to far away galaxies. Thanks to iGEM I'm 1/4 of the way there...<br />
<br />
<br />
'''Stacy Hung''': a.k.a. Mini Wheats<br />
<br />
With a B.Sc. Honours Biology and Bioinformatics from the University of Waterloo, Stacy is currently a 3rd year Ph.D. student at the University of Toronto. Her main focus is to identify novel enzyme drug targets against malaria by studying the metabolic networks of these parasites. She is inspired by anything that is new, exciting, and can have a long-term impact for making the world a better place -- iGEM is certainly one of these things.<br />
<br />
<br />
'''Daniel Wong''': a.k.a. The Architect<br />
<br />
Daniel Wong received his BASc in Engineering Science biomedical option at the University of Toronto. He is currently with the Institute of Biomaterials and Biomedical Engineering, working toward his PhD. He works in the Cochlear Implant Laboratory at the Hospital for Sick Children, developing neuroimaging algorithms for the analysis of multichannel EEG data. As design team lead for this year's iGEM team, he guided the design team in developing the protocols for creating the team's biobrick parts. His academic interests include neuroimaging and systems modelling. To relax, he enjoys a good round of golf or social salsa dancing.<br />
<br />
<br />
'''Conrad Lochovsky''': a.k.a. The Invisible Man<br />
<br />
Conrad Lochovsky completed his BASc in Biomedical Engineering in Toronto and is currently pursuing his MASc in the exciting area of microfluidics. With a minor in Economics, Conrad played a very important role as our treasurer. He has also been involved with past Toronto iGEM teams: 2006(design/lab), 2007(design/lab/finance) and is active on the executive of several other campus clubs.<br />
<br />
<br />
'''Natalie Yeung''': a.k.a. The Strategist <br />
<br />
I'm a graduate student at the University of Toronto's iSchool (sometimes known as the Faculty of Information). Having been involved in iGEM previously, it's been my privilege to see other people catch the synthetic biology bug each year. This team is a great example of the creativity of multidisciplinary groups, as well as iGEM's potential to be a catalyst for innovation (and some great stories!).<br />
<br />
<br />
'''Farhan Raja''': a.k.a. Dr. Zoidberg<br />
<br />
I did my undergrad in chemical engineering, and now I'm doing a Masters in Biochemistry. My grad work has to do with applying computational techniques (eg. FBA) towards the reconstruction and analysis of pathogenic metabolism. I am considering of a few different options for the future, but I think it will somehow involve synthetic biology because I find it very exciting. <br />
<br />
<br />
'''Kenny Zhan''': a.k.a. The Mad Scientist<br />
<br />
Hi everyone my name is Kenny Zhan and I am a third year undergraduate student. I am currently pursuing a specialization in biochemistry at the University of Toronto. This year I have been part of the iGEM design team at UofT and during the summer I have been fortunate enough to be part of the roster team that works in the lab to bring the design into reality. I find synthetic biology fascinating as I have an interest in developing new techniques and procedures to support the rapidly expanding field of biological sciences. In my free time I enjoy activities such as hiking, biking, ultimate and geocaching. Also you will see me from time to time updating our lab wiki. Hope to see you all down at the jamboree in Boston come October.<br />
<br />
<br />
'''Yen Leung''': a.k.a ElastiGirl<br />
<br />
Yen Leung has been an invaluable member of the iGem Wet lab team. She has always been around the lab helping out, doing experiments and keeping my (Kenny) craziness (when I come up with crazy ideas) and messiness in check. Currently Yen is pursuing a specialist degree in Nutrition and Neuroscience at the University of Toronto and in September '09 she will be entering her third year.<br />
<br />
<br />
'''Meah Gao''': a.k.a. The Bionic Woman<br />
<br />
Hi everyone! I am currently a 3rd-year undergraduate student at the University of Toronto specializing in Pathobiology and majoring in Cell and Systems biology. This year as part of the Toronto Mars Discovery iGEM team, my job is to apply bioinformatics methods to identify potential protein candidates for enzymatic channeling and explore alternative microcompartment platforms. Previously, I have also been involved in projects in Neurophysiology and Cellular & Molecular Biology. My current research interest lies in genomics studies using bioinformatics tools. <br />
<br />
<br />
'''James Juras''': a.k.a. The Sporadic Action Man<br />
<br />
Hey there, I'm a virgo and enjoy long snowboarding adventures in the mountains. Also in my spare time I'm a 4th year undergraduate specializing in Neuroscience at the University of Toronto. This summer I've been doing lots of work all over the place, but mainly my job has been to design the wiki you're presently navigating.</div>FRhttp://2009.igem.org/Team:TorontoMaRSDiscovery/ModelingTeam:TorontoMaRSDiscovery/Modeling2009-10-21T14:15:38Z<p>FR: /* Summary */</p>
<hr />
<div>[[image:To_igem_wiki_banner.jpg|965px]]<br />
{| style="color:white;background-color:#99CCFF;" height:100px cellpadding="2" cellspacing="0" border="0" width="100%" align="center" class="menu"<br />
!align="center"|[[Team:TorontoMaRSDiscovery|Home]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Team|The Team]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Project|The Project]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Parts|BioBricks]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Modeling|Modeling]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Bioinformatics|Bioinformatics]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Safety|Safety]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Notebook|Notebook]]<br />
|}<br />
<br><br />
<br />
<br />
=Summary=<br />
<br />
A kinetic model of our system has been constructed. Approximate parameter values were gathered from online resources to represent all processes up to the production of the eCFP and Encapsulin proteins. Current simulations predict the production of these two proteins at various initial concentrations of IPTG and aTc effector molecules. A sensitivity analysis reveals that the rate of constitutive expression of lacI and tetR has the greatest effect on eCFP and Encapsulin concentrations. Furthermore, we have outlined approaches for the detailed modelling of the eCFP degredation/maturation and Encapsulin assembly pathways.<br />
<br />
<br />
The initial simulations will be used to identify a critical concentration of Encapsulin mononomer required for microcompartment assembly. To strengthen the model, the constitutive expression rate of BBa_J23100 (our most sensitive parameter) will be experimentally determined. Subsequently, a detailed model of Encapsulin assembly will be integrated into the current model, and its parameters filled-in using parameter-scanning methods and experiments outlined in the relevant references. By comparing experimental measures of microcompartment formation with that predicted by the kinetic model, we aim to gain insight on the mechanisms of Encapsulin assembly.<br />
<br />
=Model=<br />
Our model is based on the following design (See Project Page for a full description of this system).<br />
[[image:BioBrick.png|thumb|centre|The Encapsulator]]<br />
<br />
The reaction framework was mainly generated using the [http://synbioss.sourceforge.net/ SynBioSS Designer (a really useful modeling tool for iGEM teams)], which also provides default parameter values. These parameter values have been gathered from various literature [http://neptune.cems.umn.edu/designer/designer_defaults.pdf sources], and should be taken as approximations. All units were taken to be (1 / molarity^n-1 * s), where n is the order of the reaction. For example, for the reaction 2 lacI --> lacI2, n = 2, thus the rate constant has the units 1/molarity*s. <br />
<br />
The pathways for the expressed proteins, eCFPt and Encapsulin, need to be modeled in more detail. For example, in this basic model eCFPt is degraded via a first order reaction and Encapsulin makes a dimer complex. However, in reality fluorescent proteins have been shown to degreade via Micheales-menton kinetics and Encapsulin is thought to make a complex of about 60 monomers. These issues will be addressed in future work.<br />
<br />
'''The reactions can be accessed here:'''<br />
<br />
[[The Encapsulator Model]] (opens new page)<br />
<br />
[[Media:Uft_mod_Rxns2.xls|Download Encapsulator Model ]] (download Excel file)<br />
<br />
=Simulations=<br />
<br />
All simulations were carried out using the [https://2009.igem.org/Partner_Offers SimBiology Matlab Toolbox], which was freely available to iGEM teams. <br />
<br />
===Accumulation of eCFP at Different Initial Concentrations of IPTG===<br />
<br />
[[Image:uft_mod_cfp-iptg.png | 900px]]<br />
<br />
The IPTG effector eventually loses effect, and the eCFP concentration approaches a maximum. This happens because the IPTG proteins eventually ''tie up'' all available LacI4 proteins, leaving the transcription and translation of eCFP to operate at its maxiumum rate. <br />
<br />
===Accumulation of Encapsulin monomer at Different Initial Concentrations of aTc===<br />
<br />
[[Image:uft_mod_enc-atc.png | 900px]]<br />
<br />
(NOTE: in order to observe Encapsulin monomer levels, the above simulations were carried out without any Encapsulin assembly reactions in place)<br />
<br />
The production of Encapsulin occurs at a slower rate than eCFP because the BBa_R0040 promoter has two tetR binding sites, resulting in more repression and more off-pathway scenarios. Thus, the Encapsulin concentration also seems assymptotic but at higher concentrations of aTc (relative to IPTG). <br />
<br />
It seems beneficial to have the Encapsulin protein under control of the BBa_R0040-tetR-aTc construct because at zero levels of aTc we can have essentially zero levels of Encapsulin (whereas even at zero levels of IPTG, there is still significantly more eCFP). This will enable us to probe extremely low concentrations of Encapsulin monomer when testing for optimal Encapsulin assembly conditions. The disadvantage is that if Encapsulin assembly requires a very high initial concentration of Encapsulin monomer, we would have to wait a long time to see microcompartments. If this later scenario is observed, it may be better to switch the eCFP and Encapsulin expression systems.<br />
<br />
===Sensitivity Analysis===<br />
<br />
Since all of our parameters are approximations from literature sources, those which have the greatest affect on system dynamics (ie. the most ''sensitive'' parameters) would be leading candidates to be experimentally determined. Currently we are interested in the parameters that have the greatest effect on the production of eCFP and Encapsulin. Ideally, it would be best to tighten-up the model by experimentally determining these, before incorporating the largely unexplored Encapsulin assembly pathways. <br />
<br />
<br />
'''1) Sensitivity of eCFP Production'''<br />
<br />
[[Image:uft_mod_SAecfp.png | centre | 600px]]<br />
<br />
<br />
<br />
'''2) Sensitivity of Encapsulin Production'''<br />
<br />
[[Image:uft_mod_SAenc.png | centre | 600px]]<br />
<br />
Parameters 1 and 2 correspond to the rates of constitutive expression of the repressors lacI and tetR respectively. Thus, it is predicted that eCFP and Encapsulin production is largely sensitive to the expression rates of lacI and tetR. <br />
<br />
The specific constitutive promoter used in our construct is BBa_J23100. In our model, this was given the generic rate of 1E-10 molarity\s by SynBioSS based on a variety of empirically-fitted protein expression rates found in literature. This generic approach to assigning parameter values is a suitable fist-step, but our sensitivity results suggest that experimentally determining the expression rate of BBa_J23100 should significantly improve our model's predictive capability.<br />
<br />
=Future Work=<br />
<br />
Improvements to the basic model presented above can be separated into three areas; 1) performing experiments to determine parameter values that are specific to our system, 2) more detailed modeling of eCFPt behavior, 3) more detailed modeling of Encapsulin assembly. <br />
<br />
The experiments required to determine general transcription and translation parameters need to be further researched, so this will be skipped over for now. Here we will discuss the more interesting areas – the detailed modeling of eCFP and Encapsulin pathways. This will be accomplished by incorporating previous modeling efforts that are applicable to the eCFP and Encapsulin proteins. <br />
<br />
===Maturation and Degredation of eCFP===<br />
<br />
The expression and degradation of [http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=95514&blobtype=pdf Green Fluorescent Protein (GFP) was modeled previously]. This paper noted that GFP must mature before going into fluorescent phase, and GFP degradation was shown to follow M-M kinetics, as depicted below. This paper also outlined how the degradation parameters could be derived for any expression system using only simple fluorescence and optical density measurements.<br />
<br />
[[Image:uft_mod_ecfp1.png | centre | thumb | Degredation and maturation pathways for eCFP. (Leveau and Lindow 2001)]]<br />
<br />
<br />
The GFP maturation and degradation parameters found in this paper were:<br />
<br />
<html><br />
<centre><br />
<table><br />
<tr><td> m = 0.0004279 1/s </td></tr><br />
<tr><td> Vmax = 2E-10 molality/s </td></tr><br />
<tr><td> Km = 9E-13 molality/s </td></tr><br />
<tr><td> </td></tr><br />
</table><br />
</centre><br />
</html><br />
<br />
<br />
Assuming eCFP would behave similarly to eGFP, the following additional reactions would be included in the model:<br />
<br />
<html><br />
<table><br />
<tr> <td><b> Maturation </b></td> <td> </td> </tr><br />
<tr> <td> eCFPt --> F_eCFPT </td> <td> 0.0004279 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Degradation </b></td> <td> </td> </tr><br />
<tr> <td> eCFPt --> </td> <td> Vmax = 2E-10 </td> </tr><br />
<tr> <td> </td> <td> Km = 9E-13 </td> </tr><br />
<tr> <td> F_eCFPt --> </td> <td> Vmax = 2E-10 </td> </tr><br />
<tr> <td> </td> <td> Km = 9E-13 </td> </tr><br />
</table><br />
</html><br />
<br />
===Assembly of Encapsulin Microcompartments===<br />
<br />
Though Encapsulin microcompartment assembly is not well-studied, it has been theorized to resemble the assembly of viral capsids. Thus, we could look to this relatively well-studied phenomenon as a representation of Encapsulin microcompartment assembly.<br />
<br />
Adam Zlotnick has published models of viral capsid assembly using different approaches. An early paper described an equilibrium model of assembly for a 12-unit polyhedral capsid head, and a more recent paper used a kinetic model that could be applied to many examples of spherical polymerization. We will consider how each approach could be incorporated as a representation of Encapsulin assembly.<br />
<br />
<br />
'''1) Equilibrim Approach to Encapsulin Assembly'''<br />
<br />
Zlotnick's [[Media:Uft_mod_to_build_a_virus_capsid.pdf|equilibrium-based model]] consists of reactions from an initial monomer subunit leading to a final capsid product. The sequential reactions take into account DeltaG for contact (Kn'), and parameters describing path degeneracy (varies for different intermediates).<br />
[[image:uft_mod_encap1.png|centre|thumb|Kn for assembly subunits based on path degeneracy. (Zlotnick 1994)]]<br />
<br />
<br />
'''2) Kinetic Model of Spherical Polymerization'''<br />
<br />
A [http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1302223/pdf/12124301.pdf general kinetic model for the spherical polyermization] process is shown below. In our case, the initial monomer subunit concentration (''u'') would represent our expressed Encapsulin BioBrick, and the number of monomers in the final assembly (''N'') is thought to be 60. All of the included parameters can be calculated from the four basic parameters; the microscopic, per-contact equilibrium constant (KAcon), the nucleus size (nuc), the nucleation on-rate (f_nuc), and the elongation on-rate (f_elong). The referenced paper describes methods to aquire these parameters from kinetic experiments, and provides examples for N = 12 and 30 unit viral capsid assemblies.<br />
[[image:uft_mod_encap2.png| centre | thumb |System of ODEs to represent spherical polymerization, where ''u'' is the initial subunit concentration, ''m'' is the "mth" intermediate species, and ''N'' is the number of monomers in the final assembly. (Endres and Zlotnick 2002)]]<br />
<br />
<br />
<br />
Zlotnick's models also describe two important features of spherical polymerization that we should also expect to observe in Encapsulin assembly: kinetic trapping and nucleation. A kinetic trap occurs when the initial monomer subunit concentration or the release of Gibbs free energy (deltaG) of the first assembly reaction is too high. This results in over-initiation of assembly and the reactions quickly become starved for subunits. Kinetic trapping is prevented by nucleation, where the initial reactions occur at a slower rate because the first few intermediates in a series of reactions are less stable than downstream products. Essentially, nucleation serves as a “slow first step” that regulates the assembly pathway. <br />
<br />
It will be interesting to note how the translational dynamics of Encapsulin interplay with its assembly dynamics. Since our system does not start with any initial concentration of Encapsulin, there will be an optimum rate of production that essentially serves the role of nucleation – avoiding kinetic traps while still maintaining a maximum production of full Encapsulin assemblies.<br />
<br />
=References=<br />
<br />
1. Hill AD, Tomshine JR, Weeding EM, Sotiropoulos V, Kaznessis YN. ''SynBioSS: the synthetic biology modeling suite.'' Bioinformatics. 2008 Nov 1;24(21):2551-3. Epub 2008 Aug 30.<br />
[http://neptune.cems.umn.edu/designer/interface1.php SynBioSS Web Designer]<br />
<br />
2. Leveau JH, Lindow SE. ''Predictive and interpretive simulation of green fluorescent protein expression in<br />
reporter bacteria.'' J Bacteriol. 2001 Dec;183(23):6752-62.<br />
<br />
3. Endres D, Zlotnick A. ''Model-based analysis of assembly kinetics for virus capsids or other spherical<br />
polymers.'' Biophys J. 2002 Aug;83(2):1217-30.</div>FRhttp://2009.igem.org/Team:TorontoMaRSDiscovery/ModelingTeam:TorontoMaRSDiscovery/Modeling2009-10-21T14:11:12Z<p>FR: /* Future Work */</p>
<hr />
<div>[[image:To_igem_wiki_banner.jpg|965px]]<br />
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!align="center"|[[Team:TorontoMaRSDiscovery|Home]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Team|The Team]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Project|The Project]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Parts|BioBricks]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Modeling|Modeling]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Bioinformatics|Bioinformatics]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Safety|Safety]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Notebook|Notebook]]<br />
|}<br />
<br><br />
<br />
<br />
=Summary=<br />
<br />
A kinetic model of our system has been constructed. Approximate parameter values were gathered from online resources to represent all processes up to the production of the eCFP and Encapsulin proteins. Current simulations predict the production of these two proteins at various initial concentrations of IPTG and aTc effector molecules. A sensitivity analysis reveals that the rate of constitutive expression of lacI and tetR has the greatest affect on eCFP and Encapsulin concentrations. Furthermore, we have outlined approaches for the detailed modelling of the eCFP degredation/maturation and Encapsulin assembly pathways.<br />
<br />
<br />
The initial simulations will be used to identify a critical concentration of Encapsulin mononomer required for microcompartment assembly. To strengthen the model, the constitutive expression rate of BBa_J23100 as used in our construct will be measured. Subsequently, a detailed model of Encapsulin assembly will be integrated into the current model, and its parameters filled-in using parameter-scanning methods and experiments outlined in the relevant references. By comparing experimental measures of microcompartment formation with that predicted by the kinetic model, we aim to gain insight on the mechanisms of Encapsulin assembly.<br />
<br />
=Model=<br />
Our model is based on the following design (See Project Page for a full description of this system).<br />
[[image:BioBrick.png|thumb|centre|The Encapsulator]]<br />
<br />
The reaction framework was mainly generated using the [http://synbioss.sourceforge.net/ SynBioSS Designer (a really useful modeling tool for iGEM teams)], which also provides default parameter values. These parameter values have been gathered from various literature [http://neptune.cems.umn.edu/designer/designer_defaults.pdf sources], and should be taken as approximations. All units were taken to be (1 / molarity^n-1 * s), where n is the order of the reaction. For example, for the reaction 2 lacI --> lacI2, n = 2, thus the rate constant has the units 1/molarity*s. <br />
<br />
The pathways for the expressed proteins, eCFPt and Encapsulin, need to be modeled in more detail. For example, in this basic model eCFPt is degraded via a first order reaction and Encapsulin makes a dimer complex. However, in reality fluorescent proteins have been shown to degreade via Micheales-menton kinetics and Encapsulin is thought to make a complex of about 60 monomers. These issues will be addressed in future work.<br />
<br />
'''The reactions can be accessed here:'''<br />
<br />
[[The Encapsulator Model]] (opens new page)<br />
<br />
[[Media:Uft_mod_Rxns2.xls|Download Encapsulator Model ]] (download Excel file)<br />
<br />
=Simulations=<br />
<br />
All simulations were carried out using the [https://2009.igem.org/Partner_Offers SimBiology Matlab Toolbox], which was freely available to iGEM teams. <br />
<br />
===Accumulation of eCFP at Different Initial Concentrations of IPTG===<br />
<br />
[[Image:uft_mod_cfp-iptg.png | 900px]]<br />
<br />
The IPTG effector eventually loses effect, and the eCFP concentration approaches a maximum. This happens because the IPTG proteins eventually ''tie up'' all available LacI4 proteins, leaving the transcription and translation of eCFP to operate at its maxiumum rate. <br />
<br />
===Accumulation of Encapsulin monomer at Different Initial Concentrations of aTc===<br />
<br />
[[Image:uft_mod_enc-atc.png | 900px]]<br />
<br />
(NOTE: in order to observe Encapsulin monomer levels, the above simulations were carried out without any Encapsulin assembly reactions in place)<br />
<br />
The production of Encapsulin occurs at a slower rate than eCFP because the BBa_R0040 promoter has two tetR binding sites, resulting in more repression and more off-pathway scenarios. Thus, the Encapsulin concentration also seems assymptotic but at higher concentrations of aTc (relative to IPTG). <br />
<br />
It seems beneficial to have the Encapsulin protein under control of the BBa_R0040-tetR-aTc construct because at zero levels of aTc we can have essentially zero levels of Encapsulin (whereas even at zero levels of IPTG, there is still significantly more eCFP). This will enable us to probe extremely low concentrations of Encapsulin monomer when testing for optimal Encapsulin assembly conditions. The disadvantage is that if Encapsulin assembly requires a very high initial concentration of Encapsulin monomer, we would have to wait a long time to see microcompartments. If this later scenario is observed, it may be better to switch the eCFP and Encapsulin expression systems.<br />
<br />
===Sensitivity Analysis===<br />
<br />
Since all of our parameters are approximations from literature sources, those which have the greatest affect on system dynamics (ie. the most ''sensitive'' parameters) would be leading candidates to be experimentally determined. Currently we are interested in the parameters that have the greatest effect on the production of eCFP and Encapsulin. Ideally, it would be best to tighten-up the model by experimentally determining these, before incorporating the largely unexplored Encapsulin assembly pathways. <br />
<br />
<br />
'''1) Sensitivity of eCFP Production'''<br />
<br />
[[Image:uft_mod_SAecfp.png | centre | 600px]]<br />
<br />
<br />
<br />
'''2) Sensitivity of Encapsulin Production'''<br />
<br />
[[Image:uft_mod_SAenc.png | centre | 600px]]<br />
<br />
Parameters 1 and 2 correspond to the rates of constitutive expression of the repressors lacI and tetR respectively. Thus, it is predicted that eCFP and Encapsulin production is largely sensitive to the expression rates of lacI and tetR. <br />
<br />
The specific constitutive promoter used in our construct is BBa_J23100. In our model, this was given the generic rate of 1E-10 molarity\s by SynBioSS based on a variety of empirically-fitted protein expression rates found in literature. This generic approach to assigning parameter values is a suitable fist-step, but our sensitivity results suggest that experimentally determining the expression rate of BBa_J23100 should significantly improve our model's predictive capability.<br />
<br />
=Future Work=<br />
<br />
Improvements to the basic model presented above can be separated into three areas; 1) performing experiments to determine parameter values that are specific to our system, 2) more detailed modeling of eCFPt behavior, 3) more detailed modeling of Encapsulin assembly. <br />
<br />
The experiments required to determine general transcription and translation parameters need to be further researched, so this will be skipped over for now. Here we will discuss the more interesting areas – the detailed modeling of eCFP and Encapsulin pathways. This will be accomplished by incorporating previous modeling efforts that are applicable to the eCFP and Encapsulin proteins. <br />
<br />
===Maturation and Degredation of eCFP===<br />
<br />
The expression and degradation of [http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=95514&blobtype=pdf Green Fluorescent Protein (GFP) was modeled previously]. This paper noted that GFP must mature before going into fluorescent phase, and GFP degradation was shown to follow M-M kinetics, as depicted below. This paper also outlined how the degradation parameters could be derived for any expression system using only simple fluorescence and optical density measurements.<br />
<br />
[[Image:uft_mod_ecfp1.png | centre | thumb | Degredation and maturation pathways for eCFP. (Leveau and Lindow 2001)]]<br />
<br />
<br />
The GFP maturation and degradation parameters found in this paper were:<br />
<br />
<html><br />
<centre><br />
<table><br />
<tr><td> m = 0.0004279 1/s </td></tr><br />
<tr><td> Vmax = 2E-10 molality/s </td></tr><br />
<tr><td> Km = 9E-13 molality/s </td></tr><br />
<tr><td> </td></tr><br />
</table><br />
</centre><br />
</html><br />
<br />
<br />
Assuming eCFP would behave similarly to eGFP, the following additional reactions would be included in the model:<br />
<br />
<html><br />
<table><br />
<tr> <td><b> Maturation </b></td> <td> </td> </tr><br />
<tr> <td> eCFPt --> F_eCFPT </td> <td> 0.0004279 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Degradation </b></td> <td> </td> </tr><br />
<tr> <td> eCFPt --> </td> <td> Vmax = 2E-10 </td> </tr><br />
<tr> <td> </td> <td> Km = 9E-13 </td> </tr><br />
<tr> <td> F_eCFPt --> </td> <td> Vmax = 2E-10 </td> </tr><br />
<tr> <td> </td> <td> Km = 9E-13 </td> </tr><br />
</table><br />
</html><br />
<br />
===Assembly of Encapsulin Microcompartments===<br />
<br />
Though Encapsulin microcompartment assembly is not well-studied, it has been theorized to resemble the assembly of viral capsids. Thus, we could look to this relatively well-studied phenomenon as a representation of Encapsulin microcompartment assembly.<br />
<br />
Adam Zlotnick has published models of viral capsid assembly using different approaches. An early paper described an equilibrium model of assembly for a 12-unit polyhedral capsid head, and a more recent paper used a kinetic model that could be applied to many examples of spherical polymerization. We will consider how each approach could be incorporated as a representation of Encapsulin assembly.<br />
<br />
<br />
'''1) Equilibrim Approach to Encapsulin Assembly'''<br />
<br />
Zlotnick's [[Media:Uft_mod_to_build_a_virus_capsid.pdf|equilibrium-based model]] consists of reactions from an initial monomer subunit leading to a final capsid product. The sequential reactions take into account DeltaG for contact (Kn'), and parameters describing path degeneracy (varies for different intermediates).<br />
[[image:uft_mod_encap1.png|centre|thumb|Kn for assembly subunits based on path degeneracy. (Zlotnick 1994)]]<br />
<br />
<br />
'''2) Kinetic Model of Spherical Polymerization'''<br />
<br />
A [http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1302223/pdf/12124301.pdf general kinetic model for the spherical polyermization] process is shown below. In our case, the initial monomer subunit concentration (''u'') would represent our expressed Encapsulin BioBrick, and the number of monomers in the final assembly (''N'') is thought to be 60. All of the included parameters can be calculated from the four basic parameters; the microscopic, per-contact equilibrium constant (KAcon), the nucleus size (nuc), the nucleation on-rate (f_nuc), and the elongation on-rate (f_elong). The referenced paper describes methods to aquire these parameters from kinetic experiments, and provides examples for N = 12 and 30 unit viral capsid assemblies.<br />
[[image:uft_mod_encap2.png| centre | thumb |System of ODEs to represent spherical polymerization, where ''u'' is the initial subunit concentration, ''m'' is the "mth" intermediate species, and ''N'' is the number of monomers in the final assembly. (Endres and Zlotnick 2002)]]<br />
<br />
<br />
<br />
Zlotnick's models also describe two important features of spherical polymerization that we should also expect to observe in Encapsulin assembly: kinetic trapping and nucleation. A kinetic trap occurs when the initial monomer subunit concentration or the release of Gibbs free energy (deltaG) of the first assembly reaction is too high. This results in over-initiation of assembly and the reactions quickly become starved for subunits. Kinetic trapping is prevented by nucleation, where the initial reactions occur at a slower rate because the first few intermediates in a series of reactions are less stable than downstream products. Essentially, nucleation serves as a “slow first step” that regulates the assembly pathway. <br />
<br />
It will be interesting to note how the translational dynamics of Encapsulin interplay with its assembly dynamics. Since our system does not start with any initial concentration of Encapsulin, there will be an optimum rate of production that essentially serves the role of nucleation – avoiding kinetic traps while still maintaining a maximum production of full Encapsulin assemblies.<br />
<br />
=References=<br />
<br />
1. Hill AD, Tomshine JR, Weeding EM, Sotiropoulos V, Kaznessis YN. ''SynBioSS: the synthetic biology modeling suite.'' Bioinformatics. 2008 Nov 1;24(21):2551-3. Epub 2008 Aug 30.<br />
[http://neptune.cems.umn.edu/designer/interface1.php SynBioSS Web Designer]<br />
<br />
2. Leveau JH, Lindow SE. ''Predictive and interpretive simulation of green fluorescent protein expression in<br />
reporter bacteria.'' J Bacteriol. 2001 Dec;183(23):6752-62.<br />
<br />
3. Endres D, Zlotnick A. ''Model-based analysis of assembly kinetics for virus capsids or other spherical<br />
polymers.'' Biophys J. 2002 Aug;83(2):1217-30.</div>FRhttp://2009.igem.org/Team:TorontoMaRSDiscovery/ModelingTeam:TorontoMaRSDiscovery/Modeling2009-10-21T14:08:12Z<p>FR: /* Assembly of Encapsulin Microcompartments */</p>
<hr />
<div>[[image:To_igem_wiki_banner.jpg|965px]]<br />
{| style="color:white;background-color:#99CCFF;" height:100px cellpadding="2" cellspacing="0" border="0" width="100%" align="center" class="menu"<br />
!align="center"|[[Team:TorontoMaRSDiscovery|Home]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Team|The Team]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Project|The Project]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Parts|BioBricks]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Modeling|Modeling]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Bioinformatics|Bioinformatics]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Safety|Safety]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Notebook|Notebook]]<br />
|}<br />
<br><br />
<br />
<br />
=Summary=<br />
<br />
A kinetic model of our system has been constructed. Approximate parameter values were gathered from online resources to represent all processes up to the production of the eCFP and Encapsulin proteins. Current simulations predict the production of these two proteins at various initial concentrations of IPTG and aTc effector molecules. A sensitivity analysis reveals that the rate of constitutive expression of lacI and tetR has the greatest affect on eCFP and Encapsulin concentrations. Furthermore, we have outlined approaches for the detailed modelling of the eCFP degredation/maturation and Encapsulin assembly pathways.<br />
<br />
<br />
The initial simulations will be used to identify a critical concentration of Encapsulin mononomer required for microcompartment assembly. To strengthen the model, the constitutive expression rate of BBa_J23100 as used in our construct will be measured. Subsequently, a detailed model of Encapsulin assembly will be integrated into the current model, and its parameters filled-in using parameter-scanning methods and experiments outlined in the relevant references. By comparing experimental measures of microcompartment formation with that predicted by the kinetic model, we aim to gain insight on the mechanisms of Encapsulin assembly.<br />
<br />
=Model=<br />
Our model is based on the following design (See Project Page for a full description of this system).<br />
[[image:BioBrick.png|thumb|centre|The Encapsulator]]<br />
<br />
The reaction framework was mainly generated using the [http://synbioss.sourceforge.net/ SynBioSS Designer (a really useful modeling tool for iGEM teams)], which also provides default parameter values. These parameter values have been gathered from various literature [http://neptune.cems.umn.edu/designer/designer_defaults.pdf sources], and should be taken as approximations. All units were taken to be (1 / molarity^n-1 * s), where n is the order of the reaction. For example, for the reaction 2 lacI --> lacI2, n = 2, thus the rate constant has the units 1/molarity*s. <br />
<br />
The pathways for the expressed proteins, eCFPt and Encapsulin, need to be modeled in more detail. For example, in this basic model eCFPt is degraded via a first order reaction and Encapsulin makes a dimer complex. However, in reality fluorescent proteins have been shown to degreade via Micheales-menton kinetics and Encapsulin is thought to make a complex of about 60 monomers. These issues will be addressed in future work.<br />
<br />
'''The reactions can be accessed here:'''<br />
<br />
[[The Encapsulator Model]] (opens new page)<br />
<br />
[[Media:Uft_mod_Rxns2.xls|Download Encapsulator Model ]] (download Excel file)<br />
<br />
=Simulations=<br />
<br />
All simulations were carried out using the [https://2009.igem.org/Partner_Offers SimBiology Matlab Toolbox], which was freely available to iGEM teams. <br />
<br />
===Accumulation of eCFP at Different Initial Concentrations of IPTG===<br />
<br />
[[Image:uft_mod_cfp-iptg.png | 900px]]<br />
<br />
The IPTG effector eventually loses effect, and the eCFP concentration approaches a maximum. This happens because the IPTG proteins eventually ''tie up'' all available LacI4 proteins, leaving the transcription and translation of eCFP to operate at its maxiumum rate. <br />
<br />
===Accumulation of Encapsulin monomer at Different Initial Concentrations of aTc===<br />
<br />
[[Image:uft_mod_enc-atc.png | 900px]]<br />
<br />
(NOTE: in order to observe Encapsulin monomer levels, the above simulations were carried out without any Encapsulin assembly reactions in place)<br />
<br />
The production of Encapsulin occurs at a slower rate than eCFP because the BBa_R0040 promoter has two tetR binding sites, resulting in more repression and more off-pathway scenarios. Thus, the Encapsulin concentration also seems assymptotic but at higher concentrations of aTc (relative to IPTG). <br />
<br />
It seems beneficial to have the Encapsulin protein under control of the BBa_R0040-tetR-aTc construct because at zero levels of aTc we can have essentially zero levels of Encapsulin (whereas even at zero levels of IPTG, there is still significantly more eCFP). This will enable us to probe extremely low concentrations of Encapsulin monomer when testing for optimal Encapsulin assembly conditions. The disadvantage is that if Encapsulin assembly requires a very high initial concentration of Encapsulin monomer, we would have to wait a long time to see microcompartments. If this later scenario is observed, it may be better to switch the eCFP and Encapsulin expression systems.<br />
<br />
===Sensitivity Analysis===<br />
<br />
Since all of our parameters are approximations from literature sources, those which have the greatest affect on system dynamics (ie. the most ''sensitive'' parameters) would be leading candidates to be experimentally determined. Currently we are interested in the parameters that have the greatest effect on the production of eCFP and Encapsulin. Ideally, it would be best to tighten-up the model by experimentally determining these, before incorporating the largely unexplored Encapsulin assembly pathways. <br />
<br />
<br />
'''1) Sensitivity of eCFP Production'''<br />
<br />
[[Image:uft_mod_SAecfp.png | centre | 600px]]<br />
<br />
<br />
<br />
'''2) Sensitivity of Encapsulin Production'''<br />
<br />
[[Image:uft_mod_SAenc.png | centre | 600px]]<br />
<br />
Parameters 1 and 2 correspond to the rates of constitutive expression of the repressors lacI and tetR respectively. Thus, it is predicted that eCFP and Encapsulin production is largely sensitive to the expression rates of lacI and tetR. <br />
<br />
The specific constitutive promoter used in our construct is BBa_J23100. In our model, this was given the generic rate of 1E-10 molarity\s by SynBioSS based on a variety of empirically-fitted protein expression rates found in literature. This generic approach to assigning parameter values is a suitable fist-step, but our sensitivity results suggest that experimentally determining the expression rate of BBa_J23100 should significantly improve our model's predictive capability.<br />
<br />
=Future Work=<br />
<br />
Improvements to the basic model presented above can be separated into three areas; 1) performing experiments to determine parameter values that are specific to our system, 2) more detailed modeling of eCFPt behavior, 3) more detailed modeling of Encapsulin assembly. <br />
<br />
The experiments required to determine general transcription and translation parameters need to be further researched, so this will be skipped over for now. Here we will discuss the more interesting areas – the detailed modeling of eCFP and Encapsulin pathways. This will be accomplished by incorporating previous modeling efforts that are applicable to the eCFP and Encapsulin proteins. <br />
<br />
===Maturation and Degredation of eCFP===<br />
<br />
The expression and degradation of [http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=95514&blobtype=pdf Green Fluorescent Protein (GFP) was modeled previously]. This paper noted that GFP must mature before going into fluorescent phase, and GFP degradation was shown to follow M-M kinetics, as depicted below. This paper also outlined how the degradation parameters could be derived for any expression system using only simple fluorescence and optical density measurements.<br />
<br />
[[Image:uft_mod_ecfp1.png | centre | thumb | Degredation and maturation pathways for eCFP. (Leveau and Lindow 2001)]]<br />
<br />
<br />
The GFP maturation and degradation parameters found in this paper were:<br />
<br />
<html><br />
<centre><br />
<table><br />
<tr><td> m = 0.0004279 1/s </td></tr><br />
<tr><td> Vmax = 2E-10 molality/s </td></tr><br />
<tr><td> Km = 9E-13 molality/s </td></tr><br />
<tr><td> </td></tr><br />
</table><br />
</centre><br />
</html><br />
<br />
<br />
Assuming eCFP would behave similarly to eGFP, the following additional reactions would be included in the model:<br />
<br />
<html><br />
<table><br />
<tr> <td><b> Maturation </b></td> <td> </td> </tr><br />
<tr> <td> eCFPt --> F_eCFPT </td> <td> 0.0004279 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Degradation </b></td> <td> </td> </tr><br />
<tr> <td> eCFPt --> </td> <td> Vmax = 2E-10 </td> </tr><br />
<tr> <td> </td> <td> Km = 9E-13 </td> </tr><br />
<tr> <td> F_eCFPt --> </td> <td> Vmax = 2E-10 </td> </tr><br />
<tr> <td> </td> <td> Km = 9E-13 </td> </tr><br />
</table><br />
</html><br />
<br />
===Assembly of Encapsulin Microcompartments===<br />
<br />
Though Encapsulin microcompartment assembly is not well-studied, it has been theorized to resemble the assembly of viral capsids. Thus, we could look to this relatively well-studied phenomenon as a representation of Encapsulin microcompartment assembly.<br />
<br />
Adam Zlotnick has published models of viral capsid assembly using different approaches. An early paper described an equilibrium model of assembly for a 12-unit polyhedral capsid head, and a more recent paper used a kinetic model that could be applied to many examples of spherical polymerization. We will consider how each approach could be incorporated as a representation of Encapsulin assembly.<br />
<br />
<br />
'''1) Equilibrim Approach to Encapsulin Assembly'''<br />
<br />
Zlotnick's [[Media:Uft_mod_to_build_a_virus_capsid.pdf|equilibrium-based model]] consists of reactions from an initial monomer subunit leading to a final capsid product. The sequential reactions take into account DeltaG for contact (Kn'), and parameters describing path degeneracy (varies for different intermediates).<br />
[[image:uft_mod_encap1.png|centre|thumb|Kn for assembly subunits based on path degeneracy. (Zlotnick 1994)]]<br />
<br />
<br />
'''2) Kinetic Model of Spherical Polymerization'''<br />
<br />
A [http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1302223/pdf/12124301.pdf general kinetic model for the spherical polyermization] process is shown below. In our case, the initial monomer subunit concentration (''u'') would represent our expressed Encapsulin BioBrick, and the number of monomers in the final assembly (''N'') is thought to be 60. All of the included parameters can be calculated from the four basic parameters; the microscopic, per-contact equilibrium constant (KAcon), the nucleus size (nuc), the nucleation on-rate (f_nuc), and the elongation on-rate (f_elong). The referenced paper describes methods to aquire these parameters from kinetic experiments, and provides examples for N = 12 and 30 unit viral capsid assemblies.<br />
[[image:uft_mod_encap2.png| centre | thumb |System of ODEs to represent spherical polymerization, where ''u'' is the initial subunit concentration, ''m'' is the "mth" intermediate species, and ''N'' is the number of monomers in the final assembly. (Endres and Zlotnick 2002)]]<br />
<br />
<br />
<br />
Zlotnick's models also describe two important features of spherical polymerization that we should also expect to observe in Encapsulin assembly: kinetic trapping and nucleation. A kinetic trap occurs when the initial monomer subunit concentration or the deltaG of the first assembly reaction is too high. This results in over-initiation of assembly and quickly the reactions become starved for subunits. Kinetic trapping is prevented by the inclusion of nucleation, where the initial reactions occur at a slower rate because the first few intermediates in a series of reactions are less stable than downstream products. Essentially, nucleation serves as a “slow first step” that regulates the assembly pathway. <br />
<br />
It will be interesting to note how the translational dynamics of Encapsulin interplay with its assembly dynamics. Since our system does not start with any initial concentration of Encapsulin, there will be an optimum rate of production that essentially serves the role of nucleation – avoiding kinetic traps while still maintaining a maximum production of full Encapsulin assemblies.<br />
<br />
=References=<br />
<br />
1. Hill AD, Tomshine JR, Weeding EM, Sotiropoulos V, Kaznessis YN. ''SynBioSS: the synthetic biology modeling suite.'' Bioinformatics. 2008 Nov 1;24(21):2551-3. Epub 2008 Aug 30.<br />
[http://neptune.cems.umn.edu/designer/interface1.php SynBioSS Web Designer]<br />
<br />
2. Leveau JH, Lindow SE. ''Predictive and interpretive simulation of green fluorescent protein expression in<br />
reporter bacteria.'' J Bacteriol. 2001 Dec;183(23):6752-62.<br />
<br />
3. Endres D, Zlotnick A. ''Model-based analysis of assembly kinetics for virus capsids or other spherical<br />
polymers.'' Biophys J. 2002 Aug;83(2):1217-30.</div>FRhttp://2009.igem.org/Team:TorontoMaRSDiscovery/ModelingTeam:TorontoMaRSDiscovery/Modeling2009-10-21T14:07:56Z<p>FR: /* Assembly of Encapsulin Microcompartments */</p>
<hr />
<div>[[image:To_igem_wiki_banner.jpg|965px]]<br />
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!align="center"|[[Team:TorontoMaRSDiscovery/Notebook|Notebook]]<br />
|}<br />
<br><br />
<br />
<br />
=Summary=<br />
<br />
A kinetic model of our system has been constructed. Approximate parameter values were gathered from online resources to represent all processes up to the production of the eCFP and Encapsulin proteins. Current simulations predict the production of these two proteins at various initial concentrations of IPTG and aTc effector molecules. A sensitivity analysis reveals that the rate of constitutive expression of lacI and tetR has the greatest affect on eCFP and Encapsulin concentrations. Furthermore, we have outlined approaches for the detailed modelling of the eCFP degredation/maturation and Encapsulin assembly pathways.<br />
<br />
<br />
The initial simulations will be used to identify a critical concentration of Encapsulin mononomer required for microcompartment assembly. To strengthen the model, the constitutive expression rate of BBa_J23100 as used in our construct will be measured. Subsequently, a detailed model of Encapsulin assembly will be integrated into the current model, and its parameters filled-in using parameter-scanning methods and experiments outlined in the relevant references. By comparing experimental measures of microcompartment formation with that predicted by the kinetic model, we aim to gain insight on the mechanisms of Encapsulin assembly.<br />
<br />
=Model=<br />
Our model is based on the following design (See Project Page for a full description of this system).<br />
[[image:BioBrick.png|thumb|centre|The Encapsulator]]<br />
<br />
The reaction framework was mainly generated using the [http://synbioss.sourceforge.net/ SynBioSS Designer (a really useful modeling tool for iGEM teams)], which also provides default parameter values. These parameter values have been gathered from various literature [http://neptune.cems.umn.edu/designer/designer_defaults.pdf sources], and should be taken as approximations. All units were taken to be (1 / molarity^n-1 * s), where n is the order of the reaction. For example, for the reaction 2 lacI --> lacI2, n = 2, thus the rate constant has the units 1/molarity*s. <br />
<br />
The pathways for the expressed proteins, eCFPt and Encapsulin, need to be modeled in more detail. For example, in this basic model eCFPt is degraded via a first order reaction and Encapsulin makes a dimer complex. However, in reality fluorescent proteins have been shown to degreade via Micheales-menton kinetics and Encapsulin is thought to make a complex of about 60 monomers. These issues will be addressed in future work.<br />
<br />
'''The reactions can be accessed here:'''<br />
<br />
[[The Encapsulator Model]] (opens new page)<br />
<br />
[[Media:Uft_mod_Rxns2.xls|Download Encapsulator Model ]] (download Excel file)<br />
<br />
=Simulations=<br />
<br />
All simulations were carried out using the [https://2009.igem.org/Partner_Offers SimBiology Matlab Toolbox], which was freely available to iGEM teams. <br />
<br />
===Accumulation of eCFP at Different Initial Concentrations of IPTG===<br />
<br />
[[Image:uft_mod_cfp-iptg.png | 900px]]<br />
<br />
The IPTG effector eventually loses effect, and the eCFP concentration approaches a maximum. This happens because the IPTG proteins eventually ''tie up'' all available LacI4 proteins, leaving the transcription and translation of eCFP to operate at its maxiumum rate. <br />
<br />
===Accumulation of Encapsulin monomer at Different Initial Concentrations of aTc===<br />
<br />
[[Image:uft_mod_enc-atc.png | 900px]]<br />
<br />
(NOTE: in order to observe Encapsulin monomer levels, the above simulations were carried out without any Encapsulin assembly reactions in place)<br />
<br />
The production of Encapsulin occurs at a slower rate than eCFP because the BBa_R0040 promoter has two tetR binding sites, resulting in more repression and more off-pathway scenarios. Thus, the Encapsulin concentration also seems assymptotic but at higher concentrations of aTc (relative to IPTG). <br />
<br />
It seems beneficial to have the Encapsulin protein under control of the BBa_R0040-tetR-aTc construct because at zero levels of aTc we can have essentially zero levels of Encapsulin (whereas even at zero levels of IPTG, there is still significantly more eCFP). This will enable us to probe extremely low concentrations of Encapsulin monomer when testing for optimal Encapsulin assembly conditions. The disadvantage is that if Encapsulin assembly requires a very high initial concentration of Encapsulin monomer, we would have to wait a long time to see microcompartments. If this later scenario is observed, it may be better to switch the eCFP and Encapsulin expression systems.<br />
<br />
===Sensitivity Analysis===<br />
<br />
Since all of our parameters are approximations from literature sources, those which have the greatest affect on system dynamics (ie. the most ''sensitive'' parameters) would be leading candidates to be experimentally determined. Currently we are interested in the parameters that have the greatest effect on the production of eCFP and Encapsulin. Ideally, it would be best to tighten-up the model by experimentally determining these, before incorporating the largely unexplored Encapsulin assembly pathways. <br />
<br />
<br />
'''1) Sensitivity of eCFP Production'''<br />
<br />
[[Image:uft_mod_SAecfp.png | centre | 600px]]<br />
<br />
<br />
<br />
'''2) Sensitivity of Encapsulin Production'''<br />
<br />
[[Image:uft_mod_SAenc.png | centre | 600px]]<br />
<br />
Parameters 1 and 2 correspond to the rates of constitutive expression of the repressors lacI and tetR respectively. Thus, it is predicted that eCFP and Encapsulin production is largely sensitive to the expression rates of lacI and tetR. <br />
<br />
The specific constitutive promoter used in our construct is BBa_J23100. In our model, this was given the generic rate of 1E-10 molarity\s by SynBioSS based on a variety of empirically-fitted protein expression rates found in literature. This generic approach to assigning parameter values is a suitable fist-step, but our sensitivity results suggest that experimentally determining the expression rate of BBa_J23100 should significantly improve our model's predictive capability.<br />
<br />
=Future Work=<br />
<br />
Improvements to the basic model presented above can be separated into three areas; 1) performing experiments to determine parameter values that are specific to our system, 2) more detailed modeling of eCFPt behavior, 3) more detailed modeling of Encapsulin assembly. <br />
<br />
The experiments required to determine general transcription and translation parameters need to be further researched, so this will be skipped over for now. Here we will discuss the more interesting areas – the detailed modeling of eCFP and Encapsulin pathways. This will be accomplished by incorporating previous modeling efforts that are applicable to the eCFP and Encapsulin proteins. <br />
<br />
===Maturation and Degredation of eCFP===<br />
<br />
The expression and degradation of [http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=95514&blobtype=pdf Green Fluorescent Protein (GFP) was modeled previously]. This paper noted that GFP must mature before going into fluorescent phase, and GFP degradation was shown to follow M-M kinetics, as depicted below. This paper also outlined how the degradation parameters could be derived for any expression system using only simple fluorescence and optical density measurements.<br />
<br />
[[Image:uft_mod_ecfp1.png | centre | thumb | Degredation and maturation pathways for eCFP. (Leveau and Lindow 2001)]]<br />
<br />
<br />
The GFP maturation and degradation parameters found in this paper were:<br />
<br />
<html><br />
<centre><br />
<table><br />
<tr><td> m = 0.0004279 1/s </td></tr><br />
<tr><td> Vmax = 2E-10 molality/s </td></tr><br />
<tr><td> Km = 9E-13 molality/s </td></tr><br />
<tr><td> </td></tr><br />
</table><br />
</centre><br />
</html><br />
<br />
<br />
Assuming eCFP would behave similarly to eGFP, the following additional reactions would be included in the model:<br />
<br />
<html><br />
<table><br />
<tr> <td><b> Maturation </b></td> <td> </td> </tr><br />
<tr> <td> eCFPt --> F_eCFPT </td> <td> 0.0004279 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Degradation </b></td> <td> </td> </tr><br />
<tr> <td> eCFPt --> </td> <td> Vmax = 2E-10 </td> </tr><br />
<tr> <td> </td> <td> Km = 9E-13 </td> </tr><br />
<tr> <td> F_eCFPt --> </td> <td> Vmax = 2E-10 </td> </tr><br />
<tr> <td> </td> <td> Km = 9E-13 </td> </tr><br />
</table><br />
</html><br />
<br />
===Assembly of Encapsulin Microcompartments===<br />
<br />
Though Encapsulin microcompartment assembly is not well-studied, it has been theorized to resemble the assembly of viral capsids. Thus, we could look to this relatively well-studied phenomenon as a representation of Encapsulin microcompartment assembly.<br />
<br />
Adam Zlotnick has published models of viral capsid assembly using different approaches. An early paper described an equilibrium model of assembly for a 12-unit polyhedral capsid head, and a more recent paper used a kinetic model that could be applied to many examples of spherical polymerization. We will consider how each approach could be incorporated as a representation of Encapsulin assembly.<br />
<br />
<br />
'''1) Equilibrim Approach to Encapsulin Assembly'''<br />
<br />
Zlotnick's [[Media:Uft_mod_to_build_a_virus_capsid.pdf|Equilibrium-based model]] consists of reactions from an initial monomer subunit leading to a final capsid product. The sequential reactions take into account DeltaG for contact (Kn'), and parameters describing path degeneracy (varies for different intermediates).<br />
[[image:uft_mod_encap1.png|centre|thumb|Kn for assembly subunits based on path degeneracy. (Zlotnick 1994)]]<br />
<br />
<br />
'''2) Kinetic Model of Spherical Polymerization'''<br />
<br />
A [http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1302223/pdf/12124301.pdf general kinetic model for the spherical polyermization] process is shown below. In our case, the initial monomer subunit concentration (''u'') would represent our expressed Encapsulin BioBrick, and the number of monomers in the final assembly (''N'') is thought to be 60. All of the included parameters can be calculated from the four basic parameters; the microscopic, per-contact equilibrium constant (KAcon), the nucleus size (nuc), the nucleation on-rate (f_nuc), and the elongation on-rate (f_elong). The referenced paper describes methods to aquire these parameters from kinetic experiments, and provides examples for N = 12 and 30 unit viral capsid assemblies.<br />
[[image:uft_mod_encap2.png| centre | thumb |System of ODEs to represent spherical polymerization, where ''u'' is the initial subunit concentration, ''m'' is the "mth" intermediate species, and ''N'' is the number of monomers in the final assembly. (Endres and Zlotnick 2002)]]<br />
<br />
<br />
<br />
Zlotnick's models also describe two important features of spherical polymerization that we should also expect to observe in Encapsulin assembly: kinetic trapping and nucleation. A kinetic trap occurs when the initial monomer subunit concentration or the deltaG of the first assembly reaction is too high. This results in over-initiation of assembly and quickly the reactions become starved for subunits. Kinetic trapping is prevented by the inclusion of nucleation, where the initial reactions occur at a slower rate because the first few intermediates in a series of reactions are less stable than downstream products. Essentially, nucleation serves as a “slow first step” that regulates the assembly pathway. <br />
<br />
It will be interesting to note how the translational dynamics of Encapsulin interplay with its assembly dynamics. Since our system does not start with any initial concentration of Encapsulin, there will be an optimum rate of production that essentially serves the role of nucleation – avoiding kinetic traps while still maintaining a maximum production of full Encapsulin assemblies.<br />
<br />
=References=<br />
<br />
1. Hill AD, Tomshine JR, Weeding EM, Sotiropoulos V, Kaznessis YN. ''SynBioSS: the synthetic biology modeling suite.'' Bioinformatics. 2008 Nov 1;24(21):2551-3. Epub 2008 Aug 30.<br />
[http://neptune.cems.umn.edu/designer/interface1.php SynBioSS Web Designer]<br />
<br />
2. Leveau JH, Lindow SE. ''Predictive and interpretive simulation of green fluorescent protein expression in<br />
reporter bacteria.'' J Bacteriol. 2001 Dec;183(23):6752-62.<br />
<br />
3. Endres D, Zlotnick A. ''Model-based analysis of assembly kinetics for virus capsids or other spherical<br />
polymers.'' Biophys J. 2002 Aug;83(2):1217-30.</div>FRhttp://2009.igem.org/Team:TorontoMaRSDiscovery/ModelingTeam:TorontoMaRSDiscovery/Modeling2009-10-21T14:06:54Z<p>FR: /* Maturation and Degredation of eCFP */</p>
<hr />
<div>[[image:To_igem_wiki_banner.jpg|965px]]<br />
{| style="color:white;background-color:#99CCFF;" height:100px cellpadding="2" cellspacing="0" border="0" width="100%" align="center" class="menu"<br />
!align="center"|[[Team:TorontoMaRSDiscovery|Home]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Team|The Team]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Project|The Project]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Parts|BioBricks]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Modeling|Modeling]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Bioinformatics|Bioinformatics]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Safety|Safety]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Notebook|Notebook]]<br />
|}<br />
<br><br />
<br />
<br />
=Summary=<br />
<br />
A kinetic model of our system has been constructed. Approximate parameter values were gathered from online resources to represent all processes up to the production of the eCFP and Encapsulin proteins. Current simulations predict the production of these two proteins at various initial concentrations of IPTG and aTc effector molecules. A sensitivity analysis reveals that the rate of constitutive expression of lacI and tetR has the greatest affect on eCFP and Encapsulin concentrations. Furthermore, we have outlined approaches for the detailed modelling of the eCFP degredation/maturation and Encapsulin assembly pathways.<br />
<br />
<br />
The initial simulations will be used to identify a critical concentration of Encapsulin mononomer required for microcompartment assembly. To strengthen the model, the constitutive expression rate of BBa_J23100 as used in our construct will be measured. Subsequently, a detailed model of Encapsulin assembly will be integrated into the current model, and its parameters filled-in using parameter-scanning methods and experiments outlined in the relevant references. By comparing experimental measures of microcompartment formation with that predicted by the kinetic model, we aim to gain insight on the mechanisms of Encapsulin assembly.<br />
<br />
=Model=<br />
Our model is based on the following design (See Project Page for a full description of this system).<br />
[[image:BioBrick.png|thumb|centre|The Encapsulator]]<br />
<br />
The reaction framework was mainly generated using the [http://synbioss.sourceforge.net/ SynBioSS Designer (a really useful modeling tool for iGEM teams)], which also provides default parameter values. These parameter values have been gathered from various literature [http://neptune.cems.umn.edu/designer/designer_defaults.pdf sources], and should be taken as approximations. All units were taken to be (1 / molarity^n-1 * s), where n is the order of the reaction. For example, for the reaction 2 lacI --> lacI2, n = 2, thus the rate constant has the units 1/molarity*s. <br />
<br />
The pathways for the expressed proteins, eCFPt and Encapsulin, need to be modeled in more detail. For example, in this basic model eCFPt is degraded via a first order reaction and Encapsulin makes a dimer complex. However, in reality fluorescent proteins have been shown to degreade via Micheales-menton kinetics and Encapsulin is thought to make a complex of about 60 monomers. These issues will be addressed in future work.<br />
<br />
'''The reactions can be accessed here:'''<br />
<br />
[[The Encapsulator Model]] (opens new page)<br />
<br />
[[Media:Uft_mod_Rxns2.xls|Download Encapsulator Model ]] (download Excel file)<br />
<br />
=Simulations=<br />
<br />
All simulations were carried out using the [https://2009.igem.org/Partner_Offers SimBiology Matlab Toolbox], which was freely available to iGEM teams. <br />
<br />
===Accumulation of eCFP at Different Initial Concentrations of IPTG===<br />
<br />
[[Image:uft_mod_cfp-iptg.png | 900px]]<br />
<br />
The IPTG effector eventually loses effect, and the eCFP concentration approaches a maximum. This happens because the IPTG proteins eventually ''tie up'' all available LacI4 proteins, leaving the transcription and translation of eCFP to operate at its maxiumum rate. <br />
<br />
===Accumulation of Encapsulin monomer at Different Initial Concentrations of aTc===<br />
<br />
[[Image:uft_mod_enc-atc.png | 900px]]<br />
<br />
(NOTE: in order to observe Encapsulin monomer levels, the above simulations were carried out without any Encapsulin assembly reactions in place)<br />
<br />
The production of Encapsulin occurs at a slower rate than eCFP because the BBa_R0040 promoter has two tetR binding sites, resulting in more repression and more off-pathway scenarios. Thus, the Encapsulin concentration also seems assymptotic but at higher concentrations of aTc (relative to IPTG). <br />
<br />
It seems beneficial to have the Encapsulin protein under control of the BBa_R0040-tetR-aTc construct because at zero levels of aTc we can have essentially zero levels of Encapsulin (whereas even at zero levels of IPTG, there is still significantly more eCFP). This will enable us to probe extremely low concentrations of Encapsulin monomer when testing for optimal Encapsulin assembly conditions. The disadvantage is that if Encapsulin assembly requires a very high initial concentration of Encapsulin monomer, we would have to wait a long time to see microcompartments. If this later scenario is observed, it may be better to switch the eCFP and Encapsulin expression systems.<br />
<br />
===Sensitivity Analysis===<br />
<br />
Since all of our parameters are approximations from literature sources, those which have the greatest affect on system dynamics (ie. the most ''sensitive'' parameters) would be leading candidates to be experimentally determined. Currently we are interested in the parameters that have the greatest effect on the production of eCFP and Encapsulin. Ideally, it would be best to tighten-up the model by experimentally determining these, before incorporating the largely unexplored Encapsulin assembly pathways. <br />
<br />
<br />
'''1) Sensitivity of eCFP Production'''<br />
<br />
[[Image:uft_mod_SAecfp.png | centre | 600px]]<br />
<br />
<br />
<br />
'''2) Sensitivity of Encapsulin Production'''<br />
<br />
[[Image:uft_mod_SAenc.png | centre | 600px]]<br />
<br />
Parameters 1 and 2 correspond to the rates of constitutive expression of the repressors lacI and tetR respectively. Thus, it is predicted that eCFP and Encapsulin production is largely sensitive to the expression rates of lacI and tetR. <br />
<br />
The specific constitutive promoter used in our construct is BBa_J23100. In our model, this was given the generic rate of 1E-10 molarity\s by SynBioSS based on a variety of empirically-fitted protein expression rates found in literature. This generic approach to assigning parameter values is a suitable fist-step, but our sensitivity results suggest that experimentally determining the expression rate of BBa_J23100 should significantly improve our model's predictive capability.<br />
<br />
=Future Work=<br />
<br />
Improvements to the basic model presented above can be separated into three areas; 1) performing experiments to determine parameter values that are specific to our system, 2) more detailed modeling of eCFPt behavior, 3) more detailed modeling of Encapsulin assembly. <br />
<br />
The experiments required to determine general transcription and translation parameters need to be further researched, so this will be skipped over for now. Here we will discuss the more interesting areas – the detailed modeling of eCFP and Encapsulin pathways. This will be accomplished by incorporating previous modeling efforts that are applicable to the eCFP and Encapsulin proteins. <br />
<br />
===Maturation and Degredation of eCFP===<br />
<br />
The expression and degradation of [http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=95514&blobtype=pdf Green Fluorescent Protein (GFP) was modeled previously]. This paper noted that GFP must mature before going into fluorescent phase, and GFP degradation was shown to follow M-M kinetics, as depicted below. This paper also outlined how the degradation parameters could be derived for any expression system using only simple fluorescence and optical density measurements.<br />
<br />
[[Image:uft_mod_ecfp1.png | centre | thumb | Degredation and maturation pathways for eCFP. (Leveau and Lindow 2001)]]<br />
<br />
<br />
The GFP maturation and degradation parameters found in this paper were:<br />
<br />
<html><br />
<centre><br />
<table><br />
<tr><td> m = 0.0004279 1/s </td></tr><br />
<tr><td> Vmax = 2E-10 molality/s </td></tr><br />
<tr><td> Km = 9E-13 molality/s </td></tr><br />
<tr><td> </td></tr><br />
</table><br />
</centre><br />
</html><br />
<br />
<br />
Assuming eCFP would behave similarly to eGFP, the following additional reactions would be included in the model:<br />
<br />
<html><br />
<table><br />
<tr> <td><b> Maturation </b></td> <td> </td> </tr><br />
<tr> <td> eCFPt --> F_eCFPT </td> <td> 0.0004279 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Degradation </b></td> <td> </td> </tr><br />
<tr> <td> eCFPt --> </td> <td> Vmax = 2E-10 </td> </tr><br />
<tr> <td> </td> <td> Km = 9E-13 </td> </tr><br />
<tr> <td> F_eCFPt --> </td> <td> Vmax = 2E-10 </td> </tr><br />
<tr> <td> </td> <td> Km = 9E-13 </td> </tr><br />
</table><br />
</html><br />
<br />
===Assembly of Encapsulin Microcompartments===<br />
<br />
Though Encapsulin microcompartment assembly is not well-studied, it has been theorized to resemble the assembly of viral capsids. Thus, we could look to this relatively well-studied phenomenon as a representation of Encapsulin microcompartment assembly.<br />
<br />
Adam Zlotnick has published models of viral capsid assembly using different approaches. An early paper described an equilibrium model of assembly for a 12 Unit polyhedral capsid head, and a more recent paper used a kinetic model that could be applied to many examples of spherical polymerization. We will consider how each approach could be incorporated as a representation of Encapsulin assembly.<br />
<br />
<br />
'''1) Equilibrim Approach to Encapsulin Assembly'''<br />
<br />
Zlotnick's [[Media:Uft_mod_to_build_a_virus_capsid.pdf|Equilibrium-based model]] consists of reactions from an initial monomer subunit leading to a final capsid product. The sequential reactions take into account DeltaG for contact (Kn'), and parameters describing path degeneracy (varies for different intermediates).<br />
[[image:uft_mod_encap1.png|centre|thumb|Kn for assembly subunits based on path degeneracy. (Zlotnick 1994)]]<br />
<br />
<br />
'''2) Kinetic Model of Spherical Polymerization'''<br />
<br />
A [http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1302223/pdf/12124301.pdf general kinetic model for the spherical polyermization] process is shown below. In our case, the initial monomer subunit concentration (''u'') would represent our expressed Encapsulin BioBrick, and the number of monomers in the final assembly (''N'') is thought to be 60. All of the included parameters can be calculated from the four basic parameters; the microscopic, per-contact equilibrium constant (KAcon), the nucleus size (nuc), the nucleation on-rate (f_nuc), and the elongation on-rate (f_elong). The referenced paper describes methods to aquire these parameters from kinetic experiments, and provides examples for N = 12 and 30 unit viral capsid assemblies.<br />
[[image:uft_mod_encap2.png| centre | thumb |System of ODEs to represent spherical polymerization, where ''u'' is the initial subunit concentration, ''m'' is the "mth" intermediate species, and ''N'' is the number of monomers in the final assembly. (Endres and Zlotnick 2002)]]<br />
<br />
<br />
<br />
Zlotnick's models also describe two important features of spherical polymerization that we should also expect to observe in Encapsulin assembly: kinetic trapping and nucleation. A kinetic trap occurs when the initial monomer subunit concentration or the deltaG of the first assembly reaction is too high. This results in over-initiation of assembly and quickly the reactions become starved for subunits. Kinetic trapping is prevented by the inclusion of nucleation, where the initial reactions occur at a slower rate because the first few intermediates in a series of reactions are less stable than downstream products. Essentially, nucleation serves as a “slow first step” that regulates the assembly pathway. <br />
<br />
It will be interesting to note how the translational dynamics of Encapsulin interplay with its assembly dynamics. Since our system does not start with any initial concentration of Encapsulin, there will be an optimum rate of production that essentially serves the role of nucleation – avoiding kinetic traps while still maintaining a maximum production of full Encapsulin assemblies.<br />
<br />
=References=<br />
<br />
1. Hill AD, Tomshine JR, Weeding EM, Sotiropoulos V, Kaznessis YN. ''SynBioSS: the synthetic biology modeling suite.'' Bioinformatics. 2008 Nov 1;24(21):2551-3. Epub 2008 Aug 30.<br />
[http://neptune.cems.umn.edu/designer/interface1.php SynBioSS Web Designer]<br />
<br />
2. Leveau JH, Lindow SE. ''Predictive and interpretive simulation of green fluorescent protein expression in<br />
reporter bacteria.'' J Bacteriol. 2001 Dec;183(23):6752-62.<br />
<br />
3. Endres D, Zlotnick A. ''Model-based analysis of assembly kinetics for virus capsids or other spherical<br />
polymers.'' Biophys J. 2002 Aug;83(2):1217-30.</div>FRhttp://2009.igem.org/Team:TorontoMaRSDiscovery/ModelingTeam:TorontoMaRSDiscovery/Modeling2009-10-21T14:06:17Z<p>FR: /* Maturation and Degredation of eCFP */</p>
<hr />
<div>[[image:To_igem_wiki_banner.jpg|965px]]<br />
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!align="center"|[[Team:TorontoMaRSDiscovery|Home]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Team|The Team]]<br />
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!align="center"|[[Team:TorontoMaRSDiscovery/Parts|BioBricks]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Modeling|Modeling]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Bioinformatics|Bioinformatics]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Safety|Safety]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Notebook|Notebook]]<br />
|}<br />
<br><br />
<br />
<br />
=Summary=<br />
<br />
A kinetic model of our system has been constructed. Approximate parameter values were gathered from online resources to represent all processes up to the production of the eCFP and Encapsulin proteins. Current simulations predict the production of these two proteins at various initial concentrations of IPTG and aTc effector molecules. A sensitivity analysis reveals that the rate of constitutive expression of lacI and tetR has the greatest affect on eCFP and Encapsulin concentrations. Furthermore, we have outlined approaches for the detailed modelling of the eCFP degredation/maturation and Encapsulin assembly pathways.<br />
<br />
<br />
The initial simulations will be used to identify a critical concentration of Encapsulin mononomer required for microcompartment assembly. To strengthen the model, the constitutive expression rate of BBa_J23100 as used in our construct will be measured. Subsequently, a detailed model of Encapsulin assembly will be integrated into the current model, and its parameters filled-in using parameter-scanning methods and experiments outlined in the relevant references. By comparing experimental measures of microcompartment formation with that predicted by the kinetic model, we aim to gain insight on the mechanisms of Encapsulin assembly.<br />
<br />
=Model=<br />
Our model is based on the following design (See Project Page for a full description of this system).<br />
[[image:BioBrick.png|thumb|centre|The Encapsulator]]<br />
<br />
The reaction framework was mainly generated using the [http://synbioss.sourceforge.net/ SynBioSS Designer (a really useful modeling tool for iGEM teams)], which also provides default parameter values. These parameter values have been gathered from various literature [http://neptune.cems.umn.edu/designer/designer_defaults.pdf sources], and should be taken as approximations. All units were taken to be (1 / molarity^n-1 * s), where n is the order of the reaction. For example, for the reaction 2 lacI --> lacI2, n = 2, thus the rate constant has the units 1/molarity*s. <br />
<br />
The pathways for the expressed proteins, eCFPt and Encapsulin, need to be modeled in more detail. For example, in this basic model eCFPt is degraded via a first order reaction and Encapsulin makes a dimer complex. However, in reality fluorescent proteins have been shown to degreade via Micheales-menton kinetics and Encapsulin is thought to make a complex of about 60 monomers. These issues will be addressed in future work.<br />
<br />
'''The reactions can be accessed here:'''<br />
<br />
[[The Encapsulator Model]] (opens new page)<br />
<br />
[[Media:Uft_mod_Rxns2.xls|Download Encapsulator Model ]] (download Excel file)<br />
<br />
=Simulations=<br />
<br />
All simulations were carried out using the [https://2009.igem.org/Partner_Offers SimBiology Matlab Toolbox], which was freely available to iGEM teams. <br />
<br />
===Accumulation of eCFP at Different Initial Concentrations of IPTG===<br />
<br />
[[Image:uft_mod_cfp-iptg.png | 900px]]<br />
<br />
The IPTG effector eventually loses effect, and the eCFP concentration approaches a maximum. This happens because the IPTG proteins eventually ''tie up'' all available LacI4 proteins, leaving the transcription and translation of eCFP to operate at its maxiumum rate. <br />
<br />
===Accumulation of Encapsulin monomer at Different Initial Concentrations of aTc===<br />
<br />
[[Image:uft_mod_enc-atc.png | 900px]]<br />
<br />
(NOTE: in order to observe Encapsulin monomer levels, the above simulations were carried out without any Encapsulin assembly reactions in place)<br />
<br />
The production of Encapsulin occurs at a slower rate than eCFP because the BBa_R0040 promoter has two tetR binding sites, resulting in more repression and more off-pathway scenarios. Thus, the Encapsulin concentration also seems assymptotic but at higher concentrations of aTc (relative to IPTG). <br />
<br />
It seems beneficial to have the Encapsulin protein under control of the BBa_R0040-tetR-aTc construct because at zero levels of aTc we can have essentially zero levels of Encapsulin (whereas even at zero levels of IPTG, there is still significantly more eCFP). This will enable us to probe extremely low concentrations of Encapsulin monomer when testing for optimal Encapsulin assembly conditions. The disadvantage is that if Encapsulin assembly requires a very high initial concentration of Encapsulin monomer, we would have to wait a long time to see microcompartments. If this later scenario is observed, it may be better to switch the eCFP and Encapsulin expression systems.<br />
<br />
===Sensitivity Analysis===<br />
<br />
Since all of our parameters are approximations from literature sources, those which have the greatest affect on system dynamics (ie. the most ''sensitive'' parameters) would be leading candidates to be experimentally determined. Currently we are interested in the parameters that have the greatest effect on the production of eCFP and Encapsulin. Ideally, it would be best to tighten-up the model by experimentally determining these, before incorporating the largely unexplored Encapsulin assembly pathways. <br />
<br />
<br />
'''1) Sensitivity of eCFP Production'''<br />
<br />
[[Image:uft_mod_SAecfp.png | centre | 600px]]<br />
<br />
<br />
<br />
'''2) Sensitivity of Encapsulin Production'''<br />
<br />
[[Image:uft_mod_SAenc.png | centre | 600px]]<br />
<br />
Parameters 1 and 2 correspond to the rates of constitutive expression of the repressors lacI and tetR respectively. Thus, it is predicted that eCFP and Encapsulin production is largely sensitive to the expression rates of lacI and tetR. <br />
<br />
The specific constitutive promoter used in our construct is BBa_J23100. In our model, this was given the generic rate of 1E-10 molarity\s by SynBioSS based on a variety of empirically-fitted protein expression rates found in literature. This generic approach to assigning parameter values is a suitable fist-step, but our sensitivity results suggest that experimentally determining the expression rate of BBa_J23100 should significantly improve our model's predictive capability.<br />
<br />
=Future Work=<br />
<br />
Improvements to the basic model presented above can be separated into three areas; 1) performing experiments to determine parameter values that are specific to our system, 2) more detailed modeling of eCFPt behavior, 3) more detailed modeling of Encapsulin assembly. <br />
<br />
The experiments required to determine general transcription and translation parameters need to be further researched, so this will be skipped over for now. Here we will discuss the more interesting areas – the detailed modeling of eCFP and Encapsulin pathways. This will be accomplished by incorporating previous modeling efforts that are applicable to the eCFP and Encapsulin proteins. <br />
<br />
===Maturation and Degredation of eCFP===<br />
<br />
The expression and degradation of [http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=95514&blobtype=pdf Green Fluorescent Protein (GFP) was modeled previously]. This paper noted that GFP must mature before going into fluorescent phase, and GFP degradation was shown to follow M-M kinetics, as depicted below. This paper also outlined how the degradation parameters could be derived for any expression system using only simple fluorescence and optical density measurements.<br />
<br />
[[Image:uft_mod_ecfp1.png | centre | thumb | Degredation and maturation pathways for eCFP. (Leveau and Lindow 2001)]]<br />
<br />
<br />
The GFP maturation and degradation parameters found in this paper were:<br />
<br />
<html><br />
<centre><br />
<table><br />
<tr><td> m = 0.0004279 1/s </td></tr><br />
<tr><td> Vmax = 2E-10 molality/s </td></tr><br />
<tr><td> Km = 9E-13 molality/s </td></tr><br />
<tr><td> </td></tr><br />
</table><br />
</centre><br />
</html><br />
<br />
<br />
Assuming eCFP would behave similarly to eGFP, the following additional reactions would be included in the model:<br />
<br />
<html><br />
<table><br />
<tr> <td><b> Maturation </b></td> <td> </td> </tr><br />
<tr> <td> eCFPt --> F_eCFPT </td> <td> 0.0004279 </td> </tr><br />
<tr> <td> Enc2:eCFPt --> Enc2:F_eCFPt </td> <td> 0.0004279 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Degradation </b></td> <td> </td> </tr><br />
<tr> <td> eCFPt --> </td> <td> Vmax = 2E-10 </td> </tr><br />
<tr> <td> </td> <td> Km = 9E-13 </td> </tr><br />
<tr> <td> F_eCFPt --> </td> <td> Vmax = 2E-10 </td> </tr><br />
<tr> <td> </td> <td> Km = 9E-13 </td> </tr><br />
</table><br />
</html><br />
<br />
===Assembly of Encapsulin Microcompartments===<br />
<br />
Though Encapsulin microcompartment assembly is not well-studied, it has been theorized to resemble the assembly of viral capsids. Thus, we could look to this relatively well-studied phenomenon as a representation of Encapsulin microcompartment assembly.<br />
<br />
Adam Zlotnick has published models of viral capsid assembly using different approaches. An early paper described an equilibrium model of assembly for a 12 Unit polyhedral capsid head, and a more recent paper used a kinetic model that could be applied to many examples of spherical polymerization. We will consider how each approach could be incorporated as a representation of Encapsulin assembly.<br />
<br />
<br />
'''1) Equilibrim Approach to Encapsulin Assembly'''<br />
<br />
Zlotnick's [[Media:Uft_mod_to_build_a_virus_capsid.pdf|Equilibrium-based model]] consists of reactions from an initial monomer subunit leading to a final capsid product. The sequential reactions take into account DeltaG for contact (Kn'), and parameters describing path degeneracy (varies for different intermediates).<br />
[[image:uft_mod_encap1.png|centre|thumb|Kn for assembly subunits based on path degeneracy. (Zlotnick 1994)]]<br />
<br />
<br />
'''2) Kinetic Model of Spherical Polymerization'''<br />
<br />
A [http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1302223/pdf/12124301.pdf general kinetic model for the spherical polyermization] process is shown below. In our case, the initial monomer subunit concentration (''u'') would represent our expressed Encapsulin BioBrick, and the number of monomers in the final assembly (''N'') is thought to be 60. All of the included parameters can be calculated from the four basic parameters; the microscopic, per-contact equilibrium constant (KAcon), the nucleus size (nuc), the nucleation on-rate (f_nuc), and the elongation on-rate (f_elong). The referenced paper describes methods to aquire these parameters from kinetic experiments, and provides examples for N = 12 and 30 unit viral capsid assemblies.<br />
[[image:uft_mod_encap2.png| centre | thumb |System of ODEs to represent spherical polymerization, where ''u'' is the initial subunit concentration, ''m'' is the "mth" intermediate species, and ''N'' is the number of monomers in the final assembly. (Endres and Zlotnick 2002)]]<br />
<br />
<br />
<br />
Zlotnick's models also describe two important features of spherical polymerization that we should also expect to observe in Encapsulin assembly: kinetic trapping and nucleation. A kinetic trap occurs when the initial monomer subunit concentration or the deltaG of the first assembly reaction is too high. This results in over-initiation of assembly and quickly the reactions become starved for subunits. Kinetic trapping is prevented by the inclusion of nucleation, where the initial reactions occur at a slower rate because the first few intermediates in a series of reactions are less stable than downstream products. Essentially, nucleation serves as a “slow first step” that regulates the assembly pathway. <br />
<br />
It will be interesting to note how the translational dynamics of Encapsulin interplay with its assembly dynamics. Since our system does not start with any initial concentration of Encapsulin, there will be an optimum rate of production that essentially serves the role of nucleation – avoiding kinetic traps while still maintaining a maximum production of full Encapsulin assemblies.<br />
<br />
=References=<br />
<br />
1. Hill AD, Tomshine JR, Weeding EM, Sotiropoulos V, Kaznessis YN. ''SynBioSS: the synthetic biology modeling suite.'' Bioinformatics. 2008 Nov 1;24(21):2551-3. Epub 2008 Aug 30.<br />
[http://neptune.cems.umn.edu/designer/interface1.php SynBioSS Web Designer]<br />
<br />
2. Leveau JH, Lindow SE. ''Predictive and interpretive simulation of green fluorescent protein expression in<br />
reporter bacteria.'' J Bacteriol. 2001 Dec;183(23):6752-62.<br />
<br />
3. Endres D, Zlotnick A. ''Model-based analysis of assembly kinetics for virus capsids or other spherical<br />
polymers.'' Biophys J. 2002 Aug;83(2):1217-30.</div>FRhttp://2009.igem.org/Team:TorontoMaRSDiscovery/ModelingTeam:TorontoMaRSDiscovery/Modeling2009-10-21T14:05:26Z<p>FR: /* Maturation and Degredation of eCFP */</p>
<hr />
<div>[[image:To_igem_wiki_banner.jpg|965px]]<br />
{| style="color:white;background-color:#99CCFF;" height:100px cellpadding="2" cellspacing="0" border="0" width="100%" align="center" class="menu"<br />
!align="center"|[[Team:TorontoMaRSDiscovery|Home]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Team|The Team]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Project|The Project]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Parts|BioBricks]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Modeling|Modeling]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Bioinformatics|Bioinformatics]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Safety|Safety]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Notebook|Notebook]]<br />
|}<br />
<br><br />
<br />
<br />
=Summary=<br />
<br />
A kinetic model of our system has been constructed. Approximate parameter values were gathered from online resources to represent all processes up to the production of the eCFP and Encapsulin proteins. Current simulations predict the production of these two proteins at various initial concentrations of IPTG and aTc effector molecules. A sensitivity analysis reveals that the rate of constitutive expression of lacI and tetR has the greatest affect on eCFP and Encapsulin concentrations. Furthermore, we have outlined approaches for the detailed modelling of the eCFP degredation/maturation and Encapsulin assembly pathways.<br />
<br />
<br />
The initial simulations will be used to identify a critical concentration of Encapsulin mononomer required for microcompartment assembly. To strengthen the model, the constitutive expression rate of BBa_J23100 as used in our construct will be measured. Subsequently, a detailed model of Encapsulin assembly will be integrated into the current model, and its parameters filled-in using parameter-scanning methods and experiments outlined in the relevant references. By comparing experimental measures of microcompartment formation with that predicted by the kinetic model, we aim to gain insight on the mechanisms of Encapsulin assembly.<br />
<br />
=Model=<br />
Our model is based on the following design (See Project Page for a full description of this system).<br />
[[image:BioBrick.png|thumb|centre|The Encapsulator]]<br />
<br />
The reaction framework was mainly generated using the [http://synbioss.sourceforge.net/ SynBioSS Designer (a really useful modeling tool for iGEM teams)], which also provides default parameter values. These parameter values have been gathered from various literature [http://neptune.cems.umn.edu/designer/designer_defaults.pdf sources], and should be taken as approximations. All units were taken to be (1 / molarity^n-1 * s), where n is the order of the reaction. For example, for the reaction 2 lacI --> lacI2, n = 2, thus the rate constant has the units 1/molarity*s. <br />
<br />
The pathways for the expressed proteins, eCFPt and Encapsulin, need to be modeled in more detail. For example, in this basic model eCFPt is degraded via a first order reaction and Encapsulin makes a dimer complex. However, in reality fluorescent proteins have been shown to degreade via Micheales-menton kinetics and Encapsulin is thought to make a complex of about 60 monomers. These issues will be addressed in future work.<br />
<br />
'''The reactions can be accessed here:'''<br />
<br />
[[The Encapsulator Model]] (opens new page)<br />
<br />
[[Media:Uft_mod_Rxns2.xls|Download Encapsulator Model ]] (download Excel file)<br />
<br />
=Simulations=<br />
<br />
All simulations were carried out using the [https://2009.igem.org/Partner_Offers SimBiology Matlab Toolbox], which was freely available to iGEM teams. <br />
<br />
===Accumulation of eCFP at Different Initial Concentrations of IPTG===<br />
<br />
[[Image:uft_mod_cfp-iptg.png | 900px]]<br />
<br />
The IPTG effector eventually loses effect, and the eCFP concentration approaches a maximum. This happens because the IPTG proteins eventually ''tie up'' all available LacI4 proteins, leaving the transcription and translation of eCFP to operate at its maxiumum rate. <br />
<br />
===Accumulation of Encapsulin monomer at Different Initial Concentrations of aTc===<br />
<br />
[[Image:uft_mod_enc-atc.png | 900px]]<br />
<br />
(NOTE: in order to observe Encapsulin monomer levels, the above simulations were carried out without any Encapsulin assembly reactions in place)<br />
<br />
The production of Encapsulin occurs at a slower rate than eCFP because the BBa_R0040 promoter has two tetR binding sites, resulting in more repression and more off-pathway scenarios. Thus, the Encapsulin concentration also seems assymptotic but at higher concentrations of aTc (relative to IPTG). <br />
<br />
It seems beneficial to have the Encapsulin protein under control of the BBa_R0040-tetR-aTc construct because at zero levels of aTc we can have essentially zero levels of Encapsulin (whereas even at zero levels of IPTG, there is still significantly more eCFP). This will enable us to probe extremely low concentrations of Encapsulin monomer when testing for optimal Encapsulin assembly conditions. The disadvantage is that if Encapsulin assembly requires a very high initial concentration of Encapsulin monomer, we would have to wait a long time to see microcompartments. If this later scenario is observed, it may be better to switch the eCFP and Encapsulin expression systems.<br />
<br />
===Sensitivity Analysis===<br />
<br />
Since all of our parameters are approximations from literature sources, those which have the greatest affect on system dynamics (ie. the most ''sensitive'' parameters) would be leading candidates to be experimentally determined. Currently we are interested in the parameters that have the greatest effect on the production of eCFP and Encapsulin. Ideally, it would be best to tighten-up the model by experimentally determining these, before incorporating the largely unexplored Encapsulin assembly pathways. <br />
<br />
<br />
'''1) Sensitivity of eCFP Production'''<br />
<br />
[[Image:uft_mod_SAecfp.png | centre | 600px]]<br />
<br />
<br />
<br />
'''2) Sensitivity of Encapsulin Production'''<br />
<br />
[[Image:uft_mod_SAenc.png | centre | 600px]]<br />
<br />
Parameters 1 and 2 correspond to the rates of constitutive expression of the repressors lacI and tetR respectively. Thus, it is predicted that eCFP and Encapsulin production is largely sensitive to the expression rates of lacI and tetR. <br />
<br />
The specific constitutive promoter used in our construct is BBa_J23100. In our model, this was given the generic rate of 1E-10 molarity\s by SynBioSS based on a variety of empirically-fitted protein expression rates found in literature. This generic approach to assigning parameter values is a suitable fist-step, but our sensitivity results suggest that experimentally determining the expression rate of BBa_J23100 should significantly improve our model's predictive capability.<br />
<br />
=Future Work=<br />
<br />
Improvements to the basic model presented above can be separated into three areas; 1) performing experiments to determine parameter values that are specific to our system, 2) more detailed modeling of eCFPt behavior, 3) more detailed modeling of Encapsulin assembly. <br />
<br />
The experiments required to determine general transcription and translation parameters need to be further researched, so this will be skipped over for now. Here we will discuss the more interesting areas – the detailed modeling of eCFP and Encapsulin pathways. This will be accomplished by incorporating previous modeling efforts that are applicable to the eCFP and Encapsulin proteins. <br />
<br />
===Maturation and Degredation of eCFP===<br />
<br />
The expression and degradation of [http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=95514&blobtype=pdf Green Fluorescent Protein (GFP) was modeled previously]. This paper noted that GFP must mature before going into fluorescent phase, and GFP degradation was shown to follow M-M kinetics, as depicted below. This paper also outlined how the degradation parameters could be derived for any expression system using only simple fluorescence and optical density measurements.<br />
<br />
[[Image:uft_mod_ecfp1.png | centre | thumb | Degredation and maturation pathways for eCFP. (Leveau and Lindow 2001)]]<br />
<br />
<br />
The GFP maturation and degradation parameters found in this paper were:<br />
<br />
<html><br />
<centre><br />
<table><br />
<tr><td> m = 0.0004279 1/s </td></tr><br />
<tr><td> Vmax = 2E-10 molality/s </td></tr><br />
<tr><td> Km = 9E-13 molality/s </td></tr><br />
<tr><td> </td></tr><br />
</table><br />
</centre><br />
</html><br />
<br />
<br />
Assuming eCFP would behave similarly to eGFP, the following additional reactions would be included in the model:<br />
<br />
<html><br />
<table><br />
<tr> <td><b> Maturation </b></td> <td> </td> </tr><br />
<tr> <td> eCFPt --> F_eCFPT </td> <td> 0.0004279 </td> </tr><br />
<tr> <td> Enc2:eCFPt --> Enc2:F_eCFPt </td> <td> 0.0004279 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Encapsulation </b></td> <td> </td> </tr><br />
<tr> <td> Enc2 + F_eCFPt --> Enc2:F_eCFPt </td> <td> 100 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Degradation </b></td> <td> </td> </tr><br />
<tr> <td> eCFPt --> </td> <td> Vmax = 2E-10 </td> </tr><br />
<tr> <td> </td> <td> Km = 9E-13 </td> </tr><br />
<tr> <td> F_eCFPt --> </td> <td> Vmax = 2E-10 </td> </tr><br />
<tr> <td> </td> <td> Km = 9E-13 </td> </tr><br />
</table><br />
</html><br />
<br />
===Assembly of Encapsulin Microcompartments===<br />
<br />
Though Encapsulin microcompartment assembly is not well-studied, it has been theorized to resemble the assembly of viral capsids. Thus, we could look to this relatively well-studied phenomenon as a representation of Encapsulin microcompartment assembly.<br />
<br />
Adam Zlotnick has published models of viral capsid assembly using different approaches. An early paper described an equilibrium model of assembly for a 12 Unit polyhedral capsid head, and a more recent paper used a kinetic model that could be applied to many examples of spherical polymerization. We will consider how each approach could be incorporated as a representation of Encapsulin assembly.<br />
<br />
<br />
'''1) Equilibrim Approach to Encapsulin Assembly'''<br />
<br />
Zlotnick's [[Media:Uft_mod_to_build_a_virus_capsid.pdf|Equilibrium-based model]] consists of reactions from an initial monomer subunit leading to a final capsid product. The sequential reactions take into account DeltaG for contact (Kn'), and parameters describing path degeneracy (varies for different intermediates).<br />
[[image:uft_mod_encap1.png|centre|thumb|Kn for assembly subunits based on path degeneracy. (Zlotnick 1994)]]<br />
<br />
<br />
'''2) Kinetic Model of Spherical Polymerization'''<br />
<br />
A [http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1302223/pdf/12124301.pdf general kinetic model for the spherical polyermization] process is shown below. In our case, the initial monomer subunit concentration (''u'') would represent our expressed Encapsulin BioBrick, and the number of monomers in the final assembly (''N'') is thought to be 60. All of the included parameters can be calculated from the four basic parameters; the microscopic, per-contact equilibrium constant (KAcon), the nucleus size (nuc), the nucleation on-rate (f_nuc), and the elongation on-rate (f_elong). The referenced paper describes methods to aquire these parameters from kinetic experiments, and provides examples for N = 12 and 30 unit viral capsid assemblies.<br />
[[image:uft_mod_encap2.png| centre | thumb |System of ODEs to represent spherical polymerization, where ''u'' is the initial subunit concentration, ''m'' is the "mth" intermediate species, and ''N'' is the number of monomers in the final assembly. (Endres and Zlotnick 2002)]]<br />
<br />
<br />
<br />
Zlotnick's models also describe two important features of spherical polymerization that we should also expect to observe in Encapsulin assembly: kinetic trapping and nucleation. A kinetic trap occurs when the initial monomer subunit concentration or the deltaG of the first assembly reaction is too high. This results in over-initiation of assembly and quickly the reactions become starved for subunits. Kinetic trapping is prevented by the inclusion of nucleation, where the initial reactions occur at a slower rate because the first few intermediates in a series of reactions are less stable than downstream products. Essentially, nucleation serves as a “slow first step” that regulates the assembly pathway. <br />
<br />
It will be interesting to note how the translational dynamics of Encapsulin interplay with its assembly dynamics. Since our system does not start with any initial concentration of Encapsulin, there will be an optimum rate of production that essentially serves the role of nucleation – avoiding kinetic traps while still maintaining a maximum production of full Encapsulin assemblies.<br />
<br />
=References=<br />
<br />
1. Hill AD, Tomshine JR, Weeding EM, Sotiropoulos V, Kaznessis YN. ''SynBioSS: the synthetic biology modeling suite.'' Bioinformatics. 2008 Nov 1;24(21):2551-3. Epub 2008 Aug 30.<br />
[http://neptune.cems.umn.edu/designer/interface1.php SynBioSS Web Designer]<br />
<br />
2. Leveau JH, Lindow SE. ''Predictive and interpretive simulation of green fluorescent protein expression in<br />
reporter bacteria.'' J Bacteriol. 2001 Dec;183(23):6752-62.<br />
<br />
3. Endres D, Zlotnick A. ''Model-based analysis of assembly kinetics for virus capsids or other spherical<br />
polymers.'' Biophys J. 2002 Aug;83(2):1217-30.</div>FRhttp://2009.igem.org/Team:TorontoMaRSDiscovery/ModelingTeam:TorontoMaRSDiscovery/Modeling2009-10-21T14:04:52Z<p>FR: /* Degredation of eCFP */</p>
<hr />
<div>[[image:To_igem_wiki_banner.jpg|965px]]<br />
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|}<br />
<br><br />
<br />
<br />
=Summary=<br />
<br />
A kinetic model of our system has been constructed. Approximate parameter values were gathered from online resources to represent all processes up to the production of the eCFP and Encapsulin proteins. Current simulations predict the production of these two proteins at various initial concentrations of IPTG and aTc effector molecules. A sensitivity analysis reveals that the rate of constitutive expression of lacI and tetR has the greatest affect on eCFP and Encapsulin concentrations. Furthermore, we have outlined approaches for the detailed modelling of the eCFP degredation/maturation and Encapsulin assembly pathways.<br />
<br />
<br />
The initial simulations will be used to identify a critical concentration of Encapsulin mononomer required for microcompartment assembly. To strengthen the model, the constitutive expression rate of BBa_J23100 as used in our construct will be measured. Subsequently, a detailed model of Encapsulin assembly will be integrated into the current model, and its parameters filled-in using parameter-scanning methods and experiments outlined in the relevant references. By comparing experimental measures of microcompartment formation with that predicted by the kinetic model, we aim to gain insight on the mechanisms of Encapsulin assembly.<br />
<br />
=Model=<br />
Our model is based on the following design (See Project Page for a full description of this system).<br />
[[image:BioBrick.png|thumb|centre|The Encapsulator]]<br />
<br />
The reaction framework was mainly generated using the [http://synbioss.sourceforge.net/ SynBioSS Designer (a really useful modeling tool for iGEM teams)], which also provides default parameter values. These parameter values have been gathered from various literature [http://neptune.cems.umn.edu/designer/designer_defaults.pdf sources], and should be taken as approximations. All units were taken to be (1 / molarity^n-1 * s), where n is the order of the reaction. For example, for the reaction 2 lacI --> lacI2, n = 2, thus the rate constant has the units 1/molarity*s. <br />
<br />
The pathways for the expressed proteins, eCFPt and Encapsulin, need to be modeled in more detail. For example, in this basic model eCFPt is degraded via a first order reaction and Encapsulin makes a dimer complex. However, in reality fluorescent proteins have been shown to degreade via Micheales-menton kinetics and Encapsulin is thought to make a complex of about 60 monomers. These issues will be addressed in future work.<br />
<br />
'''The reactions can be accessed here:'''<br />
<br />
[[The Encapsulator Model]] (opens new page)<br />
<br />
[[Media:Uft_mod_Rxns2.xls|Download Encapsulator Model ]] (download Excel file)<br />
<br />
=Simulations=<br />
<br />
All simulations were carried out using the [https://2009.igem.org/Partner_Offers SimBiology Matlab Toolbox], which was freely available to iGEM teams. <br />
<br />
===Accumulation of eCFP at Different Initial Concentrations of IPTG===<br />
<br />
[[Image:uft_mod_cfp-iptg.png | 900px]]<br />
<br />
The IPTG effector eventually loses effect, and the eCFP concentration approaches a maximum. This happens because the IPTG proteins eventually ''tie up'' all available LacI4 proteins, leaving the transcription and translation of eCFP to operate at its maxiumum rate. <br />
<br />
===Accumulation of Encapsulin monomer at Different Initial Concentrations of aTc===<br />
<br />
[[Image:uft_mod_enc-atc.png | 900px]]<br />
<br />
(NOTE: in order to observe Encapsulin monomer levels, the above simulations were carried out without any Encapsulin assembly reactions in place)<br />
<br />
The production of Encapsulin occurs at a slower rate than eCFP because the BBa_R0040 promoter has two tetR binding sites, resulting in more repression and more off-pathway scenarios. Thus, the Encapsulin concentration also seems assymptotic but at higher concentrations of aTc (relative to IPTG). <br />
<br />
It seems beneficial to have the Encapsulin protein under control of the BBa_R0040-tetR-aTc construct because at zero levels of aTc we can have essentially zero levels of Encapsulin (whereas even at zero levels of IPTG, there is still significantly more eCFP). This will enable us to probe extremely low concentrations of Encapsulin monomer when testing for optimal Encapsulin assembly conditions. The disadvantage is that if Encapsulin assembly requires a very high initial concentration of Encapsulin monomer, we would have to wait a long time to see microcompartments. If this later scenario is observed, it may be better to switch the eCFP and Encapsulin expression systems.<br />
<br />
===Sensitivity Analysis===<br />
<br />
Since all of our parameters are approximations from literature sources, those which have the greatest affect on system dynamics (ie. the most ''sensitive'' parameters) would be leading candidates to be experimentally determined. Currently we are interested in the parameters that have the greatest effect on the production of eCFP and Encapsulin. Ideally, it would be best to tighten-up the model by experimentally determining these, before incorporating the largely unexplored Encapsulin assembly pathways. <br />
<br />
<br />
'''1) Sensitivity of eCFP Production'''<br />
<br />
[[Image:uft_mod_SAecfp.png | centre | 600px]]<br />
<br />
<br />
<br />
'''2) Sensitivity of Encapsulin Production'''<br />
<br />
[[Image:uft_mod_SAenc.png | centre | 600px]]<br />
<br />
Parameters 1 and 2 correspond to the rates of constitutive expression of the repressors lacI and tetR respectively. Thus, it is predicted that eCFP and Encapsulin production is largely sensitive to the expression rates of lacI and tetR. <br />
<br />
The specific constitutive promoter used in our construct is BBa_J23100. In our model, this was given the generic rate of 1E-10 molarity\s by SynBioSS based on a variety of empirically-fitted protein expression rates found in literature. This generic approach to assigning parameter values is a suitable fist-step, but our sensitivity results suggest that experimentally determining the expression rate of BBa_J23100 should significantly improve our model's predictive capability.<br />
<br />
=Future Work=<br />
<br />
Improvements to the basic model presented above can be separated into three areas; 1) performing experiments to determine parameter values that are specific to our system, 2) more detailed modeling of eCFPt behavior, 3) more detailed modeling of Encapsulin assembly. <br />
<br />
The experiments required to determine general transcription and translation parameters need to be further researched, so this will be skipped over for now. Here we will discuss the more interesting areas – the detailed modeling of eCFP and Encapsulin pathways. This will be accomplished by incorporating previous modeling efforts that are applicable to the eCFP and Encapsulin proteins. <br />
<br />
===Maturation and Degredation of eCFP===<br />
<br />
The expression and degradation of [http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=95514&blobtype=pdf Green Fluorescent Protein (GFP) was modeled previously]. This paper noted that GFP must mature before going into fluorescent phase, and GFP degradation was shown to follow M-M kinetics, as depicted below. This paper also outlined how the degradation parameters could be derived for any expression system using only simple fluorescence and optical density measurements.<br />
<br />
[[Image:uft_mod_ecfp1.png | centre | thumb | Degredation and maturation pathways for eCFP. (Leveau and Lindow 2001)]]<br />
<br />
<br />
The GFP maturation and degradation parameters found in this paper were:<br />
<br />
<html><br />
<centre><br />
<table><br />
<tr><td> m = 0.0004279 1/s </td></tr><br />
<tr><td> Vmax = 2E-10 molality/s </td></tr><br />
<tr><td> Km = 9E-13 molality/s </td></tr><br />
<tr><td> </td></tr><br />
</table><br />
</centre><br />
</html><br />
<br />
<br />
Assuming eCFPt would behave similarly to eGFP, the following additional reactions would be included in the model:<br />
<br />
<html><br />
<table><br />
<tr> <td><b> Maturation </b></td> <td> </td> </tr><br />
<tr> <td> eCFPt --> F_eCFPT </td> <td> 0.0004279 </td> </tr><br />
<tr> <td> Enc2:eCFPt --> Enc2:F_eCFPt </td> <td> 0.0004279 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Encapsulation </b></td> <td> </td> </tr><br />
<tr> <td> Enc2 + F_eCFPt --> Enc2:F_eCFPt </td> <td> 100 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Degradation </b></td> <td> </td> </tr><br />
<tr> <td> eCFPt --> </td> <td> Vmax = 2E-10 </td> </tr><br />
<tr> <td> </td> <td> Km = 9E-13 </td> </tr><br />
<tr> <td> F_eCFPt --> </td> <td> Vmax = 2E-10 </td> </tr><br />
<tr> <td> </td> <td> Km = 9E-13 </td> </tr><br />
</table><br />
</html><br />
<br />
===Assembly of Encapsulin Microcompartments===<br />
<br />
Though Encapsulin microcompartment assembly is not well-studied, it has been theorized to resemble the assembly of viral capsids. Thus, we could look to this relatively well-studied phenomenon as a representation of Encapsulin microcompartment assembly.<br />
<br />
Adam Zlotnick has published models of viral capsid assembly using different approaches. An early paper described an equilibrium model of assembly for a 12 Unit polyhedral capsid head, and a more recent paper used a kinetic model that could be applied to many examples of spherical polymerization. We will consider how each approach could be incorporated as a representation of Encapsulin assembly.<br />
<br />
<br />
'''1) Equilibrim Approach to Encapsulin Assembly'''<br />
<br />
Zlotnick's [[Media:Uft_mod_to_build_a_virus_capsid.pdf|Equilibrium-based model]] consists of reactions from an initial monomer subunit leading to a final capsid product. The sequential reactions take into account DeltaG for contact (Kn'), and parameters describing path degeneracy (varies for different intermediates).<br />
[[image:uft_mod_encap1.png|centre|thumb|Kn for assembly subunits based on path degeneracy. (Zlotnick 1994)]]<br />
<br />
<br />
'''2) Kinetic Model of Spherical Polymerization'''<br />
<br />
A [http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1302223/pdf/12124301.pdf general kinetic model for the spherical polyermization] process is shown below. In our case, the initial monomer subunit concentration (''u'') would represent our expressed Encapsulin BioBrick, and the number of monomers in the final assembly (''N'') is thought to be 60. All of the included parameters can be calculated from the four basic parameters; the microscopic, per-contact equilibrium constant (KAcon), the nucleus size (nuc), the nucleation on-rate (f_nuc), and the elongation on-rate (f_elong). The referenced paper describes methods to aquire these parameters from kinetic experiments, and provides examples for N = 12 and 30 unit viral capsid assemblies.<br />
[[image:uft_mod_encap2.png| centre | thumb |System of ODEs to represent spherical polymerization, where ''u'' is the initial subunit concentration, ''m'' is the "mth" intermediate species, and ''N'' is the number of monomers in the final assembly. (Endres and Zlotnick 2002)]]<br />
<br />
<br />
<br />
Zlotnick's models also describe two important features of spherical polymerization that we should also expect to observe in Encapsulin assembly: kinetic trapping and nucleation. A kinetic trap occurs when the initial monomer subunit concentration or the deltaG of the first assembly reaction is too high. This results in over-initiation of assembly and quickly the reactions become starved for subunits. Kinetic trapping is prevented by the inclusion of nucleation, where the initial reactions occur at a slower rate because the first few intermediates in a series of reactions are less stable than downstream products. Essentially, nucleation serves as a “slow first step” that regulates the assembly pathway. <br />
<br />
It will be interesting to note how the translational dynamics of Encapsulin interplay with its assembly dynamics. Since our system does not start with any initial concentration of Encapsulin, there will be an optimum rate of production that essentially serves the role of nucleation – avoiding kinetic traps while still maintaining a maximum production of full Encapsulin assemblies.<br />
<br />
=References=<br />
<br />
1. Hill AD, Tomshine JR, Weeding EM, Sotiropoulos V, Kaznessis YN. ''SynBioSS: the synthetic biology modeling suite.'' Bioinformatics. 2008 Nov 1;24(21):2551-3. Epub 2008 Aug 30.<br />
[http://neptune.cems.umn.edu/designer/interface1.php SynBioSS Web Designer]<br />
<br />
2. Leveau JH, Lindow SE. ''Predictive and interpretive simulation of green fluorescent protein expression in<br />
reporter bacteria.'' J Bacteriol. 2001 Dec;183(23):6752-62.<br />
<br />
3. Endres D, Zlotnick A. ''Model-based analysis of assembly kinetics for virus capsids or other spherical<br />
polymers.'' Biophys J. 2002 Aug;83(2):1217-30.</div>FRhttp://2009.igem.org/Team:TorontoMaRSDiscovery/ModelingTeam:TorontoMaRSDiscovery/Modeling2009-10-21T14:03:34Z<p>FR: /* Sensitivity Analysis */</p>
<hr />
<div>[[image:To_igem_wiki_banner.jpg|965px]]<br />
{| style="color:white;background-color:#99CCFF;" height:100px cellpadding="2" cellspacing="0" border="0" width="100%" align="center" class="menu"<br />
!align="center"|[[Team:TorontoMaRSDiscovery|Home]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Team|The Team]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Project|The Project]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Parts|BioBricks]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Modeling|Modeling]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Bioinformatics|Bioinformatics]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Safety|Safety]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Notebook|Notebook]]<br />
|}<br />
<br><br />
<br />
<br />
=Summary=<br />
<br />
A kinetic model of our system has been constructed. Approximate parameter values were gathered from online resources to represent all processes up to the production of the eCFP and Encapsulin proteins. Current simulations predict the production of these two proteins at various initial concentrations of IPTG and aTc effector molecules. A sensitivity analysis reveals that the rate of constitutive expression of lacI and tetR has the greatest affect on eCFP and Encapsulin concentrations. Furthermore, we have outlined approaches for the detailed modelling of the eCFP degredation/maturation and Encapsulin assembly pathways.<br />
<br />
<br />
The initial simulations will be used to identify a critical concentration of Encapsulin mononomer required for microcompartment assembly. To strengthen the model, the constitutive expression rate of BBa_J23100 as used in our construct will be measured. Subsequently, a detailed model of Encapsulin assembly will be integrated into the current model, and its parameters filled-in using parameter-scanning methods and experiments outlined in the relevant references. By comparing experimental measures of microcompartment formation with that predicted by the kinetic model, we aim to gain insight on the mechanisms of Encapsulin assembly.<br />
<br />
=Model=<br />
Our model is based on the following design (See Project Page for a full description of this system).<br />
[[image:BioBrick.png|thumb|centre|The Encapsulator]]<br />
<br />
The reaction framework was mainly generated using the [http://synbioss.sourceforge.net/ SynBioSS Designer (a really useful modeling tool for iGEM teams)], which also provides default parameter values. These parameter values have been gathered from various literature [http://neptune.cems.umn.edu/designer/designer_defaults.pdf sources], and should be taken as approximations. All units were taken to be (1 / molarity^n-1 * s), where n is the order of the reaction. For example, for the reaction 2 lacI --> lacI2, n = 2, thus the rate constant has the units 1/molarity*s. <br />
<br />
The pathways for the expressed proteins, eCFPt and Encapsulin, need to be modeled in more detail. For example, in this basic model eCFPt is degraded via a first order reaction and Encapsulin makes a dimer complex. However, in reality fluorescent proteins have been shown to degreade via Micheales-menton kinetics and Encapsulin is thought to make a complex of about 60 monomers. These issues will be addressed in future work.<br />
<br />
'''The reactions can be accessed here:'''<br />
<br />
[[The Encapsulator Model]] (opens new page)<br />
<br />
[[Media:Uft_mod_Rxns2.xls|Download Encapsulator Model ]] (download Excel file)<br />
<br />
=Simulations=<br />
<br />
All simulations were carried out using the [https://2009.igem.org/Partner_Offers SimBiology Matlab Toolbox], which was freely available to iGEM teams. <br />
<br />
===Accumulation of eCFP at Different Initial Concentrations of IPTG===<br />
<br />
[[Image:uft_mod_cfp-iptg.png | 900px]]<br />
<br />
The IPTG effector eventually loses effect, and the eCFP concentration approaches a maximum. This happens because the IPTG proteins eventually ''tie up'' all available LacI4 proteins, leaving the transcription and translation of eCFP to operate at its maxiumum rate. <br />
<br />
===Accumulation of Encapsulin monomer at Different Initial Concentrations of aTc===<br />
<br />
[[Image:uft_mod_enc-atc.png | 900px]]<br />
<br />
(NOTE: in order to observe Encapsulin monomer levels, the above simulations were carried out without any Encapsulin assembly reactions in place)<br />
<br />
The production of Encapsulin occurs at a slower rate than eCFP because the BBa_R0040 promoter has two tetR binding sites, resulting in more repression and more off-pathway scenarios. Thus, the Encapsulin concentration also seems assymptotic but at higher concentrations of aTc (relative to IPTG). <br />
<br />
It seems beneficial to have the Encapsulin protein under control of the BBa_R0040-tetR-aTc construct because at zero levels of aTc we can have essentially zero levels of Encapsulin (whereas even at zero levels of IPTG, there is still significantly more eCFP). This will enable us to probe extremely low concentrations of Encapsulin monomer when testing for optimal Encapsulin assembly conditions. The disadvantage is that if Encapsulin assembly requires a very high initial concentration of Encapsulin monomer, we would have to wait a long time to see microcompartments. If this later scenario is observed, it may be better to switch the eCFP and Encapsulin expression systems.<br />
<br />
===Sensitivity Analysis===<br />
<br />
Since all of our parameters are approximations from literature sources, those which have the greatest affect on system dynamics (ie. the most ''sensitive'' parameters) would be leading candidates to be experimentally determined. Currently we are interested in the parameters that have the greatest effect on the production of eCFP and Encapsulin. Ideally, it would be best to tighten-up the model by experimentally determining these, before incorporating the largely unexplored Encapsulin assembly pathways. <br />
<br />
<br />
'''1) Sensitivity of eCFP Production'''<br />
<br />
[[Image:uft_mod_SAecfp.png | centre | 600px]]<br />
<br />
<br />
<br />
'''2) Sensitivity of Encapsulin Production'''<br />
<br />
[[Image:uft_mod_SAenc.png | centre | 600px]]<br />
<br />
Parameters 1 and 2 correspond to the rates of constitutive expression of the repressors lacI and tetR respectively. Thus, it is predicted that eCFP and Encapsulin production is largely sensitive to the expression rates of lacI and tetR. <br />
<br />
The specific constitutive promoter used in our construct is BBa_J23100. In our model, this was given the generic rate of 1E-10 molarity\s by SynBioSS based on a variety of empirically-fitted protein expression rates found in literature. This generic approach to assigning parameter values is a suitable fist-step, but our sensitivity results suggest that experimentally determining the expression rate of BBa_J23100 should significantly improve our model's predictive capability.<br />
<br />
=Future Work=<br />
<br />
Improvements to the basic model presented above can be separated into three areas; 1) performing experiments to determine parameter values that are specific to our system, 2) more detailed modeling of eCFPt behavior, 3) more detailed modeling of Encapsulin assembly. <br />
<br />
The experiments required to determine general transcription and translation parameters need to be further researched, so this will be skipped over for now. Here we will discuss the more interesting areas – the detailed modeling of eCFP and Encapsulin pathways. This will be accomplished by incorporating previous modeling efforts that are applicable to the eCFP and Encapsulin proteins. <br />
<br />
===Degredation of eCFP===<br />
<br />
The expression and degradation of [http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=95514&blobtype=pdf Green Fluorescent Protein (GFP) was modeled previously]. This paper noted that GFP must mature before going into fluorescent phase, and GFP degradation was shown to follow M-M kinetics, as depicted below. This paper also outlined how the degradation parameters could be derived for any expression system using only simple fluorescence and optical density measurements.<br />
<br />
[[Image:uft_mod_ecfp1.png | centre | thumb | Degredation and maturation pathways for eCFP. (Leveau and Lindow 2001)]]<br />
<br />
<br />
The GFP maturation and degradation parameters found in this paper were:<br />
<br />
<html><br />
<centre><br />
<table><br />
<tr><td> m = 0.0004279 1/s </td></tr><br />
<tr><td> Vmax = 2E-10 molality/s </td></tr><br />
<tr><td> Km = 9E-13 molality/s </td></tr><br />
<tr><td> </td></tr><br />
</table><br />
</centre><br />
</html><br />
<br />
<br />
Assuming eCFPt would behave similarly to eGFP, the following additional reactions would be included in the model:<br />
<br />
<html><br />
<table><br />
<tr> <td><b> Maturation </b></td> <td> </td> </tr><br />
<tr> <td> eCFPt --> F_eCFPT </td> <td> 0.0004279 </td> </tr><br />
<tr> <td> Enc2:eCFPt --> Enc2:F_eCFPt </td> <td> 0.0004279 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Encapsulation </b></td> <td> </td> </tr><br />
<tr> <td> Enc2 + F_eCFPt --> Enc2:F_eCFPt </td> <td> 100 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Degradation </b></td> <td> </td> </tr><br />
<tr> <td> eCFPt --> </td> <td> Vmax = 2E-10 </td> </tr><br />
<tr> <td> </td> <td> Km = 9E-13 </td> </tr><br />
<tr> <td> F_eCFPt --> </td> <td> Vmax = 2E-10 </td> </tr><br />
<tr> <td> </td> <td> Km = 9E-13 </td> </tr><br />
</table><br />
</html><br />
<br />
===Assembly of Encapsulin Microcompartments===<br />
<br />
Though Encapsulin microcompartment assembly is not well-studied, it has been theorized to resemble the assembly of viral capsids. Thus, we could look to this relatively well-studied phenomenon as a representation of Encapsulin microcompartment assembly.<br />
<br />
Adam Zlotnick has published models of viral capsid assembly using different approaches. An early paper described an equilibrium model of assembly for a 12 Unit polyhedral capsid head, and a more recent paper used a kinetic model that could be applied to many examples of spherical polymerization. We will consider how each approach could be incorporated as a representation of Encapsulin assembly.<br />
<br />
<br />
'''1) Equilibrim Approach to Encapsulin Assembly'''<br />
<br />
Zlotnick's [[Media:Uft_mod_to_build_a_virus_capsid.pdf|Equilibrium-based model]] consists of reactions from an initial monomer subunit leading to a final capsid product. The sequential reactions take into account DeltaG for contact (Kn'), and parameters describing path degeneracy (varies for different intermediates).<br />
[[image:uft_mod_encap1.png|centre|thumb|Kn for assembly subunits based on path degeneracy. (Zlotnick 1994)]]<br />
<br />
<br />
'''2) Kinetic Model of Spherical Polymerization'''<br />
<br />
A [http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1302223/pdf/12124301.pdf general kinetic model for the spherical polyermization] process is shown below. In our case, the initial monomer subunit concentration (''u'') would represent our expressed Encapsulin BioBrick, and the number of monomers in the final assembly (''N'') is thought to be 60. All of the included parameters can be calculated from the four basic parameters; the microscopic, per-contact equilibrium constant (KAcon), the nucleus size (nuc), the nucleation on-rate (f_nuc), and the elongation on-rate (f_elong). The referenced paper describes methods to aquire these parameters from kinetic experiments, and provides examples for N = 12 and 30 unit viral capsid assemblies.<br />
[[image:uft_mod_encap2.png| centre | thumb |System of ODEs to represent spherical polymerization, where ''u'' is the initial subunit concentration, ''m'' is the "mth" intermediate species, and ''N'' is the number of monomers in the final assembly. (Endres and Zlotnick 2002)]]<br />
<br />
<br />
<br />
Zlotnick's models also describe two important features of spherical polymerization that we should also expect to observe in Encapsulin assembly: kinetic trapping and nucleation. A kinetic trap occurs when the initial monomer subunit concentration or the deltaG of the first assembly reaction is too high. This results in over-initiation of assembly and quickly the reactions become starved for subunits. Kinetic trapping is prevented by the inclusion of nucleation, where the initial reactions occur at a slower rate because the first few intermediates in a series of reactions are less stable than downstream products. Essentially, nucleation serves as a “slow first step” that regulates the assembly pathway. <br />
<br />
It will be interesting to note how the translational dynamics of Encapsulin interplay with its assembly dynamics. Since our system does not start with any initial concentration of Encapsulin, there will be an optimum rate of production that essentially serves the role of nucleation – avoiding kinetic traps while still maintaining a maximum production of full Encapsulin assemblies.<br />
<br />
=References=<br />
<br />
1. Hill AD, Tomshine JR, Weeding EM, Sotiropoulos V, Kaznessis YN. ''SynBioSS: the synthetic biology modeling suite.'' Bioinformatics. 2008 Nov 1;24(21):2551-3. Epub 2008 Aug 30.<br />
[http://neptune.cems.umn.edu/designer/interface1.php SynBioSS Web Designer]<br />
<br />
2. Leveau JH, Lindow SE. ''Predictive and interpretive simulation of green fluorescent protein expression in<br />
reporter bacteria.'' J Bacteriol. 2001 Dec;183(23):6752-62.<br />
<br />
3. Endres D, Zlotnick A. ''Model-based analysis of assembly kinetics for virus capsids or other spherical<br />
polymers.'' Biophys J. 2002 Aug;83(2):1217-30.</div>FRhttp://2009.igem.org/Team:TorontoMaRSDiscovery/ModelingTeam:TorontoMaRSDiscovery/Modeling2009-10-21T14:02:16Z<p>FR: /* Sensitivity Analysis */</p>
<hr />
<div>[[image:To_igem_wiki_banner.jpg|965px]]<br />
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!align="center"|[[Team:TorontoMaRSDiscovery|Home]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Team|The Team]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Project|The Project]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Parts|BioBricks]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Modeling|Modeling]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Bioinformatics|Bioinformatics]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Safety|Safety]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Notebook|Notebook]]<br />
|}<br />
<br><br />
<br />
<br />
=Summary=<br />
<br />
A kinetic model of our system has been constructed. Approximate parameter values were gathered from online resources to represent all processes up to the production of the eCFP and Encapsulin proteins. Current simulations predict the production of these two proteins at various initial concentrations of IPTG and aTc effector molecules. A sensitivity analysis reveals that the rate of constitutive expression of lacI and tetR has the greatest affect on eCFP and Encapsulin concentrations. Furthermore, we have outlined approaches for the detailed modelling of the eCFP degredation/maturation and Encapsulin assembly pathways.<br />
<br />
<br />
The initial simulations will be used to identify a critical concentration of Encapsulin mononomer required for microcompartment assembly. To strengthen the model, the constitutive expression rate of BBa_J23100 as used in our construct will be measured. Subsequently, a detailed model of Encapsulin assembly will be integrated into the current model, and its parameters filled-in using parameter-scanning methods and experiments outlined in the relevant references. By comparing experimental measures of microcompartment formation with that predicted by the kinetic model, we aim to gain insight on the mechanisms of Encapsulin assembly.<br />
<br />
=Model=<br />
Our model is based on the following design (See Project Page for a full description of this system).<br />
[[image:BioBrick.png|thumb|centre|The Encapsulator]]<br />
<br />
The reaction framework was mainly generated using the [http://synbioss.sourceforge.net/ SynBioSS Designer (a really useful modeling tool for iGEM teams)], which also provides default parameter values. These parameter values have been gathered from various literature [http://neptune.cems.umn.edu/designer/designer_defaults.pdf sources], and should be taken as approximations. All units were taken to be (1 / molarity^n-1 * s), where n is the order of the reaction. For example, for the reaction 2 lacI --> lacI2, n = 2, thus the rate constant has the units 1/molarity*s. <br />
<br />
The pathways for the expressed proteins, eCFPt and Encapsulin, need to be modeled in more detail. For example, in this basic model eCFPt is degraded via a first order reaction and Encapsulin makes a dimer complex. However, in reality fluorescent proteins have been shown to degreade via Micheales-menton kinetics and Encapsulin is thought to make a complex of about 60 monomers. These issues will be addressed in future work.<br />
<br />
'''The reactions can be accessed here:'''<br />
<br />
[[The Encapsulator Model]] (opens new page)<br />
<br />
[[Media:Uft_mod_Rxns2.xls|Download Encapsulator Model ]] (download Excel file)<br />
<br />
=Simulations=<br />
<br />
All simulations were carried out using the [https://2009.igem.org/Partner_Offers SimBiology Matlab Toolbox], which was freely available to iGEM teams. <br />
<br />
===Accumulation of eCFP at Different Initial Concentrations of IPTG===<br />
<br />
[[Image:uft_mod_cfp-iptg.png | 900px]]<br />
<br />
The IPTG effector eventually loses effect, and the eCFP concentration approaches a maximum. This happens because the IPTG proteins eventually ''tie up'' all available LacI4 proteins, leaving the transcription and translation of eCFP to operate at its maxiumum rate. <br />
<br />
===Accumulation of Encapsulin monomer at Different Initial Concentrations of aTc===<br />
<br />
[[Image:uft_mod_enc-atc.png | 900px]]<br />
<br />
(NOTE: in order to observe Encapsulin monomer levels, the above simulations were carried out without any Encapsulin assembly reactions in place)<br />
<br />
The production of Encapsulin occurs at a slower rate than eCFP because the BBa_R0040 promoter has two tetR binding sites, resulting in more repression and more off-pathway scenarios. Thus, the Encapsulin concentration also seems assymptotic but at higher concentrations of aTc (relative to IPTG). <br />
<br />
It seems beneficial to have the Encapsulin protein under control of the BBa_R0040-tetR-aTc construct because at zero levels of aTc we can have essentially zero levels of Encapsulin (whereas even at zero levels of IPTG, there is still significantly more eCFP). This will enable us to probe extremely low concentrations of Encapsulin monomer when testing for optimal Encapsulin assembly conditions. The disadvantage is that if Encapsulin assembly requires a very high initial concentration of Encapsulin monomer, we would have to wait a long time to see microcompartments. If this later scenario is observed, it may be better to switch the eCFP and Encapsulin expression systems.<br />
<br />
===Sensitivity Analysis===<br />
<br />
Since all of our parameters are approximations from literature sources, those which have the greatest affect on system dynamics (ie. the most ''sensitive'' parameters) would be leading candidates to be experimentally determined. Currently we are interested in the parameters that have the greatest effect on the production of eCFP and Encapsulin. Ideally, it would be best to tighten-up the model by experimentally determining these, before incorporating the largely unexplored Encapsulin assembly pathways. <br />
<br />
<br />
'''1) Sensitivity of eCFP Production'''<br />
<br />
[[Image:uft_mod_SAecfp.png | centre | 600px]]<br />
<br />
<br />
<br />
'''2) Sensitivity of Encapsulin Production'''<br />
<br />
[[Image:uft_mod_SAenc.png | centre | 600px]]<br />
<br />
Parameters 1 and 2 correspond to the rates of constitutive expression of the lacI and tetR repressors respectively. Thus, it is predicted that eCFP and Encapsulin production is largely sensitive to the expression rates of lacI and tetR. <br />
<br />
The specific constitutive promoter used in our construct is BBa_J23100. In our model, this was given the generic rate of 1E-10 molarity\s by SynBioSS based on a variety of empirically-fitted protein expression rates found in literature. This generic approach to assigning parameter values is a suitable fist-step, but our sensitivity results suggest that experimentally determining the expression rate of BBa_J23100 should significantly improve our model's predictive capability.<br />
<br />
=Future Work=<br />
<br />
Improvements to the basic model presented above can be separated into three areas; 1) performing experiments to determine parameter values that are specific to our system, 2) more detailed modeling of eCFPt behavior, 3) more detailed modeling of Encapsulin assembly. <br />
<br />
The experiments required to determine general transcription and translation parameters need to be further researched, so this will be skipped over for now. Here we will discuss the more interesting areas – the detailed modeling of eCFP and Encapsulin pathways. This will be accomplished by incorporating previous modeling efforts that are applicable to the eCFP and Encapsulin proteins. <br />
<br />
===Degredation of eCFP===<br />
<br />
The expression and degradation of [http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=95514&blobtype=pdf Green Fluorescent Protein (GFP) was modeled previously]. This paper noted that GFP must mature before going into fluorescent phase, and GFP degradation was shown to follow M-M kinetics, as depicted below. This paper also outlined how the degradation parameters could be derived for any expression system using only simple fluorescence and optical density measurements.<br />
<br />
[[Image:uft_mod_ecfp1.png | centre | thumb | Degredation and maturation pathways for eCFP. (Leveau and Lindow 2001)]]<br />
<br />
<br />
The GFP maturation and degradation parameters found in this paper were:<br />
<br />
<html><br />
<centre><br />
<table><br />
<tr><td> m = 0.0004279 1/s </td></tr><br />
<tr><td> Vmax = 2E-10 molality/s </td></tr><br />
<tr><td> Km = 9E-13 molality/s </td></tr><br />
<tr><td> </td></tr><br />
</table><br />
</centre><br />
</html><br />
<br />
<br />
Assuming eCFPt would behave similarly to eGFP, the following additional reactions would be included in the model:<br />
<br />
<html><br />
<table><br />
<tr> <td><b> Maturation </b></td> <td> </td> </tr><br />
<tr> <td> eCFPt --> F_eCFPT </td> <td> 0.0004279 </td> </tr><br />
<tr> <td> Enc2:eCFPt --> Enc2:F_eCFPt </td> <td> 0.0004279 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Encapsulation </b></td> <td> </td> </tr><br />
<tr> <td> Enc2 + F_eCFPt --> Enc2:F_eCFPt </td> <td> 100 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Degradation </b></td> <td> </td> </tr><br />
<tr> <td> eCFPt --> </td> <td> Vmax = 2E-10 </td> </tr><br />
<tr> <td> </td> <td> Km = 9E-13 </td> </tr><br />
<tr> <td> F_eCFPt --> </td> <td> Vmax = 2E-10 </td> </tr><br />
<tr> <td> </td> <td> Km = 9E-13 </td> </tr><br />
</table><br />
</html><br />
<br />
===Assembly of Encapsulin Microcompartments===<br />
<br />
Though Encapsulin microcompartment assembly is not well-studied, it has been theorized to resemble the assembly of viral capsids. Thus, we could look to this relatively well-studied phenomenon as a representation of Encapsulin microcompartment assembly.<br />
<br />
Adam Zlotnick has published models of viral capsid assembly using different approaches. An early paper described an equilibrium model of assembly for a 12 Unit polyhedral capsid head, and a more recent paper used a kinetic model that could be applied to many examples of spherical polymerization. We will consider how each approach could be incorporated as a representation of Encapsulin assembly.<br />
<br />
<br />
'''1) Equilibrim Approach to Encapsulin Assembly'''<br />
<br />
Zlotnick's [[Media:Uft_mod_to_build_a_virus_capsid.pdf|Equilibrium-based model]] consists of reactions from an initial monomer subunit leading to a final capsid product. The sequential reactions take into account DeltaG for contact (Kn'), and parameters describing path degeneracy (varies for different intermediates).<br />
[[image:uft_mod_encap1.png|centre|thumb|Kn for assembly subunits based on path degeneracy. (Zlotnick 1994)]]<br />
<br />
<br />
'''2) Kinetic Model of Spherical Polymerization'''<br />
<br />
A [http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1302223/pdf/12124301.pdf general kinetic model for the spherical polyermization] process is shown below. In our case, the initial monomer subunit concentration (''u'') would represent our expressed Encapsulin BioBrick, and the number of monomers in the final assembly (''N'') is thought to be 60. All of the included parameters can be calculated from the four basic parameters; the microscopic, per-contact equilibrium constant (KAcon), the nucleus size (nuc), the nucleation on-rate (f_nuc), and the elongation on-rate (f_elong). The referenced paper describes methods to aquire these parameters from kinetic experiments, and provides examples for N = 12 and 30 unit viral capsid assemblies.<br />
[[image:uft_mod_encap2.png| centre | thumb |System of ODEs to represent spherical polymerization, where ''u'' is the initial subunit concentration, ''m'' is the "mth" intermediate species, and ''N'' is the number of monomers in the final assembly. (Endres and Zlotnick 2002)]]<br />
<br />
<br />
<br />
Zlotnick's models also describe two important features of spherical polymerization that we should also expect to observe in Encapsulin assembly: kinetic trapping and nucleation. A kinetic trap occurs when the initial monomer subunit concentration or the deltaG of the first assembly reaction is too high. This results in over-initiation of assembly and quickly the reactions become starved for subunits. Kinetic trapping is prevented by the inclusion of nucleation, where the initial reactions occur at a slower rate because the first few intermediates in a series of reactions are less stable than downstream products. Essentially, nucleation serves as a “slow first step” that regulates the assembly pathway. <br />
<br />
It will be interesting to note how the translational dynamics of Encapsulin interplay with its assembly dynamics. Since our system does not start with any initial concentration of Encapsulin, there will be an optimum rate of production that essentially serves the role of nucleation – avoiding kinetic traps while still maintaining a maximum production of full Encapsulin assemblies.<br />
<br />
=References=<br />
<br />
1. Hill AD, Tomshine JR, Weeding EM, Sotiropoulos V, Kaznessis YN. ''SynBioSS: the synthetic biology modeling suite.'' Bioinformatics. 2008 Nov 1;24(21):2551-3. Epub 2008 Aug 30.<br />
[http://neptune.cems.umn.edu/designer/interface1.php SynBioSS Web Designer]<br />
<br />
2. Leveau JH, Lindow SE. ''Predictive and interpretive simulation of green fluorescent protein expression in<br />
reporter bacteria.'' J Bacteriol. 2001 Dec;183(23):6752-62.<br />
<br />
3. Endres D, Zlotnick A. ''Model-based analysis of assembly kinetics for virus capsids or other spherical<br />
polymers.'' Biophys J. 2002 Aug;83(2):1217-30.</div>FRhttp://2009.igem.org/Team:TorontoMaRSDiscovery/ModelingTeam:TorontoMaRSDiscovery/Modeling2009-10-21T13:59:03Z<p>FR: /* Model */</p>
<hr />
<div>[[image:To_igem_wiki_banner.jpg|965px]]<br />
{| style="color:white;background-color:#99CCFF;" height:100px cellpadding="2" cellspacing="0" border="0" width="100%" align="center" class="menu"<br />
!align="center"|[[Team:TorontoMaRSDiscovery|Home]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Team|The Team]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Project|The Project]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Parts|BioBricks]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Modeling|Modeling]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Bioinformatics|Bioinformatics]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Safety|Safety]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Notebook|Notebook]]<br />
|}<br />
<br><br />
<br />
<br />
=Summary=<br />
<br />
A kinetic model of our system has been constructed. Approximate parameter values were gathered from online resources to represent all processes up to the production of the eCFP and Encapsulin proteins. Current simulations predict the production of these two proteins at various initial concentrations of IPTG and aTc effector molecules. A sensitivity analysis reveals that the rate of constitutive expression of lacI and tetR has the greatest affect on eCFP and Encapsulin concentrations. Furthermore, we have outlined approaches for the detailed modelling of the eCFP degredation/maturation and Encapsulin assembly pathways.<br />
<br />
<br />
The initial simulations will be used to identify a critical concentration of Encapsulin mononomer required for microcompartment assembly. To strengthen the model, the constitutive expression rate of BBa_J23100 as used in our construct will be measured. Subsequently, a detailed model of Encapsulin assembly will be integrated into the current model, and its parameters filled-in using parameter-scanning methods and experiments outlined in the relevant references. By comparing experimental measures of microcompartment formation with that predicted by the kinetic model, we aim to gain insight on the mechanisms of Encapsulin assembly.<br />
<br />
=Model=<br />
Our model is based on the following design (See Project Page for a full description of this system).<br />
[[image:BioBrick.png|thumb|centre|The Encapsulator]]<br />
<br />
The reaction framework was mainly generated using the [http://synbioss.sourceforge.net/ SynBioSS Designer (a really useful modeling tool for iGEM teams)], which also provides default parameter values. These parameter values have been gathered from various literature [http://neptune.cems.umn.edu/designer/designer_defaults.pdf sources], and should be taken as approximations. All units were taken to be (1 / molarity^n-1 * s), where n is the order of the reaction. For example, for the reaction 2 lacI --> lacI2, n = 2, thus the rate constant has the units 1/molarity*s. <br />
<br />
The pathways for the expressed proteins, eCFPt and Encapsulin, need to be modeled in more detail. For example, in this basic model eCFPt is degraded via a first order reaction and Encapsulin makes a dimer complex. However, in reality fluorescent proteins have been shown to degreade via Micheales-menton kinetics and Encapsulin is thought to make a complex of about 60 monomers. These issues will be addressed in future work.<br />
<br />
'''The reactions can be accessed here:'''<br />
<br />
[[The Encapsulator Model]] (opens new page)<br />
<br />
[[Media:Uft_mod_Rxns2.xls|Download Encapsulator Model ]] (download Excel file)<br />
<br />
=Simulations=<br />
<br />
All simulations were carried out using the [https://2009.igem.org/Partner_Offers SimBiology Matlab Toolbox], which was freely available to iGEM teams. <br />
<br />
===Accumulation of eCFP at Different Initial Concentrations of IPTG===<br />
<br />
[[Image:uft_mod_cfp-iptg.png | 900px]]<br />
<br />
The IPTG effector eventually loses effect, and the eCFP concentration approaches a maximum. This happens because the IPTG proteins eventually ''tie up'' all available LacI4 proteins, leaving the transcription and translation of eCFP to operate at its maxiumum rate. <br />
<br />
===Accumulation of Encapsulin monomer at Different Initial Concentrations of aTc===<br />
<br />
[[Image:uft_mod_enc-atc.png | 900px]]<br />
<br />
(NOTE: in order to observe Encapsulin monomer levels, the above simulations were carried out without any Encapsulin assembly reactions in place)<br />
<br />
The production of Encapsulin occurs at a slower rate than eCFP because the BBa_R0040 promoter has two tetR binding sites, resulting in more repression and more off-pathway scenarios. Thus, the Encapsulin concentration also seems assymptotic but at higher concentrations of aTc (relative to IPTG). <br />
<br />
It seems beneficial to have the Encapsulin protein under control of the BBa_R0040-tetR-aTc construct because at zero levels of aTc we can have essentially zero levels of Encapsulin (whereas even at zero levels of IPTG, there is still significantly more eCFP). This will enable us to probe extremely low concentrations of Encapsulin monomer when testing for optimal Encapsulin assembly conditions. The disadvantage is that if Encapsulin assembly requires a very high initial concentration of Encapsulin monomer, we would have to wait a long time to see microcompartments. If this later scenario is observed, it may be better to switch the eCFP and Encapsulin expression systems.<br />
<br />
===Sensitivity Analysis===<br />
<br />
Since all of our parameters are approximations from literature sources, those which have the greatest affect on system dynamics (ie. the most ''sensitive'' parameters) would be leading candidates to be experimentally determined. Currently we are interested in which parameters have the greatest effect on the production of eCFP and Encapsulin. Ideally, it would be best to experimentally determine these to "tighten-up" the model before incorporating the largely unexplored Encapsulin assembly pathways. <br />
<br />
<br />
'''1) Sensitivity of eCFP Production'''<br />
<br />
[[Image:uft_mod_SAecfp.png | centre | 600px]]<br />
<br />
<br />
<br />
'''2) Sensitivity of Encapsulin Production'''<br />
<br />
[[Image:uft_mod_SAenc.png | centre | 600px]]<br />
<br />
Parameters 1 and 2 correspond to the rates of constitutive expression of the lacI and tetR repressors respectively. Thus, it can be seen that eCFP and Encapsulin production is largely sensitive to the expression rates of lacI and tetR. <br />
<br />
The specific constitutive promoter used in our construct is BBa_J23100. In our model, this was given the generic rate of 1E-10 molarity\s by SynBioSS based on a variety of empirically-fitted protein expression rates found in literature. This generic approach to assigning parameter values is a suitable fist-step, but our sensitivity results suggest that experimentally determining the expression rate of our specific constitutive promoter should significantly improve our model's predictive capability.<br />
<br />
=Future Work=<br />
<br />
Improvements to the basic model presented above can be separated into three areas; 1) performing experiments to determine parameter values that are specific to our system, 2) more detailed modeling of eCFPt behavior, 3) more detailed modeling of Encapsulin assembly. <br />
<br />
The experiments required to determine general transcription and translation parameters need to be further researched, so this will be skipped over for now. Here we will discuss the more interesting areas – the detailed modeling of eCFP and Encapsulin pathways. This will be accomplished by incorporating previous modeling efforts that are applicable to the eCFP and Encapsulin proteins. <br />
<br />
===Degredation of eCFP===<br />
<br />
The expression and degradation of [http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=95514&blobtype=pdf Green Fluorescent Protein (GFP) was modeled previously]. This paper noted that GFP must mature before going into fluorescent phase, and GFP degradation was shown to follow M-M kinetics, as depicted below. This paper also outlined how the degradation parameters could be derived for any expression system using only simple fluorescence and optical density measurements.<br />
<br />
[[Image:uft_mod_ecfp1.png | centre | thumb | Degredation and maturation pathways for eCFP. (Leveau and Lindow 2001)]]<br />
<br />
<br />
The GFP maturation and degradation parameters found in this paper were:<br />
<br />
<html><br />
<centre><br />
<table><br />
<tr><td> m = 0.0004279 1/s </td></tr><br />
<tr><td> Vmax = 2E-10 molality/s </td></tr><br />
<tr><td> Km = 9E-13 molality/s </td></tr><br />
<tr><td> </td></tr><br />
</table><br />
</centre><br />
</html><br />
<br />
<br />
Assuming eCFPt would behave similarly to eGFP, the following additional reactions would be included in the model:<br />
<br />
<html><br />
<table><br />
<tr> <td><b> Maturation </b></td> <td> </td> </tr><br />
<tr> <td> eCFPt --> F_eCFPT </td> <td> 0.0004279 </td> </tr><br />
<tr> <td> Enc2:eCFPt --> Enc2:F_eCFPt </td> <td> 0.0004279 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Encapsulation </b></td> <td> </td> </tr><br />
<tr> <td> Enc2 + F_eCFPt --> Enc2:F_eCFPt </td> <td> 100 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Degradation </b></td> <td> </td> </tr><br />
<tr> <td> eCFPt --> </td> <td> Vmax = 2E-10 </td> </tr><br />
<tr> <td> </td> <td> Km = 9E-13 </td> </tr><br />
<tr> <td> F_eCFPt --> </td> <td> Vmax = 2E-10 </td> </tr><br />
<tr> <td> </td> <td> Km = 9E-13 </td> </tr><br />
</table><br />
</html><br />
<br />
===Assembly of Encapsulin Microcompartments===<br />
<br />
Though Encapsulin microcompartment assembly is not well-studied, it has been theorized to resemble the assembly of viral capsids. Thus, we could look to this relatively well-studied phenomenon as a representation of Encapsulin microcompartment assembly.<br />
<br />
Adam Zlotnick has published models of viral capsid assembly using different approaches. An early paper described an equilibrium model of assembly for a 12 Unit polyhedral capsid head, and a more recent paper used a kinetic model that could be applied to many examples of spherical polymerization. We will consider how each approach could be incorporated as a representation of Encapsulin assembly.<br />
<br />
<br />
'''1) Equilibrim Approach to Encapsulin Assembly'''<br />
<br />
Zlotnick's [[Media:Uft_mod_to_build_a_virus_capsid.pdf|Equilibrium-based model]] consists of reactions from an initial monomer subunit leading to a final capsid product. The sequential reactions take into account DeltaG for contact (Kn'), and parameters describing path degeneracy (varies for different intermediates).<br />
[[image:uft_mod_encap1.png|centre|thumb|Kn for assembly subunits based on path degeneracy. (Zlotnick 1994)]]<br />
<br />
<br />
'''2) Kinetic Model of Spherical Polymerization'''<br />
<br />
A [http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1302223/pdf/12124301.pdf general kinetic model for the spherical polyermization] process is shown below. In our case, the initial monomer subunit concentration (''u'') would represent our expressed Encapsulin BioBrick, and the number of monomers in the final assembly (''N'') is thought to be 60. All of the included parameters can be calculated from the four basic parameters; the microscopic, per-contact equilibrium constant (KAcon), the nucleus size (nuc), the nucleation on-rate (f_nuc), and the elongation on-rate (f_elong). The referenced paper describes methods to aquire these parameters from kinetic experiments, and provides examples for N = 12 and 30 unit viral capsid assemblies.<br />
[[image:uft_mod_encap2.png| centre | thumb |System of ODEs to represent spherical polymerization, where ''u'' is the initial subunit concentration, ''m'' is the "mth" intermediate species, and ''N'' is the number of monomers in the final assembly. (Endres and Zlotnick 2002)]]<br />
<br />
<br />
<br />
Zlotnick's models also describe two important features of spherical polymerization that we should also expect to observe in Encapsulin assembly: kinetic trapping and nucleation. A kinetic trap occurs when the initial monomer subunit concentration or the deltaG of the first assembly reaction is too high. This results in over-initiation of assembly and quickly the reactions become starved for subunits. Kinetic trapping is prevented by the inclusion of nucleation, where the initial reactions occur at a slower rate because the first few intermediates in a series of reactions are less stable than downstream products. Essentially, nucleation serves as a “slow first step” that regulates the assembly pathway. <br />
<br />
It will be interesting to note how the translational dynamics of Encapsulin interplay with its assembly dynamics. Since our system does not start with any initial concentration of Encapsulin, there will be an optimum rate of production that essentially serves the role of nucleation – avoiding kinetic traps while still maintaining a maximum production of full Encapsulin assemblies.<br />
<br />
=References=<br />
<br />
1. Hill AD, Tomshine JR, Weeding EM, Sotiropoulos V, Kaznessis YN. ''SynBioSS: the synthetic biology modeling suite.'' Bioinformatics. 2008 Nov 1;24(21):2551-3. Epub 2008 Aug 30.<br />
[http://neptune.cems.umn.edu/designer/interface1.php SynBioSS Web Designer]<br />
<br />
2. Leveau JH, Lindow SE. ''Predictive and interpretive simulation of green fluorescent protein expression in<br />
reporter bacteria.'' J Bacteriol. 2001 Dec;183(23):6752-62.<br />
<br />
3. Endres D, Zlotnick A. ''Model-based analysis of assembly kinetics for virus capsids or other spherical<br />
polymers.'' Biophys J. 2002 Aug;83(2):1217-30.</div>FRhttp://2009.igem.org/Team:TorontoMaRSDiscovery/ModelingTeam:TorontoMaRSDiscovery/Modeling2009-10-21T07:52:12Z<p>FR: /* Sensitivity Analysis */</p>
<hr />
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<br><br />
<br />
<br />
=Summary=<br />
<br />
A kinetic model of our system has been constructed. Approximate parameter values were gathered from online resources to represent all processes up to the production of the eCFP and Encapsulin proteins. Current simulations predict the production of these two proteins at various initial concentrations of IPTG and aTc effector molecules. A sensitivity analysis reveals that the rate of constitutive expression of lacI and tetR has the greatest affect on eCFP and Encapsulin concentrations. Furthermore, we have outlined approaches for the detailed modelling of the eCFP degredation/maturation and Encapsulin assembly pathways.<br />
<br />
<br />
The initial simulations will be used to identify a critical concentration of Encapsulin mononomer required for microcompartment assembly. To strengthen the model, the constitutive expression rate of BBa_J23100 as used in our construct will be measured. Subsequently, a detailed model of Encapsulin assembly will be integrated into the current model, and its parameters filled-in using parameter-scanning methods and experiments outlined in the relevant references. By comparing experimental measures of microcompartment formation with that predicted by the kinetic model, we aim to gain insight on the mechanisms of Encapsulin assembly.<br />
<br />
=Model=<br />
Our model is based on the following design (See Project Page for a full description of this system).<br />
[[image:BioBrick.png|thumb|centre|The Encapsulator]]<br />
<br />
The reaction framework was mainly generated using the [http://synbioss.sourceforge.net/ SynBioSS Designer (a really useful modeling tool for iGEM teams)], which also provides default parameter values. These parameter values have been gathered from various literature [http://neptune.cems.umn.edu/designer/designer_defaults.pdf sources], and should be taken as approximations. All units were taken to be (1 / molarity^n-1 * s), where n is the order of the reaction. For example, for the reaction 2 lacI --> lacI2, n = 2, thus the rate constant has the units 1/molarity*s. <br />
<br />
The pathways for the expressed proteins, eCFPt and Encapsulin, need to be modeled in more detail. For example, in this basic model eCFPt is degraded via a first order reaction and Encapsulin makes a dimer complex. However, in reality fluorescent proteins have been shown to degreade via Micheales-menton kinetics and Encapsulin is thought to make a complex of about 60 monomers. These issues will be addressed in future work.<br />
<br />
The reactions can be accessed here:<br />
<br />
[[The Encapsulator Model]] (opens new page)<br />
<br />
[[Media:Uft_mod_Rxns2.xls|The Encapsulator Model ]] (download Excel file)<br />
<br />
=Simulations=<br />
<br />
All simulations were carried out using the [https://2009.igem.org/Partner_Offers SimBiology Matlab Toolbox], which was freely available to iGEM teams. <br />
<br />
===Accumulation of eCFP at Different Initial Concentrations of IPTG===<br />
<br />
[[Image:uft_mod_cfp-iptg.png | 900px]]<br />
<br />
The IPTG effector eventually loses effect, and the eCFP concentration approaches a maximum. This happens because the IPTG proteins eventually ''tie up'' all available LacI4 proteins, leaving the transcription and translation of eCFP to operate at its maxiumum rate. <br />
<br />
===Accumulation of Encapsulin monomer at Different Initial Concentrations of aTc===<br />
<br />
[[Image:uft_mod_enc-atc.png | 900px]]<br />
<br />
(NOTE: in order to observe Encapsulin monomer levels, the above simulations were carried out without any Encapsulin assembly reactions in place)<br />
<br />
The production of Encapsulin occurs at a slower rate than eCFP because the BBa_R0040 promoter has two tetR binding sites, resulting in more repression and more off-pathway scenarios. Thus, the Encapsulin concentration also seems assymptotic but at higher concentrations of aTc (relative to IPTG). <br />
<br />
It seems beneficial to have the Encapsulin protein under control of the BBa_R0040-tetR-aTc construct because at zero levels of aTc we can have essentially zero levels of Encapsulin (whereas even at zero levels of IPTG, there is still significantly more eCFP). This will enable us to probe extremely low concentrations of Encapsulin monomer when testing for optimal Encapsulin assembly conditions. The disadvantage is that if Encapsulin assembly requires a very high initial concentration of Encapsulin monomer, we would have to wait a long time to see microcompartments. If this later scenario is observed, it may be better to switch the eCFP and Encapsulin expression systems.<br />
<br />
===Sensitivity Analysis===<br />
<br />
Since all of our parameters are approximations from literature sources, those which have the greatest affect on system dynamics (ie. the most ''sensitive'' parameters) would be leading candidates to be experimentally determined. Currently we are interested in which parameters have the greatest effect on the production of eCFP and Encapsulin. Ideally, it would be best to experimentally determine these to "tighten-up" the model before incorporating the largely unexplored Encapsulin assembly pathways. <br />
<br />
<br />
'''1) Sensitivity of eCFP Production'''<br />
<br />
[[Image:uft_mod_SAecfp.png | centre | 600px]]<br />
<br />
<br />
<br />
'''2) Sensitivity of Encapsulin Production'''<br />
<br />
[[Image:uft_mod_SAenc.png | centre | 600px]]<br />
<br />
Parameters 1 and 2 correspond to the rates of constitutive expression of the lacI and tetR repressors respectively. Thus, it can be seen that eCFP and Encapsulin production is largely sensitive to the expression rates of lacI and tetR. <br />
<br />
The specific constitutive promoter used in our construct is BBa_J23100. In our model, this was given the generic rate of 1E-10 molarity\s by SynBioSS based on a variety of empirically-fitted protein expression rates found in literature. This generic approach to assigning parameter values is a suitable fist-step, but our sensitivity results suggest that experimentally determining the expression rate of our specific constitutive promoter should significantly improve our model's predictive capability.<br />
<br />
=Future Work=<br />
<br />
Improvements to the basic model presented above can be separated into three areas; 1) performing experiments to determine parameter values that are specific to our system, 2) more detailed modeling of eCFPt behavior, 3) more detailed modeling of Encapsulin assembly. <br />
<br />
The experiments required to determine general transcription and translation parameters need to be further researched, so this will be skipped over for now. Here we will discuss the more interesting areas – the detailed modeling of eCFP and Encapsulin pathways. This will be accomplished by incorporating previous modeling efforts that are applicable to the eCFP and Encapsulin proteins. <br />
<br />
===Degredation of eCFP===<br />
<br />
The expression and degradation of [http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=95514&blobtype=pdf Green Fluorescent Protein (GFP) was modeled previously]. This paper noted that GFP must mature before going into fluorescent phase, and GFP degradation was shown to follow M-M kinetics, as depicted below. This paper also outlined how the degradation parameters could be derived for any expression system using only simple fluorescence and optical density measurements.<br />
<br />
[[Image:uft_mod_ecfp1.png | centre | thumb | Degredation and maturation pathways for eCFP. (Leveau and Lindow 2001)]]<br />
<br />
<br />
The GFP maturation and degradation parameters found in this paper were:<br />
<br />
<html><br />
<centre><br />
<table><br />
<tr><td> m = 0.0004279 1/s </td></tr><br />
<tr><td> Vmax = 2E-10 molality/s </td></tr><br />
<tr><td> Km = 9E-13 molality/s </td></tr><br />
<tr><td> </td></tr><br />
</table><br />
</centre><br />
</html><br />
<br />
<br />
Assuming eCFPt would behave similarly to eGFP, the following additional reactions would be included in the model:<br />
<br />
<html><br />
<table><br />
<tr> <td><b> Maturation </b></td> <td> </td> </tr><br />
<tr> <td> eCFPt --> F_eCFPT </td> <td> 0.0004279 </td> </tr><br />
<tr> <td> Enc2:eCFPt --> Enc2:F_eCFPt </td> <td> 0.0004279 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Encapsulation </b></td> <td> </td> </tr><br />
<tr> <td> Enc2 + F_eCFPt --> Enc2:F_eCFPt </td> <td> 100 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Degradation </b></td> <td> </td> </tr><br />
<tr> <td> eCFPt --> </td> <td> Vmax = 2E-10 </td> </tr><br />
<tr> <td> </td> <td> Km = 9E-13 </td> </tr><br />
<tr> <td> F_eCFPt --> </td> <td> Vmax = 2E-10 </td> </tr><br />
<tr> <td> </td> <td> Km = 9E-13 </td> </tr><br />
</table><br />
</html><br />
<br />
===Assembly of Encapsulin Microcompartments===<br />
<br />
Though Encapsulin microcompartment assembly is not well-studied, it has been theorized to resemble the assembly of viral capsids. Thus, we could look to this relatively well-studied phenomenon as a representation of Encapsulin microcompartment assembly.<br />
<br />
Adam Zlotnick has published models of viral capsid assembly using different approaches. An early paper described an equilibrium model of assembly for a 12 Unit polyhedral capsid head, and a more recent paper used a kinetic model that could be applied to many examples of spherical polymerization. We will consider how each approach could be incorporated as a representation of Encapsulin assembly.<br />
<br />
<br />
'''1) Equilibrim Approach to Encapsulin Assembly'''<br />
<br />
Zlotnick's [[Media:Uft_mod_to_build_a_virus_capsid.pdf|Equilibrium-based model]] consists of reactions from an initial monomer subunit leading to a final capsid product. The sequential reactions take into account DeltaG for contact (Kn'), and parameters describing path degeneracy (varies for different intermediates).<br />
[[image:uft_mod_encap1.png|centre|thumb|Kn for assembly subunits based on path degeneracy. (Zlotnick 1994)]]<br />
<br />
<br />
'''2) Kinetic Model of Spherical Polymerization'''<br />
<br />
A [http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1302223/pdf/12124301.pdf general kinetic model for the spherical polyermization] process is shown below. In our case, the initial monomer subunit concentration (''u'') would represent our expressed Encapsulin BioBrick, and the number of monomers in the final assembly (''N'') is thought to be 60. All of the included parameters can be calculated from the four basic parameters; the microscopic, per-contact equilibrium constant (KAcon), the nucleus size (nuc), the nucleation on-rate (f_nuc), and the elongation on-rate (f_elong). The referenced paper describes methods to aquire these parameters from kinetic experiments, and provides examples for N = 12 and 30 unit viral capsid assemblies.<br />
[[image:uft_mod_encap2.png| centre | thumb |System of ODEs to represent spherical polymerization, where ''u'' is the initial subunit concentration, ''m'' is the "mth" intermediate species, and ''N'' is the number of monomers in the final assembly. (Endres and Zlotnick 2002)]]<br />
<br />
<br />
<br />
Zlotnick's models also describe two important features of spherical polymerization that we should also expect to observe in Encapsulin assembly: kinetic trapping and nucleation. A kinetic trap occurs when the initial monomer subunit concentration or the deltaG of the first assembly reaction is too high. This results in over-initiation of assembly and quickly the reactions become starved for subunits. Kinetic trapping is prevented by the inclusion of nucleation, where the initial reactions occur at a slower rate because the first few intermediates in a series of reactions are less stable than downstream products. Essentially, nucleation serves as a “slow first step” that regulates the assembly pathway. <br />
<br />
It will be interesting to note how the translational dynamics of Encapsulin interplay with its assembly dynamics. Since our system does not start with any initial concentration of Encapsulin, there will be an optimum rate of production that essentially serves the role of nucleation – avoiding kinetic traps while still maintaining a maximum production of full Encapsulin assemblies.<br />
<br />
=References=<br />
<br />
1. Hill AD, Tomshine JR, Weeding EM, Sotiropoulos V, Kaznessis YN. ''SynBioSS: the synthetic biology modeling suite.'' Bioinformatics. 2008 Nov 1;24(21):2551-3. Epub 2008 Aug 30.<br />
[http://neptune.cems.umn.edu/designer/interface1.php SynBioSS Web Designer]<br />
<br />
2. Leveau JH, Lindow SE. ''Predictive and interpretive simulation of green fluorescent protein expression in<br />
reporter bacteria.'' J Bacteriol. 2001 Dec;183(23):6752-62.<br />
<br />
3. Endres D, Zlotnick A. ''Model-based analysis of assembly kinetics for virus capsids or other spherical<br />
polymers.'' Biophys J. 2002 Aug;83(2):1217-30.</div>FRhttp://2009.igem.org/The_Encapsulator_ModelThe Encapsulator Model2009-10-21T07:50:55Z<p>FR: New page: ==Reactions== <html> <table> <tr> <td><b><u>Reaction</u></b></td> <td><b><u>Rate Constant</u></b></td> </tr> <tr> <td> </td> <td> </td> </tr> <tr> <td> </td> <td> </td> </tr> <tr> <...</p>
<hr />
<div>==Reactions==<br />
<br />
<html><br />
<table><br />
<tr><br />
<td><b><u>Reaction</u></b></td><br />
<td><b><u>Rate Constant</u></b></td><br />
</tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<br />
<br />
<tr> <td><b> Constitutive Expression </b></td> <td> </td> </tr><br />
<tr> <td> --> lacl4 </td> <td> 1E-10 </td> </tr><br />
<tr> <td> --> tetR2 </td> <td> 1E-10 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Multimerization </b></td> <td> </td> </tr><br />
<tr> <td> 2 lacI --> lacI2 </td> <td> 1E+09 </td> </tr><br />
<tr> <td> lacI2 --> 2 lacI </td> <td> 10 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> 2 lacI2 --> lacI4 </td> <td> 1E+09 </td> </tr><br />
<tr> <td> lacI4 --> 2 lacI2 </td> <td> 10 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> 2 tetR --> tetR2 </td> <td> 1E+09 </td> </tr><br />
<tr> <td> tetR2 --> 2 tetR </td> <td> 10 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Transcription</b> </td> <td> </td> </tr><br />
<tr> <td> RNAp + BBa_R0010 + LacI_binding_site --> RNAp:BBa_R0010:LacI_binding_site </td> <td> 10000000 </td> </tr><br />
<tr> <td> RNAp:BBa_R0010:LacI_binding_site --> RNAp + BBa_R0010 + LacI_binding_site </td> <td> 0.057 </td> </tr><br />
<tr> <td> RNAp:BBa_R0010:LacI_binding_site --> RNAp:BBa_R0010:LacI_binding_site* </td> <td> 0.1 </td> </tr><br />
<tr> <td> RNAp:BBa_R0010:LacI_binding_site* --> RNAp:DNA_eCFPt + BBa_R0010 + LacI_binding_site </td> <td> 30 </td> </tr><br />
<tr> <td> RNAp:DNA_eCFPt --> RNAp + mRNA_eCFPt </td> <td> 0.035 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> RNAp + BBa_R0040 + TetR_1 + TetR_2 --> RNAp:BBa_R0040:TetR_1:TetR_2 </td> <td> 10000000 </td> </tr><br />
<tr> <td> RNAp:BBa_R0040:TetR_1:TetR_2 --> RNAp + BBa_R0040 + TetR_1 + TetR_2 </td> <td> 0.057 </td> </tr><br />
<tr> <td> RNAp:BBa_R0040:TetR_1:TetR_2 --> RNAp:BBa_R0040:TetR_1:TetR_2* </td> <td> 0.1 </td> </tr><br />
<tr> <td> RNAp:BBa_R0040:TetR_1:TetR_2* --> RNAp:DNA_Enc + BBa_R0040 + TetR_1 + TetR_2 </td> <td> 30 </td> </tr><br />
<tr> <td> RNAp:DNA_Enc --> RNAp + mRNA_Enc </td> <td> 0.0375 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Translation </b></td> <td> </td> </tr><br />
<tr> <td> rib + mRNA_eCFPt --> rib:mRNA_eCFPt </td> <td> 100000 </td> </tr><br />
<tr> <td> rib:mRNA_eCFPt --> rib:mRNA_eCFPt_1 + mRNA_eCFPt </td> <td> 33 </td> </tr><br />
<tr> <td> rib:mRNA_eCFPt_1 --> rib + eCFPt </td> <td> 0.1154 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> rib + mRNA_Enc --> rib:mRNA_Enc </td> <td> 100000 </td> </tr><br />
<tr> <td> rib:mRNA_Enc --> rib:mRNA_Enc_1 + mRNA_Enc </td> <td> 33 </td> </tr><br />
<tr> <td> rib:mRNA_Enc_1 --> rib + Enc </td> <td> 0.1234 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Protein-DNA </b></td> <td> </td> </tr><br />
<tr> <td> lacI4 + nsDNA --> lacI4:nsDNA </td> <td> 1000 </td> </tr><br />
<tr> <td> lacI4:nsDNA --> lacI4 + nsDNA </td> <td> 1.6225 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> lacI4 + LacI_binding_site --> lacI4:LacI_binding_site </td> <td> 1E+09 </td> </tr><br />
<tr> <td> lacI4:LacI_binding_site --> lacI4 + LacI_binding_site </td> <td> 0.005 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> tetR2 + nsDNA --> tetR2:nsDNA </td> <td> 1000 </td> </tr><br />
<tr> <td> tetR2:nsDNA --> tetR2 + nsDNA </td> <td> 1.6225 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> tetR2 + TetR_1 --> tetR2:TetR_1 </td> <td> 1E+09 </td> </tr><br />
<tr> <td> tetR2:TetR_1 --> tetR2 + TetR_1 </td> <td> 0.005 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> tetR2 + TetR_2 --> tetR2:TetR_2 </td> <td> 1E+09 </td> </tr><br />
<tr> <td> tetR2:TetR_2 --> tetR2 + TetR_2 </td> <td> 0.005 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Protein - Effector - DNA </b></td> <td> </td> </tr><br />
<tr> <td> lacI4 + IPTG --> lacI4:IPTG </td> <td> 50000000 </td> </tr><br />
<tr> <td> lacI4:IPTG --> lacI4 + IPTG </td> <td> 0.1 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> lacI4:IPTG + LacI_binding_site --> lacI4:IPTG:LacI_binding_site </td> <td> 1E+09 </td> </tr><br />
<tr> <td> lacI4:IPTG:LacI_binding_site --> lacI4:IPTG + LacI_binding_site </td> <td> 0.7 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> lacI4:LacI_binding_site + IPTG --> lacI4:IPTG:LacI_binding_site </td> <td> 1000000 </td> </tr><br />
<tr> <td> lacI4:IPTG:LacI_binding_site --> lacI4:LacI_binding_site + IPTG </td> <td> 0.4 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> lacI4:IPTG + nsDNA --> lacI4:IPTG:nsDNA </td> <td> 1000 </td> </tr><br />
<tr> <td> lacI4:IPTG:nsDNA --> lacI4:IPTG + nsDNA </td> <td> 1.6225 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> lacI4:nsDNA + IPTG --> lacI4:IPTG:nsDNA </td> <td> 1000 </td> </tr><br />
<tr> <td> lacI4:IPTG:nsDNA --> lacI4:nsDNA + IPTG </td> <td> 1.6225 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> tetR2 + aTc --> tetR2:aTc </td> <td> 50000000 </td> </tr><br />
<tr> <td> tetR2:aTc --> tetR2 + aTc </td> <td> 0.1 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> tetR2:aTc + TetR_1 --> tetR2:aTc:TetR_1 </td> <td> 1E+09 </td> </tr><br />
<tr> <td> tetR2:aTc:TetR_1 --> tetR2:aTc + TetR_1 </td> <td> 0.7 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> tetR2:TetR_1 + aTc --> tetR2:aTc:TetR_1 </td> <td> 1000000 </td> </tr><br />
<tr> <td> tetR2:aTc:TetR_1 --> tetR2:TetR_1 + aTc </td> <td> 0.4 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> tetR2:aTc + TetR_2 --> tetR2:aTc:TetR_2 </td> <td> 1E+09 </td> </tr><br />
<tr> <td> tetR2:aTc:TetR_2 --> tetR2:aTc + TetR_2 </td> <td> 0.7 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> tetR2:TetR_2 + aTc --> tetR2:aTc:TetR_2 </td> <td> 1000000 </td> </tr><br />
<tr> <td> tetR2:aTc:TetR_2 --> tetR2:TetR_2 + aTc </td> <td> 0.4 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> tetR2:aTc + nsDNA --> tetR2:aTc:nsDNA </td> <td> 1000 </td> </tr><br />
<tr> <td> tetR2:aTc:nsDNA --> tetR2:aTc + nsDNA </td> <td> 1.6225 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> tetR2:nsDNA + aTc --> tetR2:aTc:nsDNA </td> <td> 1000 </td> </tr><br />
<tr> <td> tetR2:aTc:nsDNA --> tetR2:nsDNA + aTc </td> <td> 1.6225 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Degradation</b> </td> <td> </td> </tr><br />
<tr> <td> lacI4 --> </td> <td> 0.000289 </td> </tr><br />
<tr> <td> tetR2 --> </td> <td> 0.000289 </td> </tr><br />
<tr> <td> mRNA_eCFPt --> </td> <td> 0.0015 </td> </tr><br />
<tr> <td> mRNA_Enc --> </td> <td> 0.0015 </td> </tr><br />
<tr> <td> eCFPt --> </td> <td> 0.000289 </td> </tr><br />
<tr> <td> Enc --> </td> <td> 0.000289 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Dilution</b> </td> <td> </td> </tr><br />
<tr> <td> lacI4:nsDNA --> nsDNA </td> <td> 0.000193 </td> </tr><br />
<tr> <td> tetR2:nsDNA --> nsDNA </td> <td> 0.000193 </td> </tr><br />
<tr> <td> lacI4:IPTG --> IPTG </td> <td> 0.000289 </td> </tr><br />
<tr> <td> tetR2:aTc --> aTc </td> <td> 0.000289 </td> </tr><br />
<tr> <td> lacI4:IPTG:nsDNA --> IPTG + nsDNA </td> <td> 0.000193 </td> </tr><br />
<tr> <td> tetR2:aTc:nsDNA --> aTc + nsDNA </td> <td> 0.000193 </td> </tr><br />
</table><br />
</html></div>FRhttp://2009.igem.org/Team:TorontoMaRSDiscovery/ModelingTeam:TorontoMaRSDiscovery/Modeling2009-10-21T07:48:50Z<p>FR: /* Model */</p>
<hr />
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<br><br />
<br />
<br />
=Summary=<br />
<br />
A kinetic model of our system has been constructed. Approximate parameter values were gathered from online resources to represent all processes up to the production of the eCFP and Encapsulin proteins. Current simulations predict the production of these two proteins at various initial concentrations of IPTG and aTc effector molecules. A sensitivity analysis reveals that the rate of constitutive expression of lacI and tetR has the greatest affect on eCFP and Encapsulin concentrations. Furthermore, we have outlined approaches for the detailed modelling of the eCFP degredation/maturation and Encapsulin assembly pathways.<br />
<br />
<br />
The initial simulations will be used to identify a critical concentration of Encapsulin mononomer required for microcompartment assembly. To strengthen the model, the constitutive expression rate of BBa_J23100 as used in our construct will be measured. Subsequently, a detailed model of Encapsulin assembly will be integrated into the current model, and its parameters filled-in using parameter-scanning methods and experiments outlined in the relevant references. By comparing experimental measures of microcompartment formation with that predicted by the kinetic model, we aim to gain insight on the mechanisms of Encapsulin assembly.<br />
<br />
=Model=<br />
Our model is based on the following design (See Project Page for a full description of this system).<br />
[[image:BioBrick.png|thumb|centre|The Encapsulator]]<br />
<br />
The reaction framework was mainly generated using the [http://synbioss.sourceforge.net/ SynBioSS Designer (a really useful modeling tool for iGEM teams)], which also provides default parameter values. These parameter values have been gathered from various literature [http://neptune.cems.umn.edu/designer/designer_defaults.pdf sources], and should be taken as approximations. All units were taken to be (1 / molarity^n-1 * s), where n is the order of the reaction. For example, for the reaction 2 lacI --> lacI2, n = 2, thus the rate constant has the units 1/molarity*s. <br />
<br />
The pathways for the expressed proteins, eCFPt and Encapsulin, need to be modeled in more detail. For example, in this basic model eCFPt is degraded via a first order reaction and Encapsulin makes a dimer complex. However, in reality fluorescent proteins have been shown to degreade via Micheales-menton kinetics and Encapsulin is thought to make a complex of about 60 monomers. These issues will be addressed in future work.<br />
<br />
The reactions can be accessed here:<br />
<br />
[[The Encapsulator Model]] (opens new page)<br />
<br />
[[Media:Uft_mod_Rxns2.xls|The Encapsulator Model ]] (download Excel file)<br />
<br />
=Simulations=<br />
<br />
All simulations were carried out using the [https://2009.igem.org/Partner_Offers SimBiology Matlab Toolbox], which was freely available to iGEM teams. <br />
<br />
===Accumulation of eCFP at Different Initial Concentrations of IPTG===<br />
<br />
[[Image:uft_mod_cfp-iptg.png | 900px]]<br />
<br />
The IPTG effector eventually loses effect, and the eCFP concentration approaches a maximum. This happens because the IPTG proteins eventually ''tie up'' all available LacI4 proteins, leaving the transcription and translation of eCFP to operate at its maxiumum rate. <br />
<br />
===Accumulation of Encapsulin monomer at Different Initial Concentrations of aTc===<br />
<br />
[[Image:uft_mod_enc-atc.png | 900px]]<br />
<br />
(NOTE: in order to observe Encapsulin monomer levels, the above simulations were carried out without any Encapsulin assembly reactions in place)<br />
<br />
The production of Encapsulin occurs at a slower rate than eCFP because the BBa_R0040 promoter has two tetR binding sites, resulting in more repression and more off-pathway scenarios. Thus, the Encapsulin concentration also seems assymptotic but at higher concentrations of aTc (relative to IPTG). <br />
<br />
It seems beneficial to have the Encapsulin protein under control of the BBa_R0040-tetR-aTc construct because at zero levels of aTc we can have essentially zero levels of Encapsulin (whereas even at zero levels of IPTG, there is still significantly more eCFP). This will enable us to probe extremely low concentrations of Encapsulin monomer when testing for optimal Encapsulin assembly conditions. The disadvantage is that if Encapsulin assembly requires a very high initial concentration of Encapsulin monomer, we would have to wait a long time to see microcompartments. If this later scenario is observed, it may be better to switch the eCFP and Encapsulin expression systems.<br />
<br />
===Sensitivity Analysis===<br />
<br />
Since all of our parameters are approximations from literature sources, those which have the greatest affect on system dynamics (ie. the most ''sensitive'' parameters) would be leading candidates to be experimentally determined. Currently we are interested in which parameters have the greatest effect on the production of eCFP and Encapsulin. Ideally, it would be best to experimentally determine these to "tighten-up" the model before incorporating the largely unexplored Encapsulin assembly pathways. <br />
<br />
<br />
'''1) Sensitivity of eCFP Production'''<br />
<br />
[[Image:uft_mod_SAecfp.png | centre | 900px]]<br />
<br />
<br />
<br />
'''2) Sensitivity of Encapsulin Production'''<br />
<br />
[[Image:uft_mod_SAenc.png | centre | 900px]]<br />
<br />
Parameters 1 and 2 correspond to the rates of constitutive expression of the lacI and tetR repressors respectively. Thus, it can be seen that eCFP and Encapsulin production is largely sensitive to the expression rates of lacI and tetR. <br />
<br />
The specific constitutive promoter used in our construct is BBa_J23100. In our model, this was given the generic rate of 1E-10 molarity\s by SynBioSS based on a variety of empirically-fitted protein expression rates found in literature. This generic approach to assigning parameter values is a suitable fist-step, but our sensitivity results suggest that experimentally determining the expression rate of our specific constitutive promoter should significantly improve our model's predictive capability.<br />
<br />
=Future Work=<br />
<br />
Improvements to the basic model presented above can be separated into three areas; 1) performing experiments to determine parameter values that are specific to our system, 2) more detailed modeling of eCFPt behavior, 3) more detailed modeling of Encapsulin assembly. <br />
<br />
The experiments required to determine general transcription and translation parameters need to be further researched, so this will be skipped over for now. Here we will discuss the more interesting areas – the detailed modeling of eCFP and Encapsulin pathways. This will be accomplished by incorporating previous modeling efforts that are applicable to the eCFP and Encapsulin proteins. <br />
<br />
===Degredation of eCFP===<br />
<br />
The expression and degradation of [http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=95514&blobtype=pdf Green Fluorescent Protein (GFP) was modeled previously]. This paper noted that GFP must mature before going into fluorescent phase, and GFP degradation was shown to follow M-M kinetics, as depicted below. This paper also outlined how the degradation parameters could be derived for any expression system using only simple fluorescence and optical density measurements.<br />
<br />
[[Image:uft_mod_ecfp1.png | centre | thumb | Degredation and maturation pathways for eCFP. (Leveau and Lindow 2001)]]<br />
<br />
<br />
The GFP maturation and degradation parameters found in this paper were:<br />
<br />
<html><br />
<centre><br />
<table><br />
<tr><td> m = 0.0004279 1/s </td></tr><br />
<tr><td> Vmax = 2E-10 molality/s </td></tr><br />
<tr><td> Km = 9E-13 molality/s </td></tr><br />
<tr><td> </td></tr><br />
</table><br />
</centre><br />
</html><br />
<br />
<br />
Assuming eCFPt would behave similarly to eGFP, the following additional reactions would be included in the model:<br />
<br />
<html><br />
<table><br />
<tr> <td><b> Maturation </b></td> <td> </td> </tr><br />
<tr> <td> eCFPt --> F_eCFPT </td> <td> 0.0004279 </td> </tr><br />
<tr> <td> Enc2:eCFPt --> Enc2:F_eCFPt </td> <td> 0.0004279 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Encapsulation </b></td> <td> </td> </tr><br />
<tr> <td> Enc2 + F_eCFPt --> Enc2:F_eCFPt </td> <td> 100 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Degradation </b></td> <td> </td> </tr><br />
<tr> <td> eCFPt --> </td> <td> Vmax = 2E-10 </td> </tr><br />
<tr> <td> </td> <td> Km = 9E-13 </td> </tr><br />
<tr> <td> F_eCFPt --> </td> <td> Vmax = 2E-10 </td> </tr><br />
<tr> <td> </td> <td> Km = 9E-13 </td> </tr><br />
</table><br />
</html><br />
<br />
===Assembly of Encapsulin Microcompartments===<br />
<br />
Though Encapsulin microcompartment assembly is not well-studied, it has been theorized to resemble the assembly of viral capsids. Thus, we could look to this relatively well-studied phenomenon as a representation of Encapsulin microcompartment assembly.<br />
<br />
Adam Zlotnick has published models of viral capsid assembly using different approaches. An early paper described an equilibrium model of assembly for a 12 Unit polyhedral capsid head, and a more recent paper used a kinetic model that could be applied to many examples of spherical polymerization. We will consider how each approach could be incorporated as a representation of Encapsulin assembly.<br />
<br />
<br />
'''1) Equilibrim Approach to Encapsulin Assembly'''<br />
<br />
Zlotnick's [[Media:Uft_mod_to_build_a_virus_capsid.pdf|Equilibrium-based model]] consists of reactions from an initial monomer subunit leading to a final capsid product. The sequential reactions take into account DeltaG for contact (Kn'), and parameters describing path degeneracy (varies for different intermediates).<br />
[[image:uft_mod_encap1.png|centre|thumb|Kn for assembly subunits based on path degeneracy. (Zlotnick 1994)]]<br />
<br />
<br />
'''2) Kinetic Model of Spherical Polymerization'''<br />
<br />
A [http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1302223/pdf/12124301.pdf general kinetic model for the spherical polyermization] process is shown below. In our case, the initial monomer subunit concentration (''u'') would represent our expressed Encapsulin BioBrick, and the number of monomers in the final assembly (''N'') is thought to be 60. All of the included parameters can be calculated from the four basic parameters; the microscopic, per-contact equilibrium constant (KAcon), the nucleus size (nuc), the nucleation on-rate (f_nuc), and the elongation on-rate (f_elong). The referenced paper describes methods to aquire these parameters from kinetic experiments, and provides examples for N = 12 and 30 unit viral capsid assemblies.<br />
[[image:uft_mod_encap2.png| centre | thumb |System of ODEs to represent spherical polymerization, where ''u'' is the initial subunit concentration, ''m'' is the "mth" intermediate species, and ''N'' is the number of monomers in the final assembly. (Endres and Zlotnick 2002)]]<br />
<br />
<br />
<br />
Zlotnick's models also describe two important features of spherical polymerization that we should also expect to observe in Encapsulin assembly: kinetic trapping and nucleation. A kinetic trap occurs when the initial monomer subunit concentration or the deltaG of the first assembly reaction is too high. This results in over-initiation of assembly and quickly the reactions become starved for subunits. Kinetic trapping is prevented by the inclusion of nucleation, where the initial reactions occur at a slower rate because the first few intermediates in a series of reactions are less stable than downstream products. Essentially, nucleation serves as a “slow first step” that regulates the assembly pathway. <br />
<br />
It will be interesting to note how the translational dynamics of Encapsulin interplay with its assembly dynamics. Since our system does not start with any initial concentration of Encapsulin, there will be an optimum rate of production that essentially serves the role of nucleation – avoiding kinetic traps while still maintaining a maximum production of full Encapsulin assemblies.<br />
<br />
=References=<br />
<br />
1. Hill AD, Tomshine JR, Weeding EM, Sotiropoulos V, Kaznessis YN. ''SynBioSS: the synthetic biology modeling suite.'' Bioinformatics. 2008 Nov 1;24(21):2551-3. Epub 2008 Aug 30.<br />
[http://neptune.cems.umn.edu/designer/interface1.php SynBioSS Web Designer]<br />
<br />
2. Leveau JH, Lindow SE. ''Predictive and interpretive simulation of green fluorescent protein expression in<br />
reporter bacteria.'' J Bacteriol. 2001 Dec;183(23):6752-62.<br />
<br />
3. Endres D, Zlotnick A. ''Model-based analysis of assembly kinetics for virus capsids or other spherical<br />
polymers.'' Biophys J. 2002 Aug;83(2):1217-30.</div>FRhttp://2009.igem.org/Team:TorontoMaRSDiscovery/ModelingTeam:TorontoMaRSDiscovery/Modeling2009-10-21T07:47:43Z<p>FR: /* Model */</p>
<hr />
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|}<br />
<br><br />
<br />
<br />
=Summary=<br />
<br />
A kinetic model of our system has been constructed. Approximate parameter values were gathered from online resources to represent all processes up to the production of the eCFP and Encapsulin proteins. Current simulations predict the production of these two proteins at various initial concentrations of IPTG and aTc effector molecules. A sensitivity analysis reveals that the rate of constitutive expression of lacI and tetR has the greatest affect on eCFP and Encapsulin concentrations. Furthermore, we have outlined approaches for the detailed modelling of the eCFP degredation/maturation and Encapsulin assembly pathways.<br />
<br />
<br />
The initial simulations will be used to identify a critical concentration of Encapsulin mononomer required for microcompartment assembly. To strengthen the model, the constitutive expression rate of BBa_J23100 as used in our construct will be measured. Subsequently, a detailed model of Encapsulin assembly will be integrated into the current model, and its parameters filled-in using parameter-scanning methods and experiments outlined in the relevant references. By comparing experimental measures of microcompartment formation with that predicted by the kinetic model, we aim to gain insight on the mechanisms of Encapsulin assembly.<br />
<br />
=Model=<br />
Our model is based on the following design (See Project Page for a full description of this system).<br />
[[image:BioBrick.png|thumb|centre|The Encapsulator]]<br />
<br />
The reaction framework was mainly generated using the [http://synbioss.sourceforge.net/ SynBioSS Designer (a really useful modeling tool for iGEM teams)], which also provides default parameter values. These parameter values have been gathered from various literature [http://neptune.cems.umn.edu/designer/designer_defaults.pdf sources], and should be taken as approximations. All units were taken to be (1 / molarity^n-1 * s), where n is the order of the reaction. For example, for the reaction 2 lacI --> lacI2, n = 2, thus the rate constant has the units 1/molarity*s. <br />
<br />
The pathways for the expressed proteins, eCFPt and Encapsulin, need to be modeled in more detail. For example, in this basic model eCFPt is degraded via a first order reaction and Encapsulin makes a dimer complex. However, in reality fluorescent proteins have been shown to degreade via Micheales-menton kinetics and Encapsulin is thought to make a complex of about 60 monomers. These issues will be addressed in future work.<br />
<br />
The reactions can be accessed here:<br />
<br />
[[Model (opens new page)]]<br />
<br />
[[Media:Uft_mod_Rxns2.xls|The Encapsulator Model ]] (download Excel file)<br />
<br />
=Simulations=<br />
<br />
All simulations were carried out using the [https://2009.igem.org/Partner_Offers SimBiology Matlab Toolbox], which was freely available to iGEM teams. <br />
<br />
===Accumulation of eCFP at Different Initial Concentrations of IPTG===<br />
<br />
[[Image:uft_mod_cfp-iptg.png | 900px]]<br />
<br />
The IPTG effector eventually loses effect, and the eCFP concentration approaches a maximum. This happens because the IPTG proteins eventually ''tie up'' all available LacI4 proteins, leaving the transcription and translation of eCFP to operate at its maxiumum rate. <br />
<br />
===Accumulation of Encapsulin monomer at Different Initial Concentrations of aTc===<br />
<br />
[[Image:uft_mod_enc-atc.png | 900px]]<br />
<br />
(NOTE: in order to observe Encapsulin monomer levels, the above simulations were carried out without any Encapsulin assembly reactions in place)<br />
<br />
The production of Encapsulin occurs at a slower rate than eCFP because the BBa_R0040 promoter has two tetR binding sites, resulting in more repression and more off-pathway scenarios. Thus, the Encapsulin concentration also seems assymptotic but at higher concentrations of aTc (relative to IPTG). <br />
<br />
It seems beneficial to have the Encapsulin protein under control of the BBa_R0040-tetR-aTc construct because at zero levels of aTc we can have essentially zero levels of Encapsulin (whereas even at zero levels of IPTG, there is still significantly more eCFP). This will enable us to probe extremely low concentrations of Encapsulin monomer when testing for optimal Encapsulin assembly conditions. The disadvantage is that if Encapsulin assembly requires a very high initial concentration of Encapsulin monomer, we would have to wait a long time to see microcompartments. If this later scenario is observed, it may be better to switch the eCFP and Encapsulin expression systems.<br />
<br />
===Sensitivity Analysis===<br />
<br />
Since all of our parameters are approximations from literature sources, those which have the greatest affect on system dynamics (ie. the most ''sensitive'' parameters) would be leading candidates to be experimentally determined. Currently we are interested in which parameters have the greatest effect on the production of eCFP and Encapsulin. Ideally, it would be best to experimentally determine these to "tighten-up" the model before incorporating the largely unexplored Encapsulin assembly pathways. <br />
<br />
<br />
'''1) Sensitivity of eCFP Production'''<br />
<br />
[[Image:uft_mod_SAecfp.png | centre | 900px]]<br />
<br />
<br />
<br />
'''2) Sensitivity of Encapsulin Production'''<br />
<br />
[[Image:uft_mod_SAenc.png | centre | 900px]]<br />
<br />
Parameters 1 and 2 correspond to the rates of constitutive expression of the lacI and tetR repressors respectively. Thus, it can be seen that eCFP and Encapsulin production is largely sensitive to the expression rates of lacI and tetR. <br />
<br />
The specific constitutive promoter used in our construct is BBa_J23100. In our model, this was given the generic rate of 1E-10 molarity\s by SynBioSS based on a variety of empirically-fitted protein expression rates found in literature. This generic approach to assigning parameter values is a suitable fist-step, but our sensitivity results suggest that experimentally determining the expression rate of our specific constitutive promoter should significantly improve our model's predictive capability.<br />
<br />
=Future Work=<br />
<br />
Improvements to the basic model presented above can be separated into three areas; 1) performing experiments to determine parameter values that are specific to our system, 2) more detailed modeling of eCFPt behavior, 3) more detailed modeling of Encapsulin assembly. <br />
<br />
The experiments required to determine general transcription and translation parameters need to be further researched, so this will be skipped over for now. Here we will discuss the more interesting areas – the detailed modeling of eCFP and Encapsulin pathways. This will be accomplished by incorporating previous modeling efforts that are applicable to the eCFP and Encapsulin proteins. <br />
<br />
===Degredation of eCFP===<br />
<br />
The expression and degradation of [http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=95514&blobtype=pdf Green Fluorescent Protein (GFP) was modeled previously]. This paper noted that GFP must mature before going into fluorescent phase, and GFP degradation was shown to follow M-M kinetics, as depicted below. This paper also outlined how the degradation parameters could be derived for any expression system using only simple fluorescence and optical density measurements.<br />
<br />
[[Image:uft_mod_ecfp1.png | centre | thumb | Degredation and maturation pathways for eCFP. (Leveau and Lindow 2001)]]<br />
<br />
<br />
The GFP maturation and degradation parameters found in this paper were:<br />
<br />
<html><br />
<centre><br />
<table><br />
<tr><td> m = 0.0004279 1/s </td></tr><br />
<tr><td> Vmax = 2E-10 molality/s </td></tr><br />
<tr><td> Km = 9E-13 molality/s </td></tr><br />
<tr><td> </td></tr><br />
</table><br />
</centre><br />
</html><br />
<br />
<br />
Assuming eCFPt would behave similarly to eGFP, the following additional reactions would be included in the model:<br />
<br />
<html><br />
<table><br />
<tr> <td><b> Maturation </b></td> <td> </td> </tr><br />
<tr> <td> eCFPt --> F_eCFPT </td> <td> 0.0004279 </td> </tr><br />
<tr> <td> Enc2:eCFPt --> Enc2:F_eCFPt </td> <td> 0.0004279 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Encapsulation </b></td> <td> </td> </tr><br />
<tr> <td> Enc2 + F_eCFPt --> Enc2:F_eCFPt </td> <td> 100 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Degradation </b></td> <td> </td> </tr><br />
<tr> <td> eCFPt --> </td> <td> Vmax = 2E-10 </td> </tr><br />
<tr> <td> </td> <td> Km = 9E-13 </td> </tr><br />
<tr> <td> F_eCFPt --> </td> <td> Vmax = 2E-10 </td> </tr><br />
<tr> <td> </td> <td> Km = 9E-13 </td> </tr><br />
</table><br />
</html><br />
<br />
===Assembly of Encapsulin Microcompartments===<br />
<br />
Though Encapsulin microcompartment assembly is not well-studied, it has been theorized to resemble the assembly of viral capsids. Thus, we could look to this relatively well-studied phenomenon as a representation of Encapsulin microcompartment assembly.<br />
<br />
Adam Zlotnick has published models of viral capsid assembly using different approaches. An early paper described an equilibrium model of assembly for a 12 Unit polyhedral capsid head, and a more recent paper used a kinetic model that could be applied to many examples of spherical polymerization. We will consider how each approach could be incorporated as a representation of Encapsulin assembly.<br />
<br />
<br />
'''1) Equilibrim Approach to Encapsulin Assembly'''<br />
<br />
Zlotnick's [[Media:Uft_mod_to_build_a_virus_capsid.pdf|Equilibrium-based model]] consists of reactions from an initial monomer subunit leading to a final capsid product. The sequential reactions take into account DeltaG for contact (Kn'), and parameters describing path degeneracy (varies for different intermediates).<br />
[[image:uft_mod_encap1.png|centre|thumb|Kn for assembly subunits based on path degeneracy. (Zlotnick 1994)]]<br />
<br />
<br />
'''2) Kinetic Model of Spherical Polymerization'''<br />
<br />
A [http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1302223/pdf/12124301.pdf general kinetic model for the spherical polyermization] process is shown below. In our case, the initial monomer subunit concentration (''u'') would represent our expressed Encapsulin BioBrick, and the number of monomers in the final assembly (''N'') is thought to be 60. All of the included parameters can be calculated from the four basic parameters; the microscopic, per-contact equilibrium constant (KAcon), the nucleus size (nuc), the nucleation on-rate (f_nuc), and the elongation on-rate (f_elong). The referenced paper describes methods to aquire these parameters from kinetic experiments, and provides examples for N = 12 and 30 unit viral capsid assemblies.<br />
[[image:uft_mod_encap2.png| centre | thumb |System of ODEs to represent spherical polymerization, where ''u'' is the initial subunit concentration, ''m'' is the "mth" intermediate species, and ''N'' is the number of monomers in the final assembly. (Endres and Zlotnick 2002)]]<br />
<br />
<br />
<br />
Zlotnick's models also describe two important features of spherical polymerization that we should also expect to observe in Encapsulin assembly: kinetic trapping and nucleation. A kinetic trap occurs when the initial monomer subunit concentration or the deltaG of the first assembly reaction is too high. This results in over-initiation of assembly and quickly the reactions become starved for subunits. Kinetic trapping is prevented by the inclusion of nucleation, where the initial reactions occur at a slower rate because the first few intermediates in a series of reactions are less stable than downstream products. Essentially, nucleation serves as a “slow first step” that regulates the assembly pathway. <br />
<br />
It will be interesting to note how the translational dynamics of Encapsulin interplay with its assembly dynamics. Since our system does not start with any initial concentration of Encapsulin, there will be an optimum rate of production that essentially serves the role of nucleation – avoiding kinetic traps while still maintaining a maximum production of full Encapsulin assemblies.<br />
<br />
=References=<br />
<br />
1. Hill AD, Tomshine JR, Weeding EM, Sotiropoulos V, Kaznessis YN. ''SynBioSS: the synthetic biology modeling suite.'' Bioinformatics. 2008 Nov 1;24(21):2551-3. Epub 2008 Aug 30.<br />
[http://neptune.cems.umn.edu/designer/interface1.php SynBioSS Web Designer]<br />
<br />
2. Leveau JH, Lindow SE. ''Predictive and interpretive simulation of green fluorescent protein expression in<br />
reporter bacteria.'' J Bacteriol. 2001 Dec;183(23):6752-62.<br />
<br />
3. Endres D, Zlotnick A. ''Model-based analysis of assembly kinetics for virus capsids or other spherical<br />
polymers.'' Biophys J. 2002 Aug;83(2):1217-30.</div>FRhttp://2009.igem.org/Model_(opens_new_page)Model (opens new page)2009-10-21T07:45:25Z<p>FR: </p>
<hr />
<div>==Reactions==<br />
<br />
<html><br />
<table><br />
<tr><br />
<td><b><u>Reaction</u></b></td><br />
<td><b><u>Rate Constant</u></b></td><br />
</tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<br />
<br />
<tr> <td><b> Constitutive Expression </b></td> <td> </td> </tr><br />
<tr> <td> --> lacl4 </td> <td> 1E-10 </td> </tr><br />
<tr> <td> --> tetR2 </td> <td> 1E-10 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Multimerization </b></td> <td> </td> </tr><br />
<tr> <td> 2 lacI --> lacI2 </td> <td> 1E+09 </td> </tr><br />
<tr> <td> lacI2 --> 2 lacI </td> <td> 10 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> 2 lacI2 --> lacI4 </td> <td> 1E+09 </td> </tr><br />
<tr> <td> lacI4 --> 2 lacI2 </td> <td> 10 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> 2 tetR --> tetR2 </td> <td> 1E+09 </td> </tr><br />
<tr> <td> tetR2 --> 2 tetR </td> <td> 10 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Transcription</b> </td> <td> </td> </tr><br />
<tr> <td> RNAp + BBa_R0010 + LacI_binding_site --> RNAp:BBa_R0010:LacI_binding_site </td> <td> 10000000 </td> </tr><br />
<tr> <td> RNAp:BBa_R0010:LacI_binding_site --> RNAp + BBa_R0010 + LacI_binding_site </td> <td> 0.057 </td> </tr><br />
<tr> <td> RNAp:BBa_R0010:LacI_binding_site --> RNAp:BBa_R0010:LacI_binding_site* </td> <td> 0.1 </td> </tr><br />
<tr> <td> RNAp:BBa_R0010:LacI_binding_site* --> RNAp:DNA_eCFPt + BBa_R0010 + LacI_binding_site </td> <td> 30 </td> </tr><br />
<tr> <td> RNAp:DNA_eCFPt --> RNAp + mRNA_eCFPt </td> <td> 0.035 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> RNAp + BBa_R0040 + TetR_1 + TetR_2 --> RNAp:BBa_R0040:TetR_1:TetR_2 </td> <td> 10000000 </td> </tr><br />
<tr> <td> RNAp:BBa_R0040:TetR_1:TetR_2 --> RNAp + BBa_R0040 + TetR_1 + TetR_2 </td> <td> 0.057 </td> </tr><br />
<tr> <td> RNAp:BBa_R0040:TetR_1:TetR_2 --> RNAp:BBa_R0040:TetR_1:TetR_2* </td> <td> 0.1 </td> </tr><br />
<tr> <td> RNAp:BBa_R0040:TetR_1:TetR_2* --> RNAp:DNA_Enc + BBa_R0040 + TetR_1 + TetR_2 </td> <td> 30 </td> </tr><br />
<tr> <td> RNAp:DNA_Enc --> RNAp + mRNA_Enc </td> <td> 0.0375 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Translation </b></td> <td> </td> </tr><br />
<tr> <td> rib + mRNA_eCFPt --> rib:mRNA_eCFPt </td> <td> 100000 </td> </tr><br />
<tr> <td> rib:mRNA_eCFPt --> rib:mRNA_eCFPt_1 + mRNA_eCFPt </td> <td> 33 </td> </tr><br />
<tr> <td> rib:mRNA_eCFPt_1 --> rib + eCFPt </td> <td> 0.1154 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> rib + mRNA_Enc --> rib:mRNA_Enc </td> <td> 100000 </td> </tr><br />
<tr> <td> rib:mRNA_Enc --> rib:mRNA_Enc_1 + mRNA_Enc </td> <td> 33 </td> </tr><br />
<tr> <td> rib:mRNA_Enc_1 --> rib + Enc </td> <td> 0.1234 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Protein-DNA </b></td> <td> </td> </tr><br />
<tr> <td> lacI4 + nsDNA --> lacI4:nsDNA </td> <td> 1000 </td> </tr><br />
<tr> <td> lacI4:nsDNA --> lacI4 + nsDNA </td> <td> 1.6225 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> lacI4 + LacI_binding_site --> lacI4:LacI_binding_site </td> <td> 1.00E+09 </td> </tr><br />
<tr> <td> lacI4:LacI_binding_site --> lacI4 + LacI_binding_site </td> <td> 0.005 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> tetR2 + nsDNA --> tetR2:nsDNA </td> <td> 1000 </td> </tr><br />
<tr> <td> tetR2:nsDNA --> tetR2 + nsDNA </td> <td> 1.6225 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> tetR2 + TetR_1 --> tetR2:TetR_1 </td> <td> 1.00E+09 </td> </tr><br />
<tr> <td> tetR2:TetR_1 --> tetR2 + TetR_1 </td> <td> 0.005 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> tetR2 + TetR_2 --> tetR2:TetR_2 </td> <td> 1.00E+09 </td> </tr><br />
<tr> <td> tetR2:TetR_2 --> tetR2 + TetR_2 </td> <td> 0.005 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Protein - Effector - DNA </b></td> <td> </td> </tr><br />
<tr> <td> lacI4 + IPTG --> lacI4:IPTG </td> <td> 50000000 </td> </tr><br />
<tr> <td> lacI4:IPTG --> lacI4 + IPTG </td> <td> 0.1 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> lacI4:IPTG + LacI_binding_site --> lacI4:IPTG:LacI_binding_site </td> <td> 1.00E+09 </td> </tr><br />
<tr> <td> lacI4:IPTG:LacI_binding_site --> lacI4:IPTG + LacI_binding_site </td> <td> 0.7 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> lacI4:LacI_binding_site + IPTG --> lacI4:IPTG:LacI_binding_site </td> <td> 1000000 </td> </tr><br />
<tr> <td> lacI4:IPTG:LacI_binding_site --> lacI4:LacI_binding_site + IPTG </td> <td> 0.4 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> lacI4:IPTG + nsDNA --> lacI4:IPTG:nsDNA </td> <td> 1000 </td> </tr><br />
<tr> <td> lacI4:IPTG:nsDNA --> lacI4:IPTG + nsDNA </td> <td> 1.6225 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> lacI4:nsDNA + IPTG --> lacI4:IPTG:nsDNA </td> <td> 1000 </td> </tr><br />
<tr> <td> lacI4:IPTG:nsDNA --> lacI4:nsDNA + IPTG </td> <td> 1.6225 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> tetR2 + aTc --> tetR2:aTc </td> <td> 50000000 </td> </tr><br />
<tr> <td> tetR2:aTc --> tetR2 + aTc </td> <td> 0.1 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> tetR2:aTc + TetR_1 --> tetR2:aTc:TetR_1 </td> <td> 1.00E+09 </td> </tr><br />
<tr> <td> tetR2:aTc:TetR_1 --> tetR2:aTc + TetR_1 </td> <td> 0.7 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> tetR2:TetR_1 + aTc --> tetR2:aTc:TetR_1 </td> <td> 1000000 </td> </tr><br />
<tr> <td> tetR2:aTc:TetR_1 --> tetR2:TetR_1 + aTc </td> <td> 0.4 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> tetR2:aTc + TetR_2 --> tetR2:aTc:TetR_2 </td> <td> 1.00E+09 </td> </tr><br />
<tr> <td> tetR2:aTc:TetR_2 --> tetR2:aTc + TetR_2 </td> <td> 0.7 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> tetR2:TetR_2 + aTc --> tetR2:aTc:TetR_2 </td> <td> 1000000 </td> </tr><br />
<tr> <td> tetR2:aTc:TetR_2 --> tetR2:TetR_2 + aTc </td> <td> 0.4 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> tetR2:aTc + nsDNA --> tetR2:aTc:nsDNA </td> <td> 1000 </td> </tr><br />
<tr> <td> tetR2:aTc:nsDNA --> tetR2:aTc + nsDNA </td> <td> 1.6225 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> tetR2:nsDNA + aTc --> tetR2:aTc:nsDNA </td> <td> 1000 </td> </tr><br />
<tr> <td> tetR2:aTc:nsDNA --> tetR2:nsDNA + aTc </td> <td> 1.6225 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Degradation</b> </td> <td> </td> </tr><br />
<tr> <td> lacI4 --> </td> <td> 0.000289 </td> </tr><br />
<tr> <td> tetR2 --> </td> <td> 0.000289 </td> </tr><br />
<tr> <td> mRNA_eCFPt --> </td> <td> 0.0015 </td> </tr><br />
<tr> <td> mRNA_Enc --> </td> <td> 0.0015 </td> </tr><br />
<tr> <td> eCFPt --> </td> <td> 0.000289 </td> </tr><br />
<tr> <td> Enc --> </td> <td> 0.000289 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Dilution</b> </td> <td> </td> </tr><br />
<tr> <td> lacI4:nsDNA --> nsDNA </td> <td> 0.000193 </td> </tr><br />
<tr> <td> tetR2:nsDNA --> nsDNA </td> <td> 0.000193 </td> </tr><br />
<tr> <td> lacI4:IPTG --> IPTG </td> <td> 0.000289 </td> </tr><br />
<tr> <td> tetR2:aTc --> aTc </td> <td> 0.000289 </td> </tr><br />
<tr> <td> lacI4:IPTG:nsDNA --> IPTG + nsDNA </td> <td> 0.000193 </td> </tr><br />
<tr> <td> tetR2:aTc:nsDNA --> aTc + nsDNA </td> <td> 0.000193 </td> </tr><br />
</table><br />
</html></div>FRhttp://2009.igem.org/Model_(opens_new_page)Model (opens new page)2009-10-21T07:44:42Z<p>FR: New page: =Model Reactions= <html> <table> <tr> <td><b><u>Reaction</u></b></td> <td><b><u>Rate Constant</u></b></td> </tr> <tr> <td> </td> <td> </td> </tr> <tr> <td> </td> <td> </td> </tr> <t...</p>
<hr />
<div>=Model Reactions=<br />
<br />
<html><br />
<table><br />
<tr><br />
<td><b><u>Reaction</u></b></td><br />
<td><b><u>Rate Constant</u></b></td><br />
</tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<br />
<br />
<tr> <td><b> Constitutive Expression </b></td> <td> </td> </tr><br />
<tr> <td> --> lacl4 </td> <td> 1E-10 </td> </tr><br />
<tr> <td> --> tetR2 </td> <td> 1E-10 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Multimerization </b></td> <td> </td> </tr><br />
<tr> <td> 2 lacI --> lacI2 </td> <td> 1E+09 </td> </tr><br />
<tr> <td> lacI2 --> 2 lacI </td> <td> 10 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> 2 lacI2 --> lacI4 </td> <td> 1E+09 </td> </tr><br />
<tr> <td> lacI4 --> 2 lacI2 </td> <td> 10 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> 2 tetR --> tetR2 </td> <td> 1E+09 </td> </tr><br />
<tr> <td> tetR2 --> 2 tetR </td> <td> 10 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Transcription</b> </td> <td> </td> </tr><br />
<tr> <td> RNAp + BBa_R0010 + LacI_binding_site --> RNAp:BBa_R0010:LacI_binding_site </td> <td> 10000000 </td> </tr><br />
<tr> <td> RNAp:BBa_R0010:LacI_binding_site --> RNAp + BBa_R0010 + LacI_binding_site </td> <td> 0.057 </td> </tr><br />
<tr> <td> RNAp:BBa_R0010:LacI_binding_site --> RNAp:BBa_R0010:LacI_binding_site* </td> <td> 0.1 </td> </tr><br />
<tr> <td> RNAp:BBa_R0010:LacI_binding_site* --> RNAp:DNA_eCFPt + BBa_R0010 + LacI_binding_site </td> <td> 30 </td> </tr><br />
<tr> <td> RNAp:DNA_eCFPt --> RNAp + mRNA_eCFPt </td> <td> 0.035 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> RNAp + BBa_R0040 + TetR_1 + TetR_2 --> RNAp:BBa_R0040:TetR_1:TetR_2 </td> <td> 10000000 </td> </tr><br />
<tr> <td> RNAp:BBa_R0040:TetR_1:TetR_2 --> RNAp + BBa_R0040 + TetR_1 + TetR_2 </td> <td> 0.057 </td> </tr><br />
<tr> <td> RNAp:BBa_R0040:TetR_1:TetR_2 --> RNAp:BBa_R0040:TetR_1:TetR_2* </td> <td> 0.1 </td> </tr><br />
<tr> <td> RNAp:BBa_R0040:TetR_1:TetR_2* --> RNAp:DNA_Enc + BBa_R0040 + TetR_1 + TetR_2 </td> <td> 30 </td> </tr><br />
<tr> <td> RNAp:DNA_Enc --> RNAp + mRNA_Enc </td> <td> 0.0375 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Translation </b></td> <td> </td> </tr><br />
<tr> <td> rib + mRNA_eCFPt --> rib:mRNA_eCFPt </td> <td> 100000 </td> </tr><br />
<tr> <td> rib:mRNA_eCFPt --> rib:mRNA_eCFPt_1 + mRNA_eCFPt </td> <td> 33 </td> </tr><br />
<tr> <td> rib:mRNA_eCFPt_1 --> rib + eCFPt </td> <td> 0.1154 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> rib + mRNA_Enc --> rib:mRNA_Enc </td> <td> 100000 </td> </tr><br />
<tr> <td> rib:mRNA_Enc --> rib:mRNA_Enc_1 + mRNA_Enc </td> <td> 33 </td> </tr><br />
<tr> <td> rib:mRNA_Enc_1 --> rib + Enc </td> <td> 0.1234 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Protein-DNA </b></td> <td> </td> </tr><br />
<tr> <td> lacI4 + nsDNA --> lacI4:nsDNA </td> <td> 1000 </td> </tr><br />
<tr> <td> lacI4:nsDNA --> lacI4 + nsDNA </td> <td> 1.6225 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> lacI4 + LacI_binding_site --> lacI4:LacI_binding_site </td> <td> 1.00E+09 </td> </tr><br />
<tr> <td> lacI4:LacI_binding_site --> lacI4 + LacI_binding_site </td> <td> 0.005 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> tetR2 + nsDNA --> tetR2:nsDNA </td> <td> 1000 </td> </tr><br />
<tr> <td> tetR2:nsDNA --> tetR2 + nsDNA </td> <td> 1.6225 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> tetR2 + TetR_1 --> tetR2:TetR_1 </td> <td> 1.00E+09 </td> </tr><br />
<tr> <td> tetR2:TetR_1 --> tetR2 + TetR_1 </td> <td> 0.005 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> tetR2 + TetR_2 --> tetR2:TetR_2 </td> <td> 1.00E+09 </td> </tr><br />
<tr> <td> tetR2:TetR_2 --> tetR2 + TetR_2 </td> <td> 0.005 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Protein - Effector - DNA </b></td> <td> </td> </tr><br />
<tr> <td> lacI4 + IPTG --> lacI4:IPTG </td> <td> 50000000 </td> </tr><br />
<tr> <td> lacI4:IPTG --> lacI4 + IPTG </td> <td> 0.1 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> lacI4:IPTG + LacI_binding_site --> lacI4:IPTG:LacI_binding_site </td> <td> 1.00E+09 </td> </tr><br />
<tr> <td> lacI4:IPTG:LacI_binding_site --> lacI4:IPTG + LacI_binding_site </td> <td> 0.7 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> lacI4:LacI_binding_site + IPTG --> lacI4:IPTG:LacI_binding_site </td> <td> 1000000 </td> </tr><br />
<tr> <td> lacI4:IPTG:LacI_binding_site --> lacI4:LacI_binding_site + IPTG </td> <td> 0.4 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> lacI4:IPTG + nsDNA --> lacI4:IPTG:nsDNA </td> <td> 1000 </td> </tr><br />
<tr> <td> lacI4:IPTG:nsDNA --> lacI4:IPTG + nsDNA </td> <td> 1.6225 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> lacI4:nsDNA + IPTG --> lacI4:IPTG:nsDNA </td> <td> 1000 </td> </tr><br />
<tr> <td> lacI4:IPTG:nsDNA --> lacI4:nsDNA + IPTG </td> <td> 1.6225 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> tetR2 + aTc --> tetR2:aTc </td> <td> 50000000 </td> </tr><br />
<tr> <td> tetR2:aTc --> tetR2 + aTc </td> <td> 0.1 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> tetR2:aTc + TetR_1 --> tetR2:aTc:TetR_1 </td> <td> 1.00E+09 </td> </tr><br />
<tr> <td> tetR2:aTc:TetR_1 --> tetR2:aTc + TetR_1 </td> <td> 0.7 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> tetR2:TetR_1 + aTc --> tetR2:aTc:TetR_1 </td> <td> 1000000 </td> </tr><br />
<tr> <td> tetR2:aTc:TetR_1 --> tetR2:TetR_1 + aTc </td> <td> 0.4 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> tetR2:aTc + TetR_2 --> tetR2:aTc:TetR_2 </td> <td> 1.00E+09 </td> </tr><br />
<tr> <td> tetR2:aTc:TetR_2 --> tetR2:aTc + TetR_2 </td> <td> 0.7 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> tetR2:TetR_2 + aTc --> tetR2:aTc:TetR_2 </td> <td> 1000000 </td> </tr><br />
<tr> <td> tetR2:aTc:TetR_2 --> tetR2:TetR_2 + aTc </td> <td> 0.4 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> tetR2:aTc + nsDNA --> tetR2:aTc:nsDNA </td> <td> 1000 </td> </tr><br />
<tr> <td> tetR2:aTc:nsDNA --> tetR2:aTc + nsDNA </td> <td> 1.6225 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> tetR2:nsDNA + aTc --> tetR2:aTc:nsDNA </td> <td> 1000 </td> </tr><br />
<tr> <td> tetR2:aTc:nsDNA --> tetR2:nsDNA + aTc </td> <td> 1.6225 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Degradation</b> </td> <td> </td> </tr><br />
<tr> <td> lacI4 --> </td> <td> 0.000289 </td> </tr><br />
<tr> <td> tetR2 --> </td> <td> 0.000289 </td> </tr><br />
<tr> <td> mRNA_eCFPt --> </td> <td> 0.0015 </td> </tr><br />
<tr> <td> mRNA_Enc --> </td> <td> 0.0015 </td> </tr><br />
<tr> <td> eCFPt --> </td> <td> 0.000289 </td> </tr><br />
<tr> <td> Enc --> </td> <td> 0.000289 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Dilution</b> </td> <td> </td> </tr><br />
<tr> <td> lacI4:nsDNA --> nsDNA </td> <td> 0.000193 </td> </tr><br />
<tr> <td> tetR2:nsDNA --> nsDNA </td> <td> 0.000193 </td> </tr><br />
<tr> <td> lacI4:IPTG --> IPTG </td> <td> 0.000289 </td> </tr><br />
<tr> <td> tetR2:aTc --> aTc </td> <td> 0.000289 </td> </tr><br />
<tr> <td> lacI4:IPTG:nsDNA --> IPTG + nsDNA </td> <td> 0.000193 </td> </tr><br />
<tr> <td> tetR2:aTc:nsDNA --> aTc + nsDNA </td> <td> 0.000193 </td> </tr><br />
</table><br />
</html></div>FRhttp://2009.igem.org/Team:TorontoMaRSDiscovery/ModelingTeam:TorontoMaRSDiscovery/Modeling2009-10-21T07:41:47Z<p>FR: /* Model */</p>
<hr />
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<br><br />
<br />
<br />
=Summary=<br />
<br />
A kinetic model of our system has been constructed. Approximate parameter values were gathered from online resources to represent all processes up to the production of the eCFP and Encapsulin proteins. Current simulations predict the production of these two proteins at various initial concentrations of IPTG and aTc effector molecules. A sensitivity analysis reveals that the rate of constitutive expression of lacI and tetR has the greatest affect on eCFP and Encapsulin concentrations. Furthermore, we have outlined approaches for the detailed modelling of the eCFP degredation/maturation and Encapsulin assembly pathways.<br />
<br />
<br />
The initial simulations will be used to identify a critical concentration of Encapsulin mononomer required for microcompartment assembly. To strengthen the model, the constitutive expression rate of BBa_J23100 as used in our construct will be measured. Subsequently, a detailed model of Encapsulin assembly will be integrated into the current model, and its parameters filled-in using parameter-scanning methods and experiments outlined in the relevant references. By comparing experimental measures of microcompartment formation with that predicted by the kinetic model, we aim to gain insight on the mechanisms of Encapsulin assembly.<br />
<br />
=Model=<br />
Our model is based on the following design (See Project Page for a full description of this system).<br />
[[image:BioBrick.png|thumb|centre|The Encapsulator]]<br />
<br />
The reaction framework was mainly generated using the [http://synbioss.sourceforge.net/ SynBioSS Designer (a really useful modeling tool for iGEM teams)], which also provides default parameter values. These parameter values have been gathered from various literature [http://neptune.cems.umn.edu/designer/designer_defaults.pdf sources], and should be taken as approximations. All units were taken to be (1 / molarity^n-1 * s), where n is the order of the reaction. For example, for the reaction 2 lacI --> lacI2, n = 2, thus the rate constant has the units 1/molarity*s. <br />
<br />
The pathways for the expressed proteins, eCFPt and Encapsulin, need to be modeled in more detail. For example, in this basic model eCFPt is degraded via a first order reaction and Encapsulin makes a dimer complex. However, in reality fluorescent proteins have been shown to degreade via Micheales-menton kinetics and Encapsulin is thought to make a complex of about 60 monomers. These issues will be addressed in future work.<br />
<br />
The reactions can be accessed here:<br />
<br />
[[Model (opens new page)]]<br />
<br />
[[Media:Uft_mod_Rxns2.xls|Model (download Excel file)]]<br />
<br />
=Simulations=<br />
<br />
All simulations were carried out using the [https://2009.igem.org/Partner_Offers SimBiology Matlab Toolbox], which was freely available to iGEM teams. <br />
<br />
===Accumulation of eCFP at Different Initial Concentrations of IPTG===<br />
<br />
[[Image:uft_mod_cfp-iptg.png | 900px]]<br />
<br />
The IPTG effector eventually loses effect, and the eCFP concentration approaches a maximum. This happens because the IPTG proteins eventually ''tie up'' all available LacI4 proteins, leaving the transcription and translation of eCFP to operate at its maxiumum rate. <br />
<br />
===Accumulation of Encapsulin monomer at Different Initial Concentrations of aTc===<br />
<br />
[[Image:uft_mod_enc-atc.png | 900px]]<br />
<br />
(NOTE: in order to observe Encapsulin monomer levels, the above simulations were carried out without any Encapsulin assembly reactions in place)<br />
<br />
The production of Encapsulin occurs at a slower rate than eCFP because the BBa_R0040 promoter has two tetR binding sites, resulting in more repression and more off-pathway scenarios. Thus, the Encapsulin concentration also seems assymptotic but at higher concentrations of aTc (relative to IPTG). <br />
<br />
It seems beneficial to have the Encapsulin protein under control of the BBa_R0040-tetR-aTc construct because at zero levels of aTc we can have essentially zero levels of Encapsulin (whereas even at zero levels of IPTG, there is still significantly more eCFP). This will enable us to probe extremely low concentrations of Encapsulin monomer when testing for optimal Encapsulin assembly conditions. The disadvantage is that if Encapsulin assembly requires a very high initial concentration of Encapsulin monomer, we would have to wait a long time to see microcompartments. If this later scenario is observed, it may be better to switch the eCFP and Encapsulin expression systems.<br />
<br />
===Sensitivity Analysis===<br />
<br />
Since all of our parameters are approximations from literature sources, those which have the greatest affect on system dynamics (ie. the most ''sensitive'' parameters) would be leading candidates to be experimentally determined. Currently we are interested in which parameters have the greatest effect on the production of eCFP and Encapsulin. Ideally, it would be best to experimentally determine these to "tighten-up" the model before incorporating the largely unexplored Encapsulin assembly pathways. <br />
<br />
<br />
'''1) Sensitivity of eCFP Production'''<br />
<br />
[[Image:uft_mod_SAecfp.png | centre | 900px]]<br />
<br />
<br />
<br />
'''2) Sensitivity of Encapsulin Production'''<br />
<br />
[[Image:uft_mod_SAenc.png | centre | 900px]]<br />
<br />
Parameters 1 and 2 correspond to the rates of constitutive expression of the lacI and tetR repressors respectively. Thus, it can be seen that eCFP and Encapsulin production is largely sensitive to the expression rates of lacI and tetR. <br />
<br />
The specific constitutive promoter used in our construct is BBa_J23100. In our model, this was given the generic rate of 1E-10 molarity\s by SynBioSS based on a variety of empirically-fitted protein expression rates found in literature. This generic approach to assigning parameter values is a suitable fist-step, but our sensitivity results suggest that experimentally determining the expression rate of our specific constitutive promoter should significantly improve our model's predictive capability.<br />
<br />
=Future Work=<br />
<br />
Improvements to the basic model presented above can be separated into three areas; 1) performing experiments to determine parameter values that are specific to our system, 2) more detailed modeling of eCFPt behavior, 3) more detailed modeling of Encapsulin assembly. <br />
<br />
The experiments required to determine general transcription and translation parameters need to be further researched, so this will be skipped over for now. Here we will discuss the more interesting areas – the detailed modeling of eCFP and Encapsulin pathways. This will be accomplished by incorporating previous modeling efforts that are applicable to the eCFP and Encapsulin proteins. <br />
<br />
===Degredation of eCFP===<br />
<br />
The expression and degradation of [http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=95514&blobtype=pdf Green Fluorescent Protein (GFP) was modeled previously]. This paper noted that GFP must mature before going into fluorescent phase, and GFP degradation was shown to follow M-M kinetics, as depicted below. This paper also outlined how the degradation parameters could be derived for any expression system using only simple fluorescence and optical density measurements.<br />
<br />
[[Image:uft_mod_ecfp1.png | centre | thumb | Degredation and maturation pathways for eCFP. (Leveau and Lindow 2001)]]<br />
<br />
<br />
The GFP maturation and degradation parameters found in this paper were:<br />
<br />
<html><br />
<centre><br />
<table><br />
<tr><td> m = 0.0004279 1/s </td></tr><br />
<tr><td> Vmax = 2E-10 molality/s </td></tr><br />
<tr><td> Km = 9E-13 molality/s </td></tr><br />
<tr><td> </td></tr><br />
</table><br />
</centre><br />
</html><br />
<br />
<br />
Assuming eCFPt would behave similarly to eGFP, the following additional reactions would be included in the model:<br />
<br />
<html><br />
<table><br />
<tr> <td><b> Maturation </b></td> <td> </td> </tr><br />
<tr> <td> eCFPt --> F_eCFPT </td> <td> 0.0004279 </td> </tr><br />
<tr> <td> Enc2:eCFPt --> Enc2:F_eCFPt </td> <td> 0.0004279 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Encapsulation </b></td> <td> </td> </tr><br />
<tr> <td> Enc2 + F_eCFPt --> Enc2:F_eCFPt </td> <td> 100 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Degradation </b></td> <td> </td> </tr><br />
<tr> <td> eCFPt --> </td> <td> Vmax = 2E-10 </td> </tr><br />
<tr> <td> </td> <td> Km = 9E-13 </td> </tr><br />
<tr> <td> F_eCFPt --> </td> <td> Vmax = 2E-10 </td> </tr><br />
<tr> <td> </td> <td> Km = 9E-13 </td> </tr><br />
</table><br />
</html><br />
<br />
===Assembly of Encapsulin Microcompartments===<br />
<br />
Though Encapsulin microcompartment assembly is not well-studied, it has been theorized to resemble the assembly of viral capsids. Thus, we could look to this relatively well-studied phenomenon as a representation of Encapsulin microcompartment assembly.<br />
<br />
Adam Zlotnick has published models of viral capsid assembly using different approaches. An early paper described an equilibrium model of assembly for a 12 Unit polyhedral capsid head, and a more recent paper used a kinetic model that could be applied to many examples of spherical polymerization. We will consider how each approach could be incorporated as a representation of Encapsulin assembly.<br />
<br />
<br />
'''1) Equilibrim Approach to Encapsulin Assembly'''<br />
<br />
Zlotnick's [[Media:Uft_mod_to_build_a_virus_capsid.pdf|Equilibrium-based model]] consists of reactions from an initial monomer subunit leading to a final capsid product. The sequential reactions take into account DeltaG for contact (Kn'), and parameters describing path degeneracy (varies for different intermediates).<br />
[[image:uft_mod_encap1.png|centre|thumb|Kn for assembly subunits based on path degeneracy. (Zlotnick 1994)]]<br />
<br />
<br />
'''2) Kinetic Model of Spherical Polymerization'''<br />
<br />
A [http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1302223/pdf/12124301.pdf general kinetic model for the spherical polyermization] process is shown below. In our case, the initial monomer subunit concentration (''u'') would represent our expressed Encapsulin BioBrick, and the number of monomers in the final assembly (''N'') is thought to be 60. All of the included parameters can be calculated from the four basic parameters; the microscopic, per-contact equilibrium constant (KAcon), the nucleus size (nuc), the nucleation on-rate (f_nuc), and the elongation on-rate (f_elong). The referenced paper describes methods to aquire these parameters from kinetic experiments, and provides examples for N = 12 and 30 unit viral capsid assemblies.<br />
[[image:uft_mod_encap2.png| centre | thumb |System of ODEs to represent spherical polymerization, where ''u'' is the initial subunit concentration, ''m'' is the "mth" intermediate species, and ''N'' is the number of monomers in the final assembly. (Endres and Zlotnick 2002)]]<br />
<br />
<br />
<br />
Zlotnick's models also describe two important features of spherical polymerization that we should also expect to observe in Encapsulin assembly: kinetic trapping and nucleation. A kinetic trap occurs when the initial monomer subunit concentration or the deltaG of the first assembly reaction is too high. This results in over-initiation of assembly and quickly the reactions become starved for subunits. Kinetic trapping is prevented by the inclusion of nucleation, where the initial reactions occur at a slower rate because the first few intermediates in a series of reactions are less stable than downstream products. Essentially, nucleation serves as a “slow first step” that regulates the assembly pathway. <br />
<br />
It will be interesting to note how the translational dynamics of Encapsulin interplay with its assembly dynamics. Since our system does not start with any initial concentration of Encapsulin, there will be an optimum rate of production that essentially serves the role of nucleation – avoiding kinetic traps while still maintaining a maximum production of full Encapsulin assemblies.<br />
<br />
=References=<br />
<br />
1. Hill AD, Tomshine JR, Weeding EM, Sotiropoulos V, Kaznessis YN. ''SynBioSS: the synthetic biology modeling suite.'' Bioinformatics. 2008 Nov 1;24(21):2551-3. Epub 2008 Aug 30.<br />
[http://neptune.cems.umn.edu/designer/interface1.php SynBioSS Web Designer]<br />
<br />
2. Leveau JH, Lindow SE. ''Predictive and interpretive simulation of green fluorescent protein expression in<br />
reporter bacteria.'' J Bacteriol. 2001 Dec;183(23):6752-62.<br />
<br />
3. Endres D, Zlotnick A. ''Model-based analysis of assembly kinetics for virus capsids or other spherical<br />
polymers.'' Biophys J. 2002 Aug;83(2):1217-30.</div>FRhttp://2009.igem.org/Team:TorontoMaRSDiscovery/ModelingTeam:TorontoMaRSDiscovery/Modeling2009-10-21T07:40:57Z<p>FR: /* Summary */</p>
<hr />
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<br><br />
<br />
<br />
=Summary=<br />
<br />
A kinetic model of our system has been constructed. Approximate parameter values were gathered from online resources to represent all processes up to the production of the eCFP and Encapsulin proteins. Current simulations predict the production of these two proteins at various initial concentrations of IPTG and aTc effector molecules. A sensitivity analysis reveals that the rate of constitutive expression of lacI and tetR has the greatest affect on eCFP and Encapsulin concentrations. Furthermore, we have outlined approaches for the detailed modelling of the eCFP degredation/maturation and Encapsulin assembly pathways.<br />
<br />
<br />
The initial simulations will be used to identify a critical concentration of Encapsulin mononomer required for microcompartment assembly. To strengthen the model, the constitutive expression rate of BBa_J23100 as used in our construct will be measured. Subsequently, a detailed model of Encapsulin assembly will be integrated into the current model, and its parameters filled-in using parameter-scanning methods and experiments outlined in the relevant references. By comparing experimental measures of microcompartment formation with that predicted by the kinetic model, we aim to gain insight on the mechanisms of Encapsulin assembly.<br />
<br />
=Model=<br />
Our model is based on the following design (See Project Page for a full description of this system).<br />
[[image:BioBrick.png|thumb|centre|The Encapsulator]]<br />
<br />
The reaction framework was mainly generated using the [http://synbioss.sourceforge.net/ SynBioSS Designer (a really useful modeling tool for iGEM teams)], which also provides default parameter values. These parameter values have been gathered from various literature [http://neptune.cems.umn.edu/designer/designer_defaults.pdf sources], and should be taken as approximations. All units were taken to be (1 / molarity^n-1 * s), where n is the order of the reaction. For example, for the reaction 2 lacI --> lacI2, n = 2, thus the rate constant has the units 1/molarity*s. <br />
<br />
The pathways for the expressed proteins, eCFPt and Encapsulin, need to be modeled in more detail. For example, in this basic model eCFPt is degraded via a first order reaction and Encapsulin makes a dimer complex. However, in reality fluorescent proteins have been shown to degreade via Micheales-menton kinetics and Encapsulin is thought to make a complex of about 60 monomers. These issues will be addressed in future work.<br />
<br />
The reactions can be accessed here:<br />
<br />
[[Model (open new page)]]<br />
<br />
[[Media:Uft_mod_Rxns2.xls|Model (download Excel file)]]<br />
<br />
=Simulations=<br />
<br />
All simulations were carried out using the [https://2009.igem.org/Partner_Offers SimBiology Matlab Toolbox], which was freely available to iGEM teams. <br />
<br />
===Accumulation of eCFP at Different Initial Concentrations of IPTG===<br />
<br />
[[Image:uft_mod_cfp-iptg.png | 900px]]<br />
<br />
The IPTG effector eventually loses effect, and the eCFP concentration approaches a maximum. This happens because the IPTG proteins eventually ''tie up'' all available LacI4 proteins, leaving the transcription and translation of eCFP to operate at its maxiumum rate. <br />
<br />
===Accumulation of Encapsulin monomer at Different Initial Concentrations of aTc===<br />
<br />
[[Image:uft_mod_enc-atc.png | 900px]]<br />
<br />
(NOTE: in order to observe Encapsulin monomer levels, the above simulations were carried out without any Encapsulin assembly reactions in place)<br />
<br />
The production of Encapsulin occurs at a slower rate than eCFP because the BBa_R0040 promoter has two tetR binding sites, resulting in more repression and more off-pathway scenarios. Thus, the Encapsulin concentration also seems assymptotic but at higher concentrations of aTc (relative to IPTG). <br />
<br />
It seems beneficial to have the Encapsulin protein under control of the BBa_R0040-tetR-aTc construct because at zero levels of aTc we can have essentially zero levels of Encapsulin (whereas even at zero levels of IPTG, there is still significantly more eCFP). This will enable us to probe extremely low concentrations of Encapsulin monomer when testing for optimal Encapsulin assembly conditions. The disadvantage is that if Encapsulin assembly requires a very high initial concentration of Encapsulin monomer, we would have to wait a long time to see microcompartments. If this later scenario is observed, it may be better to switch the eCFP and Encapsulin expression systems.<br />
<br />
===Sensitivity Analysis===<br />
<br />
Since all of our parameters are approximations from literature sources, those which have the greatest affect on system dynamics (ie. the most ''sensitive'' parameters) would be leading candidates to be experimentally determined. Currently we are interested in which parameters have the greatest effect on the production of eCFP and Encapsulin. Ideally, it would be best to experimentally determine these to "tighten-up" the model before incorporating the largely unexplored Encapsulin assembly pathways. <br />
<br />
<br />
'''1) Sensitivity of eCFP Production'''<br />
<br />
[[Image:uft_mod_SAecfp.png | centre | 900px]]<br />
<br />
<br />
<br />
'''2) Sensitivity of Encapsulin Production'''<br />
<br />
[[Image:uft_mod_SAenc.png | centre | 900px]]<br />
<br />
Parameters 1 and 2 correspond to the rates of constitutive expression of the lacI and tetR repressors respectively. Thus, it can be seen that eCFP and Encapsulin production is largely sensitive to the expression rates of lacI and tetR. <br />
<br />
The specific constitutive promoter used in our construct is BBa_J23100. In our model, this was given the generic rate of 1E-10 molarity\s by SynBioSS based on a variety of empirically-fitted protein expression rates found in literature. This generic approach to assigning parameter values is a suitable fist-step, but our sensitivity results suggest that experimentally determining the expression rate of our specific constitutive promoter should significantly improve our model's predictive capability.<br />
<br />
=Future Work=<br />
<br />
Improvements to the basic model presented above can be separated into three areas; 1) performing experiments to determine parameter values that are specific to our system, 2) more detailed modeling of eCFPt behavior, 3) more detailed modeling of Encapsulin assembly. <br />
<br />
The experiments required to determine general transcription and translation parameters need to be further researched, so this will be skipped over for now. Here we will discuss the more interesting areas – the detailed modeling of eCFP and Encapsulin pathways. This will be accomplished by incorporating previous modeling efforts that are applicable to the eCFP and Encapsulin proteins. <br />
<br />
===Degredation of eCFP===<br />
<br />
The expression and degradation of [http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=95514&blobtype=pdf Green Fluorescent Protein (GFP) was modeled previously]. This paper noted that GFP must mature before going into fluorescent phase, and GFP degradation was shown to follow M-M kinetics, as depicted below. This paper also outlined how the degradation parameters could be derived for any expression system using only simple fluorescence and optical density measurements.<br />
<br />
[[Image:uft_mod_ecfp1.png | centre | thumb | Degredation and maturation pathways for eCFP. (Leveau and Lindow 2001)]]<br />
<br />
<br />
The GFP maturation and degradation parameters found in this paper were:<br />
<br />
<html><br />
<centre><br />
<table><br />
<tr><td> m = 0.0004279 1/s </td></tr><br />
<tr><td> Vmax = 2E-10 molality/s </td></tr><br />
<tr><td> Km = 9E-13 molality/s </td></tr><br />
<tr><td> </td></tr><br />
</table><br />
</centre><br />
</html><br />
<br />
<br />
Assuming eCFPt would behave similarly to eGFP, the following additional reactions would be included in the model:<br />
<br />
<html><br />
<table><br />
<tr> <td><b> Maturation </b></td> <td> </td> </tr><br />
<tr> <td> eCFPt --> F_eCFPT </td> <td> 0.0004279 </td> </tr><br />
<tr> <td> Enc2:eCFPt --> Enc2:F_eCFPt </td> <td> 0.0004279 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Encapsulation </b></td> <td> </td> </tr><br />
<tr> <td> Enc2 + F_eCFPt --> Enc2:F_eCFPt </td> <td> 100 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Degradation </b></td> <td> </td> </tr><br />
<tr> <td> eCFPt --> </td> <td> Vmax = 2E-10 </td> </tr><br />
<tr> <td> </td> <td> Km = 9E-13 </td> </tr><br />
<tr> <td> F_eCFPt --> </td> <td> Vmax = 2E-10 </td> </tr><br />
<tr> <td> </td> <td> Km = 9E-13 </td> </tr><br />
</table><br />
</html><br />
<br />
===Assembly of Encapsulin Microcompartments===<br />
<br />
Though Encapsulin microcompartment assembly is not well-studied, it has been theorized to resemble the assembly of viral capsids. Thus, we could look to this relatively well-studied phenomenon as a representation of Encapsulin microcompartment assembly.<br />
<br />
Adam Zlotnick has published models of viral capsid assembly using different approaches. An early paper described an equilibrium model of assembly for a 12 Unit polyhedral capsid head, and a more recent paper used a kinetic model that could be applied to many examples of spherical polymerization. We will consider how each approach could be incorporated as a representation of Encapsulin assembly.<br />
<br />
<br />
'''1) Equilibrim Approach to Encapsulin Assembly'''<br />
<br />
Zlotnick's [[Media:Uft_mod_to_build_a_virus_capsid.pdf|Equilibrium-based model]] consists of reactions from an initial monomer subunit leading to a final capsid product. The sequential reactions take into account DeltaG for contact (Kn'), and parameters describing path degeneracy (varies for different intermediates).<br />
[[image:uft_mod_encap1.png|centre|thumb|Kn for assembly subunits based on path degeneracy. (Zlotnick 1994)]]<br />
<br />
<br />
'''2) Kinetic Model of Spherical Polymerization'''<br />
<br />
A [http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1302223/pdf/12124301.pdf general kinetic model for the spherical polyermization] process is shown below. In our case, the initial monomer subunit concentration (''u'') would represent our expressed Encapsulin BioBrick, and the number of monomers in the final assembly (''N'') is thought to be 60. All of the included parameters can be calculated from the four basic parameters; the microscopic, per-contact equilibrium constant (KAcon), the nucleus size (nuc), the nucleation on-rate (f_nuc), and the elongation on-rate (f_elong). The referenced paper describes methods to aquire these parameters from kinetic experiments, and provides examples for N = 12 and 30 unit viral capsid assemblies.<br />
[[image:uft_mod_encap2.png| centre | thumb |System of ODEs to represent spherical polymerization, where ''u'' is the initial subunit concentration, ''m'' is the "mth" intermediate species, and ''N'' is the number of monomers in the final assembly. (Endres and Zlotnick 2002)]]<br />
<br />
<br />
<br />
Zlotnick's models also describe two important features of spherical polymerization that we should also expect to observe in Encapsulin assembly: kinetic trapping and nucleation. A kinetic trap occurs when the initial monomer subunit concentration or the deltaG of the first assembly reaction is too high. This results in over-initiation of assembly and quickly the reactions become starved for subunits. Kinetic trapping is prevented by the inclusion of nucleation, where the initial reactions occur at a slower rate because the first few intermediates in a series of reactions are less stable than downstream products. Essentially, nucleation serves as a “slow first step” that regulates the assembly pathway. <br />
<br />
It will be interesting to note how the translational dynamics of Encapsulin interplay with its assembly dynamics. Since our system does not start with any initial concentration of Encapsulin, there will be an optimum rate of production that essentially serves the role of nucleation – avoiding kinetic traps while still maintaining a maximum production of full Encapsulin assemblies.<br />
<br />
=References=<br />
<br />
1. Hill AD, Tomshine JR, Weeding EM, Sotiropoulos V, Kaznessis YN. ''SynBioSS: the synthetic biology modeling suite.'' Bioinformatics. 2008 Nov 1;24(21):2551-3. Epub 2008 Aug 30.<br />
[http://neptune.cems.umn.edu/designer/interface1.php SynBioSS Web Designer]<br />
<br />
2. Leveau JH, Lindow SE. ''Predictive and interpretive simulation of green fluorescent protein expression in<br />
reporter bacteria.'' J Bacteriol. 2001 Dec;183(23):6752-62.<br />
<br />
3. Endres D, Zlotnick A. ''Model-based analysis of assembly kinetics for virus capsids or other spherical<br />
polymers.'' Biophys J. 2002 Aug;83(2):1217-30.</div>FRhttp://2009.igem.org/Team:TorontoMaRSDiscovery/ModelingTeam:TorontoMaRSDiscovery/Modeling2009-10-21T07:34:40Z<p>FR: /* Assembly of Encapsulin Microcompartments */</p>
<hr />
<div>[[image:To_igem_wiki_banner.jpg|965px]]<br />
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!align="center"|[[Team:TorontoMaRSDiscovery/Parts|BioBricks]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Modeling|Modeling]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Bioinformatics|Bioinformatics]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Safety|Safety]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Notebook|Notebook]]<br />
|}<br />
<br><br />
<br />
<br />
=Summary=<br />
<br />
A kinetic model of our system has been constructed. Approximate parameter values were gathered from online resources to represent all processes up to the production of the eCFP and Encapsulin proteins. Current simulations predict the production of these two proteins at various initial concentrations of IPTG and aTc effector molecules. Furthermore, we have outlined approaches for the detailed modelling of the eCFP degredation/maturation and Encapsulin assembly pathways.<br />
<br />
<br />
The initial simulations will be used to identify the critical concentration of Encapsulin mononomer required for microcompartment assembly. Subsequently, a detailed model of Encapsulin assembly will be integrated into the current model, and its parameters filled-in using parameter-scanning methods and experiments outlined in the relevant references. By comparing experimental measures of microcompartment formation with that predicted by the kinetic model, we aim to gain insight on the mechanisms of Encapsulin assembly.<br />
<br />
=Model=<br />
Our model is based on the following design (See Project Page for a full description of this system).<br />
[[image:BioBrick.png|thumb|centre|The Encapsulator]]<br />
<br />
The reaction framework was mainly generated using the [http://synbioss.sourceforge.net/ SynBioSS Designer (a really useful modeling tool for iGEM teams)], which also provides default parameter values. These parameter values have been gathered from various literature [http://neptune.cems.umn.edu/designer/designer_defaults.pdf sources], and should be taken as approximations. All units were taken to be (1 / molarity^n-1 * s), where n is the order of the reaction. For example, for the reaction 2 lacI --> lacI2, n = 2, thus the rate constant has the units 1/molarity*s. <br />
<br />
The pathways for the expressed proteins, eCFPt and Encapsulin, need to be modeled in more detail. For example, in this basic model eCFPt is degraded via a first order reaction and Encapsulin makes a dimer complex. However, in reality fluorescent proteins have been shown to degreade via Micheales-menton kinetics and Encapsulin is thought to make a complex of about 60 monomers. These issues will be addressed in future work.<br />
<br />
The reactions can be accessed here:<br />
<br />
[[Model (open new page)]]<br />
<br />
[[Media:Uft_mod_Rxns2.xls|Model (download Excel file)]]<br />
<br />
=Simulations=<br />
<br />
All simulations were carried out using the [https://2009.igem.org/Partner_Offers SimBiology Matlab Toolbox], which was freely available to iGEM teams. <br />
<br />
===Accumulation of eCFP at Different Initial Concentrations of IPTG===<br />
<br />
[[Image:uft_mod_cfp-iptg.png | 900px]]<br />
<br />
The IPTG effector eventually loses effect, and the eCFP concentration approaches a maximum. This happens because the IPTG proteins eventually ''tie up'' all available LacI4 proteins, leaving the transcription and translation of eCFP to operate at its maxiumum rate. <br />
<br />
===Accumulation of Encapsulin monomer at Different Initial Concentrations of aTc===<br />
<br />
[[Image:uft_mod_enc-atc.png | 900px]]<br />
<br />
(NOTE: in order to observe Encapsulin monomer levels, the above simulations were carried out without any Encapsulin assembly reactions in place)<br />
<br />
The production of Encapsulin occurs at a slower rate than eCFP because the BBa_R0040 promoter has two tetR binding sites, resulting in more repression and more off-pathway scenarios. Thus, the Encapsulin concentration also seems assymptotic but at higher concentrations of aTc (relative to IPTG). <br />
<br />
It seems beneficial to have the Encapsulin protein under control of the BBa_R0040-tetR-aTc construct because at zero levels of aTc we can have essentially zero levels of Encapsulin (whereas even at zero levels of IPTG, there is still significantly more eCFP). This will enable us to probe extremely low concentrations of Encapsulin monomer when testing for optimal Encapsulin assembly conditions. The disadvantage is that if Encapsulin assembly requires a very high initial concentration of Encapsulin monomer, we would have to wait a long time to see microcompartments. If this later scenario is observed, it may be better to switch the eCFP and Encapsulin expression systems.<br />
<br />
===Sensitivity Analysis===<br />
<br />
Since all of our parameters are approximations from literature sources, those which have the greatest affect on system dynamics (ie. the most ''sensitive'' parameters) would be leading candidates to be experimentally determined. Currently we are interested in which parameters have the greatest effect on the production of eCFP and Encapsulin. Ideally, it would be best to experimentally determine these to "tighten-up" the model before incorporating the largely unexplored Encapsulin assembly pathways. <br />
<br />
<br />
'''1) Sensitivity of eCFP Production'''<br />
<br />
[[Image:uft_mod_SAecfp.png | centre | 900px]]<br />
<br />
<br />
<br />
'''2) Sensitivity of Encapsulin Production'''<br />
<br />
[[Image:uft_mod_SAenc.png | centre | 900px]]<br />
<br />
Parameters 1 and 2 correspond to the rates of constitutive expression of the lacI and tetR repressors respectively. Thus, it can be seen that eCFP and Encapsulin production is largely sensitive to the expression rates of lacI and tetR. <br />
<br />
The specific constitutive promoter used in our construct is BBa_J23100. In our model, this was given the generic rate of 1E-10 molarity\s by SynBioSS based on a variety of empirically-fitted protein expression rates found in literature. This generic approach to assigning parameter values is a suitable fist-step, but our sensitivity results suggest that experimentally determining the expression rate of our specific constitutive promoter should significantly improve our model's predictive capability.<br />
<br />
=Future Work=<br />
<br />
Improvements to the basic model presented above can be separated into three areas; 1) performing experiments to determine parameter values that are specific to our system, 2) more detailed modeling of eCFPt behavior, 3) more detailed modeling of Encapsulin assembly. <br />
<br />
The experiments required to determine general transcription and translation parameters need to be further researched, so this will be skipped over for now. Here we will discuss the more interesting areas – the detailed modeling of eCFP and Encapsulin pathways. This will be accomplished by incorporating previous modeling efforts that are applicable to the eCFP and Encapsulin proteins. <br />
<br />
===Degredation of eCFP===<br />
<br />
The expression and degradation of [http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=95514&blobtype=pdf Green Fluorescent Protein (GFP) was modeled previously]. This paper noted that GFP must mature before going into fluorescent phase, and GFP degradation was shown to follow M-M kinetics, as depicted below. This paper also outlined how the degradation parameters could be derived for any expression system using only simple fluorescence and optical density measurements.<br />
<br />
[[Image:uft_mod_ecfp1.png | centre | thumb | Degredation and maturation pathways for eCFP. (Leveau and Lindow 2001)]]<br />
<br />
<br />
The GFP maturation and degradation parameters found in this paper were:<br />
<br />
<html><br />
<centre><br />
<table><br />
<tr><td> m = 0.0004279 1/s </td></tr><br />
<tr><td> Vmax = 2E-10 molality/s </td></tr><br />
<tr><td> Km = 9E-13 molality/s </td></tr><br />
<tr><td> </td></tr><br />
</table><br />
</centre><br />
</html><br />
<br />
<br />
Assuming eCFPt would behave similarly to eGFP, the following additional reactions would be included in the model:<br />
<br />
<html><br />
<table><br />
<tr> <td><b> Maturation </b></td> <td> </td> </tr><br />
<tr> <td> eCFPt --> F_eCFPT </td> <td> 0.0004279 </td> </tr><br />
<tr> <td> Enc2:eCFPt --> Enc2:F_eCFPt </td> <td> 0.0004279 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Encapsulation </b></td> <td> </td> </tr><br />
<tr> <td> Enc2 + F_eCFPt --> Enc2:F_eCFPt </td> <td> 100 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Degradation </b></td> <td> </td> </tr><br />
<tr> <td> eCFPt --> </td> <td> Vmax = 2E-10 </td> </tr><br />
<tr> <td> </td> <td> Km = 9E-13 </td> </tr><br />
<tr> <td> F_eCFPt --> </td> <td> Vmax = 2E-10 </td> </tr><br />
<tr> <td> </td> <td> Km = 9E-13 </td> </tr><br />
</table><br />
</html><br />
<br />
===Assembly of Encapsulin Microcompartments===<br />
<br />
Though Encapsulin microcompartment assembly is not well-studied, it has been theorized to resemble the assembly of viral capsids. Thus, we could look to this relatively well-studied phenomenon as a representation of Encapsulin microcompartment assembly.<br />
<br />
Adam Zlotnick has published models of viral capsid assembly using different approaches. An early paper described an equilibrium model of assembly for a 12 Unit polyhedral capsid head, and a more recent paper used a kinetic model that could be applied to many examples of spherical polymerization. We will consider how each approach could be incorporated as a representation of Encapsulin assembly.<br />
<br />
<br />
'''1) Equilibrim Approach to Encapsulin Assembly'''<br />
<br />
Zlotnick's [[Media:Uft_mod_to_build_a_virus_capsid.pdf|Equilibrium-based model]] consists of reactions from an initial monomer subunit leading to a final capsid product. The sequential reactions take into account DeltaG for contact (Kn'), and parameters describing path degeneracy (varies for different intermediates).<br />
[[image:uft_mod_encap1.png|centre|thumb|Kn for assembly subunits based on path degeneracy. (Zlotnick 1994)]]<br />
<br />
<br />
'''2) Kinetic Model of Spherical Polymerization'''<br />
<br />
A [http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1302223/pdf/12124301.pdf general kinetic model for the spherical polyermization] process is shown below. In our case, the initial monomer subunit concentration (''u'') would represent our expressed Encapsulin BioBrick, and the number of monomers in the final assembly (''N'') is thought to be 60. All of the included parameters can be calculated from the four basic parameters; the microscopic, per-contact equilibrium constant (KAcon), the nucleus size (nuc), the nucleation on-rate (f_nuc), and the elongation on-rate (f_elong). The referenced paper describes methods to aquire these parameters from kinetic experiments, and provides examples for N = 12 and 30 unit viral capsid assemblies.<br />
[[image:uft_mod_encap2.png| centre | thumb |System of ODEs to represent spherical polymerization, where ''u'' is the initial subunit concentration, ''m'' is the "mth" intermediate species, and ''N'' is the number of monomers in the final assembly. (Endres and Zlotnick 2002)]]<br />
<br />
<br />
<br />
Zlotnick's models also describe two important features of spherical polymerization that we should also expect to observe in Encapsulin assembly: kinetic trapping and nucleation. A kinetic trap occurs when the initial monomer subunit concentration or the deltaG of the first assembly reaction is too high. This results in over-initiation of assembly and quickly the reactions become starved for subunits. Kinetic trapping is prevented by the inclusion of nucleation, where the initial reactions occur at a slower rate because the first few intermediates in a series of reactions are less stable than downstream products. Essentially, nucleation serves as a “slow first step” that regulates the assembly pathway. <br />
<br />
It will be interesting to note how the translational dynamics of Encapsulin interplay with its assembly dynamics. Since our system does not start with any initial concentration of Encapsulin, there will be an optimum rate of production that essentially serves the role of nucleation – avoiding kinetic traps while still maintaining a maximum production of full Encapsulin assemblies.<br />
<br />
=References=<br />
<br />
1. Hill AD, Tomshine JR, Weeding EM, Sotiropoulos V, Kaznessis YN. ''SynBioSS: the synthetic biology modeling suite.'' Bioinformatics. 2008 Nov 1;24(21):2551-3. Epub 2008 Aug 30.<br />
[http://neptune.cems.umn.edu/designer/interface1.php SynBioSS Web Designer]<br />
<br />
2. Leveau JH, Lindow SE. ''Predictive and interpretive simulation of green fluorescent protein expression in<br />
reporter bacteria.'' J Bacteriol. 2001 Dec;183(23):6752-62.<br />
<br />
3. Endres D, Zlotnick A. ''Model-based analysis of assembly kinetics for virus capsids or other spherical<br />
polymers.'' Biophys J. 2002 Aug;83(2):1217-30.</div>FRhttp://2009.igem.org/Team:TorontoMaRSDiscovery/ModelingTeam:TorontoMaRSDiscovery/Modeling2009-10-21T07:31:32Z<p>FR: /* Future Work */</p>
<hr />
<div>[[image:To_igem_wiki_banner.jpg|965px]]<br />
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!align="center"|[[Team:TorontoMaRSDiscovery|Home]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Team|The Team]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Project|The Project]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Parts|BioBricks]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Modeling|Modeling]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Bioinformatics|Bioinformatics]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Safety|Safety]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Notebook|Notebook]]<br />
|}<br />
<br><br />
<br />
<br />
=Summary=<br />
<br />
A kinetic model of our system has been constructed. Approximate parameter values were gathered from online resources to represent all processes up to the production of the eCFP and Encapsulin proteins. Current simulations predict the production of these two proteins at various initial concentrations of IPTG and aTc effector molecules. Furthermore, we have outlined approaches for the detailed modelling of the eCFP degredation/maturation and Encapsulin assembly pathways.<br />
<br />
<br />
The initial simulations will be used to identify the critical concentration of Encapsulin mononomer required for microcompartment assembly. Subsequently, a detailed model of Encapsulin assembly will be integrated into the current model, and its parameters filled-in using parameter-scanning methods and experiments outlined in the relevant references. By comparing experimental measures of microcompartment formation with that predicted by the kinetic model, we aim to gain insight on the mechanisms of Encapsulin assembly.<br />
<br />
=Model=<br />
Our model is based on the following design (See Project Page for a full description of this system).<br />
[[image:BioBrick.png|thumb|centre|The Encapsulator]]<br />
<br />
The reaction framework was mainly generated using the [http://synbioss.sourceforge.net/ SynBioSS Designer (a really useful modeling tool for iGEM teams)], which also provides default parameter values. These parameter values have been gathered from various literature [http://neptune.cems.umn.edu/designer/designer_defaults.pdf sources], and should be taken as approximations. All units were taken to be (1 / molarity^n-1 * s), where n is the order of the reaction. For example, for the reaction 2 lacI --> lacI2, n = 2, thus the rate constant has the units 1/molarity*s. <br />
<br />
The pathways for the expressed proteins, eCFPt and Encapsulin, need to be modeled in more detail. For example, in this basic model eCFPt is degraded via a first order reaction and Encapsulin makes a dimer complex. However, in reality fluorescent proteins have been shown to degreade via Micheales-menton kinetics and Encapsulin is thought to make a complex of about 60 monomers. These issues will be addressed in future work.<br />
<br />
The reactions can be accessed here:<br />
<br />
[[Model (open new page)]]<br />
<br />
[[Media:Uft_mod_Rxns2.xls|Model (download Excel file)]]<br />
<br />
=Simulations=<br />
<br />
All simulations were carried out using the [https://2009.igem.org/Partner_Offers SimBiology Matlab Toolbox], which was freely available to iGEM teams. <br />
<br />
===Accumulation of eCFP at Different Initial Concentrations of IPTG===<br />
<br />
[[Image:uft_mod_cfp-iptg.png | 900px]]<br />
<br />
The IPTG effector eventually loses effect, and the eCFP concentration approaches a maximum. This happens because the IPTG proteins eventually ''tie up'' all available LacI4 proteins, leaving the transcription and translation of eCFP to operate at its maxiumum rate. <br />
<br />
===Accumulation of Encapsulin monomer at Different Initial Concentrations of aTc===<br />
<br />
[[Image:uft_mod_enc-atc.png | 900px]]<br />
<br />
(NOTE: in order to observe Encapsulin monomer levels, the above simulations were carried out without any Encapsulin assembly reactions in place)<br />
<br />
The production of Encapsulin occurs at a slower rate than eCFP because the BBa_R0040 promoter has two tetR binding sites, resulting in more repression and more off-pathway scenarios. Thus, the Encapsulin concentration also seems assymptotic but at higher concentrations of aTc (relative to IPTG). <br />
<br />
It seems beneficial to have the Encapsulin protein under control of the BBa_R0040-tetR-aTc construct because at zero levels of aTc we can have essentially zero levels of Encapsulin (whereas even at zero levels of IPTG, there is still significantly more eCFP). This will enable us to probe extremely low concentrations of Encapsulin monomer when testing for optimal Encapsulin assembly conditions. The disadvantage is that if Encapsulin assembly requires a very high initial concentration of Encapsulin monomer, we would have to wait a long time to see microcompartments. If this later scenario is observed, it may be better to switch the eCFP and Encapsulin expression systems.<br />
<br />
===Sensitivity Analysis===<br />
<br />
Since all of our parameters are approximations from literature sources, those which have the greatest affect on system dynamics (ie. the most ''sensitive'' parameters) would be leading candidates to be experimentally determined. Currently we are interested in which parameters have the greatest effect on the production of eCFP and Encapsulin. Ideally, it would be best to experimentally determine these to "tighten-up" the model before incorporating the largely unexplored Encapsulin assembly pathways. <br />
<br />
<br />
'''1) Sensitivity of eCFP Production'''<br />
<br />
[[Image:uft_mod_SAecfp.png | centre | 900px]]<br />
<br />
<br />
<br />
'''2) Sensitivity of Encapsulin Production'''<br />
<br />
[[Image:uft_mod_SAenc.png | centre | 900px]]<br />
<br />
Parameters 1 and 2 correspond to the rates of constitutive expression of the lacI and tetR repressors respectively. Thus, it can be seen that eCFP and Encapsulin production is largely sensitive to the expression rates of lacI and tetR. <br />
<br />
The specific constitutive promoter used in our construct is BBa_J23100. In our model, this was given the generic rate of 1E-10 molarity\s by SynBioSS based on a variety of empirically-fitted protein expression rates found in literature. This generic approach to assigning parameter values is a suitable fist-step, but our sensitivity results suggest that experimentally determining the expression rate of our specific constitutive promoter should significantly improve our model's predictive capability.<br />
<br />
=Future Work=<br />
<br />
Improvements to the basic model presented above can be separated into three areas; 1) performing experiments to determine parameter values that are specific to our system, 2) more detailed modeling of eCFPt behavior, 3) more detailed modeling of Encapsulin assembly. <br />
<br />
The experiments required to determine general transcription and translation parameters need to be further researched, so this will be skipped over for now. Here we will discuss the more interesting areas – the detailed modeling of eCFP and Encapsulin pathways. This will be accomplished by incorporating previous modeling efforts that are applicable to the eCFP and Encapsulin proteins. <br />
<br />
===Degredation of eCFP===<br />
<br />
The expression and degradation of [http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=95514&blobtype=pdf Green Fluorescent Protein (GFP) was modeled previously]. This paper noted that GFP must mature before going into fluorescent phase, and GFP degradation was shown to follow M-M kinetics, as depicted below. This paper also outlined how the degradation parameters could be derived for any expression system using only simple fluorescence and optical density measurements.<br />
<br />
[[Image:uft_mod_ecfp1.png | centre | thumb | Degredation and maturation pathways for eCFP. (Leveau and Lindow 2001)]]<br />
<br />
<br />
The GFP maturation and degradation parameters found in this paper were:<br />
<br />
<html><br />
<centre><br />
<table><br />
<tr><td> m = 0.0004279 1/s </td></tr><br />
<tr><td> Vmax = 2E-10 molality/s </td></tr><br />
<tr><td> Km = 9E-13 molality/s </td></tr><br />
<tr><td> </td></tr><br />
</table><br />
</centre><br />
</html><br />
<br />
<br />
Assuming eCFPt would behave similarly to eGFP, the following additional reactions would be included in the model:<br />
<br />
<html><br />
<table><br />
<tr> <td><b> Maturation </b></td> <td> </td> </tr><br />
<tr> <td> eCFPt --> F_eCFPT </td> <td> 0.0004279 </td> </tr><br />
<tr> <td> Enc2:eCFPt --> Enc2:F_eCFPt </td> <td> 0.0004279 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Encapsulation </b></td> <td> </td> </tr><br />
<tr> <td> Enc2 + F_eCFPt --> Enc2:F_eCFPt </td> <td> 100 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Degradation </b></td> <td> </td> </tr><br />
<tr> <td> eCFPt --> </td> <td> Vmax = 2E-10 </td> </tr><br />
<tr> <td> </td> <td> Km = 9E-13 </td> </tr><br />
<tr> <td> F_eCFPt --> </td> <td> Vmax = 2E-10 </td> </tr><br />
<tr> <td> </td> <td> Km = 9E-13 </td> </tr><br />
</table><br />
</html><br />
<br />
===Assembly of Encapsulin Microcompartments===<br />
<br />
Though Encapsulin microcompartment assembly is not well-studied, it has been theorized to resemble the assembly of viral capsids. Thus, we could look to this relatively well-studied phenomenon as a representation of Encapsulin microcompartment assembly.<br />
<br />
Adam Zlotnick has published models of viral capsid assembly using different approaches. An early paper described an equilibrium model of assembly for a 12 Unit polyhedral capsid head, and a more recent paper used a kinetic model that could be applied to many examples of spherical polymerization. We will consider how each approach could be incorporated as a representation of Encapsulin assembly.<br />
<br />
'''1) Equilibrim Approach to Encapsulin Assembly'''<br />
<br />
Zlotnick's [[Media:Uft_mod_to_build_a_virus_capsid.pdf|Equilibrium-based model]] consists of reactions from an initial monomer subunit leading to a final capsid product. The sequential reactions take into account DeltaG for contact (Kn'), and parameters describing path degeneracy (varies for different intermediates).<br />
[[image:uft_mod_encap1.png|centre|thumb|Kn for assembly subunits based on path degeneracy. (Zlotnick 1994)]]<br />
<br />
Simulations from a preliminary incorporation of this approach are shown below. In this version of our basic model, Encapsulin assembles in a series of first order reactions. However, for simplicity, the rate constants are kept identical and do not take path degeneracy into account.<br />
<br />
<html><br />
<table><br />
<tr> <td><b> Encapsulin Assembly </b></td> <td> </td> </tr><br />
<tr> <td> 2 Enc --> Enc2 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 Enc2 --> Enc4 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 En4 --> Enc8 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 Enc8 --> Enc16 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 Enc16 --> Enc32 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 Enc16 --> Enc64 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td><b> Encapsulation </b></td> <td> </td> </tr><br />
<tr> <td> Enc64 + eCFPt --> Enc64:eCFPt </td> <td> 1.00E2 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
</table><br />
</html><br />
<br />
[[Image:uft_mod_enc1.png |frameless|300px]][[Image:uft_mod_enc2.png |frameless|300px]][[Image:uft_mod_enc3.png |frameless|300px]]<br />
<br />
<gallery caption=Equilibrium-based Encapsulin Assembly width=600px height=150px><br />
<center><br />
image:uft_mod_enc1.png<br />
image:uft_mod_enc2.png<br />
image:uft_mod_enc3.png<br />
</center><br />
</gallery><br />
<br />
Encapsulin assembly intermediates are observed to quickly come to a steady state. The last intermediate ''Enc64'' is the most depleted probably because of the formation of ''Enc64:eCFPt'' complex. Formation of ''Enc64:eCFPt'' then mirrors the production of ''eCFPt''. <br />
<br />
<br />
'''2) Kinetic Model of Spherical Polymerization'''<br />
<br />
A [http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1302223/pdf/12124301.pdf general kinetic model for the spherical polyermization] process is shown below. In our case, the initial monomer subunit concentration (''u'') would represent our expressed Encapsulin BioBrick, and the number of monomers in the final assembly (''N'') is thought to be 60. All of the included parameters can be calculated from the four basic parameters; the microscopic, per-contact equilibrium constant (KAcon), the nucleus size (nuc), the nucleation on-rate (f_nuc), and the elongation on-rate (f_elong). The referenced paper describes methods to aquire these parameters from kinetic experiments, and provides examples for N = 12 and 30 unit viral capsid assemblies.<br />
[[image:uft_mod_encap2.png| centre | thumb |System of ODEs to represent spherical polymerization, where ''u'' is the initial subunit concentration, ''m'' is the "mth" intermediate species, and ''N'' is the number of monomers in the final assembly. (Endres and Zlotnick 2002)]]<br />
<br />
<br />
<br />
Zlotnick's models also describe two important features of spherical polymerization that we should also expect to observe in Encapsulin assembly: kinetic trapping and nucleation. A kinetic trap occurs when the initial monomer subunit concentration or the deltaG of the first assembly reaction is too high. This results in over-initiation of assembly and quickly the reactions become starved for subunits. Kinetic trapping is prevented by the inclusion of nucleation, where the initial reactions occur at a slower rate because the first few intermediates in a series of reactions are less stable than downstream products. Essentially, nucleation serves as a “slow first step” that regulates the assembly pathway. <br />
<br />
It will be interesting to note how the translational dynamics of Encapsulin interplay with its assembly dynamics. Since our system does not start with any initial concentration of Encapsulin, there will be an optimum rate of production that essentially serves the role of nucleation – avoiding kinetic traps while still maintaining a maximum production of full Encapsulin assemblies.<br />
<br />
=References=<br />
<br />
1. Hill AD, Tomshine JR, Weeding EM, Sotiropoulos V, Kaznessis YN. ''SynBioSS: the synthetic biology modeling suite.'' Bioinformatics. 2008 Nov 1;24(21):2551-3. Epub 2008 Aug 30.<br />
[http://neptune.cems.umn.edu/designer/interface1.php SynBioSS Web Designer]<br />
<br />
2. Leveau JH, Lindow SE. ''Predictive and interpretive simulation of green fluorescent protein expression in<br />
reporter bacteria.'' J Bacteriol. 2001 Dec;183(23):6752-62.<br />
<br />
3. Endres D, Zlotnick A. ''Model-based analysis of assembly kinetics for virus capsids or other spherical<br />
polymers.'' Biophys J. 2002 Aug;83(2):1217-30.</div>FRhttp://2009.igem.org/Team:TorontoMaRSDiscovery/ModelingTeam:TorontoMaRSDiscovery/Modeling2009-10-21T07:30:18Z<p>FR: /* Sensitivity Analysis */</p>
<hr />
<div>[[image:To_igem_wiki_banner.jpg|965px]]<br />
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|}<br />
<br><br />
<br />
<br />
=Summary=<br />
<br />
A kinetic model of our system has been constructed. Approximate parameter values were gathered from online resources to represent all processes up to the production of the eCFP and Encapsulin proteins. Current simulations predict the production of these two proteins at various initial concentrations of IPTG and aTc effector molecules. Furthermore, we have outlined approaches for the detailed modelling of the eCFP degredation/maturation and Encapsulin assembly pathways.<br />
<br />
<br />
The initial simulations will be used to identify the critical concentration of Encapsulin mononomer required for microcompartment assembly. Subsequently, a detailed model of Encapsulin assembly will be integrated into the current model, and its parameters filled-in using parameter-scanning methods and experiments outlined in the relevant references. By comparing experimental measures of microcompartment formation with that predicted by the kinetic model, we aim to gain insight on the mechanisms of Encapsulin assembly.<br />
<br />
=Model=<br />
Our model is based on the following design (See Project Page for a full description of this system).<br />
[[image:BioBrick.png|thumb|centre|The Encapsulator]]<br />
<br />
The reaction framework was mainly generated using the [http://synbioss.sourceforge.net/ SynBioSS Designer (a really useful modeling tool for iGEM teams)], which also provides default parameter values. These parameter values have been gathered from various literature [http://neptune.cems.umn.edu/designer/designer_defaults.pdf sources], and should be taken as approximations. All units were taken to be (1 / molarity^n-1 * s), where n is the order of the reaction. For example, for the reaction 2 lacI --> lacI2, n = 2, thus the rate constant has the units 1/molarity*s. <br />
<br />
The pathways for the expressed proteins, eCFPt and Encapsulin, need to be modeled in more detail. For example, in this basic model eCFPt is degraded via a first order reaction and Encapsulin makes a dimer complex. However, in reality fluorescent proteins have been shown to degreade via Micheales-menton kinetics and Encapsulin is thought to make a complex of about 60 monomers. These issues will be addressed in future work.<br />
<br />
The reactions can be accessed here:<br />
<br />
[[Model (open new page)]]<br />
<br />
[[Media:Uft_mod_Rxns2.xls|Model (download Excel file)]]<br />
<br />
=Simulations=<br />
<br />
All simulations were carried out using the [https://2009.igem.org/Partner_Offers SimBiology Matlab Toolbox], which was freely available to iGEM teams. <br />
<br />
===Accumulation of eCFP at Different Initial Concentrations of IPTG===<br />
<br />
[[Image:uft_mod_cfp-iptg.png | 900px]]<br />
<br />
The IPTG effector eventually loses effect, and the eCFP concentration approaches a maximum. This happens because the IPTG proteins eventually ''tie up'' all available LacI4 proteins, leaving the transcription and translation of eCFP to operate at its maxiumum rate. <br />
<br />
===Accumulation of Encapsulin monomer at Different Initial Concentrations of aTc===<br />
<br />
[[Image:uft_mod_enc-atc.png | 900px]]<br />
<br />
(NOTE: in order to observe Encapsulin monomer levels, the above simulations were carried out without any Encapsulin assembly reactions in place)<br />
<br />
The production of Encapsulin occurs at a slower rate than eCFP because the BBa_R0040 promoter has two tetR binding sites, resulting in more repression and more off-pathway scenarios. Thus, the Encapsulin concentration also seems assymptotic but at higher concentrations of aTc (relative to IPTG). <br />
<br />
It seems beneficial to have the Encapsulin protein under control of the BBa_R0040-tetR-aTc construct because at zero levels of aTc we can have essentially zero levels of Encapsulin (whereas even at zero levels of IPTG, there is still significantly more eCFP). This will enable us to probe extremely low concentrations of Encapsulin monomer when testing for optimal Encapsulin assembly conditions. The disadvantage is that if Encapsulin assembly requires a very high initial concentration of Encapsulin monomer, we would have to wait a long time to see microcompartments. If this later scenario is observed, it may be better to switch the eCFP and Encapsulin expression systems.<br />
<br />
===Sensitivity Analysis===<br />
<br />
Since all of our parameters are approximations from literature sources, those which have the greatest affect on system dynamics (ie. the most ''sensitive'' parameters) would be leading candidates to be experimentally determined. Currently we are interested in which parameters have the greatest effect on the production of eCFP and Encapsulin. Ideally, it would be best to experimentally determine these to "tighten-up" the model before incorporating the largely unexplored Encapsulin assembly pathways. <br />
<br />
<br />
'''1) Sensitivity of eCFP Production'''<br />
<br />
[[Image:uft_mod_SAecfp.png | centre | 900px]]<br />
<br />
<br />
<br />
'''2) Sensitivity of Encapsulin Production'''<br />
<br />
[[Image:uft_mod_SAenc.png | centre | 900px]]<br />
<br />
Parameters 1 and 2 correspond to the rates of constitutive expression of the lacI and tetR repressors respectively. Thus, it can be seen that eCFP and Encapsulin production is largely sensitive to the expression rates of lacI and tetR. <br />
<br />
The specific constitutive promoter used in our construct is BBa_J23100. In our model, this was given the generic rate of 1E-10 molarity\s by SynBioSS based on a variety of empirically-fitted protein expression rates found in literature. This generic approach to assigning parameter values is a suitable fist-step, but our sensitivity results suggest that experimentally determining the expression rate of our specific constitutive promoter should significantly improve our model's predictive capability.<br />
<br />
=Future Work=<br />
<br />
Improvements to the basic model presented above can be separated into three areas; 1) performing experiments to determine parameter values that are specific to our system, 2) more detailed modeling of eCFPt behavior, 3) more detailed modeling of Encapsulin assembly. <br />
<br />
The experiments required to determine general transcription and translation parameters need to be further researched, so this will be skipped over for now (the proposed sensitivity analysis of the model parameters will also identify which experiments are critical). Here we will discuss the more interesting areas – the detailed modeling of eCFP and Encapsulin pathways. This will be accomplished by incorporating previous modeling efforts that are applicable to the eCFP and Encapsulin proteins. <br />
<br />
===Degredation of eCFP===<br />
<br />
The expression and degradation of [http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=95514&blobtype=pdf Green Fluorescent Protein (GFP) was modeled previously]. This paper noted that GFP must mature before going into fluorescent phase, and GFP degradation was shown to follow M-M kinetics, as depicted below. This paper also outlined how the degradation parameters could be derived for any expression system using only simple fluorescence and optical density measurements.<br />
<br />
[[Image:uft_mod_ecfp1.png | centre | thumb | Degredation and maturation pathways for eCFP. (Leveau and Lindow 2001)]]<br />
<br />
<br />
The GFP maturation and degradation parameters found in this paper were:<br />
<br />
<html><br />
<centre><br />
<table><br />
<tr><td> m = 0.0004279 1/s </td></tr><br />
<tr><td> Vmax = 2E-10 molality/s </td></tr><br />
<tr><td> Km = 9E-13 molality/s </td></tr><br />
<tr><td> </td></tr><br />
</table><br />
</centre><br />
</html><br />
<br />
<br />
Assuming eCFPt would behave similarly to eGFP, the following additional reactions would be included in the model:<br />
<br />
<html><br />
<table><br />
<tr> <td><b> Maturation </b></td> <td> </td> </tr><br />
<tr> <td> eCFPt --> F_eCFPT </td> <td> 0.0004279 </td> </tr><br />
<tr> <td> Enc2:eCFPt --> Enc2:F_eCFPt </td> <td> 0.0004279 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Encapsulation </b></td> <td> </td> </tr><br />
<tr> <td> Enc2 + F_eCFPt --> Enc2:F_eCFPt </td> <td> 100 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Degradation </b></td> <td> </td> </tr><br />
<tr> <td> eCFPt --> </td> <td> Vmax = 2E-10 </td> </tr><br />
<tr> <td> </td> <td> Km = 9E-13 </td> </tr><br />
<tr> <td> F_eCFPt --> </td> <td> Vmax = 2E-10 </td> </tr><br />
<tr> <td> </td> <td> Km = 9E-13 </td> </tr><br />
</table><br />
</html><br />
<br />
===Assembly of Encapsulin Microcompartments===<br />
<br />
Though Encapsulin microcompartment assembly is not well-studied, it has been theorized to resemble the assembly of viral capsids. Thus, we could look to this relatively well-studied phenomenon as a representation of Encapsulin microcompartment assembly.<br />
<br />
Adam Zlotnick has published models of viral capsid assembly using different approaches. An early paper described an equilibrium model of assembly for a 12 Unit polyhedral capsid head, and a more recent paper used a kinetic model that could be applied to many examples of spherical polymerization. We will consider how each approach could be incorporated as a representation of Encapsulin assembly.<br />
<br />
'''1) Equilibrim Approach to Encapsulin Assembly'''<br />
<br />
Zlotnick's [[Media:Uft_mod_to_build_a_virus_capsid.pdf|Equilibrium-based model]] consists of reactions from an initial monomer subunit leading to a final capsid product. The sequential reactions take into account DeltaG for contact (Kn'), and parameters describing path degeneracy (varies for different intermediates).<br />
[[image:uft_mod_encap1.png|centre|thumb|Kn for assembly subunits based on path degeneracy. (Zlotnick 1994)]]<br />
<br />
Simulations from a preliminary incorporation of this approach are shown below. In this version of our basic model, Encapsulin assembles in a series of first order reactions. However, for simplicity, the rate constants are kept identical and do not take path degeneracy into account.<br />
<br />
<html><br />
<table><br />
<tr> <td><b> Encapsulin Assembly </b></td> <td> </td> </tr><br />
<tr> <td> 2 Enc --> Enc2 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 Enc2 --> Enc4 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 En4 --> Enc8 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 Enc8 --> Enc16 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 Enc16 --> Enc32 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 Enc16 --> Enc64 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td><b> Encapsulation </b></td> <td> </td> </tr><br />
<tr> <td> Enc64 + eCFPt --> Enc64:eCFPt </td> <td> 1.00E2 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
</table><br />
</html><br />
<br />
[[Image:uft_mod_enc1.png |frameless|300px]][[Image:uft_mod_enc2.png |frameless|300px]][[Image:uft_mod_enc3.png |frameless|300px]]<br />
<br />
<gallery caption=Equilibrium-based Encapsulin Assembly width=600px height=150px><br />
<center><br />
image:uft_mod_enc1.png<br />
image:uft_mod_enc2.png<br />
image:uft_mod_enc3.png<br />
</center><br />
</gallery><br />
<br />
Encapsulin assembly intermediates are observed to quickly come to a steady state. The last intermediate ''Enc64'' is the most depleted probably because of the formation of ''Enc64:eCFPt'' complex. Formation of ''Enc64:eCFPt'' then mirrors the production of ''eCFPt''. <br />
<br />
<br />
'''2) Kinetic Model of Spherical Polymerization'''<br />
<br />
A [http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1302223/pdf/12124301.pdf general kinetic model for the spherical polyermization] process is shown below. In our case, the initial monomer subunit concentration (''u'') would represent our expressed Encapsulin BioBrick, and the number of monomers in the final assembly (''N'') is thought to be 60. All of the included parameters can be calculated from the four basic parameters; the microscopic, per-contact equilibrium constant (KAcon), the nucleus size (nuc), the nucleation on-rate (f_nuc), and the elongation on-rate (f_elong). The referenced paper describes methods to aquire these parameters from kinetic experiments, and provides examples for N = 12 and 30 unit viral capsid assemblies.<br />
[[image:uft_mod_encap2.png| centre | thumb |System of ODEs to represent spherical polymerization, where ''u'' is the initial subunit concentration, ''m'' is the "mth" intermediate species, and ''N'' is the number of monomers in the final assembly. (Endres and Zlotnick 2002)]]<br />
<br />
<br />
<br />
Zlotnick's models also describe two important features of spherical polymerization that we should also expect to observe in Encapsulin assembly: kinetic trapping and nucleation. A kinetic trap occurs when the initial monomer subunit concentration or the deltaG of the first assembly reaction is too high. This results in over-initiation of assembly and quickly the reactions become starved for subunits. Kinetic trapping is prevented by the inclusion of nucleation, where the initial reactions occur at a slower rate because the first few intermediates in a series of reactions are less stable than downstream products. Essentially, nucleation serves as a “slow first step” that regulates the assembly pathway. <br />
<br />
It will be interesting to note how the translational dynamics of Encapsulin interplay with its assembly dynamics. Since our system does not start with any initial concentration of Encapsulin, there will be an optimum rate of production that essentially serves the role of nucleation – avoiding kinetic traps while still maintaining a maximum production of full Encapsulin assemblies.<br />
<br />
=References=<br />
<br />
1. Hill AD, Tomshine JR, Weeding EM, Sotiropoulos V, Kaznessis YN. ''SynBioSS: the synthetic biology modeling suite.'' Bioinformatics. 2008 Nov 1;24(21):2551-3. Epub 2008 Aug 30.<br />
[http://neptune.cems.umn.edu/designer/interface1.php SynBioSS Web Designer]<br />
<br />
2. Leveau JH, Lindow SE. ''Predictive and interpretive simulation of green fluorescent protein expression in<br />
reporter bacteria.'' J Bacteriol. 2001 Dec;183(23):6752-62.<br />
<br />
3. Endres D, Zlotnick A. ''Model-based analysis of assembly kinetics for virus capsids or other spherical<br />
polymers.'' Biophys J. 2002 Aug;83(2):1217-30.</div>FRhttp://2009.igem.org/Team:TorontoMaRSDiscovery/ModelingTeam:TorontoMaRSDiscovery/Modeling2009-10-21T07:29:22Z<p>FR: /* Sensitivity Analysis */</p>
<hr />
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|}<br />
<br><br />
<br />
<br />
=Summary=<br />
<br />
A kinetic model of our system has been constructed. Approximate parameter values were gathered from online resources to represent all processes up to the production of the eCFP and Encapsulin proteins. Current simulations predict the production of these two proteins at various initial concentrations of IPTG and aTc effector molecules. Furthermore, we have outlined approaches for the detailed modelling of the eCFP degredation/maturation and Encapsulin assembly pathways.<br />
<br />
<br />
The initial simulations will be used to identify the critical concentration of Encapsulin mononomer required for microcompartment assembly. Subsequently, a detailed model of Encapsulin assembly will be integrated into the current model, and its parameters filled-in using parameter-scanning methods and experiments outlined in the relevant references. By comparing experimental measures of microcompartment formation with that predicted by the kinetic model, we aim to gain insight on the mechanisms of Encapsulin assembly.<br />
<br />
=Model=<br />
Our model is based on the following design (See Project Page for a full description of this system).<br />
[[image:BioBrick.png|thumb|centre|The Encapsulator]]<br />
<br />
The reaction framework was mainly generated using the [http://synbioss.sourceforge.net/ SynBioSS Designer (a really useful modeling tool for iGEM teams)], which also provides default parameter values. These parameter values have been gathered from various literature [http://neptune.cems.umn.edu/designer/designer_defaults.pdf sources], and should be taken as approximations. All units were taken to be (1 / molarity^n-1 * s), where n is the order of the reaction. For example, for the reaction 2 lacI --> lacI2, n = 2, thus the rate constant has the units 1/molarity*s. <br />
<br />
The pathways for the expressed proteins, eCFPt and Encapsulin, need to be modeled in more detail. For example, in this basic model eCFPt is degraded via a first order reaction and Encapsulin makes a dimer complex. However, in reality fluorescent proteins have been shown to degreade via Micheales-menton kinetics and Encapsulin is thought to make a complex of about 60 monomers. These issues will be addressed in future work.<br />
<br />
The reactions can be accessed here:<br />
<br />
[[Model (open new page)]]<br />
<br />
[[Media:Uft_mod_Rxns2.xls|Model (download Excel file)]]<br />
<br />
=Simulations=<br />
<br />
All simulations were carried out using the [https://2009.igem.org/Partner_Offers SimBiology Matlab Toolbox], which was freely available to iGEM teams. <br />
<br />
===Accumulation of eCFP at Different Initial Concentrations of IPTG===<br />
<br />
[[Image:uft_mod_cfp-iptg.png | 900px]]<br />
<br />
The IPTG effector eventually loses effect, and the eCFP concentration approaches a maximum. This happens because the IPTG proteins eventually ''tie up'' all available LacI4 proteins, leaving the transcription and translation of eCFP to operate at its maxiumum rate. <br />
<br />
===Accumulation of Encapsulin monomer at Different Initial Concentrations of aTc===<br />
<br />
[[Image:uft_mod_enc-atc.png | 900px]]<br />
<br />
(NOTE: in order to observe Encapsulin monomer levels, the above simulations were carried out without any Encapsulin assembly reactions in place)<br />
<br />
The production of Encapsulin occurs at a slower rate than eCFP because the BBa_R0040 promoter has two tetR binding sites, resulting in more repression and more off-pathway scenarios. Thus, the Encapsulin concentration also seems assymptotic but at higher concentrations of aTc (relative to IPTG). <br />
<br />
It seems beneficial to have the Encapsulin protein under control of the BBa_R0040-tetR-aTc construct because at zero levels of aTc we can have essentially zero levels of Encapsulin (whereas even at zero levels of IPTG, there is still significantly more eCFP). This will enable us to probe extremely low concentrations of Encapsulin monomer when testing for optimal Encapsulin assembly conditions. The disadvantage is that if Encapsulin assembly requires a very high initial concentration of Encapsulin monomer, we would have to wait a long time to see microcompartments. If this later scenario is observed, it may be better to switch the eCFP and Encapsulin expression systems.<br />
<br />
===Sensitivity Analysis===<br />
<br />
Since all of our parameters are approximations from literature sources, those which have the greatest affect on system dynamics (ie. the most ''sensitive'' parameters) would be leading candidates to be experimentally determined. Currently we are interested in which parameters have the greatest effect on the production of eCFP and Encapsulin. Ideally, it would be best to experimentally determine these to "tighten-up" the model before incorporating the largely unexplored Encapsulin assembly pathways. <br />
<br />
<br />
'''1) Sensitivity of eCFP Production'''<br />
<br />
[[Image:uft_mod_SAecfp.png | centre | 900px]]<br />
<br />
<br />
<br />
'''2) Sensitivity of Encapsulin Production'''<br />
<br />
[[Image:uft_mod_SAenc.png | centre | 900px]]<br />
<br />
Parameters 1 and 2 correspond to the rates of constitutive expression of the lacI and tetR repressors respectively. Thus, it can be seen that eCFP and Encapsulin production is largely sensitive to the expression rates of lacI and tetR. <br />
<br />
The specific constitutive promoter used in our construct is BBa_J23100. In our model, this was given the generic rate of 1E-10 molarity\s by SynBioSS based on a variety of empirically-fitted protein expression rates found in literature. This generic approach to assigning parameter values is a suitable fist-step, but our sensitivity results suggest that experimentally determining the expression rate of our specific constitutive promoter should significantly improve our model's predictive capacity.<br />
<br />
=Future Work=<br />
<br />
Improvements to the basic model presented above can be separated into three areas; 1) performing experiments to determine parameter values that are specific to our system, 2) more detailed modeling of eCFPt behavior, 3) more detailed modeling of Encapsulin assembly. <br />
<br />
The experiments required to determine general transcription and translation parameters need to be further researched, so this will be skipped over for now (the proposed sensitivity analysis of the model parameters will also identify which experiments are critical). Here we will discuss the more interesting areas – the detailed modeling of eCFP and Encapsulin pathways. This will be accomplished by incorporating previous modeling efforts that are applicable to the eCFP and Encapsulin proteins. <br />
<br />
===Degredation of eCFP===<br />
<br />
The expression and degradation of [http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=95514&blobtype=pdf Green Fluorescent Protein (GFP) was modeled previously]. This paper noted that GFP must mature before going into fluorescent phase, and GFP degradation was shown to follow M-M kinetics, as depicted below. This paper also outlined how the degradation parameters could be derived for any expression system using only simple fluorescence and optical density measurements.<br />
<br />
[[Image:uft_mod_ecfp1.png | centre | thumb | Degredation and maturation pathways for eCFP. (Leveau and Lindow 2001)]]<br />
<br />
<br />
The GFP maturation and degradation parameters found in this paper were:<br />
<br />
<html><br />
<centre><br />
<table><br />
<tr><td> m = 0.0004279 1/s </td></tr><br />
<tr><td> Vmax = 2E-10 molality/s </td></tr><br />
<tr><td> Km = 9E-13 molality/s </td></tr><br />
<tr><td> </td></tr><br />
</table><br />
</centre><br />
</html><br />
<br />
<br />
Assuming eCFPt would behave similarly to eGFP, the following additional reactions would be included in the model:<br />
<br />
<html><br />
<table><br />
<tr> <td><b> Maturation </b></td> <td> </td> </tr><br />
<tr> <td> eCFPt --> F_eCFPT </td> <td> 0.0004279 </td> </tr><br />
<tr> <td> Enc2:eCFPt --> Enc2:F_eCFPt </td> <td> 0.0004279 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Encapsulation </b></td> <td> </td> </tr><br />
<tr> <td> Enc2 + F_eCFPt --> Enc2:F_eCFPt </td> <td> 100 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Degradation </b></td> <td> </td> </tr><br />
<tr> <td> eCFPt --> </td> <td> Vmax = 2E-10 </td> </tr><br />
<tr> <td> </td> <td> Km = 9E-13 </td> </tr><br />
<tr> <td> F_eCFPt --> </td> <td> Vmax = 2E-10 </td> </tr><br />
<tr> <td> </td> <td> Km = 9E-13 </td> </tr><br />
</table><br />
</html><br />
<br />
===Assembly of Encapsulin Microcompartments===<br />
<br />
Though Encapsulin microcompartment assembly is not well-studied, it has been theorized to resemble the assembly of viral capsids. Thus, we could look to this relatively well-studied phenomenon as a representation of Encapsulin microcompartment assembly.<br />
<br />
Adam Zlotnick has published models of viral capsid assembly using different approaches. An early paper described an equilibrium model of assembly for a 12 Unit polyhedral capsid head, and a more recent paper used a kinetic model that could be applied to many examples of spherical polymerization. We will consider how each approach could be incorporated as a representation of Encapsulin assembly.<br />
<br />
'''1) Equilibrim Approach to Encapsulin Assembly'''<br />
<br />
Zlotnick's [[Media:Uft_mod_to_build_a_virus_capsid.pdf|Equilibrium-based model]] consists of reactions from an initial monomer subunit leading to a final capsid product. The sequential reactions take into account DeltaG for contact (Kn'), and parameters describing path degeneracy (varies for different intermediates).<br />
[[image:uft_mod_encap1.png|centre|thumb|Kn for assembly subunits based on path degeneracy. (Zlotnick 1994)]]<br />
<br />
Simulations from a preliminary incorporation of this approach are shown below. In this version of our basic model, Encapsulin assembles in a series of first order reactions. However, for simplicity, the rate constants are kept identical and do not take path degeneracy into account.<br />
<br />
<html><br />
<table><br />
<tr> <td><b> Encapsulin Assembly </b></td> <td> </td> </tr><br />
<tr> <td> 2 Enc --> Enc2 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 Enc2 --> Enc4 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 En4 --> Enc8 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 Enc8 --> Enc16 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 Enc16 --> Enc32 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 Enc16 --> Enc64 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td><b> Encapsulation </b></td> <td> </td> </tr><br />
<tr> <td> Enc64 + eCFPt --> Enc64:eCFPt </td> <td> 1.00E2 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
</table><br />
</html><br />
<br />
[[Image:uft_mod_enc1.png |frameless|300px]][[Image:uft_mod_enc2.png |frameless|300px]][[Image:uft_mod_enc3.png |frameless|300px]]<br />
<br />
<gallery caption=Equilibrium-based Encapsulin Assembly width=600px height=150px><br />
<center><br />
image:uft_mod_enc1.png<br />
image:uft_mod_enc2.png<br />
image:uft_mod_enc3.png<br />
</center><br />
</gallery><br />
<br />
Encapsulin assembly intermediates are observed to quickly come to a steady state. The last intermediate ''Enc64'' is the most depleted probably because of the formation of ''Enc64:eCFPt'' complex. Formation of ''Enc64:eCFPt'' then mirrors the production of ''eCFPt''. <br />
<br />
<br />
'''2) Kinetic Model of Spherical Polymerization'''<br />
<br />
A [http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1302223/pdf/12124301.pdf general kinetic model for the spherical polyermization] process is shown below. In our case, the initial monomer subunit concentration (''u'') would represent our expressed Encapsulin BioBrick, and the number of monomers in the final assembly (''N'') is thought to be 60. All of the included parameters can be calculated from the four basic parameters; the microscopic, per-contact equilibrium constant (KAcon), the nucleus size (nuc), the nucleation on-rate (f_nuc), and the elongation on-rate (f_elong). The referenced paper describes methods to aquire these parameters from kinetic experiments, and provides examples for N = 12 and 30 unit viral capsid assemblies.<br />
[[image:uft_mod_encap2.png| centre | thumb |System of ODEs to represent spherical polymerization, where ''u'' is the initial subunit concentration, ''m'' is the "mth" intermediate species, and ''N'' is the number of monomers in the final assembly. (Endres and Zlotnick 2002)]]<br />
<br />
<br />
<br />
Zlotnick's models also describe two important features of spherical polymerization that we should also expect to observe in Encapsulin assembly: kinetic trapping and nucleation. A kinetic trap occurs when the initial monomer subunit concentration or the deltaG of the first assembly reaction is too high. This results in over-initiation of assembly and quickly the reactions become starved for subunits. Kinetic trapping is prevented by the inclusion of nucleation, where the initial reactions occur at a slower rate because the first few intermediates in a series of reactions are less stable than downstream products. Essentially, nucleation serves as a “slow first step” that regulates the assembly pathway. <br />
<br />
It will be interesting to note how the translational dynamics of Encapsulin interplay with its assembly dynamics. Since our system does not start with any initial concentration of Encapsulin, there will be an optimum rate of production that essentially serves the role of nucleation – avoiding kinetic traps while still maintaining a maximum production of full Encapsulin assemblies.<br />
<br />
=References=<br />
<br />
1. Hill AD, Tomshine JR, Weeding EM, Sotiropoulos V, Kaznessis YN. ''SynBioSS: the synthetic biology modeling suite.'' Bioinformatics. 2008 Nov 1;24(21):2551-3. Epub 2008 Aug 30.<br />
[http://neptune.cems.umn.edu/designer/interface1.php SynBioSS Web Designer]<br />
<br />
2. Leveau JH, Lindow SE. ''Predictive and interpretive simulation of green fluorescent protein expression in<br />
reporter bacteria.'' J Bacteriol. 2001 Dec;183(23):6752-62.<br />
<br />
3. Endres D, Zlotnick A. ''Model-based analysis of assembly kinetics for virus capsids or other spherical<br />
polymers.'' Biophys J. 2002 Aug;83(2):1217-30.</div>FRhttp://2009.igem.org/Team:TorontoMaRSDiscovery/ModelingTeam:TorontoMaRSDiscovery/Modeling2009-10-21T07:20:56Z<p>FR: /* Model */</p>
<hr />
<div>[[image:To_igem_wiki_banner.jpg|965px]]<br />
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!align="center"|[[Team:TorontoMaRSDiscovery/Team|The Team]]<br />
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!align="center"|[[Team:TorontoMaRSDiscovery/Parts|BioBricks]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Modeling|Modeling]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Bioinformatics|Bioinformatics]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Safety|Safety]]<br />
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|}<br />
<br><br />
<br />
<br />
=Summary=<br />
<br />
A kinetic model of our system has been constructed. Approximate parameter values were gathered from online resources to represent all processes up to the production of the eCFP and Encapsulin proteins. Current simulations predict the production of these two proteins at various initial concentrations of IPTG and aTc effector molecules. Furthermore, we have outlined approaches for the detailed modelling of the eCFP degredation/maturation and Encapsulin assembly pathways.<br />
<br />
<br />
The initial simulations will be used to identify the critical concentration of Encapsulin mononomer required for microcompartment assembly. Subsequently, a detailed model of Encapsulin assembly will be integrated into the current model, and its parameters filled-in using parameter-scanning methods and experiments outlined in the relevant references. By comparing experimental measures of microcompartment formation with that predicted by the kinetic model, we aim to gain insight on the mechanisms of Encapsulin assembly.<br />
<br />
=Model=<br />
Our model is based on the following design (See Project Page for a full description of this system).<br />
[[image:BioBrick.png|thumb|centre|The Encapsulator]]<br />
<br />
The reaction framework was mainly generated using the [http://synbioss.sourceforge.net/ SynBioSS Designer (a really useful modeling tool for iGEM teams)], which also provides default parameter values. These parameter values have been gathered from various literature [http://neptune.cems.umn.edu/designer/designer_defaults.pdf sources], and should be taken as approximations. All units were taken to be (1 / molarity^n-1 * s), where n is the order of the reaction. For example, for the reaction 2 lacI --> lacI2, n = 2, thus the rate constant has the units 1/molarity*s. <br />
<br />
The pathways for the expressed proteins, eCFPt and Encapsulin, need to be modeled in more detail. For example, in this basic model eCFPt is degraded via a first order reaction and Encapsulin makes a dimer complex. However, in reality fluorescent proteins have been shown to degreade via Micheales-menton kinetics and Encapsulin is thought to make a complex of about 60 monomers. These issues will be addressed in future work.<br />
<br />
The reactions can be accessed here:<br />
<br />
[[Model (open new page)]]<br />
<br />
[[Media:Uft_mod_Rxns2.xls|Model (download Excel file)]]<br />
<br />
=Simulations=<br />
<br />
All simulations were carried out using the [https://2009.igem.org/Partner_Offers SimBiology Matlab Toolbox], which was freely available to iGEM teams. <br />
<br />
===Accumulation of eCFP at Different Initial Concentrations of IPTG===<br />
<br />
[[Image:uft_mod_cfp-iptg.png | 900px]]<br />
<br />
The IPTG effector eventually loses effect, and the eCFP concentration approaches a maximum. This happens because the IPTG proteins eventually ''tie up'' all available LacI4 proteins, leaving the transcription and translation of eCFP to operate at its maxiumum rate. <br />
<br />
===Accumulation of Encapsulin monomer at Different Initial Concentrations of aTc===<br />
<br />
[[Image:uft_mod_enc-atc.png | 900px]]<br />
<br />
(NOTE: in order to observe Encapsulin monomer levels, the above simulations were carried out without any Encapsulin assembly reactions in place)<br />
<br />
The production of Encapsulin occurs at a slower rate than eCFP because the BBa_R0040 promoter has two tetR binding sites, resulting in more repression and more off-pathway scenarios. Thus, the Encapsulin concentration also seems assymptotic but at higher concentrations of aTc (relative to IPTG). <br />
<br />
It seems beneficial to have the Encapsulin protein under control of the BBa_R0040-tetR-aTc construct because at zero levels of aTc we can have essentially zero levels of Encapsulin (whereas even at zero levels of IPTG, there is still significantly more eCFP). This will enable us to probe extremely low concentrations of Encapsulin monomer when testing for optimal Encapsulin assembly conditions. The disadvantage is that if Encapsulin assembly requires a very high initial concentration of Encapsulin monomer, we would have to wait a long time to see microcompartments. If this later scenario is observed, it may be better to switch the eCFP and Encapsulin expression systems.<br />
<br />
===Sensitivity Analysis===<br />
<br />
Since all of our parameters are approximations from literature sources, those which have the greatest affect on system dynamics (ie. the most ''sensitive'' parameters) would be leading candidates to be experimentally determined. Currently we are interested in which parameters have the greatest effect on the production of eCFP and Encapsulin. Ideally, it would be best to experimentally determine these to "tighten-up" the model before incorporating the largely unexplored Encapsulin assembly pathways. <br />
<br />
<br />
'''1) Sensitivity of eCFP Production'''<br />
<br />
[[Image:uft_mod_SAecfp.png | centre | 900px]]<br />
<br />
<br />
<br />
'''2) Sensitivity of Encapsulin Production'''<br />
<br />
[[Image:uft_mod_SAenc.png | centre | 900px]]<br />
<br />
Parameters 1 and 2 correspond to <br />
It can be seen that eCFP and Encapsulin production is largely sensitive to ''lacI_in'' and ''tetR_in'', which represent the rates of constitutive expression of the lacI and tetR repressors respectively. <br />
In our construct these are expressed using constitutive promoter bba_..., <br />
rate assigned by synbioss is...from which source<br />
The sensitivity results suggest that these rates should be experimentally determined for our system, for most accurate predictions.<br />
<br />
=Future Work=<br />
<br />
Improvements to the basic model presented above can be separated into three areas; 1) performing experiments to determine parameter values that are specific to our system, 2) more detailed modeling of eCFPt behavior, 3) more detailed modeling of Encapsulin assembly. <br />
<br />
The experiments required to determine general transcription and translation parameters need to be further researched, so this will be skipped over for now (the proposed sensitivity analysis of the model parameters will also identify which experiments are critical). Here we will discuss the more interesting areas – the detailed modeling of eCFP and Encapsulin pathways. This will be accomplished by incorporating previous modeling efforts that are applicable to the eCFP and Encapsulin proteins. <br />
<br />
===Degredation of eCFP===<br />
<br />
The expression and degradation of [http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=95514&blobtype=pdf Green Fluorescent Protein (GFP) was modeled previously]. This paper noted that GFP must mature before going into fluorescent phase, and GFP degradation was shown to follow M-M kinetics, as depicted below. This paper also outlined how the degradation parameters could be derived for any expression system using only simple fluorescence and optical density measurements.<br />
<br />
[[Image:uft_mod_ecfp1.png | centre | thumb | Degredation and maturation pathways for eCFP. (Leveau and Lindow 2001)]]<br />
<br />
<br />
The GFP maturation and degradation parameters found in this paper were:<br />
<br />
<html><br />
<centre><br />
<table><br />
<tr><td> m = 0.0004279 1/s </td></tr><br />
<tr><td> Vmax = 2E-10 molality/s </td></tr><br />
<tr><td> Km = 9E-13 molality/s </td></tr><br />
<tr><td> </td></tr><br />
</table><br />
</centre><br />
</html><br />
<br />
<br />
Assuming eCFPt would behave similarly to eGFP, the following additional reactions would be included in the model:<br />
<br />
<html><br />
<table><br />
<tr> <td><b> Maturation </b></td> <td> </td> </tr><br />
<tr> <td> eCFPt --> F_eCFPT </td> <td> 0.0004279 </td> </tr><br />
<tr> <td> Enc2:eCFPt --> Enc2:F_eCFPt </td> <td> 0.0004279 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Encapsulation </b></td> <td> </td> </tr><br />
<tr> <td> Enc2 + F_eCFPt --> Enc2:F_eCFPt </td> <td> 100 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Degradation </b></td> <td> </td> </tr><br />
<tr> <td> eCFPt --> </td> <td> Vmax = 2E-10 </td> </tr><br />
<tr> <td> </td> <td> Km = 9E-13 </td> </tr><br />
<tr> <td> F_eCFPt --> </td> <td> Vmax = 2E-10 </td> </tr><br />
<tr> <td> </td> <td> Km = 9E-13 </td> </tr><br />
</table><br />
</html><br />
<br />
===Assembly of Encapsulin Microcompartments===<br />
<br />
Though Encapsulin microcompartment assembly is not well-studied, it has been theorized to resemble the assembly of viral capsids. Thus, we could look to this relatively well-studied phenomenon as a representation of Encapsulin microcompartment assembly.<br />
<br />
Adam Zlotnick has published models of viral capsid assembly using different approaches. An early paper described an equilibrium model of assembly for a 12 Unit polyhedral capsid head, and a more recent paper used a kinetic model that could be applied to many examples of spherical polymerization. We will consider how each approach could be incorporated as a representation of Encapsulin assembly.<br />
<br />
'''1) Equilibrim Approach to Encapsulin Assembly'''<br />
<br />
Zlotnick's [[Media:Uft_mod_to_build_a_virus_capsid.pdf|Equilibrium-based model]] consists of reactions from an initial monomer subunit leading to a final capsid product. The sequential reactions take into account DeltaG for contact (Kn'), and parameters describing path degeneracy (varies for different intermediates).<br />
[[image:uft_mod_encap1.png|centre|thumb|Kn for assembly subunits based on path degeneracy. (Zlotnick 1994)]]<br />
<br />
Simulations from a preliminary incorporation of this approach are shown below. In this version of our basic model, Encapsulin assembles in a series of first order reactions. However, for simplicity, the rate constants are kept identical and do not take path degeneracy into account.<br />
<br />
<html><br />
<table><br />
<tr> <td><b> Encapsulin Assembly </b></td> <td> </td> </tr><br />
<tr> <td> 2 Enc --> Enc2 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 Enc2 --> Enc4 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 En4 --> Enc8 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 Enc8 --> Enc16 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 Enc16 --> Enc32 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 Enc16 --> Enc64 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td><b> Encapsulation </b></td> <td> </td> </tr><br />
<tr> <td> Enc64 + eCFPt --> Enc64:eCFPt </td> <td> 1.00E2 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
</table><br />
</html><br />
<br />
[[Image:uft_mod_enc1.png |frameless|300px]][[Image:uft_mod_enc2.png |frameless|300px]][[Image:uft_mod_enc3.png |frameless|300px]]<br />
<br />
<gallery caption=Equilibrium-based Encapsulin Assembly width=600px height=150px><br />
<center><br />
image:uft_mod_enc1.png<br />
image:uft_mod_enc2.png<br />
image:uft_mod_enc3.png<br />
</center><br />
</gallery><br />
<br />
Encapsulin assembly intermediates are observed to quickly come to a steady state. The last intermediate ''Enc64'' is the most depleted probably because of the formation of ''Enc64:eCFPt'' complex. Formation of ''Enc64:eCFPt'' then mirrors the production of ''eCFPt''. <br />
<br />
<br />
'''2) Kinetic Model of Spherical Polymerization'''<br />
<br />
A [http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1302223/pdf/12124301.pdf general kinetic model for the spherical polyermization] process is shown below. In our case, the initial monomer subunit concentration (''u'') would represent our expressed Encapsulin BioBrick, and the number of monomers in the final assembly (''N'') is thought to be 60. All of the included parameters can be calculated from the four basic parameters; the microscopic, per-contact equilibrium constant (KAcon), the nucleus size (nuc), the nucleation on-rate (f_nuc), and the elongation on-rate (f_elong). The referenced paper describes methods to aquire these parameters from kinetic experiments, and provides examples for N = 12 and 30 unit viral capsid assemblies.<br />
[[image:uft_mod_encap2.png| centre | thumb |System of ODEs to represent spherical polymerization, where ''u'' is the initial subunit concentration, ''m'' is the "mth" intermediate species, and ''N'' is the number of monomers in the final assembly. (Endres and Zlotnick 2002)]]<br />
<br />
<br />
<br />
Zlotnick's models also describe two important features of spherical polymerization that we should also expect to observe in Encapsulin assembly: kinetic trapping and nucleation. A kinetic trap occurs when the initial monomer subunit concentration or the deltaG of the first assembly reaction is too high. This results in over-initiation of assembly and quickly the reactions become starved for subunits. Kinetic trapping is prevented by the inclusion of nucleation, where the initial reactions occur at a slower rate because the first few intermediates in a series of reactions are less stable than downstream products. Essentially, nucleation serves as a “slow first step” that regulates the assembly pathway. <br />
<br />
It will be interesting to note how the translational dynamics of Encapsulin interplay with its assembly dynamics. Since our system does not start with any initial concentration of Encapsulin, there will be an optimum rate of production that essentially serves the role of nucleation – avoiding kinetic traps while still maintaining a maximum production of full Encapsulin assemblies.<br />
<br />
=References=<br />
<br />
1. Hill AD, Tomshine JR, Weeding EM, Sotiropoulos V, Kaznessis YN. ''SynBioSS: the synthetic biology modeling suite.'' Bioinformatics. 2008 Nov 1;24(21):2551-3. Epub 2008 Aug 30.<br />
[http://neptune.cems.umn.edu/designer/interface1.php SynBioSS Web Designer]<br />
<br />
2. Leveau JH, Lindow SE. ''Predictive and interpretive simulation of green fluorescent protein expression in<br />
reporter bacteria.'' J Bacteriol. 2001 Dec;183(23):6752-62.<br />
<br />
3. Endres D, Zlotnick A. ''Model-based analysis of assembly kinetics for virus capsids or other spherical<br />
polymers.'' Biophys J. 2002 Aug;83(2):1217-30.</div>FRhttp://2009.igem.org/Team:TorontoMaRSDiscovery/ModelingTeam:TorontoMaRSDiscovery/Modeling2009-10-21T07:04:08Z<p>FR: /* Sensitivity Analysis */</p>
<hr />
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!align="center"|[[Team:TorontoMaRSDiscovery/Safety|Safety]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Notebook|Notebook]]<br />
|}<br />
<br><br />
<br />
<br />
=Summary=<br />
<br />
A kinetic model of our system has been constructed. Approximate parameter values were gathered from online resources to represent all processes up to the production of the eCFP and Encapsulin proteins. Current simulations predict the production of these two proteins at various initial concentrations of IPTG and aTc effector molecules. Furthermore, we have outlined approaches for the detailed modelling of the eCFP degredation/maturation and Encapsulin assembly pathways.<br />
<br />
<br />
The initial simulations will be used to identify the critical concentration of Encapsulin mononomer required for microcompartment assembly. Subsequently, a detailed model of Encapsulin assembly will be integrated into the current model, and its parameters filled-in using parameter-scanning methods and experiments outlined in the relevant references. By comparing experimental measures of microcompartment formation with that predicted by the kinetic model, we aim to gain insight on the mechanisms of Encapsulin assembly.<br />
<br />
=Model=<br />
Our model is based on the following design (See Project Page for a full description of this system).<br />
[[image:BioBrick.png|thumb|centre|The Encapsulator]]<br />
<br />
The reaction framework was mainly generated using the [http://synbioss.sourceforge.net/ SynBioSS Designer (a really useful modeling tool for iGEM teams)], which also provides default parameter values. These parameter values have been gathered from various literature [http://neptune.cems.umn.edu/designer/designer_defaults.pdf sources], and should be taken as approximations. All units were taken to be (1 / molarity^n-1 * s), where n is the order of the reaction. For example, for the reaction 2 lacI --> lacI2, n = 2, thus the rate constant has the units 1/molality*s. <br />
<br />
The pathways for the expressed proteins, eCFPt and Encapsulin, need to be modeled in more detail. For example, in this basic model eCFPt is degraded via a first order reaction and Encapsulin makes a dimer complex. However, in reality fluorescent proteins have been shown to degreade via Micheales-menton kinetics and Encapsulin is thought to make a complex of about 60 monomers. These issues will be addressed in future work.<br />
<br />
The reactions can be accessed here:<br />
<br />
[[Model (open new page)]]<br />
<br />
[[Media:Uft_mod_Rxns2.xls|Model (download Excel file)]]<br />
<br />
=Simulations=<br />
<br />
All simulations were carried out using the [https://2009.igem.org/Partner_Offers SimBiology Matlab Toolbox], which was freely available to iGEM teams. <br />
<br />
===Accumulation of eCFP at Different Initial Concentrations of IPTG===<br />
<br />
[[Image:uft_mod_cfp-iptg.png | 900px]]<br />
<br />
The IPTG effector eventually loses effect, and the eCFP concentration approaches a maximum. This happens because the IPTG proteins eventually ''tie up'' all available LacI4 proteins, leaving the transcription and translation of eCFP to operate at its maxiumum rate. <br />
<br />
===Accumulation of Encapsulin monomer at Different Initial Concentrations of aTc===<br />
<br />
[[Image:uft_mod_enc-atc.png | 900px]]<br />
<br />
(NOTE: in order to observe Encapsulin monomer levels, the above simulations were carried out without any Encapsulin assembly reactions in place)<br />
<br />
The production of Encapsulin occurs at a slower rate than eCFP because the BBa_R0040 promoter has two tetR binding sites, resulting in more repression and more off-pathway scenarios. Thus, the Encapsulin concentration also seems assymptotic but at higher concentrations of aTc (relative to IPTG). <br />
<br />
It seems beneficial to have the Encapsulin protein under control of the BBa_R0040-tetR-aTc construct because at zero levels of aTc we can have essentially zero levels of Encapsulin (whereas even at zero levels of IPTG, there is still significantly more eCFP). This will enable us to probe extremely low concentrations of Encapsulin monomer when testing for optimal Encapsulin assembly conditions. The disadvantage is that if Encapsulin assembly requires a very high initial concentration of Encapsulin monomer, we would have to wait a long time to see microcompartments. If this later scenario is observed, it may be better to switch the eCFP and Encapsulin expression systems.<br />
<br />
===Sensitivity Analysis===<br />
<br />
Since all of our parameters are approximations from literature sources, those which have the greatest affect on system dynamics (ie. the most ''sensitive'' parameters) would be leading candidates to be experimentally determined. Currently we are interested in which parameters have the greatest effect on the production of eCFP and Encapsulin. Ideally, it would be best to experimentally determine these to "tighten-up" the model before incorporating the largely unexplored Encapsulin assembly pathways. <br />
<br />
<br />
'''1) Sensitivity of eCFP Production'''<br />
<br />
[[Image:uft_mod_SAecfp.png | centre | 900px]]<br />
<br />
<br />
<br />
'''2) Sensitivity of Encapsulin Production'''<br />
<br />
[[Image:uft_mod_SAenc.png | centre | 900px]]<br />
<br />
Parameters 1 and 2 correspond to <br />
It can be seen that eCFP and Encapsulin production is largely sensitive to ''lacI_in'' and ''tetR_in'', which represent the rates of constitutive expression of the lacI and tetR repressors respectively. <br />
In our construct these are expressed using constitutive promoter bba_..., <br />
rate assigned by synbioss is...from which source<br />
The sensitivity results suggest that these rates should be experimentally determined for our system, for most accurate predictions.<br />
<br />
=Future Work=<br />
<br />
Improvements to the basic model presented above can be separated into three areas; 1) performing experiments to determine parameter values that are specific to our system, 2) more detailed modeling of eCFPt behavior, 3) more detailed modeling of Encapsulin assembly. <br />
<br />
The experiments required to determine general transcription and translation parameters need to be further researched, so this will be skipped over for now (the proposed sensitivity analysis of the model parameters will also identify which experiments are critical). Here we will discuss the more interesting areas – the detailed modeling of eCFP and Encapsulin pathways. This will be accomplished by incorporating previous modeling efforts that are applicable to the eCFP and Encapsulin proteins. <br />
<br />
===Degredation of eCFP===<br />
<br />
The expression and degradation of [http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=95514&blobtype=pdf Green Fluorescent Protein (GFP) was modeled previously]. This paper noted that GFP must mature before going into fluorescent phase, and GFP degradation was shown to follow M-M kinetics, as depicted below. This paper also outlined how the degradation parameters could be derived for any expression system using only simple fluorescence and optical density measurements.<br />
<br />
[[Image:uft_mod_ecfp1.png | centre | thumb | Degredation and maturation pathways for eCFP. (Leveau and Lindow 2001)]]<br />
<br />
<br />
The GFP maturation and degradation parameters found in this paper were:<br />
<br />
<html><br />
<centre><br />
<table><br />
<tr><td> m = 0.0004279 1/s </td></tr><br />
<tr><td> Vmax = 2E-10 molality/s </td></tr><br />
<tr><td> Km = 9E-13 molality/s </td></tr><br />
<tr><td> </td></tr><br />
</table><br />
</centre><br />
</html><br />
<br />
<br />
Assuming eCFPt would behave similarly to eGFP, the following additional reactions would be included in the model:<br />
<br />
<html><br />
<table><br />
<tr> <td><b> Maturation </b></td> <td> </td> </tr><br />
<tr> <td> eCFPt --> F_eCFPT </td> <td> 0.0004279 </td> </tr><br />
<tr> <td> Enc2:eCFPt --> Enc2:F_eCFPt </td> <td> 0.0004279 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Encapsulation </b></td> <td> </td> </tr><br />
<tr> <td> Enc2 + F_eCFPt --> Enc2:F_eCFPt </td> <td> 100 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Degradation </b></td> <td> </td> </tr><br />
<tr> <td> eCFPt --> </td> <td> Vmax = 2E-10 </td> </tr><br />
<tr> <td> </td> <td> Km = 9E-13 </td> </tr><br />
<tr> <td> F_eCFPt --> </td> <td> Vmax = 2E-10 </td> </tr><br />
<tr> <td> </td> <td> Km = 9E-13 </td> </tr><br />
</table><br />
</html><br />
<br />
===Assembly of Encapsulin Microcompartments===<br />
<br />
Though Encapsulin microcompartment assembly is not well-studied, it has been theorized to resemble the assembly of viral capsids. Thus, we could look to this relatively well-studied phenomenon as a representation of Encapsulin microcompartment assembly.<br />
<br />
Adam Zlotnick has published models of viral capsid assembly using different approaches. An early paper described an equilibrium model of assembly for a 12 Unit polyhedral capsid head, and a more recent paper used a kinetic model that could be applied to many examples of spherical polymerization. We will consider how each approach could be incorporated as a representation of Encapsulin assembly.<br />
<br />
'''1) Equilibrim Approach to Encapsulin Assembly'''<br />
<br />
Zlotnick's [[Media:Uft_mod_to_build_a_virus_capsid.pdf|Equilibrium-based model]] consists of reactions from an initial monomer subunit leading to a final capsid product. The sequential reactions take into account DeltaG for contact (Kn'), and parameters describing path degeneracy (varies for different intermediates).<br />
[[image:uft_mod_encap1.png|centre|thumb|Kn for assembly subunits based on path degeneracy. (Zlotnick 1994)]]<br />
<br />
Simulations from a preliminary incorporation of this approach are shown below. In this version of our basic model, Encapsulin assembles in a series of first order reactions. However, for simplicity, the rate constants are kept identical and do not take path degeneracy into account.<br />
<br />
<html><br />
<table><br />
<tr> <td><b> Encapsulin Assembly </b></td> <td> </td> </tr><br />
<tr> <td> 2 Enc --> Enc2 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 Enc2 --> Enc4 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 En4 --> Enc8 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 Enc8 --> Enc16 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 Enc16 --> Enc32 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 Enc16 --> Enc64 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td><b> Encapsulation </b></td> <td> </td> </tr><br />
<tr> <td> Enc64 + eCFPt --> Enc64:eCFPt </td> <td> 1.00E2 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
</table><br />
</html><br />
<br />
[[Image:uft_mod_enc1.png |frameless|300px]][[Image:uft_mod_enc2.png |frameless|300px]][[Image:uft_mod_enc3.png |frameless|300px]]<br />
<br />
<gallery caption=Equilibrium-based Encapsulin Assembly width=600px height=150px><br />
<center><br />
image:uft_mod_enc1.png<br />
image:uft_mod_enc2.png<br />
image:uft_mod_enc3.png<br />
</center><br />
</gallery><br />
<br />
Encapsulin assembly intermediates are observed to quickly come to a steady state. The last intermediate ''Enc64'' is the most depleted probably because of the formation of ''Enc64:eCFPt'' complex. Formation of ''Enc64:eCFPt'' then mirrors the production of ''eCFPt''. <br />
<br />
<br />
'''2) Kinetic Model of Spherical Polymerization'''<br />
<br />
A [http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1302223/pdf/12124301.pdf general kinetic model for the spherical polyermization] process is shown below. In our case, the initial monomer subunit concentration (''u'') would represent our expressed Encapsulin BioBrick, and the number of monomers in the final assembly (''N'') is thought to be 60. All of the included parameters can be calculated from the four basic parameters; the microscopic, per-contact equilibrium constant (KAcon), the nucleus size (nuc), the nucleation on-rate (f_nuc), and the elongation on-rate (f_elong). The referenced paper describes methods to aquire these parameters from kinetic experiments, and provides examples for N = 12 and 30 unit viral capsid assemblies.<br />
[[image:uft_mod_encap2.png| centre | thumb |System of ODEs to represent spherical polymerization, where ''u'' is the initial subunit concentration, ''m'' is the "mth" intermediate species, and ''N'' is the number of monomers in the final assembly. (Endres and Zlotnick 2002)]]<br />
<br />
<br />
<br />
Zlotnick's models also describe two important features of spherical polymerization that we should also expect to observe in Encapsulin assembly: kinetic trapping and nucleation. A kinetic trap occurs when the initial monomer subunit concentration or the deltaG of the first assembly reaction is too high. This results in over-initiation of assembly and quickly the reactions become starved for subunits. Kinetic trapping is prevented by the inclusion of nucleation, where the initial reactions occur at a slower rate because the first few intermediates in a series of reactions are less stable than downstream products. Essentially, nucleation serves as a “slow first step” that regulates the assembly pathway. <br />
<br />
It will be interesting to note how the translational dynamics of Encapsulin interplay with its assembly dynamics. Since our system does not start with any initial concentration of Encapsulin, there will be an optimum rate of production that essentially serves the role of nucleation – avoiding kinetic traps while still maintaining a maximum production of full Encapsulin assemblies.<br />
<br />
=References=<br />
<br />
1. Hill AD, Tomshine JR, Weeding EM, Sotiropoulos V, Kaznessis YN. ''SynBioSS: the synthetic biology modeling suite.'' Bioinformatics. 2008 Nov 1;24(21):2551-3. Epub 2008 Aug 30.<br />
[http://neptune.cems.umn.edu/designer/interface1.php SynBioSS Web Designer]<br />
<br />
2. Leveau JH, Lindow SE. ''Predictive and interpretive simulation of green fluorescent protein expression in<br />
reporter bacteria.'' J Bacteriol. 2001 Dec;183(23):6752-62.<br />
<br />
3. Endres D, Zlotnick A. ''Model-based analysis of assembly kinetics for virus capsids or other spherical<br />
polymers.'' Biophys J. 2002 Aug;83(2):1217-30.</div>FRhttp://2009.igem.org/Team:TorontoMaRSDiscovery/ModelingTeam:TorontoMaRSDiscovery/Modeling2009-10-21T07:00:24Z<p>FR: /* Sensitivity Analysis */</p>
<hr />
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<br><br />
<br />
<br />
=Summary=<br />
<br />
A kinetic model of our system has been constructed. Approximate parameter values were gathered from online resources to represent all processes up to the production of the eCFP and Encapsulin proteins. Current simulations predict the production of these two proteins at various initial concentrations of IPTG and aTc effector molecules. Furthermore, we have outlined approaches for the detailed modelling of the eCFP degredation/maturation and Encapsulin assembly pathways.<br />
<br />
<br />
The initial simulations will be used to identify the critical concentration of Encapsulin mononomer required for microcompartment assembly. Subsequently, a detailed model of Encapsulin assembly will be integrated into the current model, and its parameters filled-in using parameter-scanning methods and experiments outlined in the relevant references. By comparing experimental measures of microcompartment formation with that predicted by the kinetic model, we aim to gain insight on the mechanisms of Encapsulin assembly.<br />
<br />
=Model=<br />
Our model is based on the following design (See Project Page for a full description of this system).<br />
[[image:BioBrick.png|thumb|centre|The Encapsulator]]<br />
<br />
The reaction framework was mainly generated using the [http://synbioss.sourceforge.net/ SynBioSS Designer (a really useful modeling tool for iGEM teams)], which also provides default parameter values. These parameter values have been gathered from various literature [http://neptune.cems.umn.edu/designer/designer_defaults.pdf sources], and should be taken as approximations. All units were taken to be (1 / molarity^n-1 * s), where n is the order of the reaction. For example, for the reaction 2 lacI --> lacI2, n = 2, thus the rate constant has the units 1/molality*s. <br />
<br />
The pathways for the expressed proteins, eCFPt and Encapsulin, need to be modeled in more detail. For example, in this basic model eCFPt is degraded via a first order reaction and Encapsulin makes a dimer complex. However, in reality fluorescent proteins have been shown to degreade via Micheales-menton kinetics and Encapsulin is thought to make a complex of about 60 monomers. These issues will be addressed in future work.<br />
<br />
The reactions can be accessed here:<br />
<br />
[[Model (open new page)]]<br />
<br />
[[Media:Uft_mod_Rxns2.xls|Model (download Excel file)]]<br />
<br />
=Simulations=<br />
<br />
All simulations were carried out using the [https://2009.igem.org/Partner_Offers SimBiology Matlab Toolbox], which was freely available to iGEM teams. <br />
<br />
===Accumulation of eCFP at Different Initial Concentrations of IPTG===<br />
<br />
[[Image:uft_mod_cfp-iptg.png | 900px]]<br />
<br />
The IPTG effector eventually loses effect, and the eCFP concentration approaches a maximum. This happens because the IPTG proteins eventually ''tie up'' all available LacI4 proteins, leaving the transcription and translation of eCFP to operate at its maxiumum rate. <br />
<br />
===Accumulation of Encapsulin monomer at Different Initial Concentrations of aTc===<br />
<br />
[[Image:uft_mod_enc-atc.png | 900px]]<br />
<br />
(NOTE: in order to observe Encapsulin monomer levels, the above simulations were carried out without any Encapsulin assembly reactions in place)<br />
<br />
The production of Encapsulin occurs at a slower rate than eCFP because the BBa_R0040 promoter has two tetR binding sites, resulting in more repression and more off-pathway scenarios. Thus, the Encapsulin concentration also seems assymptotic but at higher concentrations of aTc (relative to IPTG). <br />
<br />
It seems beneficial to have the Encapsulin protein under control of the BBa_R0040-tetR-aTc construct because at zero levels of aTc we can have essentially zero levels of Encapsulin (whereas even at zero levels of IPTG, there is still significantly more eCFP). This will enable us to probe extremely low concentrations of Encapsulin monomer when testing for optimal Encapsulin assembly conditions. The disadvantage is that if Encapsulin assembly requires a very high initial concentration of Encapsulin monomer, we would have to wait a long time to see microcompartments. If this later scenario is observed, it may be better to switch the eCFP and Encapsulin expression systems.<br />
<br />
===Sensitivity Analysis===<br />
<br />
Since all of our parameters are approximations from literature sources, those which have the greatest affect on system dynamics (ie. the most ''sensitive'' parameters) would be leading candidates to be experimentally determined. Currently we are interested in which parameters have the greatest effect on the production of eCFP and Encapsulin. Ideally, it would be best to experimentally determine these to "tighten-up" the model before incorporating the largely unexplored Encapsulin assembly pathways. <br />
<br />
<br />
'''1) Sensitivity of eCFP Production'''<br />
<br />
[[Image:uft_mod_SAecfp.png | centre | 900px]]<br />
<br />
<br />
<br />
'''2) Sensitivity of Encapsulin Production'''<br />
<br />
[[Image:uft_mod_SAenc.png | centre | 900px]]<br />
<br />
It can be seen that eCFP and Encapsulin production is largely sensitive to ''lacI_in'' and ''tetR_in'', which represent the rates of constitutive expression of the lacI and tetR repressors respectively. <br />
In our construct these are expressed using constitutive promoter bba_..., <br />
rate assigned by synbioss is...from which source<br />
The sensitivity results suggest that these rates should be experimentally determined for our system, for most accurate predictions.<br />
<br />
=Future Work=<br />
<br />
Improvements to the basic model presented above can be separated into three areas; 1) performing experiments to determine parameter values that are specific to our system, 2) more detailed modeling of eCFPt behavior, 3) more detailed modeling of Encapsulin assembly. <br />
<br />
The experiments required to determine general transcription and translation parameters need to be further researched, so this will be skipped over for now (the proposed sensitivity analysis of the model parameters will also identify which experiments are critical). Here we will discuss the more interesting areas – the detailed modeling of eCFP and Encapsulin pathways. This will be accomplished by incorporating previous modeling efforts that are applicable to the eCFP and Encapsulin proteins. <br />
<br />
===Degredation of eCFP===<br />
<br />
The expression and degradation of [http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=95514&blobtype=pdf Green Fluorescent Protein (GFP) was modeled previously]. This paper noted that GFP must mature before going into fluorescent phase, and GFP degradation was shown to follow M-M kinetics, as depicted below. This paper also outlined how the degradation parameters could be derived for any expression system using only simple fluorescence and optical density measurements.<br />
<br />
[[Image:uft_mod_ecfp1.png | centre | thumb | Degredation and maturation pathways for eCFP. (Leveau and Lindow 2001)]]<br />
<br />
<br />
The GFP maturation and degradation parameters found in this paper were:<br />
<br />
<html><br />
<centre><br />
<table><br />
<tr><td> m = 0.0004279 1/s </td></tr><br />
<tr><td> Vmax = 2E-10 molality/s </td></tr><br />
<tr><td> Km = 9E-13 molality/s </td></tr><br />
<tr><td> </td></tr><br />
</table><br />
</centre><br />
</html><br />
<br />
<br />
Assuming eCFPt would behave similarly to eGFP, the following additional reactions would be included in the model:<br />
<br />
<html><br />
<table><br />
<tr> <td><b> Maturation </b></td> <td> </td> </tr><br />
<tr> <td> eCFPt --> F_eCFPT </td> <td> 0.0004279 </td> </tr><br />
<tr> <td> Enc2:eCFPt --> Enc2:F_eCFPt </td> <td> 0.0004279 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Encapsulation </b></td> <td> </td> </tr><br />
<tr> <td> Enc2 + F_eCFPt --> Enc2:F_eCFPt </td> <td> 100 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Degradation </b></td> <td> </td> </tr><br />
<tr> <td> eCFPt --> </td> <td> Vmax = 2E-10 </td> </tr><br />
<tr> <td> </td> <td> Km = 9E-13 </td> </tr><br />
<tr> <td> F_eCFPt --> </td> <td> Vmax = 2E-10 </td> </tr><br />
<tr> <td> </td> <td> Km = 9E-13 </td> </tr><br />
</table><br />
</html><br />
<br />
===Assembly of Encapsulin Microcompartments===<br />
<br />
Though Encapsulin microcompartment assembly is not well-studied, it has been theorized to resemble the assembly of viral capsids. Thus, we could look to this relatively well-studied phenomenon as a representation of Encapsulin microcompartment assembly.<br />
<br />
Adam Zlotnick has published models of viral capsid assembly using different approaches. An early paper described an equilibrium model of assembly for a 12 Unit polyhedral capsid head, and a more recent paper used a kinetic model that could be applied to many examples of spherical polymerization. We will consider how each approach could be incorporated as a representation of Encapsulin assembly.<br />
<br />
'''1) Equilibrim Approach to Encapsulin Assembly'''<br />
<br />
Zlotnick's [[Media:Uft_mod_to_build_a_virus_capsid.pdf|Equilibrium-based model]] consists of reactions from an initial monomer subunit leading to a final capsid product. The sequential reactions take into account DeltaG for contact (Kn'), and parameters describing path degeneracy (varies for different intermediates).<br />
[[image:uft_mod_encap1.png|centre|thumb|Kn for assembly subunits based on path degeneracy. (Zlotnick 1994)]]<br />
<br />
Simulations from a preliminary incorporation of this approach are shown below. In this version of our basic model, Encapsulin assembles in a series of first order reactions. However, for simplicity, the rate constants are kept identical and do not take path degeneracy into account.<br />
<br />
<html><br />
<table><br />
<tr> <td><b> Encapsulin Assembly </b></td> <td> </td> </tr><br />
<tr> <td> 2 Enc --> Enc2 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 Enc2 --> Enc4 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 En4 --> Enc8 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 Enc8 --> Enc16 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 Enc16 --> Enc32 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 Enc16 --> Enc64 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td><b> Encapsulation </b></td> <td> </td> </tr><br />
<tr> <td> Enc64 + eCFPt --> Enc64:eCFPt </td> <td> 1.00E2 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
</table><br />
</html><br />
<br />
[[Image:uft_mod_enc1.png |frameless|300px]][[Image:uft_mod_enc2.png |frameless|300px]][[Image:uft_mod_enc3.png |frameless|300px]]<br />
<br />
<gallery caption=Equilibrium-based Encapsulin Assembly width=600px height=150px><br />
<center><br />
image:uft_mod_enc1.png<br />
image:uft_mod_enc2.png<br />
image:uft_mod_enc3.png<br />
</center><br />
</gallery><br />
<br />
Encapsulin assembly intermediates are observed to quickly come to a steady state. The last intermediate ''Enc64'' is the most depleted probably because of the formation of ''Enc64:eCFPt'' complex. Formation of ''Enc64:eCFPt'' then mirrors the production of ''eCFPt''. <br />
<br />
<br />
'''2) Kinetic Model of Spherical Polymerization'''<br />
<br />
A [http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1302223/pdf/12124301.pdf general kinetic model for the spherical polyermization] process is shown below. In our case, the initial monomer subunit concentration (''u'') would represent our expressed Encapsulin BioBrick, and the number of monomers in the final assembly (''N'') is thought to be 60. All of the included parameters can be calculated from the four basic parameters; the microscopic, per-contact equilibrium constant (KAcon), the nucleus size (nuc), the nucleation on-rate (f_nuc), and the elongation on-rate (f_elong). The referenced paper describes methods to aquire these parameters from kinetic experiments, and provides examples for N = 12 and 30 unit viral capsid assemblies.<br />
[[image:uft_mod_encap2.png| centre | thumb |System of ODEs to represent spherical polymerization, where ''u'' is the initial subunit concentration, ''m'' is the "mth" intermediate species, and ''N'' is the number of monomers in the final assembly. (Endres and Zlotnick 2002)]]<br />
<br />
<br />
<br />
Zlotnick's models also describe two important features of spherical polymerization that we should also expect to observe in Encapsulin assembly: kinetic trapping and nucleation. A kinetic trap occurs when the initial monomer subunit concentration or the deltaG of the first assembly reaction is too high. This results in over-initiation of assembly and quickly the reactions become starved for subunits. Kinetic trapping is prevented by the inclusion of nucleation, where the initial reactions occur at a slower rate because the first few intermediates in a series of reactions are less stable than downstream products. Essentially, nucleation serves as a “slow first step” that regulates the assembly pathway. <br />
<br />
It will be interesting to note how the translational dynamics of Encapsulin interplay with its assembly dynamics. Since our system does not start with any initial concentration of Encapsulin, there will be an optimum rate of production that essentially serves the role of nucleation – avoiding kinetic traps while still maintaining a maximum production of full Encapsulin assemblies.<br />
<br />
=References=<br />
<br />
1. Hill AD, Tomshine JR, Weeding EM, Sotiropoulos V, Kaznessis YN. ''SynBioSS: the synthetic biology modeling suite.'' Bioinformatics. 2008 Nov 1;24(21):2551-3. Epub 2008 Aug 30.<br />
[http://neptune.cems.umn.edu/designer/interface1.php SynBioSS Web Designer]<br />
<br />
2. Leveau JH, Lindow SE. ''Predictive and interpretive simulation of green fluorescent protein expression in<br />
reporter bacteria.'' J Bacteriol. 2001 Dec;183(23):6752-62.<br />
<br />
3. Endres D, Zlotnick A. ''Model-based analysis of assembly kinetics for virus capsids or other spherical<br />
polymers.'' Biophys J. 2002 Aug;83(2):1217-30.</div>FRhttp://2009.igem.org/File:Uft_mod_SAenc.pngFile:Uft mod SAenc.png2009-10-21T06:58:11Z<p>FR: uploaded a new version of "Image:Uft mod SAenc.png"</p>
<hr />
<div></div>FRhttp://2009.igem.org/File:Uft_mod_SAenc.pngFile:Uft mod SAenc.png2009-10-21T06:56:07Z<p>FR: </p>
<hr />
<div></div>FRhttp://2009.igem.org/Team:TorontoMaRSDiscovery/ModelingTeam:TorontoMaRSDiscovery/Modeling2009-10-21T06:55:47Z<p>FR: /* Sensitivity Analysis */</p>
<hr />
<div>[[image:To_igem_wiki_banner.jpg|965px]]<br />
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!align="center"|[[Team:TorontoMaRSDiscovery/Modeling|Modeling]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Bioinformatics|Bioinformatics]]<br />
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|}<br />
<br><br />
<br />
<br />
=Summary=<br />
<br />
A kinetic model of our system has been constructed. Approximate parameter values were gathered from online resources to represent all processes up to the production of the eCFP and Encapsulin proteins. Current simulations predict the production of these two proteins at various initial concentrations of IPTG and aTc effector molecules. Furthermore, we have outlined approaches for the detailed modelling of the eCFP degredation/maturation and Encapsulin assembly pathways.<br />
<br />
<br />
The initial simulations will be used to identify the critical concentration of Encapsulin mononomer required for microcompartment assembly. Subsequently, a detailed model of Encapsulin assembly will be integrated into the current model, and its parameters filled-in using parameter-scanning methods and experiments outlined in the relevant references. By comparing experimental measures of microcompartment formation with that predicted by the kinetic model, we aim to gain insight on the mechanisms of Encapsulin assembly.<br />
<br />
=Model=<br />
Our model is based on the following design (See Project Page for a full description of this system).<br />
[[image:BioBrick.png|thumb|centre|The Encapsulator]]<br />
<br />
The reaction framework was mainly generated using the [http://synbioss.sourceforge.net/ SynBioSS Designer (a really useful modeling tool for iGEM teams)], which also provides default parameter values. These parameter values have been gathered from various literature [http://neptune.cems.umn.edu/designer/designer_defaults.pdf sources], and should be taken as approximations. All units were taken to be (1 / molarity^n-1 * s), where n is the order of the reaction. For example, for the reaction 2 lacI --> lacI2, n = 2, thus the rate constant has the units 1/molality*s. <br />
<br />
The pathways for the expressed proteins, eCFPt and Encapsulin, need to be modeled in more detail. For example, in this basic model eCFPt is degraded via a first order reaction and Encapsulin makes a dimer complex. However, in reality fluorescent proteins have been shown to degreade via Micheales-menton kinetics and Encapsulin is thought to make a complex of about 60 monomers. These issues will be addressed in future work.<br />
<br />
The reactions can be accessed here:<br />
<br />
[[Model (open new page)]]<br />
<br />
[[Media:Uft_mod_Rxns2.xls|Model (download Excel file)]]<br />
<br />
=Simulations=<br />
<br />
All simulations were carried out using the [https://2009.igem.org/Partner_Offers SimBiology Matlab Toolbox], which was freely available to iGEM teams. <br />
<br />
===Accumulation of eCFP at Different Initial Concentrations of IPTG===<br />
<br />
[[Image:uft_mod_cfp-iptg.png | 900px]]<br />
<br />
The IPTG effector eventually loses effect, and the eCFP concentration approaches a maximum. This happens because the IPTG proteins eventually ''tie up'' all available LacI4 proteins, leaving the transcription and translation of eCFP to operate at its maxiumum rate. <br />
<br />
===Accumulation of Encapsulin monomer at Different Initial Concentrations of aTc===<br />
<br />
[[Image:uft_mod_enc-atc.png | 900px]]<br />
<br />
(NOTE: in order to observe Encapsulin monomer levels, the above simulations were carried out without any Encapsulin assembly reactions in place)<br />
<br />
The production of Encapsulin occurs at a slower rate than eCFP because the BBa_R0040 promoter has two tetR binding sites, resulting in more repression and more off-pathway scenarios. Thus, the Encapsulin concentration also seems assymptotic but at higher concentrations of aTc (relative to IPTG). <br />
<br />
It seems beneficial to have the Encapsulin protein under control of the BBa_R0040-tetR-aTc construct because at zero levels of aTc we can have essentially zero levels of Encapsulin (whereas even at zero levels of IPTG, there is still significantly more eCFP). This will enable us to probe extremely low concentrations of Encapsulin monomer when testing for optimal Encapsulin assembly conditions. The disadvantage is that if Encapsulin assembly requires a very high initial concentration of Encapsulin monomer, we would have to wait a long time to see microcompartments. If this later scenario is observed, it may be better to switch the eCFP and Encapsulin expression systems.<br />
<br />
===Sensitivity Analysis===<br />
<br />
Since all of our parameters are approximations from literature sources, those which have the greatest affect on system dynamics (ie. the most ''sensitive'' parameters) would be leading candidates to be experimentally determined. Currently we are interested in which parameters have the greatest effect on the production of eCFP and Encapsulin. Ideally, it would be best to experimentally determine these to "tighten-up" the model before incorporating the largely unexplored Encapsulin assembly pathways. <br />
<br />
'''1) Sensitivity of eCFP Production'''<br />
<br />
[[Image:uft_mod_SAecfp.png | centre]]<br />
<br />
'''2) Sensitivity of Encapsulin Production'''<br />
<br />
[[Image:uft_mod_SAenc.png | centre]]<br />
<br />
It can be seen that eCFP and Encapsulin production is largely sensitive to ''lacI_in'' and ''tetR_in'', which represent the rates of constitutive expression of the lacI and tetR repressors respectively. <br />
In our construct these are expressed using constitutive promoter bba_..., <br />
rate assigned by synbioss is...from which source<br />
The sensitivity results suggest that these rates should be experimentally determined for our system, for most accurate predictions.<br />
<br />
=Future Work=<br />
<br />
Improvements to the basic model presented above can be separated into three areas; 1) performing experiments to determine parameter values that are specific to our system, 2) more detailed modeling of eCFPt behavior, 3) more detailed modeling of Encapsulin assembly. <br />
<br />
The experiments required to determine general transcription and translation parameters need to be further researched, so this will be skipped over for now (the proposed sensitivity analysis of the model parameters will also identify which experiments are critical). Here we will discuss the more interesting areas – the detailed modeling of eCFP and Encapsulin pathways. This will be accomplished by incorporating previous modeling efforts that are applicable to the eCFP and Encapsulin proteins. <br />
<br />
===Degredation of eCFP===<br />
<br />
The expression and degradation of [http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=95514&blobtype=pdf Green Fluorescent Protein (GFP) was modeled previously]. This paper noted that GFP must mature before going into fluorescent phase, and GFP degradation was shown to follow M-M kinetics, as depicted below. This paper also outlined how the degradation parameters could be derived for any expression system using only simple fluorescence and optical density measurements.<br />
<br />
[[Image:uft_mod_ecfp1.png | centre | thumb | Degredation and maturation pathways for eCFP. (Leveau and Lindow 2001)]]<br />
<br />
<br />
The GFP maturation and degradation parameters found in this paper were:<br />
<br />
<html><br />
<centre><br />
<table><br />
<tr><td> m = 0.0004279 1/s </td></tr><br />
<tr><td> Vmax = 2E-10 molality/s </td></tr><br />
<tr><td> Km = 9E-13 molality/s </td></tr><br />
<tr><td> </td></tr><br />
</table><br />
</centre><br />
</html><br />
<br />
<br />
Assuming eCFPt would behave similarly to eGFP, the following additional reactions would be included in the model:<br />
<br />
<html><br />
<table><br />
<tr> <td><b> Maturation </b></td> <td> </td> </tr><br />
<tr> <td> eCFPt --> F_eCFPT </td> <td> 0.0004279 </td> </tr><br />
<tr> <td> Enc2:eCFPt --> Enc2:F_eCFPt </td> <td> 0.0004279 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Encapsulation </b></td> <td> </td> </tr><br />
<tr> <td> Enc2 + F_eCFPt --> Enc2:F_eCFPt </td> <td> 100 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Degradation </b></td> <td> </td> </tr><br />
<tr> <td> eCFPt --> </td> <td> Vmax = 2E-10 </td> </tr><br />
<tr> <td> </td> <td> Km = 9E-13 </td> </tr><br />
<tr> <td> F_eCFPt --> </td> <td> Vmax = 2E-10 </td> </tr><br />
<tr> <td> </td> <td> Km = 9E-13 </td> </tr><br />
</table><br />
</html><br />
<br />
===Assembly of Encapsulin Microcompartments===<br />
<br />
Though Encapsulin microcompartment assembly is not well-studied, it has been theorized to resemble the assembly of viral capsids. Thus, we could look to this relatively well-studied phenomenon as a representation of Encapsulin microcompartment assembly.<br />
<br />
Adam Zlotnick has published models of viral capsid assembly using different approaches. An early paper described an equilibrium model of assembly for a 12 Unit polyhedral capsid head, and a more recent paper used a kinetic model that could be applied to many examples of spherical polymerization. We will consider how each approach could be incorporated as a representation of Encapsulin assembly.<br />
<br />
'''1) Equilibrim Approach to Encapsulin Assembly'''<br />
<br />
Zlotnick's [[Media:Uft_mod_to_build_a_virus_capsid.pdf|Equilibrium-based model]] consists of reactions from an initial monomer subunit leading to a final capsid product. The sequential reactions take into account DeltaG for contact (Kn'), and parameters describing path degeneracy (varies for different intermediates).<br />
[[image:uft_mod_encap1.png|centre|thumb|Kn for assembly subunits based on path degeneracy. (Zlotnick 1994)]]<br />
<br />
Simulations from a preliminary incorporation of this approach are shown below. In this version of our basic model, Encapsulin assembles in a series of first order reactions. However, for simplicity, the rate constants are kept identical and do not take path degeneracy into account.<br />
<br />
<html><br />
<table><br />
<tr> <td><b> Encapsulin Assembly </b></td> <td> </td> </tr><br />
<tr> <td> 2 Enc --> Enc2 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 Enc2 --> Enc4 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 En4 --> Enc8 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 Enc8 --> Enc16 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 Enc16 --> Enc32 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 Enc16 --> Enc64 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td><b> Encapsulation </b></td> <td> </td> </tr><br />
<tr> <td> Enc64 + eCFPt --> Enc64:eCFPt </td> <td> 1.00E2 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
</table><br />
</html><br />
<br />
[[Image:uft_mod_enc1.png |frameless|300px]][[Image:uft_mod_enc2.png |frameless|300px]][[Image:uft_mod_enc3.png |frameless|300px]]<br />
<br />
<gallery caption=Equilibrium-based Encapsulin Assembly width=600px height=150px><br />
<center><br />
image:uft_mod_enc1.png<br />
image:uft_mod_enc2.png<br />
image:uft_mod_enc3.png<br />
</center><br />
</gallery><br />
<br />
Encapsulin assembly intermediates are observed to quickly come to a steady state. The last intermediate ''Enc64'' is the most depleted probably because of the formation of ''Enc64:eCFPt'' complex. Formation of ''Enc64:eCFPt'' then mirrors the production of ''eCFPt''. <br />
<br />
<br />
'''2) Kinetic Model of Spherical Polymerization'''<br />
<br />
A [http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1302223/pdf/12124301.pdf general kinetic model for the spherical polyermization] process is shown below. In our case, the initial monomer subunit concentration (''u'') would represent our expressed Encapsulin BioBrick, and the number of monomers in the final assembly (''N'') is thought to be 60. All of the included parameters can be calculated from the four basic parameters; the microscopic, per-contact equilibrium constant (KAcon), the nucleus size (nuc), the nucleation on-rate (f_nuc), and the elongation on-rate (f_elong). The referenced paper describes methods to aquire these parameters from kinetic experiments, and provides examples for N = 12 and 30 unit viral capsid assemblies.<br />
[[image:uft_mod_encap2.png| centre | thumb |System of ODEs to represent spherical polymerization, where ''u'' is the initial subunit concentration, ''m'' is the "mth" intermediate species, and ''N'' is the number of monomers in the final assembly. (Endres and Zlotnick 2002)]]<br />
<br />
<br />
<br />
Zlotnick's models also describe two important features of spherical polymerization that we should also expect to observe in Encapsulin assembly: kinetic trapping and nucleation. A kinetic trap occurs when the initial monomer subunit concentration or the deltaG of the first assembly reaction is too high. This results in over-initiation of assembly and quickly the reactions become starved for subunits. Kinetic trapping is prevented by the inclusion of nucleation, where the initial reactions occur at a slower rate because the first few intermediates in a series of reactions are less stable than downstream products. Essentially, nucleation serves as a “slow first step” that regulates the assembly pathway. <br />
<br />
It will be interesting to note how the translational dynamics of Encapsulin interplay with its assembly dynamics. Since our system does not start with any initial concentration of Encapsulin, there will be an optimum rate of production that essentially serves the role of nucleation – avoiding kinetic traps while still maintaining a maximum production of full Encapsulin assemblies.<br />
<br />
=References=<br />
<br />
1. Hill AD, Tomshine JR, Weeding EM, Sotiropoulos V, Kaznessis YN. ''SynBioSS: the synthetic biology modeling suite.'' Bioinformatics. 2008 Nov 1;24(21):2551-3. Epub 2008 Aug 30.<br />
[http://neptune.cems.umn.edu/designer/interface1.php SynBioSS Web Designer]<br />
<br />
2. Leveau JH, Lindow SE. ''Predictive and interpretive simulation of green fluorescent protein expression in<br />
reporter bacteria.'' J Bacteriol. 2001 Dec;183(23):6752-62.<br />
<br />
3. Endres D, Zlotnick A. ''Model-based analysis of assembly kinetics for virus capsids or other spherical<br />
polymers.'' Biophys J. 2002 Aug;83(2):1217-30.</div>FRhttp://2009.igem.org/Team:TorontoMaRSDiscovery/ModelingTeam:TorontoMaRSDiscovery/Modeling2009-10-21T06:55:10Z<p>FR: /* Sensitivity Analysis */</p>
<hr />
<div>[[image:To_igem_wiki_banner.jpg|965px]]<br />
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!align="center"|[[Team:TorontoMaRSDiscovery|Home]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Team|The Team]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Project|The Project]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Parts|BioBricks]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Modeling|Modeling]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Bioinformatics|Bioinformatics]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Safety|Safety]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Notebook|Notebook]]<br />
|}<br />
<br><br />
<br />
<br />
=Summary=<br />
<br />
A kinetic model of our system has been constructed. Approximate parameter values were gathered from online resources to represent all processes up to the production of the eCFP and Encapsulin proteins. Current simulations predict the production of these two proteins at various initial concentrations of IPTG and aTc effector molecules. Furthermore, we have outlined approaches for the detailed modelling of the eCFP degredation/maturation and Encapsulin assembly pathways.<br />
<br />
<br />
The initial simulations will be used to identify the critical concentration of Encapsulin mononomer required for microcompartment assembly. Subsequently, a detailed model of Encapsulin assembly will be integrated into the current model, and its parameters filled-in using parameter-scanning methods and experiments outlined in the relevant references. By comparing experimental measures of microcompartment formation with that predicted by the kinetic model, we aim to gain insight on the mechanisms of Encapsulin assembly.<br />
<br />
=Model=<br />
Our model is based on the following design (See Project Page for a full description of this system).<br />
[[image:BioBrick.png|thumb|centre|The Encapsulator]]<br />
<br />
The reaction framework was mainly generated using the [http://synbioss.sourceforge.net/ SynBioSS Designer (a really useful modeling tool for iGEM teams)], which also provides default parameter values. These parameter values have been gathered from various literature [http://neptune.cems.umn.edu/designer/designer_defaults.pdf sources], and should be taken as approximations. All units were taken to be (1 / molarity^n-1 * s), where n is the order of the reaction. For example, for the reaction 2 lacI --> lacI2, n = 2, thus the rate constant has the units 1/molality*s. <br />
<br />
The pathways for the expressed proteins, eCFPt and Encapsulin, need to be modeled in more detail. For example, in this basic model eCFPt is degraded via a first order reaction and Encapsulin makes a dimer complex. However, in reality fluorescent proteins have been shown to degreade via Micheales-menton kinetics and Encapsulin is thought to make a complex of about 60 monomers. These issues will be addressed in future work.<br />
<br />
The reactions can be accessed here:<br />
<br />
[[Model (open new page)]]<br />
<br />
[[Media:Uft_mod_Rxns2.xls|Model (download Excel file)]]<br />
<br />
=Simulations=<br />
<br />
All simulations were carried out using the [https://2009.igem.org/Partner_Offers SimBiology Matlab Toolbox], which was freely available to iGEM teams. <br />
<br />
===Accumulation of eCFP at Different Initial Concentrations of IPTG===<br />
<br />
[[Image:uft_mod_cfp-iptg.png | 900px]]<br />
<br />
The IPTG effector eventually loses effect, and the eCFP concentration approaches a maximum. This happens because the IPTG proteins eventually ''tie up'' all available LacI4 proteins, leaving the transcription and translation of eCFP to operate at its maxiumum rate. <br />
<br />
===Accumulation of Encapsulin monomer at Different Initial Concentrations of aTc===<br />
<br />
[[Image:uft_mod_enc-atc.png | 900px]]<br />
<br />
(NOTE: in order to observe Encapsulin monomer levels, the above simulations were carried out without any Encapsulin assembly reactions in place)<br />
<br />
The production of Encapsulin occurs at a slower rate than eCFP because the BBa_R0040 promoter has two tetR binding sites, resulting in more repression and more off-pathway scenarios. Thus, the Encapsulin concentration also seems assymptotic but at higher concentrations of aTc (relative to IPTG). <br />
<br />
It seems beneficial to have the Encapsulin protein under control of the BBa_R0040-tetR-aTc construct because at zero levels of aTc we can have essentially zero levels of Encapsulin (whereas even at zero levels of IPTG, there is still significantly more eCFP). This will enable us to probe extremely low concentrations of Encapsulin monomer when testing for optimal Encapsulin assembly conditions. The disadvantage is that if Encapsulin assembly requires a very high initial concentration of Encapsulin monomer, we would have to wait a long time to see microcompartments. If this later scenario is observed, it may be better to switch the eCFP and Encapsulin expression systems.<br />
<br />
===Sensitivity Analysis===<br />
<br />
Since all of our parameters are approximations from literature sources, those which have the greatest affect on system dynamics (ie. the most ''sensitive'' parameters) would be leading candidates to be experimentally determined. Currently we are interested in which parameters have the greatest effect on the production of eCFP and Encapsulin. Ideally, it would be best to experimentally determine these to "tighten-up" the model before incorporating the largely unexplored Encapsulin assembly pathways. <br />
<br />
'''1) Sensitivity of eCFP Production'''<br />
<br />
[[Image:uft_mod_SAecfp.png | centre]]<br />
<br />
'''2) Sensitivity of Encapsulin Production'''<br />
<br />
It can be seen that eCFP and Encapsulin production is largely sensitive to ''lacI_in'' and ''tetR_in'', which represent the rates of constitutive expression of the lacI and tetR repressors respectively. <br />
In our construct these are expressed using constitutive promoter bba_..., <br />
rate assigned by synbioss is...from which source<br />
The sensitivity results suggest that these rates should be experimentally determined for our system, for most accurate predictions.<br />
<br />
=Future Work=<br />
<br />
Improvements to the basic model presented above can be separated into three areas; 1) performing experiments to determine parameter values that are specific to our system, 2) more detailed modeling of eCFPt behavior, 3) more detailed modeling of Encapsulin assembly. <br />
<br />
The experiments required to determine general transcription and translation parameters need to be further researched, so this will be skipped over for now (the proposed sensitivity analysis of the model parameters will also identify which experiments are critical). Here we will discuss the more interesting areas – the detailed modeling of eCFP and Encapsulin pathways. This will be accomplished by incorporating previous modeling efforts that are applicable to the eCFP and Encapsulin proteins. <br />
<br />
===Degredation of eCFP===<br />
<br />
The expression and degradation of [http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=95514&blobtype=pdf Green Fluorescent Protein (GFP) was modeled previously]. This paper noted that GFP must mature before going into fluorescent phase, and GFP degradation was shown to follow M-M kinetics, as depicted below. This paper also outlined how the degradation parameters could be derived for any expression system using only simple fluorescence and optical density measurements.<br />
<br />
[[Image:uft_mod_ecfp1.png | centre | thumb | Degredation and maturation pathways for eCFP. (Leveau and Lindow 2001)]]<br />
<br />
<br />
The GFP maturation and degradation parameters found in this paper were:<br />
<br />
<html><br />
<centre><br />
<table><br />
<tr><td> m = 0.0004279 1/s </td></tr><br />
<tr><td> Vmax = 2E-10 molality/s </td></tr><br />
<tr><td> Km = 9E-13 molality/s </td></tr><br />
<tr><td> </td></tr><br />
</table><br />
</centre><br />
</html><br />
<br />
<br />
Assuming eCFPt would behave similarly to eGFP, the following additional reactions would be included in the model:<br />
<br />
<html><br />
<table><br />
<tr> <td><b> Maturation </b></td> <td> </td> </tr><br />
<tr> <td> eCFPt --> F_eCFPT </td> <td> 0.0004279 </td> </tr><br />
<tr> <td> Enc2:eCFPt --> Enc2:F_eCFPt </td> <td> 0.0004279 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Encapsulation </b></td> <td> </td> </tr><br />
<tr> <td> Enc2 + F_eCFPt --> Enc2:F_eCFPt </td> <td> 100 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Degradation </b></td> <td> </td> </tr><br />
<tr> <td> eCFPt --> </td> <td> Vmax = 2E-10 </td> </tr><br />
<tr> <td> </td> <td> Km = 9E-13 </td> </tr><br />
<tr> <td> F_eCFPt --> </td> <td> Vmax = 2E-10 </td> </tr><br />
<tr> <td> </td> <td> Km = 9E-13 </td> </tr><br />
</table><br />
</html><br />
<br />
===Assembly of Encapsulin Microcompartments===<br />
<br />
Though Encapsulin microcompartment assembly is not well-studied, it has been theorized to resemble the assembly of viral capsids. Thus, we could look to this relatively well-studied phenomenon as a representation of Encapsulin microcompartment assembly.<br />
<br />
Adam Zlotnick has published models of viral capsid assembly using different approaches. An early paper described an equilibrium model of assembly for a 12 Unit polyhedral capsid head, and a more recent paper used a kinetic model that could be applied to many examples of spherical polymerization. We will consider how each approach could be incorporated as a representation of Encapsulin assembly.<br />
<br />
'''1) Equilibrim Approach to Encapsulin Assembly'''<br />
<br />
Zlotnick's [[Media:Uft_mod_to_build_a_virus_capsid.pdf|Equilibrium-based model]] consists of reactions from an initial monomer subunit leading to a final capsid product. The sequential reactions take into account DeltaG for contact (Kn'), and parameters describing path degeneracy (varies for different intermediates).<br />
[[image:uft_mod_encap1.png|centre|thumb|Kn for assembly subunits based on path degeneracy. (Zlotnick 1994)]]<br />
<br />
Simulations from a preliminary incorporation of this approach are shown below. In this version of our basic model, Encapsulin assembles in a series of first order reactions. However, for simplicity, the rate constants are kept identical and do not take path degeneracy into account.<br />
<br />
<html><br />
<table><br />
<tr> <td><b> Encapsulin Assembly </b></td> <td> </td> </tr><br />
<tr> <td> 2 Enc --> Enc2 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 Enc2 --> Enc4 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 En4 --> Enc8 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 Enc8 --> Enc16 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 Enc16 --> Enc32 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 Enc16 --> Enc64 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td><b> Encapsulation </b></td> <td> </td> </tr><br />
<tr> <td> Enc64 + eCFPt --> Enc64:eCFPt </td> <td> 1.00E2 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
</table><br />
</html><br />
<br />
[[Image:uft_mod_enc1.png |frameless|300px]][[Image:uft_mod_enc2.png |frameless|300px]][[Image:uft_mod_enc3.png |frameless|300px]]<br />
<br />
<gallery caption=Equilibrium-based Encapsulin Assembly width=600px height=150px><br />
<center><br />
image:uft_mod_enc1.png<br />
image:uft_mod_enc2.png<br />
image:uft_mod_enc3.png<br />
</center><br />
</gallery><br />
<br />
Encapsulin assembly intermediates are observed to quickly come to a steady state. The last intermediate ''Enc64'' is the most depleted probably because of the formation of ''Enc64:eCFPt'' complex. Formation of ''Enc64:eCFPt'' then mirrors the production of ''eCFPt''. <br />
<br />
<br />
'''2) Kinetic Model of Spherical Polymerization'''<br />
<br />
A [http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1302223/pdf/12124301.pdf general kinetic model for the spherical polyermization] process is shown below. In our case, the initial monomer subunit concentration (''u'') would represent our expressed Encapsulin BioBrick, and the number of monomers in the final assembly (''N'') is thought to be 60. All of the included parameters can be calculated from the four basic parameters; the microscopic, per-contact equilibrium constant (KAcon), the nucleus size (nuc), the nucleation on-rate (f_nuc), and the elongation on-rate (f_elong). The referenced paper describes methods to aquire these parameters from kinetic experiments, and provides examples for N = 12 and 30 unit viral capsid assemblies.<br />
[[image:uft_mod_encap2.png| centre | thumb |System of ODEs to represent spherical polymerization, where ''u'' is the initial subunit concentration, ''m'' is the "mth" intermediate species, and ''N'' is the number of monomers in the final assembly. (Endres and Zlotnick 2002)]]<br />
<br />
<br />
<br />
Zlotnick's models also describe two important features of spherical polymerization that we should also expect to observe in Encapsulin assembly: kinetic trapping and nucleation. A kinetic trap occurs when the initial monomer subunit concentration or the deltaG of the first assembly reaction is too high. This results in over-initiation of assembly and quickly the reactions become starved for subunits. Kinetic trapping is prevented by the inclusion of nucleation, where the initial reactions occur at a slower rate because the first few intermediates in a series of reactions are less stable than downstream products. Essentially, nucleation serves as a “slow first step” that regulates the assembly pathway. <br />
<br />
It will be interesting to note how the translational dynamics of Encapsulin interplay with its assembly dynamics. Since our system does not start with any initial concentration of Encapsulin, there will be an optimum rate of production that essentially serves the role of nucleation – avoiding kinetic traps while still maintaining a maximum production of full Encapsulin assemblies.<br />
<br />
=References=<br />
<br />
1. Hill AD, Tomshine JR, Weeding EM, Sotiropoulos V, Kaznessis YN. ''SynBioSS: the synthetic biology modeling suite.'' Bioinformatics. 2008 Nov 1;24(21):2551-3. Epub 2008 Aug 30.<br />
[http://neptune.cems.umn.edu/designer/interface1.php SynBioSS Web Designer]<br />
<br />
2. Leveau JH, Lindow SE. ''Predictive and interpretive simulation of green fluorescent protein expression in<br />
reporter bacteria.'' J Bacteriol. 2001 Dec;183(23):6752-62.<br />
<br />
3. Endres D, Zlotnick A. ''Model-based analysis of assembly kinetics for virus capsids or other spherical<br />
polymers.'' Biophys J. 2002 Aug;83(2):1217-30.</div>FRhttp://2009.igem.org/File:Uft_mod_SAecfp.pngFile:Uft mod SAecfp.png2009-10-21T06:54:16Z<p>FR: uploaded a new version of "Image:Uft mod SAecfp.png"</p>
<hr />
<div></div>FRhttp://2009.igem.org/File:Uft_mod_SAecfp.pngFile:Uft mod SAecfp.png2009-10-21T06:45:01Z<p>FR: </p>
<hr />
<div></div>FRhttp://2009.igem.org/Team:TorontoMaRSDiscovery/ModelingTeam:TorontoMaRSDiscovery/Modeling2009-10-21T06:44:50Z<p>FR: /* Sensitivity Analysis */</p>
<hr />
<div>[[image:To_igem_wiki_banner.jpg|965px]]<br />
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!align="center"|[[Team:TorontoMaRSDiscovery|Home]]<br />
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!align="center"|[[Team:TorontoMaRSDiscovery/Modeling|Modeling]]<br />
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|}<br />
<br><br />
<br />
<br />
=Summary=<br />
<br />
A kinetic model of our system has been constructed. Approximate parameter values were gathered from online resources to represent all processes up to the production of the eCFP and Encapsulin proteins. Current simulations predict the production of these two proteins at various initial concentrations of IPTG and aTc effector molecules. Furthermore, we have outlined approaches for the detailed modelling of the eCFP degredation/maturation and Encapsulin assembly pathways.<br />
<br />
<br />
The initial simulations will be used to identify the critical concentration of Encapsulin mononomer required for microcompartment assembly. Subsequently, a detailed model of Encapsulin assembly will be integrated into the current model, and its parameters filled-in using parameter-scanning methods and experiments outlined in the relevant references. By comparing experimental measures of microcompartment formation with that predicted by the kinetic model, we aim to gain insight on the mechanisms of Encapsulin assembly.<br />
<br />
=Model=<br />
Our model is based on the following design (See Project Page for a full description of this system).<br />
[[image:BioBrick.png|thumb|centre|The Encapsulator]]<br />
<br />
The reaction framework was mainly generated using the [http://synbioss.sourceforge.net/ SynBioSS Designer (a really useful modeling tool for iGEM teams)], which also provides default parameter values. These parameter values have been gathered from various literature [http://neptune.cems.umn.edu/designer/designer_defaults.pdf sources], and should be taken as approximations. All units were taken to be (1 / molarity^n-1 * s), where n is the order of the reaction. For example, for the reaction 2 lacI --> lacI2, n = 2, thus the rate constant has the units 1/molality*s. <br />
<br />
The pathways for the expressed proteins, eCFPt and Encapsulin, need to be modeled in more detail. For example, in this basic model eCFPt is degraded via a first order reaction and Encapsulin makes a dimer complex. However, in reality fluorescent proteins have been shown to degreade via Micheales-menton kinetics and Encapsulin is thought to make a complex of about 60 monomers. These issues will be addressed in future work.<br />
<br />
The reactions can be accessed here:<br />
<br />
[[Model (open new page)]]<br />
<br />
[[Media:Uft_mod_Rxns2.xls|Model (download Excel file)]]<br />
<br />
=Simulations=<br />
<br />
All simulations were carried out using the [https://2009.igem.org/Partner_Offers SimBiology Matlab Toolbox], which was freely available to iGEM teams. <br />
<br />
===Accumulation of eCFP at Different Initial Concentrations of IPTG===<br />
<br />
[[Image:uft_mod_cfp-iptg.png | 900px]]<br />
<br />
The IPTG effector eventually loses effect, and the eCFP concentration approaches a maximum. This happens because the IPTG proteins eventually ''tie up'' all available LacI4 proteins, leaving the transcription and translation of eCFP to operate at its maxiumum rate. <br />
<br />
===Accumulation of Encapsulin monomer at Different Initial Concentrations of aTc===<br />
<br />
[[Image:uft_mod_enc-atc.png | 900px]]<br />
<br />
(NOTE: in order to observe Encapsulin monomer levels, the above simulations were carried out without any Encapsulin assembly reactions in place)<br />
<br />
The production of Encapsulin occurs at a slower rate than eCFP because the BBa_R0040 promoter has two tetR binding sites, resulting in more repression and more off-pathway scenarios. Thus, the Encapsulin concentration also seems assymptotic but at higher concentrations of aTc (relative to IPTG). <br />
<br />
It seems beneficial to have the Encapsulin protein under control of the BBa_R0040-tetR-aTc construct because at zero levels of aTc we can have essentially zero levels of Encapsulin (whereas even at zero levels of IPTG, there is still significantly more eCFP). This will enable us to probe extremely low concentrations of Encapsulin monomer when testing for optimal Encapsulin assembly conditions. The disadvantage is that if Encapsulin assembly requires a very high initial concentration of Encapsulin monomer, we would have to wait a long time to see microcompartments. If this later scenario is observed, it may be better to switch the eCFP and Encapsulin expression systems.<br />
<br />
===Sensitivity Analysis===<br />
<br />
Since all of our parameters are approximations from literature sources, those which have the greatest affect on system dynamics (ie. the most ''sensitive'' parameters) would be leading candidates to be experimentally determined. Currently we are interested in which parameters have the greatest effect on the production of eCFP and Encapsulin. Ideally, it would be best to experimentally determine these to "tighten-up" the model before incorporating the largely unexplored Encapsulin assembly pathways. <br />
<br />
'''1) Sensitivity of eCFP Production'''<br />
<br />
[[Image:uft_mod_SAecfp.png]]<br />
<br />
'''2) Sensitivity of Encapsulin Production'''<br />
<br />
It can be seen that eCFP and Encapsulin production is largely sensitive to ''lacI_in'' and ''tetR_in'', which represent the rates of constitutive expression of the lacI and tetR repressors respectively. <br />
In our construct these are expressed using constitutive promoter bba_..., <br />
rate assigned by synbioss is...from which source<br />
The sensitivity results suggest that these rates should be experimentally determined for our system, for most accurate predictions.<br />
<br />
=Future Work=<br />
<br />
Improvements to the basic model presented above can be separated into three areas; 1) performing experiments to determine parameter values that are specific to our system, 2) more detailed modeling of eCFPt behavior, 3) more detailed modeling of Encapsulin assembly. <br />
<br />
The experiments required to determine general transcription and translation parameters need to be further researched, so this will be skipped over for now (the proposed sensitivity analysis of the model parameters will also identify which experiments are critical). Here we will discuss the more interesting areas – the detailed modeling of eCFP and Encapsulin pathways. This will be accomplished by incorporating previous modeling efforts that are applicable to the eCFP and Encapsulin proteins. <br />
<br />
===Degredation of eCFP===<br />
<br />
The expression and degradation of [http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=95514&blobtype=pdf Green Fluorescent Protein (GFP) was modeled previously]. This paper noted that GFP must mature before going into fluorescent phase, and GFP degradation was shown to follow M-M kinetics, as depicted below. This paper also outlined how the degradation parameters could be derived for any expression system using only simple fluorescence and optical density measurements.<br />
<br />
[[Image:uft_mod_ecfp1.png | centre | thumb | Degredation and maturation pathways for eCFP. (Leveau and Lindow 2001)]]<br />
<br />
<br />
The GFP maturation and degradation parameters found in this paper were:<br />
<br />
<html><br />
<centre><br />
<table><br />
<tr><td> m = 0.0004279 1/s </td></tr><br />
<tr><td> Vmax = 2E-10 molality/s </td></tr><br />
<tr><td> Km = 9E-13 molality/s </td></tr><br />
<tr><td> </td></tr><br />
</table><br />
</centre><br />
</html><br />
<br />
<br />
Assuming eCFPt would behave similarly to eGFP, the following additional reactions would be included in the model:<br />
<br />
<html><br />
<table><br />
<tr> <td><b> Maturation </b></td> <td> </td> </tr><br />
<tr> <td> eCFPt --> F_eCFPT </td> <td> 0.0004279 </td> </tr><br />
<tr> <td> Enc2:eCFPt --> Enc2:F_eCFPt </td> <td> 0.0004279 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Encapsulation </b></td> <td> </td> </tr><br />
<tr> <td> Enc2 + F_eCFPt --> Enc2:F_eCFPt </td> <td> 100 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Degradation </b></td> <td> </td> </tr><br />
<tr> <td> eCFPt --> </td> <td> Vmax = 2E-10 </td> </tr><br />
<tr> <td> </td> <td> Km = 9E-13 </td> </tr><br />
<tr> <td> F_eCFPt --> </td> <td> Vmax = 2E-10 </td> </tr><br />
<tr> <td> </td> <td> Km = 9E-13 </td> </tr><br />
</table><br />
</html><br />
<br />
===Assembly of Encapsulin Microcompartments===<br />
<br />
Though Encapsulin microcompartment assembly is not well-studied, it has been theorized to resemble the assembly of viral capsids. Thus, we could look to this relatively well-studied phenomenon as a representation of Encapsulin microcompartment assembly.<br />
<br />
Adam Zlotnick has published models of viral capsid assembly using different approaches. An early paper described an equilibrium model of assembly for a 12 Unit polyhedral capsid head, and a more recent paper used a kinetic model that could be applied to many examples of spherical polymerization. We will consider how each approach could be incorporated as a representation of Encapsulin assembly.<br />
<br />
'''1) Equilibrim Approach to Encapsulin Assembly'''<br />
<br />
Zlotnick's [[Media:Uft_mod_to_build_a_virus_capsid.pdf|Equilibrium-based model]] consists of reactions from an initial monomer subunit leading to a final capsid product. The sequential reactions take into account DeltaG for contact (Kn'), and parameters describing path degeneracy (varies for different intermediates).<br />
[[image:uft_mod_encap1.png|centre|thumb|Kn for assembly subunits based on path degeneracy. (Zlotnick 1994)]]<br />
<br />
Simulations from a preliminary incorporation of this approach are shown below. In this version of our basic model, Encapsulin assembles in a series of first order reactions. However, for simplicity, the rate constants are kept identical and do not take path degeneracy into account.<br />
<br />
<html><br />
<table><br />
<tr> <td><b> Encapsulin Assembly </b></td> <td> </td> </tr><br />
<tr> <td> 2 Enc --> Enc2 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 Enc2 --> Enc4 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 En4 --> Enc8 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 Enc8 --> Enc16 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 Enc16 --> Enc32 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 Enc16 --> Enc64 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td><b> Encapsulation </b></td> <td> </td> </tr><br />
<tr> <td> Enc64 + eCFPt --> Enc64:eCFPt </td> <td> 1.00E2 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
</table><br />
</html><br />
<br />
[[Image:uft_mod_enc1.png |frameless|300px]][[Image:uft_mod_enc2.png |frameless|300px]][[Image:uft_mod_enc3.png |frameless|300px]]<br />
<br />
<gallery caption=Equilibrium-based Encapsulin Assembly width=600px height=150px><br />
<center><br />
image:uft_mod_enc1.png<br />
image:uft_mod_enc2.png<br />
image:uft_mod_enc3.png<br />
</center><br />
</gallery><br />
<br />
Encapsulin assembly intermediates are observed to quickly come to a steady state. The last intermediate ''Enc64'' is the most depleted probably because of the formation of ''Enc64:eCFPt'' complex. Formation of ''Enc64:eCFPt'' then mirrors the production of ''eCFPt''. <br />
<br />
<br />
'''2) Kinetic Model of Spherical Polymerization'''<br />
<br />
A [http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1302223/pdf/12124301.pdf general kinetic model for the spherical polyermization] process is shown below. In our case, the initial monomer subunit concentration (''u'') would represent our expressed Encapsulin BioBrick, and the number of monomers in the final assembly (''N'') is thought to be 60. All of the included parameters can be calculated from the four basic parameters; the microscopic, per-contact equilibrium constant (KAcon), the nucleus size (nuc), the nucleation on-rate (f_nuc), and the elongation on-rate (f_elong). The referenced paper describes methods to aquire these parameters from kinetic experiments, and provides examples for N = 12 and 30 unit viral capsid assemblies.<br />
[[image:uft_mod_encap2.png| centre | thumb |System of ODEs to represent spherical polymerization, where ''u'' is the initial subunit concentration, ''m'' is the "mth" intermediate species, and ''N'' is the number of monomers in the final assembly. (Endres and Zlotnick 2002)]]<br />
<br />
<br />
<br />
Zlotnick's models also describe two important features of spherical polymerization that we should also expect to observe in Encapsulin assembly: kinetic trapping and nucleation. A kinetic trap occurs when the initial monomer subunit concentration or the deltaG of the first assembly reaction is too high. This results in over-initiation of assembly and quickly the reactions become starved for subunits. Kinetic trapping is prevented by the inclusion of nucleation, where the initial reactions occur at a slower rate because the first few intermediates in a series of reactions are less stable than downstream products. Essentially, nucleation serves as a “slow first step” that regulates the assembly pathway. <br />
<br />
It will be interesting to note how the translational dynamics of Encapsulin interplay with its assembly dynamics. Since our system does not start with any initial concentration of Encapsulin, there will be an optimum rate of production that essentially serves the role of nucleation – avoiding kinetic traps while still maintaining a maximum production of full Encapsulin assemblies.<br />
<br />
=References=<br />
<br />
1. Hill AD, Tomshine JR, Weeding EM, Sotiropoulos V, Kaznessis YN. ''SynBioSS: the synthetic biology modeling suite.'' Bioinformatics. 2008 Nov 1;24(21):2551-3. Epub 2008 Aug 30.<br />
[http://neptune.cems.umn.edu/designer/interface1.php SynBioSS Web Designer]<br />
<br />
2. Leveau JH, Lindow SE. ''Predictive and interpretive simulation of green fluorescent protein expression in<br />
reporter bacteria.'' J Bacteriol. 2001 Dec;183(23):6752-62.<br />
<br />
3. Endres D, Zlotnick A. ''Model-based analysis of assembly kinetics for virus capsids or other spherical<br />
polymers.'' Biophys J. 2002 Aug;83(2):1217-30.</div>FRhttp://2009.igem.org/Team:TorontoMaRSDiscovery/ModelingTeam:TorontoMaRSDiscovery/Modeling2009-10-21T06:43:10Z<p>FR: /* Simulations */</p>
<hr />
<div>[[image:To_igem_wiki_banner.jpg|965px]]<br />
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!align="center"|[[Team:TorontoMaRSDiscovery|Home]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Team|The Team]]<br />
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!align="center"|[[Team:TorontoMaRSDiscovery/Modeling|Modeling]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Bioinformatics|Bioinformatics]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Safety|Safety]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Notebook|Notebook]]<br />
|}<br />
<br><br />
<br />
<br />
=Summary=<br />
<br />
A kinetic model of our system has been constructed. Approximate parameter values were gathered from online resources to represent all processes up to the production of the eCFP and Encapsulin proteins. Current simulations predict the production of these two proteins at various initial concentrations of IPTG and aTc effector molecules. Furthermore, we have outlined approaches for the detailed modelling of the eCFP degredation/maturation and Encapsulin assembly pathways.<br />
<br />
<br />
The initial simulations will be used to identify the critical concentration of Encapsulin mononomer required for microcompartment assembly. Subsequently, a detailed model of Encapsulin assembly will be integrated into the current model, and its parameters filled-in using parameter-scanning methods and experiments outlined in the relevant references. By comparing experimental measures of microcompartment formation with that predicted by the kinetic model, we aim to gain insight on the mechanisms of Encapsulin assembly.<br />
<br />
=Model=<br />
Our model is based on the following design (See Project Page for a full description of this system).<br />
[[image:BioBrick.png|thumb|centre|The Encapsulator]]<br />
<br />
The reaction framework was mainly generated using the [http://synbioss.sourceforge.net/ SynBioSS Designer (a really useful modeling tool for iGEM teams)], which also provides default parameter values. These parameter values have been gathered from various literature [http://neptune.cems.umn.edu/designer/designer_defaults.pdf sources], and should be taken as approximations. All units were taken to be (1 / molarity^n-1 * s), where n is the order of the reaction. For example, for the reaction 2 lacI --> lacI2, n = 2, thus the rate constant has the units 1/molality*s. <br />
<br />
The pathways for the expressed proteins, eCFPt and Encapsulin, need to be modeled in more detail. For example, in this basic model eCFPt is degraded via a first order reaction and Encapsulin makes a dimer complex. However, in reality fluorescent proteins have been shown to degreade via Micheales-menton kinetics and Encapsulin is thought to make a complex of about 60 monomers. These issues will be addressed in future work.<br />
<br />
The reactions can be accessed here:<br />
<br />
[[Model (open new page)]]<br />
<br />
[[Media:Uft_mod_Rxns2.xls|Model (download Excel file)]]<br />
<br />
=Simulations=<br />
<br />
All simulations were carried out using the [https://2009.igem.org/Partner_Offers SimBiology Matlab Toolbox], which was freely available to iGEM teams. <br />
<br />
===Accumulation of eCFP at Different Initial Concentrations of IPTG===<br />
<br />
[[Image:uft_mod_cfp-iptg.png | 900px]]<br />
<br />
The IPTG effector eventually loses effect, and the eCFP concentration approaches a maximum. This happens because the IPTG proteins eventually ''tie up'' all available LacI4 proteins, leaving the transcription and translation of eCFP to operate at its maxiumum rate. <br />
<br />
===Accumulation of Encapsulin monomer at Different Initial Concentrations of aTc===<br />
<br />
[[Image:uft_mod_enc-atc.png | 900px]]<br />
<br />
(NOTE: in order to observe Encapsulin monomer levels, the above simulations were carried out without any Encapsulin assembly reactions in place)<br />
<br />
The production of Encapsulin occurs at a slower rate than eCFP because the BBa_R0040 promoter has two tetR binding sites, resulting in more repression and more off-pathway scenarios. Thus, the Encapsulin concentration also seems assymptotic but at higher concentrations of aTc (relative to IPTG). <br />
<br />
It seems beneficial to have the Encapsulin protein under control of the BBa_R0040-tetR-aTc construct because at zero levels of aTc we can have essentially zero levels of Encapsulin (whereas even at zero levels of IPTG, there is still significantly more eCFP). This will enable us to probe extremely low concentrations of Encapsulin monomer when testing for optimal Encapsulin assembly conditions. The disadvantage is that if Encapsulin assembly requires a very high initial concentration of Encapsulin monomer, we would have to wait a long time to see microcompartments. If this later scenario is observed, it may be better to switch the eCFP and Encapsulin expression systems.<br />
<br />
===Sensitivity Analysis===<br />
<br />
Since all of our parameters are approximations from literature sources, those which have the greatest affect on system dynamics (ie. the most ''sensitive'' parameters) would be leading candidates to be experimentally determined. Currently we are interested in which parameters have the greatest effect on the production of eCFP and Encapsulin. Ideally, it would be best to experimentally determine these to "tighten-up" the model before incorporating the largely unexplored Encapsulin assembly pathways. <br />
<br />
'''1) Sensitivity of eCFP Production'''<br />
<br />
[[Image:uft_mod_SAecfp.bmp]]<br />
<br />
'''2) Sensitivity of Encapsulin Production'''<br />
<br />
It can be seen that eCFP and Encapsulin production is largely sensitive to ''lacI_in'' and ''tetR_in'', which represent the rates of constitutive expression of the lacI and tetR repressors respectively. <br />
In our construct these are expressed using constitutive promoter bba_..., <br />
rate assigned by synbioss is...from which source<br />
The sensitivity results suggest that these rates should be experimentally determined for our system, for most accurate predictions.<br />
<br />
=Future Work=<br />
<br />
Improvements to the basic model presented above can be separated into three areas; 1) performing experiments to determine parameter values that are specific to our system, 2) more detailed modeling of eCFPt behavior, 3) more detailed modeling of Encapsulin assembly. <br />
<br />
The experiments required to determine general transcription and translation parameters need to be further researched, so this will be skipped over for now (the proposed sensitivity analysis of the model parameters will also identify which experiments are critical). Here we will discuss the more interesting areas – the detailed modeling of eCFP and Encapsulin pathways. This will be accomplished by incorporating previous modeling efforts that are applicable to the eCFP and Encapsulin proteins. <br />
<br />
===Degredation of eCFP===<br />
<br />
The expression and degradation of [http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=95514&blobtype=pdf Green Fluorescent Protein (GFP) was modeled previously]. This paper noted that GFP must mature before going into fluorescent phase, and GFP degradation was shown to follow M-M kinetics, as depicted below. This paper also outlined how the degradation parameters could be derived for any expression system using only simple fluorescence and optical density measurements.<br />
<br />
[[Image:uft_mod_ecfp1.png | centre | thumb | Degredation and maturation pathways for eCFP. (Leveau and Lindow 2001)]]<br />
<br />
<br />
The GFP maturation and degradation parameters found in this paper were:<br />
<br />
<html><br />
<centre><br />
<table><br />
<tr><td> m = 0.0004279 1/s </td></tr><br />
<tr><td> Vmax = 2E-10 molality/s </td></tr><br />
<tr><td> Km = 9E-13 molality/s </td></tr><br />
<tr><td> </td></tr><br />
</table><br />
</centre><br />
</html><br />
<br />
<br />
Assuming eCFPt would behave similarly to eGFP, the following additional reactions would be included in the model:<br />
<br />
<html><br />
<table><br />
<tr> <td><b> Maturation </b></td> <td> </td> </tr><br />
<tr> <td> eCFPt --> F_eCFPT </td> <td> 0.0004279 </td> </tr><br />
<tr> <td> Enc2:eCFPt --> Enc2:F_eCFPt </td> <td> 0.0004279 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Encapsulation </b></td> <td> </td> </tr><br />
<tr> <td> Enc2 + F_eCFPt --> Enc2:F_eCFPt </td> <td> 100 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Degradation </b></td> <td> </td> </tr><br />
<tr> <td> eCFPt --> </td> <td> Vmax = 2E-10 </td> </tr><br />
<tr> <td> </td> <td> Km = 9E-13 </td> </tr><br />
<tr> <td> F_eCFPt --> </td> <td> Vmax = 2E-10 </td> </tr><br />
<tr> <td> </td> <td> Km = 9E-13 </td> </tr><br />
</table><br />
</html><br />
<br />
===Assembly of Encapsulin Microcompartments===<br />
<br />
Though Encapsulin microcompartment assembly is not well-studied, it has been theorized to resemble the assembly of viral capsids. Thus, we could look to this relatively well-studied phenomenon as a representation of Encapsulin microcompartment assembly.<br />
<br />
Adam Zlotnick has published models of viral capsid assembly using different approaches. An early paper described an equilibrium model of assembly for a 12 Unit polyhedral capsid head, and a more recent paper used a kinetic model that could be applied to many examples of spherical polymerization. We will consider how each approach could be incorporated as a representation of Encapsulin assembly.<br />
<br />
'''1) Equilibrim Approach to Encapsulin Assembly'''<br />
<br />
Zlotnick's [[Media:Uft_mod_to_build_a_virus_capsid.pdf|Equilibrium-based model]] consists of reactions from an initial monomer subunit leading to a final capsid product. The sequential reactions take into account DeltaG for contact (Kn'), and parameters describing path degeneracy (varies for different intermediates).<br />
[[image:uft_mod_encap1.png|centre|thumb|Kn for assembly subunits based on path degeneracy. (Zlotnick 1994)]]<br />
<br />
Simulations from a preliminary incorporation of this approach are shown below. In this version of our basic model, Encapsulin assembles in a series of first order reactions. However, for simplicity, the rate constants are kept identical and do not take path degeneracy into account.<br />
<br />
<html><br />
<table><br />
<tr> <td><b> Encapsulin Assembly </b></td> <td> </td> </tr><br />
<tr> <td> 2 Enc --> Enc2 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 Enc2 --> Enc4 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 En4 --> Enc8 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 Enc8 --> Enc16 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 Enc16 --> Enc32 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 Enc16 --> Enc64 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td><b> Encapsulation </b></td> <td> </td> </tr><br />
<tr> <td> Enc64 + eCFPt --> Enc64:eCFPt </td> <td> 1.00E2 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
</table><br />
</html><br />
<br />
[[Image:uft_mod_enc1.png |frameless|300px]][[Image:uft_mod_enc2.png |frameless|300px]][[Image:uft_mod_enc3.png |frameless|300px]]<br />
<br />
<gallery caption=Equilibrium-based Encapsulin Assembly width=600px height=150px><br />
<center><br />
image:uft_mod_enc1.png<br />
image:uft_mod_enc2.png<br />
image:uft_mod_enc3.png<br />
</center><br />
</gallery><br />
<br />
Encapsulin assembly intermediates are observed to quickly come to a steady state. The last intermediate ''Enc64'' is the most depleted probably because of the formation of ''Enc64:eCFPt'' complex. Formation of ''Enc64:eCFPt'' then mirrors the production of ''eCFPt''. <br />
<br />
<br />
'''2) Kinetic Model of Spherical Polymerization'''<br />
<br />
A [http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1302223/pdf/12124301.pdf general kinetic model for the spherical polyermization] process is shown below. In our case, the initial monomer subunit concentration (''u'') would represent our expressed Encapsulin BioBrick, and the number of monomers in the final assembly (''N'') is thought to be 60. All of the included parameters can be calculated from the four basic parameters; the microscopic, per-contact equilibrium constant (KAcon), the nucleus size (nuc), the nucleation on-rate (f_nuc), and the elongation on-rate (f_elong). The referenced paper describes methods to aquire these parameters from kinetic experiments, and provides examples for N = 12 and 30 unit viral capsid assemblies.<br />
[[image:uft_mod_encap2.png| centre | thumb |System of ODEs to represent spherical polymerization, where ''u'' is the initial subunit concentration, ''m'' is the "mth" intermediate species, and ''N'' is the number of monomers in the final assembly. (Endres and Zlotnick 2002)]]<br />
<br />
<br />
<br />
Zlotnick's models also describe two important features of spherical polymerization that we should also expect to observe in Encapsulin assembly: kinetic trapping and nucleation. A kinetic trap occurs when the initial monomer subunit concentration or the deltaG of the first assembly reaction is too high. This results in over-initiation of assembly and quickly the reactions become starved for subunits. Kinetic trapping is prevented by the inclusion of nucleation, where the initial reactions occur at a slower rate because the first few intermediates in a series of reactions are less stable than downstream products. Essentially, nucleation serves as a “slow first step” that regulates the assembly pathway. <br />
<br />
It will be interesting to note how the translational dynamics of Encapsulin interplay with its assembly dynamics. Since our system does not start with any initial concentration of Encapsulin, there will be an optimum rate of production that essentially serves the role of nucleation – avoiding kinetic traps while still maintaining a maximum production of full Encapsulin assemblies.<br />
<br />
=References=<br />
<br />
1. Hill AD, Tomshine JR, Weeding EM, Sotiropoulos V, Kaznessis YN. ''SynBioSS: the synthetic biology modeling suite.'' Bioinformatics. 2008 Nov 1;24(21):2551-3. Epub 2008 Aug 30.<br />
[http://neptune.cems.umn.edu/designer/interface1.php SynBioSS Web Designer]<br />
<br />
2. Leveau JH, Lindow SE. ''Predictive and interpretive simulation of green fluorescent protein expression in<br />
reporter bacteria.'' J Bacteriol. 2001 Dec;183(23):6752-62.<br />
<br />
3. Endres D, Zlotnick A. ''Model-based analysis of assembly kinetics for virus capsids or other spherical<br />
polymers.'' Biophys J. 2002 Aug;83(2):1217-30.</div>FRhttp://2009.igem.org/Team:TorontoMaRSDiscovery/ModelingTeam:TorontoMaRSDiscovery/Modeling2009-10-21T03:55:39Z<p>FR: /* Sensitivity Analysis */</p>
<hr />
<div>[[image:To_igem_wiki_banner.jpg|965px]]<br />
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!align="center"|[[Team:TorontoMaRSDiscovery|Home]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Team|The Team]]<br />
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!align="center"|[[Team:TorontoMaRSDiscovery/Parts|BioBricks]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Modeling|Modeling]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Bioinformatics|Bioinformatics]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Safety|Safety]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Notebook|Notebook]]<br />
|}<br />
<br><br />
<br />
<br />
=Summary=<br />
<br />
A kinetic model of our system has been constructed. Approximate parameter values were gathered from online resources to represent all processes up to the production of the eCFP and Encapsulin proteins. Current simulations predict the production of these two proteins at various initial concentrations of IPTG and aTc effector molecules. Furthermore, we have outlined approaches for the detailed modelling of the eCFP degredation/maturation and Encapsulin assembly pathways.<br />
<br />
<br />
The initial simulations will be used to identify the critical concentration of Encapsulin mononomer required for microcompartment assembly. Subsequently, a detailed model of Encapsulin assembly will be integrated into the current model, and its parameters filled-in using parameter-scanning methods and experiments outlined in the relevant references. By comparing experimental measures of microcompartment formation with that predicted by the kinetic model, we aim to gain insight on the mechanisms of Encapsulin assembly.<br />
<br />
=Model=<br />
Our model is based on the following design (See Project Page for a full description of this system).<br />
[[image:BioBrick.png|thumb|centre|The Encapsulator]]<br />
<br />
The reaction framework was mainly generated using the [http://synbioss.sourceforge.net/ SynBioSS Designer (a really useful modeling tool for iGEM teams)], which also provides default parameter values. These parameter values have been gathered from various literature [http://neptune.cems.umn.edu/designer/designer_defaults.pdf sources], and should be taken as approximations. All units were taken to be (1 / molarity^n-1 * s), where n is the order of the reaction. For example, for the reaction 2 lacI --> lacI2, n = 2, thus the rate constant has the units 1/molality*s. <br />
<br />
The pathways for the expressed proteins, eCFPt and Encapsulin, need to be modeled in more detail. For example, in this basic model eCFPt is degraded via a first order reaction and Encapsulin makes a dimer complex. However, in reality fluorescent proteins have been shown to degreade via Micheales-menton kinetics and Encapsulin is thought to make a complex of about 60 monomers. These issues will be addressed in future work.<br />
<br />
The reactions can be accessed here:<br />
<br />
[[Model (open new page)]]<br />
<br />
[[Media:Uft_mod_Rxns2.xls|Model (download Excel file)]]<br />
<br />
=Simulations=<br />
<br />
All simulations were carried out using the [https://2009.igem.org/Partner_Offers SimBiology Matlab Toolbox], which was freely available to iGEM teams. <br />
<br />
===Accumulation of eCFP at Different Initial Concentrations of IPTG===<br />
<br />
[[Image:uft_mod_cfp-iptg.png | 900px]]<br />
<br />
The IPTG effector eventually loses effect, and the eCFP concentration approaches a maximum. This happens because the IPTG proteins eventually ''tie up'' all available LacI4 proteins, leaving the transcription and translation of eCFP to operate at its maxiumum rate. <br />
<br />
===Accumulation of Encapsulin monomer at Different Initial Concentrations of aTc===<br />
<br />
[[Image:uft_mod_enc-atc.png | 900px]]<br />
<br />
(NOTE: in order to observe Encapsulin monomer levels, the above simulations were carried out without any Encapsulin assembly reactions in place)<br />
<br />
The production of Encapsulin occurs at a slower rate than eCFP because the BBa_R0040 promoter has two tetR binding sites, resulting in more repression and more off-pathway scenarios. Thus, the Encapsulin concentration also seems assymptotic but at higher concentrations of aTc (relative to IPTG). <br />
<br />
It seems beneficial to have the Encapsulin protein under control of the BBa_R0040-tetR-aTc construct because at zero levels of aTc we can have essentially zero levels of Encapsulin (whereas even at zero levels of IPTG, there is still significantly more eCFP). This will enable us to probe extremely low concentrations of Encapsulin monomer when testing for optimal Encapsulin assembly conditions. The disadvantage is that if Encapsulin assembly requires a very high initial concentration of Encapsulin monomer, we would have to wait a long time to see microcompartments. If this later scenario is observed, it may be better to switch the eCFP and Encapsulin expression systems.<br />
<br />
===Sensitivity Analysis===<br />
<br />
Since all of our parameters are approximations from literature sources, those which have the greatest affect on system dynamics (ie. the most ''sensitive'' parameters) would be leading candidates to be experimentally determined. Currently we are interested in which parameters have the greatest effect on the production of eCFP and Encapsulin. Ideally, it would be best to experimentally determine these to "tighten-up" the model before incorporating the largely unexplored Encapsulin assembly pathways. <br />
<br />
'''1) Sensitivity of eCFP Production'''<br />
<br />
'''2) Sensitivity of Encapsulin Production'''<br />
<br />
It can be seen that eCFP and Encapsulin production is largely sensitive to ''lacI_in'' and ''tetR_in'', which represent the rates of constitutive expression of the lacI and tetR repressors respectively. <br />
In our construct these are expressed using constitutive promoter bba_..., <br />
rate assigned by synbioss is...from which source<br />
The sensitivity results suggest that these rates should be experimentally determined for our system, for most accurate predictions.<br />
<br />
=Future Work=<br />
<br />
Improvements to the basic model presented above can be separated into three areas; 1) performing experiments to determine parameter values that are specific to our system, 2) more detailed modeling of eCFPt behavior, 3) more detailed modeling of Encapsulin assembly. <br />
<br />
The experiments required to determine general transcription and translation parameters need to be further researched, so this will be skipped over for now (the proposed sensitivity analysis of the model parameters will also identify which experiments are critical). Here we will discuss the more interesting areas – the detailed modeling of eCFP and Encapsulin pathways. This will be accomplished by incorporating previous modeling efforts that are applicable to the eCFP and Encapsulin proteins. <br />
<br />
===Degredation of eCFP===<br />
<br />
The expression and degradation of [http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=95514&blobtype=pdf Green Fluorescent Protein (GFP) was modeled previously]. This paper noted that GFP must mature before going into fluorescent phase, and GFP degradation was shown to follow M-M kinetics, as depicted below. This paper also outlined how the degradation parameters could be derived for any expression system using only simple fluorescence and optical density measurements.<br />
<br />
[[Image:uft_mod_ecfp1.png | centre | thumb | Degredation and maturation pathways for eCFP. (Leveau and Lindow 2001)]]<br />
<br />
<br />
The GFP maturation and degradation parameters found in this paper were:<br />
<br />
<html><br />
<centre><br />
<table><br />
<tr><td> m = 0.0004279 1/s </td></tr><br />
<tr><td> Vmax = 2E-10 molality/s </td></tr><br />
<tr><td> Km = 9E-13 molality/s </td></tr><br />
<tr><td> </td></tr><br />
</table><br />
</centre><br />
</html><br />
<br />
<br />
Assuming eCFPt would behave similarly to eGFP, the following additional reactions would be included in the model:<br />
<br />
<html><br />
<table><br />
<tr> <td><b> Maturation </b></td> <td> </td> </tr><br />
<tr> <td> eCFPt --> F_eCFPT </td> <td> 0.0004279 </td> </tr><br />
<tr> <td> Enc2:eCFPt --> Enc2:F_eCFPt </td> <td> 0.0004279 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Encapsulation </b></td> <td> </td> </tr><br />
<tr> <td> Enc2 + F_eCFPt --> Enc2:F_eCFPt </td> <td> 100 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Degradation </b></td> <td> </td> </tr><br />
<tr> <td> eCFPt --> </td> <td> Vmax = 2E-10 </td> </tr><br />
<tr> <td> </td> <td> Km = 9E-13 </td> </tr><br />
<tr> <td> F_eCFPt --> </td> <td> Vmax = 2E-10 </td> </tr><br />
<tr> <td> </td> <td> Km = 9E-13 </td> </tr><br />
</table><br />
</html><br />
<br />
===Assembly of Encapsulin Microcompartments===<br />
<br />
Though Encapsulin microcompartment assembly is not well-studied, it has been theorized to resemble the assembly of viral capsids. Thus, we could look to this relatively well-studied phenomenon as a representation of Encapsulin microcompartment assembly.<br />
<br />
Adam Zlotnick has published models of viral capsid assembly using different approaches. An early paper described an equilibrium model of assembly for a 12 Unit polyhedral capsid head, and a more recent paper used a kinetic model that could be applied to many examples of spherical polymerization. We will consider how each approach could be incorporated as a representation of Encapsulin assembly.<br />
<br />
'''1) Equilibrim Approach to Encapsulin Assembly'''<br />
<br />
Zlotnick's [[Media:Uft_mod_to_build_a_virus_capsid.pdf|Equilibrium-based model]] consists of reactions from an initial monomer subunit leading to a final capsid product. The sequential reactions take into account DeltaG for contact (Kn'), and parameters describing path degeneracy (varies for different intermediates).<br />
[[image:uft_mod_encap1.png|centre|thumb|Kn for assembly subunits based on path degeneracy. (Zlotnick 1994)]]<br />
<br />
Simulations from a preliminary incorporation of this approach are shown below. In this version of our basic model, Encapsulin assembles in a series of first order reactions. However, for simplicity, the rate constants are kept identical and do not take path degeneracy into account.<br />
<br />
<html><br />
<table><br />
<tr> <td><b> Encapsulin Assembly </b></td> <td> </td> </tr><br />
<tr> <td> 2 Enc --> Enc2 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 Enc2 --> Enc4 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 En4 --> Enc8 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 Enc8 --> Enc16 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 Enc16 --> Enc32 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 Enc16 --> Enc64 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td><b> Encapsulation </b></td> <td> </td> </tr><br />
<tr> <td> Enc64 + eCFPt --> Enc64:eCFPt </td> <td> 1.00E2 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
</table><br />
</html><br />
<br />
[[Image:uft_mod_enc1.png |frameless|300px]][[Image:uft_mod_enc2.png |frameless|300px]][[Image:uft_mod_enc3.png |frameless|300px]]<br />
<br />
<gallery caption=Equilibrium-based Encapsulin Assembly width=600px height=150px><br />
<center><br />
image:uft_mod_enc1.png<br />
image:uft_mod_enc2.png<br />
image:uft_mod_enc3.png<br />
</center><br />
</gallery><br />
<br />
Encapsulin assembly intermediates are observed to quickly come to a steady state. The last intermediate ''Enc64'' is the most depleted probably because of the formation of ''Enc64:eCFPt'' complex. Formation of ''Enc64:eCFPt'' then mirrors the production of ''eCFPt''. <br />
<br />
<br />
'''2) Kinetic Model of Spherical Polymerization'''<br />
<br />
A [http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1302223/pdf/12124301.pdf general kinetic model for the spherical polyermization] process is shown below. In our case, the initial monomer subunit concentration (''u'') would represent our expressed Encapsulin BioBrick, and the number of monomers in the final assembly (''N'') is thought to be 60. All of the included parameters can be calculated from the four basic parameters; the microscopic, per-contact equilibrium constant (KAcon), the nucleus size (nuc), the nucleation on-rate (f_nuc), and the elongation on-rate (f_elong). The referenced paper describes methods to aquire these parameters from kinetic experiments, and provides examples for N = 12 and 30 unit viral capsid assemblies.<br />
[[image:uft_mod_encap2.png| centre | thumb |System of ODEs to represent spherical polymerization, where ''u'' is the initial subunit concentration, ''m'' is the "mth" intermediate species, and ''N'' is the number of monomers in the final assembly. (Endres and Zlotnick 2002)]]<br />
<br />
<br />
<br />
Zlotnick's models also describe two important features of spherical polymerization that we should also expect to observe in Encapsulin assembly: kinetic trapping and nucleation. A kinetic trap occurs when the initial monomer subunit concentration or the deltaG of the first assembly reaction is too high. This results in over-initiation of assembly and quickly the reactions become starved for subunits. Kinetic trapping is prevented by the inclusion of nucleation, where the initial reactions occur at a slower rate because the first few intermediates in a series of reactions are less stable than downstream products. Essentially, nucleation serves as a “slow first step” that regulates the assembly pathway. <br />
<br />
It will be interesting to note how the translational dynamics of Encapsulin interplay with its assembly dynamics. Since our system does not start with any initial concentration of Encapsulin, there will be an optimum rate of production that essentially serves the role of nucleation – avoiding kinetic traps while still maintaining a maximum production of full Encapsulin assemblies.<br />
<br />
=References=<br />
<br />
1. Hill AD, Tomshine JR, Weeding EM, Sotiropoulos V, Kaznessis YN. ''SynBioSS: the synthetic biology modeling suite.'' Bioinformatics. 2008 Nov 1;24(21):2551-3. Epub 2008 Aug 30.<br />
[http://neptune.cems.umn.edu/designer/interface1.php SynBioSS Web Designer]<br />
<br />
2. Leveau JH, Lindow SE. ''Predictive and interpretive simulation of green fluorescent protein expression in<br />
reporter bacteria.'' J Bacteriol. 2001 Dec;183(23):6752-62.<br />
<br />
3. Endres D, Zlotnick A. ''Model-based analysis of assembly kinetics for virus capsids or other spherical<br />
polymers.'' Biophys J. 2002 Aug;83(2):1217-30.</div>FRhttp://2009.igem.org/Team:TorontoMaRSDiscovery/ModelingTeam:TorontoMaRSDiscovery/Modeling2009-10-21T03:40:07Z<p>FR: /* Sensitivity Analysis */</p>
<hr />
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!align="center"|[[Team:TorontoMaRSDiscovery|Home]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Team|The Team]]<br />
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!align="center"|[[Team:TorontoMaRSDiscovery/Modeling|Modeling]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Bioinformatics|Bioinformatics]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Safety|Safety]]<br />
!align="center"|[[Team:TorontoMaRSDiscovery/Notebook|Notebook]]<br />
|}<br />
<br><br />
<br />
<br />
=Summary=<br />
<br />
A kinetic model of our system has been constructed. Approximate parameter values were gathered from online resources to represent all processes up to the production of the eCFP and Encapsulin proteins. Current simulations predict the production of these two proteins at various initial concentrations of IPTG and aTc effector molecules. Furthermore, we have outlined approaches for the detailed modelling of the eCFP degredation/maturation and Encapsulin assembly pathways.<br />
<br />
<br />
The initial simulations will be used to identify the critical concentration of Encapsulin mononomer required for microcompartment assembly. Subsequently, a detailed model of Encapsulin assembly will be integrated into the current model, and its parameters filled-in using parameter-scanning methods and experiments outlined in the relevant references. By comparing experimental measures of microcompartment formation with that predicted by the kinetic model, we aim to gain insight on the mechanisms of Encapsulin assembly.<br />
<br />
=Model=<br />
Our model is based on the following design (See Project Page for a full description of this system).<br />
[[image:BioBrick.png|thumb|centre|The Encapsulator]]<br />
<br />
The reaction framework was mainly generated using the [http://synbioss.sourceforge.net/ SynBioSS Designer (a really useful modeling tool for iGEM teams)], which also provides default parameter values. These parameter values have been gathered from various literature [http://neptune.cems.umn.edu/designer/designer_defaults.pdf sources], and should be taken as approximations. All units were taken to be (1 / molarity^n-1 * s), where n is the order of the reaction. For example, for the reaction 2 lacI --> lacI2, n = 2, thus the rate constant has the units 1/molality*s. <br />
<br />
The pathways for the expressed proteins, eCFPt and Encapsulin, need to be modeled in more detail. For example, in this basic model eCFPt is degraded via a first order reaction and Encapsulin makes a dimer complex. However, in reality fluorescent proteins have been shown to degreade via Micheales-menton kinetics and Encapsulin is thought to make a complex of about 60 monomers. These issues will be addressed in future work.<br />
<br />
The reactions can be accessed here:<br />
<br />
[[Model (open new page)]]<br />
<br />
[[Media:Uft_mod_Rxns2.xls|Model (download Excel file)]]<br />
<br />
=Simulations=<br />
<br />
All simulations were carried out using the [https://2009.igem.org/Partner_Offers SimBiology Matlab Toolbox], which was freely available to iGEM teams. <br />
<br />
===Accumulation of eCFP at Different Initial Concentrations of IPTG===<br />
<br />
[[Image:uft_mod_cfp-iptg.png | 900px]]<br />
<br />
The IPTG effector eventually loses effect, and the eCFP concentration approaches a maximum. This happens because the IPTG proteins eventually ''tie up'' all available LacI4 proteins, leaving the transcription and translation of eCFP to operate at its maxiumum rate. <br />
<br />
===Accumulation of Encapsulin monomer at Different Initial Concentrations of aTc===<br />
<br />
[[Image:uft_mod_enc-atc.png | 900px]]<br />
<br />
(NOTE: in order to observe Encapsulin monomer levels, the above simulations were carried out without any Encapsulin assembly reactions in place)<br />
<br />
The production of Encapsulin occurs at a slower rate than eCFP because the BBa_R0040 promoter has two tetR binding sites, resulting in more repression and more off-pathway scenarios. Thus, the Encapsulin concentration also seems assymptotic but at higher concentrations of aTc (relative to IPTG). <br />
<br />
It seems beneficial to have the Encapsulin protein under control of the BBa_R0040-tetR-aTc construct because at zero levels of aTc we can have essentially zero levels of Encapsulin (whereas even at zero levels of IPTG, there is still significantly more eCFP). This will enable us to probe extremely low concentrations of Encapsulin monomer when testing for optimal Encapsulin assembly conditions. The disadvantage is that if Encapsulin assembly requires a very high initial concentration of Encapsulin monomer, we would have to wait a long time to see microcompartments. If this later scenario is observed, it may be better to switch the eCFP and Encapsulin expression systems.<br />
<br />
===Sensitivity Analysis===<br />
<br />
Currently we are interested in which parameters have the greatest effect on the production of eCFP and Encapsulin proteins. Since all of our parameters are approximations from literature sources, the most ''sensitive'' parameters would be leading candidates to be experimentally determined.<br />
<br />
=Future Work=<br />
<br />
Improvements to the basic model presented above can be separated into three areas; 1) performing experiments to determine parameter values that are specific to our system, 2) more detailed modeling of eCFPt behavior, 3) more detailed modeling of Encapsulin assembly. <br />
<br />
The experiments required to determine general transcription and translation parameters need to be further researched, so this will be skipped over for now (the proposed sensitivity analysis of the model parameters will also identify which experiments are critical). Here we will discuss the more interesting areas – the detailed modeling of eCFP and Encapsulin pathways. This will be accomplished by incorporating previous modeling efforts that are applicable to the eCFP and Encapsulin proteins. <br />
<br />
===Degredation of eCFP===<br />
<br />
The expression and degradation of [http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=95514&blobtype=pdf Green Fluorescent Protein (GFP) was modeled previously]. This paper noted that GFP must mature before going into fluorescent phase, and GFP degradation was shown to follow M-M kinetics, as depicted below. This paper also outlined how the degradation parameters could be derived for any expression system using only simple fluorescence and optical density measurements.<br />
<br />
[[Image:uft_mod_ecfp1.png | centre | thumb | Degredation and maturation pathways for eCFP. (Leveau and Lindow 2001)]]<br />
<br />
<br />
The GFP maturation and degradation parameters found in this paper were:<br />
<br />
<html><br />
<centre><br />
<table><br />
<tr><td> m = 0.0004279 1/s </td></tr><br />
<tr><td> Vmax = 2E-10 molality/s </td></tr><br />
<tr><td> Km = 9E-13 molality/s </td></tr><br />
<tr><td> </td></tr><br />
</table><br />
</centre><br />
</html><br />
<br />
<br />
Assuming eCFPt would behave similarly to eGFP, the following additional reactions would be included in the model:<br />
<br />
<html><br />
<table><br />
<tr> <td><b> Maturation </b></td> <td> </td> </tr><br />
<tr> <td> eCFPt --> F_eCFPT </td> <td> 0.0004279 </td> </tr><br />
<tr> <td> Enc2:eCFPt --> Enc2:F_eCFPt </td> <td> 0.0004279 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Encapsulation </b></td> <td> </td> </tr><br />
<tr> <td> Enc2 + F_eCFPt --> Enc2:F_eCFPt </td> <td> 100 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Degradation </b></td> <td> </td> </tr><br />
<tr> <td> eCFPt --> </td> <td> Vmax = 2E-10 </td> </tr><br />
<tr> <td> </td> <td> Km = 9E-13 </td> </tr><br />
<tr> <td> F_eCFPt --> </td> <td> Vmax = 2E-10 </td> </tr><br />
<tr> <td> </td> <td> Km = 9E-13 </td> </tr><br />
</table><br />
</html><br />
<br />
===Assembly of Encapsulin Microcompartments===<br />
<br />
Though Encapsulin microcompartment assembly is not well-studied, it has been theorized to resemble the assembly of viral capsids. Thus, we could look to this relatively well-studied phenomenon as a representation of Encapsulin microcompartment assembly.<br />
<br />
Adam Zlotnick has published models of viral capsid assembly using different approaches. An early paper described an equilibrium model of assembly for a 12 Unit polyhedral capsid head, and a more recent paper used a kinetic model that could be applied to many examples of spherical polymerization. We will consider how each approach could be incorporated as a representation of Encapsulin assembly.<br />
<br />
'''1) Equilibrim Approach to Encapsulin Assembly'''<br />
<br />
Zlotnick's [[Media:Uft_mod_to_build_a_virus_capsid.pdf|Equilibrium-based model]] consists of reactions from an initial monomer subunit leading to a final capsid product. The sequential reactions take into account DeltaG for contact (Kn'), and parameters describing path degeneracy (varies for different intermediates).<br />
[[image:uft_mod_encap1.png|centre|thumb|Kn for assembly subunits based on path degeneracy. (Zlotnick 1994)]]<br />
<br />
Simulations from a preliminary incorporation of this approach are shown below. In this version of our basic model, Encapsulin assembles in a series of first order reactions. However, for simplicity, the rate constants are kept identical and do not take path degeneracy into account.<br />
<br />
<html><br />
<table><br />
<tr> <td><b> Encapsulin Assembly </b></td> <td> </td> </tr><br />
<tr> <td> 2 Enc --> Enc2 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 Enc2 --> Enc4 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 En4 --> Enc8 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 Enc8 --> Enc16 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 Enc16 --> Enc32 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 Enc16 --> Enc64 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td><b> Encapsulation </b></td> <td> </td> </tr><br />
<tr> <td> Enc64 + eCFPt --> Enc64:eCFPt </td> <td> 1.00E2 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
</table><br />
</html><br />
<br />
[[Image:uft_mod_enc1.png |frameless|300px]][[Image:uft_mod_enc2.png |frameless|300px]][[Image:uft_mod_enc3.png |frameless|300px]]<br />
<br />
<gallery caption=Equilibrium-based Encapsulin Assembly width=600px height=150px><br />
<center><br />
image:uft_mod_enc1.png<br />
image:uft_mod_enc2.png<br />
image:uft_mod_enc3.png<br />
</center><br />
</gallery><br />
<br />
Encapsulin assembly intermediates are observed to quickly come to a steady state. The last intermediate ''Enc64'' is the most depleted probably because of the formation of ''Enc64:eCFPt'' complex. Formation of ''Enc64:eCFPt'' then mirrors the production of ''eCFPt''. <br />
<br />
<br />
'''2) Kinetic Model of Spherical Polymerization'''<br />
<br />
A [http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1302223/pdf/12124301.pdf general kinetic model for the spherical polyermization] process is shown below. In our case, the initial monomer subunit concentration (''u'') would represent our expressed Encapsulin BioBrick, and the number of monomers in the final assembly (''N'') is thought to be 60. All of the included parameters can be calculated from the four basic parameters; the microscopic, per-contact equilibrium constant (KAcon), the nucleus size (nuc), the nucleation on-rate (f_nuc), and the elongation on-rate (f_elong). The referenced paper describes methods to aquire these parameters from kinetic experiments, and provides examples for N = 12 and 30 unit viral capsid assemblies.<br />
[[image:uft_mod_encap2.png| centre | thumb |System of ODEs to represent spherical polymerization, where ''u'' is the initial subunit concentration, ''m'' is the "mth" intermediate species, and ''N'' is the number of monomers in the final assembly. (Endres and Zlotnick 2002)]]<br />
<br />
<br />
<br />
Zlotnick's models also describe two important features of spherical polymerization that we should also expect to observe in Encapsulin assembly: kinetic trapping and nucleation. A kinetic trap occurs when the initial monomer subunit concentration or the deltaG of the first assembly reaction is too high. This results in over-initiation of assembly and quickly the reactions become starved for subunits. Kinetic trapping is prevented by the inclusion of nucleation, where the initial reactions occur at a slower rate because the first few intermediates in a series of reactions are less stable than downstream products. Essentially, nucleation serves as a “slow first step” that regulates the assembly pathway. <br />
<br />
It will be interesting to note how the translational dynamics of Encapsulin interplay with its assembly dynamics. Since our system does not start with any initial concentration of Encapsulin, there will be an optimum rate of production that essentially serves the role of nucleation – avoiding kinetic traps while still maintaining a maximum production of full Encapsulin assemblies.<br />
<br />
=References=<br />
<br />
1. Hill AD, Tomshine JR, Weeding EM, Sotiropoulos V, Kaznessis YN. ''SynBioSS: the synthetic biology modeling suite.'' Bioinformatics. 2008 Nov 1;24(21):2551-3. Epub 2008 Aug 30.<br />
[http://neptune.cems.umn.edu/designer/interface1.php SynBioSS Web Designer]<br />
<br />
2. Leveau JH, Lindow SE. ''Predictive and interpretive simulation of green fluorescent protein expression in<br />
reporter bacteria.'' J Bacteriol. 2001 Dec;183(23):6752-62.<br />
<br />
3. Endres D, Zlotnick A. ''Model-based analysis of assembly kinetics for virus capsids or other spherical<br />
polymers.'' Biophys J. 2002 Aug;83(2):1217-30.</div>FRhttp://2009.igem.org/Team:TorontoMaRSDiscovery/ModelingTeam:TorontoMaRSDiscovery/Modeling2009-10-21T03:15:20Z<p>FR: /* Sensitivity Analysis */</p>
<hr />
<div>[[image:To_igem_wiki_banner.jpg|965px]]<br />
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|}<br />
<br><br />
<br />
<br />
=Summary=<br />
<br />
A kinetic model of our system has been constructed. Approximate parameter values were gathered from online resources to represent all processes up to the production of the eCFP and Encapsulin proteins. Current simulations predict the production of these two proteins at various initial concentrations of IPTG and aTc effector molecules. Furthermore, we have outlined approaches for the detailed modelling of the eCFP degredation/maturation and Encapsulin assembly pathways.<br />
<br />
<br />
The initial simulations will be used to identify the critical concentration of Encapsulin mononomer required for microcompartment assembly. Subsequently, a detailed model of Encapsulin assembly will be integrated into the current model, and its parameters filled-in using parameter-scanning methods and experiments outlined in the relevant references. By comparing experimental measures of microcompartment formation with that predicted by the kinetic model, we aim to gain insight on the mechanisms of Encapsulin assembly.<br />
<br />
=Model=<br />
Our model is based on the following design (See Project Page for a full description of this system).<br />
[[image:BioBrick.png|thumb|centre|The Encapsulator]]<br />
<br />
The reaction framework was mainly generated using the [http://synbioss.sourceforge.net/ SynBioSS Designer (a really useful modeling tool for iGEM teams)], which also provides default parameter values. These parameter values have been gathered from various literature [http://neptune.cems.umn.edu/designer/designer_defaults.pdf sources], and should be taken as approximations. All units were taken to be (1 / molarity^n-1 * s), where n is the order of the reaction. For example, for the reaction 2 lacI --> lacI2, n = 2, thus the rate constant has the units 1/molality*s. <br />
<br />
The pathways for the expressed proteins, eCFPt and Encapsulin, need to be modeled in more detail. For example, in this basic model eCFPt is degraded via a first order reaction and Encapsulin makes a dimer complex. However, in reality fluorescent proteins have been shown to degreade via Micheales-menton kinetics and Encapsulin is thought to make a complex of about 60 monomers. These issues will be addressed in future work.<br />
<br />
The reactions can be accessed here:<br />
<br />
[[Model (open new page)]]<br />
<br />
[[Media:Uft_mod_Rxns2.xls|Model (download Excel file)]]<br />
<br />
=Simulations=<br />
<br />
All simulations were carried out using the [https://2009.igem.org/Partner_Offers SimBiology Matlab Toolbox], which was freely available to iGEM teams. <br />
<br />
===Accumulation of eCFP at Different Initial Concentrations of IPTG===<br />
<br />
[[Image:uft_mod_cfp-iptg.png | 900px]]<br />
<br />
The IPTG effector eventually loses effect, and the eCFP concentration approaches a maximum. This happens because the IPTG proteins eventually ''tie up'' all available LacI4 proteins, leaving the transcription and translation of eCFP to operate at its maxiumum rate. <br />
<br />
===Accumulation of Encapsulin monomer at Different Initial Concentrations of aTc===<br />
<br />
[[Image:uft_mod_enc-atc.png | 900px]]<br />
<br />
(NOTE: in order to observe Encapsulin monomer levels, the above simulations were carried out without any Encapsulin assembly reactions in place)<br />
<br />
The production of Encapsulin occurs at a slower rate than eCFP because the BBa_R0040 promoter has two tetR binding sites, resulting in more repression and more off-pathway scenarios. Thus, the Encapsulin concentration also seems assymptotic but at higher concentrations of aTc (relative to IPTG). <br />
<br />
It seems beneficial to have the Encapsulin protein under control of the BBa_R0040-tetR-aTc construct because at zero levels of aTc we can have essentially zero levels of Encapsulin (whereas even at zero levels of IPTG, there is still significantly more eCFP). This will enable us to probe extremely low concentrations of Encapsulin monomer when testing for optimal Encapsulin assembly conditions. The disadvantage is that if Encapsulin assembly requires a very high initial concentration of Encapsulin monomer, we would have to wait a long time to see microcompartments. If this later scenario is observed, it may be better to switch the eCFP and Encapsulin expression systems.<br />
<br />
===Sensitivity Analysis===<br />
<br />
Currently we are interesting to note which parameters have the greatest effect on the dynamics of the system. Since the parameters in our model are approximations from literature sources, the most ''sensitive'' parameters would be leading candidates to be experimentally determined.<br />
<br />
=Future Work=<br />
<br />
Improvements to the basic model presented above can be separated into three areas; 1) performing experiments to determine parameter values that are specific to our system, 2) more detailed modeling of eCFPt behavior, 3) more detailed modeling of Encapsulin assembly. <br />
<br />
The experiments required to determine general transcription and translation parameters need to be further researched, so this will be skipped over for now (the proposed sensitivity analysis of the model parameters will also identify which experiments are critical). Here we will discuss the more interesting areas – the detailed modeling of eCFP and Encapsulin pathways. This will be accomplished by incorporating previous modeling efforts that are applicable to the eCFP and Encapsulin proteins. <br />
<br />
===Degredation of eCFP===<br />
<br />
The expression and degradation of [http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=95514&blobtype=pdf Green Fluorescent Protein (GFP) was modeled previously]. This paper noted that GFP must mature before going into fluorescent phase, and GFP degradation was shown to follow M-M kinetics, as depicted below. This paper also outlined how the degradation parameters could be derived for any expression system using only simple fluorescence and optical density measurements.<br />
<br />
[[Image:uft_mod_ecfp1.png | centre | thumb | Degredation and maturation pathways for eCFP. (Leveau and Lindow 2001)]]<br />
<br />
<br />
The GFP maturation and degradation parameters found in this paper were:<br />
<br />
<html><br />
<centre><br />
<table><br />
<tr><td> m = 0.0004279 1/s </td></tr><br />
<tr><td> Vmax = 2E-10 molality/s </td></tr><br />
<tr><td> Km = 9E-13 molality/s </td></tr><br />
<tr><td> </td></tr><br />
</table><br />
</centre><br />
</html><br />
<br />
<br />
Assuming eCFPt would behave similarly to eGFP, the following additional reactions would be included in the model:<br />
<br />
<html><br />
<table><br />
<tr> <td><b> Maturation </b></td> <td> </td> </tr><br />
<tr> <td> eCFPt --> F_eCFPT </td> <td> 0.0004279 </td> </tr><br />
<tr> <td> Enc2:eCFPt --> Enc2:F_eCFPt </td> <td> 0.0004279 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Encapsulation </b></td> <td> </td> </tr><br />
<tr> <td> Enc2 + F_eCFPt --> Enc2:F_eCFPt </td> <td> 100 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Degradation </b></td> <td> </td> </tr><br />
<tr> <td> eCFPt --> </td> <td> Vmax = 2E-10 </td> </tr><br />
<tr> <td> </td> <td> Km = 9E-13 </td> </tr><br />
<tr> <td> F_eCFPt --> </td> <td> Vmax = 2E-10 </td> </tr><br />
<tr> <td> </td> <td> Km = 9E-13 </td> </tr><br />
</table><br />
</html><br />
<br />
===Assembly of Encapsulin Microcompartments===<br />
<br />
Though Encapsulin microcompartment assembly is not well-studied, it has been theorized to resemble the assembly of viral capsids. Thus, we could look to this relatively well-studied phenomenon as a representation of Encapsulin microcompartment assembly.<br />
<br />
Adam Zlotnick has published models of viral capsid assembly using different approaches. An early paper described an equilibrium model of assembly for a 12 Unit polyhedral capsid head, and a more recent paper used a kinetic model that could be applied to many examples of spherical polymerization. We will consider how each approach could be incorporated as a representation of Encapsulin assembly.<br />
<br />
'''1) Equilibrim Approach to Encapsulin Assembly'''<br />
<br />
Zlotnick's [[Media:Uft_mod_to_build_a_virus_capsid.pdf|Equilibrium-based model]] consists of reactions from an initial monomer subunit leading to a final capsid product. The sequential reactions take into account DeltaG for contact (Kn'), and parameters describing path degeneracy (varies for different intermediates).<br />
[[image:uft_mod_encap1.png|centre|thumb|Kn for assembly subunits based on path degeneracy. (Zlotnick 1994)]]<br />
<br />
Simulations from a preliminary incorporation of this approach are shown below. In this version of our basic model, Encapsulin assembles in a series of first order reactions. However, for simplicity, the rate constants are kept identical and do not take path degeneracy into account.<br />
<br />
<html><br />
<table><br />
<tr> <td><b> Encapsulin Assembly </b></td> <td> </td> </tr><br />
<tr> <td> 2 Enc --> Enc2 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 Enc2 --> Enc4 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 En4 --> Enc8 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 Enc8 --> Enc16 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 Enc16 --> Enc32 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 Enc16 --> Enc64 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td><b> Encapsulation </b></td> <td> </td> </tr><br />
<tr> <td> Enc64 + eCFPt --> Enc64:eCFPt </td> <td> 1.00E2 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
</table><br />
</html><br />
<br />
[[Image:uft_mod_enc1.png |frameless|300px]][[Image:uft_mod_enc2.png |frameless|300px]][[Image:uft_mod_enc3.png |frameless|300px]]<br />
<br />
<gallery caption=Equilibrium-based Encapsulin Assembly width=600px height=150px><br />
<center><br />
image:uft_mod_enc1.png<br />
image:uft_mod_enc2.png<br />
image:uft_mod_enc3.png<br />
</center><br />
</gallery><br />
<br />
Encapsulin assembly intermediates are observed to quickly come to a steady state. The last intermediate ''Enc64'' is the most depleted probably because of the formation of ''Enc64:eCFPt'' complex. Formation of ''Enc64:eCFPt'' then mirrors the production of ''eCFPt''. <br />
<br />
<br />
'''2) Kinetic Model of Spherical Polymerization'''<br />
<br />
A [http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1302223/pdf/12124301.pdf general kinetic model for the spherical polyermization] process is shown below. In our case, the initial monomer subunit concentration (''u'') would represent our expressed Encapsulin BioBrick, and the number of monomers in the final assembly (''N'') is thought to be 60. All of the included parameters can be calculated from the four basic parameters; the microscopic, per-contact equilibrium constant (KAcon), the nucleus size (nuc), the nucleation on-rate (f_nuc), and the elongation on-rate (f_elong). The referenced paper describes methods to aquire these parameters from kinetic experiments, and provides examples for N = 12 and 30 unit viral capsid assemblies.<br />
[[image:uft_mod_encap2.png| centre | thumb |System of ODEs to represent spherical polymerization, where ''u'' is the initial subunit concentration, ''m'' is the "mth" intermediate species, and ''N'' is the number of monomers in the final assembly. (Endres and Zlotnick 2002)]]<br />
<br />
<br />
<br />
Zlotnick's models also describe two important features of spherical polymerization that we should also expect to observe in Encapsulin assembly: kinetic trapping and nucleation. A kinetic trap occurs when the initial monomer subunit concentration or the deltaG of the first assembly reaction is too high. This results in over-initiation of assembly and quickly the reactions become starved for subunits. Kinetic trapping is prevented by the inclusion of nucleation, where the initial reactions occur at a slower rate because the first few intermediates in a series of reactions are less stable than downstream products. Essentially, nucleation serves as a “slow first step” that regulates the assembly pathway. <br />
<br />
It will be interesting to note how the translational dynamics of Encapsulin interplay with its assembly dynamics. Since our system does not start with any initial concentration of Encapsulin, there will be an optimum rate of production that essentially serves the role of nucleation – avoiding kinetic traps while still maintaining a maximum production of full Encapsulin assemblies.<br />
<br />
=References=<br />
<br />
1. Hill AD, Tomshine JR, Weeding EM, Sotiropoulos V, Kaznessis YN. ''SynBioSS: the synthetic biology modeling suite.'' Bioinformatics. 2008 Nov 1;24(21):2551-3. Epub 2008 Aug 30.<br />
[http://neptune.cems.umn.edu/designer/interface1.php SynBioSS Web Designer]<br />
<br />
2. Leveau JH, Lindow SE. ''Predictive and interpretive simulation of green fluorescent protein expression in<br />
reporter bacteria.'' J Bacteriol. 2001 Dec;183(23):6752-62.<br />
<br />
3. Endres D, Zlotnick A. ''Model-based analysis of assembly kinetics for virus capsids or other spherical<br />
polymers.'' Biophys J. 2002 Aug;83(2):1217-30.</div>FRhttp://2009.igem.org/Team:TorontoMaRSDiscovery/ModelingTeam:TorontoMaRSDiscovery/Modeling2009-10-21T03:01:51Z<p>FR: /* Future Work */</p>
<hr />
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<br><br />
<br />
<br />
=Summary=<br />
<br />
A kinetic model of our system has been constructed. Approximate parameter values were gathered from online resources to represent all processes up to the production of the eCFP and Encapsulin proteins. Current simulations predict the production of these two proteins at various initial concentrations of IPTG and aTc effector molecules. Furthermore, we have outlined approaches for the detailed modelling of the eCFP degredation/maturation and Encapsulin assembly pathways.<br />
<br />
<br />
The initial simulations will be used to identify the critical concentration of Encapsulin mononomer required for microcompartment assembly. Subsequently, a detailed model of Encapsulin assembly will be integrated into the current model, and its parameters filled-in using parameter-scanning methods and experiments outlined in the relevant references. By comparing experimental measures of microcompartment formation with that predicted by the kinetic model, we aim to gain insight on the mechanisms of Encapsulin assembly.<br />
<br />
=Model=<br />
Our model is based on the following design (See Project Page for a full description of this system).<br />
[[image:BioBrick.png|thumb|centre|The Encapsulator]]<br />
<br />
The reaction framework was mainly generated using the [http://synbioss.sourceforge.net/ SynBioSS Designer (a really useful modeling tool for iGEM teams)], which also provides default parameter values. These parameter values have been gathered from various literature [http://neptune.cems.umn.edu/designer/designer_defaults.pdf sources], and should be taken as approximations. All units were taken to be (1 / molarity^n-1 * s), where n is the order of the reaction. For example, for the reaction 2 lacI --> lacI2, n = 2, thus the rate constant has the units 1/molality*s. <br />
<br />
The pathways for the expressed proteins, eCFPt and Encapsulin, need to be modeled in more detail. For example, in this basic model eCFPt is degraded via a first order reaction and Encapsulin makes a dimer complex. However, in reality fluorescent proteins have been shown to degreade via Micheales-menton kinetics and Encapsulin is thought to make a complex of about 60 monomers. These issues will be addressed in future work.<br />
<br />
The reactions can be accessed here:<br />
<br />
[[Model (open new page)]]<br />
<br />
[[Media:Uft_mod_Rxns2.xls|Model (download Excel file)]]<br />
<br />
=Simulations=<br />
<br />
All simulations were carried out using the [https://2009.igem.org/Partner_Offers SimBiology Matlab Toolbox], which was freely available to iGEM teams. <br />
<br />
===Accumulation of eCFP at Different Initial Concentrations of IPTG===<br />
<br />
[[Image:uft_mod_cfp-iptg.png | 900px]]<br />
<br />
The IPTG effector eventually loses effect, and the eCFP concentration approaches a maximum. This happens because the IPTG proteins eventually ''tie up'' all available LacI4 proteins, leaving the transcription and translation of eCFP to operate at its maxiumum rate. <br />
<br />
===Accumulation of Encapsulin monomer at Different Initial Concentrations of aTc===<br />
<br />
[[Image:uft_mod_enc-atc.png | 900px]]<br />
<br />
(NOTE: in order to observe Encapsulin monomer levels, the above simulations were carried out without any Encapsulin assembly reactions in place)<br />
<br />
The production of Encapsulin occurs at a slower rate than eCFP because the BBa_R0040 promoter has two tetR binding sites, resulting in more repression and more off-pathway scenarios. Thus, the Encapsulin concentration also seems assymptotic but at higher concentrations of aTc (relative to IPTG). <br />
<br />
It seems beneficial to have the Encapsulin protein under control of the BBa_R0040-tetR-aTc construct because at zero levels of aTc we can have essentially zero levels of Encapsulin (whereas even at zero levels of IPTG, there is still significantly more eCFP). This will enable us to probe extremely low concentrations of Encapsulin monomer when testing for optimal Encapsulin assembly conditions. The disadvantage is that if Encapsulin assembly requires a very high initial concentration of Encapsulin monomer, we would have to wait a long time to see microcompartments. If this later scenario is observed, it may be better to switch the eCFP and Encapsulin expression systems.<br />
<br />
===Sensitivity Analysis===<br />
<br />
It is interesting to note which parameters have the greatest effect on the dynamics of the system. Since the parameters in our model are approximations from literature sources, the most ''sensitive'' parameters would be leading candidates to be experimentally determined. <br />
<br />
''(Currently, the SimBiology Toolbox reports an "OUT OF MEMORY" error when running a sensitivity analyis on our system).''<br />
<br />
=Future Work=<br />
<br />
Improvements to the basic model presented above can be separated into three areas; 1) performing experiments to determine parameter values that are specific to our system, 2) more detailed modeling of eCFPt behavior, 3) more detailed modeling of Encapsulin assembly. <br />
<br />
The experiments required to determine general transcription and translation parameters need to be further researched, so this will be skipped over for now (the proposed sensitivity analysis of the model parameters will also identify which experiments are critical). Here we will discuss the more interesting areas – the detailed modeling of eCFP and Encapsulin pathways. This will be accomplished by incorporating previous modeling efforts that are applicable to the eCFP and Encapsulin proteins. <br />
<br />
===Degredation of eCFP===<br />
<br />
The expression and degradation of [http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=95514&blobtype=pdf Green Fluorescent Protein (GFP) was modeled previously]. This paper noted that GFP must mature before going into fluorescent phase, and GFP degradation was shown to follow M-M kinetics, as depicted below. This paper also outlined how the degradation parameters could be derived for any expression system using only simple fluorescence and optical density measurements.<br />
<br />
[[Image:uft_mod_ecfp1.png | centre | thumb | Degredation and maturation pathways for eCFP. (Leveau and Lindow 2001)]]<br />
<br />
<br />
The GFP maturation and degradation parameters found in this paper were:<br />
<br />
<html><br />
<centre><br />
<table><br />
<tr><td> m = 0.0004279 1/s </td></tr><br />
<tr><td> Vmax = 2E-10 molality/s </td></tr><br />
<tr><td> Km = 9E-13 molality/s </td></tr><br />
<tr><td> </td></tr><br />
</table><br />
</centre><br />
</html><br />
<br />
<br />
Assuming eCFPt would behave similarly to eGFP, the following additional reactions would be included in the model:<br />
<br />
<html><br />
<table><br />
<tr> <td><b> Maturation </b></td> <td> </td> </tr><br />
<tr> <td> eCFPt --> F_eCFPT </td> <td> 0.0004279 </td> </tr><br />
<tr> <td> Enc2:eCFPt --> Enc2:F_eCFPt </td> <td> 0.0004279 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Encapsulation </b></td> <td> </td> </tr><br />
<tr> <td> Enc2 + F_eCFPt --> Enc2:F_eCFPt </td> <td> 100 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Degradation </b></td> <td> </td> </tr><br />
<tr> <td> eCFPt --> </td> <td> Vmax = 2E-10 </td> </tr><br />
<tr> <td> </td> <td> Km = 9E-13 </td> </tr><br />
<tr> <td> F_eCFPt --> </td> <td> Vmax = 2E-10 </td> </tr><br />
<tr> <td> </td> <td> Km = 9E-13 </td> </tr><br />
</table><br />
</html><br />
<br />
===Assembly of Encapsulin Microcompartments===<br />
<br />
Though Encapsulin microcompartment assembly is not well-studied, it has been theorized to resemble the assembly of viral capsids. Thus, we could look to this relatively well-studied phenomenon as a representation of Encapsulin microcompartment assembly.<br />
<br />
Adam Zlotnick has published models of viral capsid assembly using different approaches. An early paper described an equilibrium model of assembly for a 12 Unit polyhedral capsid head, and a more recent paper used a kinetic model that could be applied to many examples of spherical polymerization. We will consider how each approach could be incorporated as a representation of Encapsulin assembly.<br />
<br />
'''1) Equilibrim Approach to Encapsulin Assembly'''<br />
<br />
Zlotnick's [[Media:Uft_mod_to_build_a_virus_capsid.pdf|Equilibrium-based model]] consists of reactions from an initial monomer subunit leading to a final capsid product. The sequential reactions take into account DeltaG for contact (Kn'), and parameters describing path degeneracy (varies for different intermediates).<br />
[[image:uft_mod_encap1.png|centre|thumb|Kn for assembly subunits based on path degeneracy. (Zlotnick 1994)]]<br />
<br />
Simulations from a preliminary incorporation of this approach are shown below. In this version of our basic model, Encapsulin assembles in a series of first order reactions. However, for simplicity, the rate constants are kept identical and do not take path degeneracy into account.<br />
<br />
<html><br />
<table><br />
<tr> <td><b> Encapsulin Assembly </b></td> <td> </td> </tr><br />
<tr> <td> 2 Enc --> Enc2 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 Enc2 --> Enc4 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 En4 --> Enc8 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 Enc8 --> Enc16 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 Enc16 --> Enc32 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 Enc16 --> Enc64 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td><b> Encapsulation </b></td> <td> </td> </tr><br />
<tr> <td> Enc64 + eCFPt --> Enc64:eCFPt </td> <td> 1.00E2 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
</table><br />
</html><br />
<br />
[[Image:uft_mod_enc1.png |frameless|300px]][[Image:uft_mod_enc2.png |frameless|300px]][[Image:uft_mod_enc3.png |frameless|300px]]<br />
<br />
<gallery caption=Equilibrium-based Encapsulin Assembly width=600px height=150px><br />
<center><br />
image:uft_mod_enc1.png<br />
image:uft_mod_enc2.png<br />
image:uft_mod_enc3.png<br />
</center><br />
</gallery><br />
<br />
Encapsulin assembly intermediates are observed to quickly come to a steady state. The last intermediate ''Enc64'' is the most depleted probably because of the formation of ''Enc64:eCFPt'' complex. Formation of ''Enc64:eCFPt'' then mirrors the production of ''eCFPt''. <br />
<br />
<br />
'''2) Kinetic Model of Spherical Polymerization'''<br />
<br />
A [http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1302223/pdf/12124301.pdf general kinetic model for the spherical polyermization] process is shown below. In our case, the initial monomer subunit concentration (''u'') would represent our expressed Encapsulin BioBrick, and the number of monomers in the final assembly (''N'') is thought to be 60. All of the included parameters can be calculated from the four basic parameters; the microscopic, per-contact equilibrium constant (KAcon), the nucleus size (nuc), the nucleation on-rate (f_nuc), and the elongation on-rate (f_elong). The referenced paper describes methods to aquire these parameters from kinetic experiments, and provides examples for N = 12 and 30 unit viral capsid assemblies.<br />
[[image:uft_mod_encap2.png| centre | thumb |System of ODEs to represent spherical polymerization, where ''u'' is the initial subunit concentration, ''m'' is the "mth" intermediate species, and ''N'' is the number of monomers in the final assembly. (Endres and Zlotnick 2002)]]<br />
<br />
<br />
<br />
Zlotnick's models also describe two important features of spherical polymerization that we should also expect to observe in Encapsulin assembly: kinetic trapping and nucleation. A kinetic trap occurs when the initial monomer subunit concentration or the deltaG of the first assembly reaction is too high. This results in over-initiation of assembly and quickly the reactions become starved for subunits. Kinetic trapping is prevented by the inclusion of nucleation, where the initial reactions occur at a slower rate because the first few intermediates in a series of reactions are less stable than downstream products. Essentially, nucleation serves as a “slow first step” that regulates the assembly pathway. <br />
<br />
It will be interesting to note how the translational dynamics of Encapsulin interplay with its assembly dynamics. Since our system does not start with any initial concentration of Encapsulin, there will be an optimum rate of production that essentially serves the role of nucleation – avoiding kinetic traps while still maintaining a maximum production of full Encapsulin assemblies.<br />
<br />
=References=<br />
<br />
1. Hill AD, Tomshine JR, Weeding EM, Sotiropoulos V, Kaznessis YN. ''SynBioSS: the synthetic biology modeling suite.'' Bioinformatics. 2008 Nov 1;24(21):2551-3. Epub 2008 Aug 30.<br />
[http://neptune.cems.umn.edu/designer/interface1.php SynBioSS Web Designer]<br />
<br />
2. Leveau JH, Lindow SE. ''Predictive and interpretive simulation of green fluorescent protein expression in<br />
reporter bacteria.'' J Bacteriol. 2001 Dec;183(23):6752-62.<br />
<br />
3. Endres D, Zlotnick A. ''Model-based analysis of assembly kinetics for virus capsids or other spherical<br />
polymers.'' Biophys J. 2002 Aug;83(2):1217-30.</div>FRhttp://2009.igem.org/Team:TorontoMaRSDiscovery/ModelingTeam:TorontoMaRSDiscovery/Modeling2009-10-21T02:52:18Z<p>FR: /* Future Work */</p>
<hr />
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|}<br />
<br><br />
<br />
<br />
=Summary=<br />
<br />
A kinetic model of our system has been constructed. Approximate parameter values were gathered from online resources to represent all processes up to the production of the eCFP and Encapsulin proteins. Current simulations predict the production of these two proteins at various initial concentrations of IPTG and aTc effector molecules. Furthermore, we have outlined approaches for the detailed modelling of the eCFP degredation/maturation and Encapsulin assembly pathways.<br />
<br />
<br />
The initial simulations will be used to identify the critical concentration of Encapsulin mononomer required for microcompartment assembly. Subsequently, a detailed model of Encapsulin assembly will be integrated into the current model, and its parameters filled-in using parameter-scanning methods and experiments outlined in the relevant references. By comparing experimental measures of microcompartment formation with that predicted by the kinetic model, we aim to gain insight on the mechanisms of Encapsulin assembly.<br />
<br />
=Model=<br />
Our model is based on the following design (See Project Page for a full description of this system).<br />
[[image:BioBrick.png|thumb|centre|The Encapsulator]]<br />
<br />
The reaction framework was mainly generated using the [http://synbioss.sourceforge.net/ SynBioSS Designer (a really useful modeling tool for iGEM teams)], which also provides default parameter values. These parameter values have been gathered from various literature [http://neptune.cems.umn.edu/designer/designer_defaults.pdf sources], and should be taken as approximations. All units were taken to be (1 / molarity^n-1 * s), where n is the order of the reaction. For example, for the reaction 2 lacI --> lacI2, n = 2, thus the rate constant has the units 1/molality*s. <br />
<br />
The pathways for the expressed proteins, eCFPt and Encapsulin, need to be modeled in more detail. For example, in this basic model eCFPt is degraded via a first order reaction and Encapsulin makes a dimer complex. However, in reality fluorescent proteins have been shown to degreade via Micheales-menton kinetics and Encapsulin is thought to make a complex of about 60 monomers. These issues will be addressed in future work.<br />
<br />
The reactions can be accessed here:<br />
<br />
[[Model (open new page)]]<br />
<br />
[[Media:Uft_mod_Rxns2.xls|Model (download Excel file)]]<br />
<br />
=Simulations=<br />
<br />
All simulations were carried out using the [https://2009.igem.org/Partner_Offers SimBiology Matlab Toolbox], which was freely available to iGEM teams. <br />
<br />
===Accumulation of eCFP at Different Initial Concentrations of IPTG===<br />
<br />
[[Image:uft_mod_cfp-iptg.png | 900px]]<br />
<br />
The IPTG effector eventually loses effect, and the eCFP concentration approaches a maximum. This happens because the IPTG proteins eventually ''tie up'' all available LacI4 proteins, leaving the transcription and translation of eCFP to operate at its maxiumum rate. <br />
<br />
===Accumulation of Encapsulin monomer at Different Initial Concentrations of aTc===<br />
<br />
[[Image:uft_mod_enc-atc.png | 900px]]<br />
<br />
(NOTE: in order to observe Encapsulin monomer levels, the above simulations were carried out without any Encapsulin assembly reactions in place)<br />
<br />
The production of Encapsulin occurs at a slower rate than eCFP because the BBa_R0040 promoter has two tetR binding sites, resulting in more repression and more off-pathway scenarios. Thus, the Encapsulin concentration also seems assymptotic but at higher concentrations of aTc (relative to IPTG). <br />
<br />
It seems beneficial to have the Encapsulin protein under control of the BBa_R0040-tetR-aTc construct because at zero levels of aTc we can have essentially zero levels of Encapsulin (whereas even at zero levels of IPTG, there is still significantly more eCFP). This will enable us to probe extremely low concentrations of Encapsulin monomer when testing for optimal Encapsulin assembly conditions. The disadvantage is that if Encapsulin assembly requires a very high initial concentration of Encapsulin monomer, we would have to wait a long time to see microcompartments. If this later scenario is observed, it may be better to switch the eCFP and Encapsulin expression systems.<br />
<br />
===Sensitivity Analysis===<br />
<br />
It is interesting to note which parameters have the greatest effect on the dynamics of the system. Since the parameters in our model are approximations from literature sources, the most ''sensitive'' parameters would be leading candidates to be experimentally determined. <br />
<br />
''(Currently, the SimBiology Toolbox reports an "OUT OF MEMORY" error when running a sensitivity analyis on our system).''<br />
<br />
=Future Work=<br />
<br />
Improvements to the basic model presented above can be separated into three areas; 1) performing experiments to determine parameter values that are specific to our system, 2) more detailed modeling of eCFPt behavior, 3) more detailed modeling of Encapsulin assembly. <br />
<br />
The experiments required to determine general transcription and translation parameters need to be further researched, so this will be skipped over for now (the proposed sensitivity analysis of the model parameters will also identify which experiments are critical). Here we will discuss the more interesting areas – the detailed modeling of eCFP and Encapsulin pathways. This will be accomplished by incorporating previous modeling efforts that are applicable to the eCFP and Encapsulin proteins. <br />
<br />
===Degredation of eCFP===<br />
<br />
The expression and degradation of [http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=95514&blobtype=pdf Green Fluorescent Protein (GFP) was modeled previously]. This paper noted that GFP must mature before going into fluorescent phase, and GFP degradation was shown to follow M-M kinetics, as depicted below. This paper also outlined how the degradation parameters could be derived for any expression system using only simple fluorescence and optical density measurements.<br />
<br />
[[Image:uft_mod_ecfp1.png | centre | thumb | Degredation and maturation pathways for eCFP. (Leveau and Lindow 2001)]]<br />
<br />
<br />
The GFP maturation and degradation parameters found in this paper were:<br />
<br />
<html><br />
<centre><br />
<table><br />
<tr><td> m = 0.0004279 1/s </td></tr><br />
<tr><td> Vmax = 2E-10 molality/s </td></tr><br />
<tr><td> Km = 9E-13 molality/s </td></tr><br />
<tr><td> </td></tr><br />
</table><br />
</centre><br />
</html><br />
<br />
<br />
Assuming eCFPt would behave similarly to eGFP, the following additional reactions would be included in the model:<br />
<br />
<html><br />
<table><br />
<tr> <td><b> Maturation </b></td> <td> </td> </tr><br />
<tr> <td> eCFPt --> F_eCFPT </td> <td> 0.0004279 </td> </tr><br />
<tr> <td> Enc2:eCFPt --> Enc2:F_eCFPt </td> <td> 0.0004279 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Encapsulation </b></td> <td> </td> </tr><br />
<tr> <td> Enc2 + F_eCFPt --> Enc2:F_eCFPt </td> <td> 100 </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td> </td> <td> </td> </tr><br />
<tr> <td><b> Degradation </b></td> <td> </td> </tr><br />
<tr> <td> eCFPt --> </td> <td> Vmax = 2E-10 </td> </tr><br />
<tr> <td> </td> <td> Km = 9E-13 </td> </tr><br />
<tr> <td> F_eCFPt --> </td> <td> Vmax = 2E-10 </td> </tr><br />
<tr> <td> </td> <td> Km = 9E-13 </td> </tr><br />
</table><br />
</html><br />
<br />
===Assembly of Encapsulin Microcompartments===<br />
<br />
Though Encapsulin microcompartment assembly is not well-studied, it has been theorized to resemble the assembly of viral capsids. Thus, we could look to this relatively well-studied phenomenon as a representation of Encapsulin microcompartment assembly.<br />
<br />
Adam Zlotnick has published models of viral capsid assembly using different approaches. An early paper described an equilibrium model of assembly for a 12 Unit polyhedral capsid head, and a more recent paper used a kinetic model that could be applied to many examples of spherical polymerization. We will consider how each approach could be incorporated as a representation of Encapsulin assembly.<br />
<br />
'''1) Equilibrim Approach to Encapsulin Assembly'''<br />
<br />
Zlotnick's [[Media:Uft_mod_to_build_a_virus_capsid.pdf|Equilibrium-based model]] consists of reactions from an initial monomer subunit leading to a final capsid product. The sequential reactions take into account DeltaG for contact (Kn'), and parameters describing path degeneracy (varies for different intermediates).<br />
[[image:uft_mod_encap1.png|centre|thumb|Kn for assembly subunits based on path degeneracy. (Zlotnick 1994)]]<br />
<br />
Simulations from a preliminary incorporation of this approach are shown below. In this version of our basic model, Encapsulin assembles in a series of first order reactions. However, for simplicity, the rate constants are kept identical and do not take path degeneracy into account.<br />
<br />
<html><br />
<table><br />
<tr> <td><b> Encapsulin Assembly </b></td> <td> </td> </tr><br />
<tr> <td> 2 Enc --> Enc2 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 Enc2 --> Enc4 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 En4 --> Enc8 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 Enc8 --> Enc16 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 Enc16 --> Enc32 </td> <td> 1.00E9 </td> </tr><br />
<tr> <td> 2 Enc16 --> Enc64 </td> <td> 1.00E9 </td> </tr><br />
</table><br />
</html><br />
<br />
[[Image:uft_mod_enc1.png |frameless|300px]][[Image:uft_mod_enc2.png |frameless|300px]][[Image:uft_mod_enc3.png |frameless|300px]]<br />
<br />
<gallery caption=Equilibrium-based Encapsulin Assembly width=600px height=150px><br />
<center><br />
image:uft_mod_enc1.png<br />
image:uft_mod_enc2.png<br />
image:uft_mod_enc3.png<br />
</center><br />
</gallery><br />
<br />
Encapsulin assembly intermediates are observed to quickly come to a steady state. The last intermediate ''Enc64'' is the most depleted probably because of the formation of ''Enc64:eCFPt'' complex. Formation of ''Enc64:eCFPt'' then mirrors the production of ''eCFPt''. <br />
<br />
<br />
'''2) Kinetic Model of Spherical Polymerization'''<br />
<br />
A [http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1302223/pdf/12124301.pdf general kinetic model for the spherical polyermization] process is shown below. In our case, the initial monomer subunit concentration (''u'') would represent our expressed Encapsulin BioBrick, and the number of monomers in the final assembly (''N'') is thought to be 60. All of the included parameters can be calculated from the four basic parameters; the microscopic, per-contact equilibrium constant (KAcon), the nucleus size (nuc), the nucleation on-rate (f_nuc), and the elongation on-rate (f_elong). The referenced paper describes methods to aquire these parameters from kinetic experiments, and provides examples for N = 12 and 30 unit viral capsid assemblies.<br />
[[image:uft_mod_encap2.png| centre | thumb |System of ODEs to represent spherical polymerization, where ''u'' is the initial subunit concentration, ''m'' is the "mth" intermediate species, and ''N'' is the number of monomers in the final assembly. (Endres and Zlotnick 2002)]]<br />
<br />
<br />
<br />
Zlotnick's models also describe two important features of spherical polymerization that we should also expect to observe in Encapsulin assembly: kinetic trapping and nucleation. A kinetic trap occurs when the initial monomer subunit concentration or the deltaG of the first assembly reaction is too high. This results in over-initiation of assembly and quickly the reactions become starved for subunits. Kinetic trapping is prevented by the inclusion of nucleation, where the initial reactions occur at a slower rate because the first few intermediates in a series of reactions are less stable than downstream products. Essentially, nucleation serves as a “slow first step” that regulates the assembly pathway. <br />
<br />
It will be interesting to note how the translational dynamics of Encapsulin interplay with its assembly dynamics. Since our system does not start with any initial concentration of Encapsulin, there will be an optimum rate of production that essentially serves the role of nucleation – avoiding kinetic traps while still maintaining a maximum production of full Encapsulin assemblies.<br />
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=References=<br />
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[http://neptune.cems.umn.edu/designer/interface1.php SynBioSS Web Designer]<br />
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3. Endres D, Zlotnick A. ''Model-based analysis of assembly kinetics for virus capsids or other spherical<br />
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