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| + | Modeling<span class="art-PostHeader"></span> </h2> |
| + | </div> |
| + | <p><span style="font-size: 20pt; line-height: 115%;">Contents<o:p></o:p></span></p> |
| + | <p style="margin-left: 32.2pt; text-indent: -18pt;"><!--[if !supportLists]--><span |
| + | style="font-size: 12pt; line-height: 115%;"><span style="">1.<span |
| + | style="font-family: "Times New Roman"; font-style: normal; font-variant: normal; font-weight: normal; font-size: 7pt; line-height: normal; font-size-adjust: none; font-stretch: normal;"> |
| + | </span></span></span><!--[endif]--><span |
| + | style="font-size: 12pt; line-height: 115%;">Introduction<o:p></o:p></span></p> |
| + | <p style="margin-left: 32.2pt; text-indent: -18pt;"><!--[if !supportLists]--><span |
| + | style="font-size: 12pt; line-height: 115%;"><span style="">2.<span |
| + | style="font-family: "Times New Roman"; font-style: normal; font-variant: normal; font-weight: normal; font-size: 7pt; line-height: normal; font-size-adjust: none; font-stretch: normal;"> |
| + | </span></span></span><!--[endif]--><span |
| + | style="font-size: 12pt; line-height: 115%;">Model |
| + | 1: ‘Ready’ – |
| + | ‘Steady‘- cut<o:p></o:p></span></p> |
| + | <p style="margin-left: 72pt;"><span |
| + | style="font-size: 12pt; line-height: 115%;">2.1 |
| + | Reaction |
| + | kinetics<o:p></o:p></span></p> |
| + | <p style="margin-left: 72pt;"><span |
| + | style="font-size: 12pt; line-height: 115%;">2.2. |
| + | ODEs<o:p></o:p></span></p> |
| + | <p style="margin-left: 72pt;"><span |
| + | style="font-size: 12pt; line-height: 115%;">2.3 |
| + | Stimulating temperature dependence for a set of parameters<o:p></o:p></span></p> |
| + | <p style="margin-left: 72pt;"><span |
| + | style="font-size: 12pt; line-height: 115%;">2.4. |
| + | Discussion<o:p></o:p></span></p> |
| + | <p style="margin-left: 32.2pt; text-indent: -18pt;"><!--[if !supportLists]--><span |
| + | style="font-size: 12pt; line-height: 115%;"><span style="">3.<span |
| + | style="font-family: "Times New Roman"; font-style: normal; font-variant: normal; font-weight: normal; font-size: 7pt; line-height: normal; font-size-adjust: none; font-stretch: normal;"> |
| + | </span></span></span><!--[endif]--><span |
| + | style="font-size: 12pt; line-height: 115%;">Model |
| + | 2: bind - ‘Ready’- ‘Steady’- |
| + | cut <o:p></o:p></span></p> |
| + | <p style="margin-left: 72pt;"><span |
| + | style="font-size: 12pt; line-height: 115%;">3.1 |
| + | Reaction |
| + | kinetics<o:p></o:p></span></p> |
| + | <p style="margin-left: 72pt;"><span |
| + | style="font-size: 12pt; line-height: 115%;">3.2 |
| + | ODE’s<o:p></o:p></span></p> |
| + | <p style="margin-left: 35.4pt; text-indent: 35.4pt;"><span |
| + | style="font-size: 12pt; line-height: 115%;">3.3 |
| + | Different concentrations of Fok_a and Fok_i<o:p></o:p></span></p> |
| + | <p style="margin-left: 35.4pt; text-indent: 35.4pt;"><span |
| + | style="font-size: 12pt; line-height: 115%;">3.3.1 |
| + | Discussion</span><span |
| + | style="font-size: 12pt; line-height: 115%;"><o:p></o:p></span> |
| + | </p> |
| + | <p style="margin-left: 32.2pt; text-indent: -18pt;"><span |
| + | style="font-size: 12pt; line-height: 115%;"><o:p></o:p></span></p> |
| + | <p style="margin-left: 32.2pt; text-indent: -18pt;"><comment |
| + | title="[if !supportLists]" |
| + | xmlns="http://disruptive-innovations.com/zoo/nvu"><img |
| + | src="chrome://editor/content/images/tag-comment.gif" /><!--[if !supportLists]--></comment><span |
| + | style="font-size: 12pt; line-height: 115%;"><span style="">4.<span |
| + | style="font-family: "Times New Roman"; font-style: normal; font-variant: normal; font-weight: normal; font-size: 7pt; line-height: normal; font-size-adjust: none; font-stretch: normal;"> |
| + | </span></span></span> <span |
| + | style="font-size: 12pt; line-height: 115%;">Results</span><span |
| + | style="font-size: 12pt; line-height: 115%;"><o:p></o:p></span> |
| + | </p> |
| + | <p style="margin-left: 32.2pt; text-indent: -18pt;"><span |
| + | style="font-size: 12pt; line-height: 115%;"><o:p></o:p></span></p> |
| + | <p style="margin-left: 32.2pt; text-indent: -18pt;"><comment |
| + | title="[if !supportLists]" |
| + | xmlns="http://disruptive-innovations.com/zoo/nvu"><img |
| + | src="chrome://editor/content/images/tag-comment.gif" /><!--[if !supportLists]--></comment><span |
| + | style="font-size: 12pt; line-height: 115%;"><span style="">5.<span |
| + | style="font-family: "Times New Roman"; font-style: normal; font-variant: normal; font-weight: normal; font-size: 7pt; line-height: normal; font-size-adjust: none; font-stretch: normal;"> |
| + | </span></span></span> <span |
| + | style="font-size: 12pt; line-height: 115%;">Literature</span><span |
| + | style="font-size: 12pt; line-height: 115%;"></span></p> |
| + | <p style="margin-left: 32.2pt; text-indent: -18pt;"><span |
| + | style="font-size: 12pt; line-height: 115%;"><o:p></o:p></span></p> |
| + | <p><span style="font-size: 20pt; line-height: 115%;" |
| + | lang="EN-GB"><o:p> </o:p></span></p> |
| + | <p><span style="font-size: 20pt; line-height: 115%;" |
| + | lang="EN-GB">1. |
| + | Introduction<o:p></o:p></span></p> |
| + | <p><span style="">Endonucleases |
| + | are restriction enzymes cutting single (ss) - or double (ds) - stranded |
| + | DNA at |
| + | specific nucleotide sequences. They are found in bacteria and classify |
| + | in three |
| + | different types of those enzymes, which are categorized in different |
| + | groups. |
| + | The restriction enzyme of our interest, FokI, belongs to class two, |
| + | which means |
| + | that it cuts the DNA strand directly after the restriction site.<span |
| + | style=""> </span><o:p></o:p></span></p> |
| + | <p><span style=""><span style=""> </span>With |
| + | this model we tried to |
| + | simulate a |
| + | universal enzyme. <o:p></o:p></span></p> |
| + | <p><span style="">Whereas |
| + | for |
| + | cutting determined substrate is ds DNA, two DNA pieces are the |
| + | products, the |
| + | measurable output resulting from the reaction. <o:p></o:p></span></p> |
| + | <p><span style="">To |
| + | analyze |
| + | the process, first the dimerization of the two protein domains needs to |
| + | proceed. Therefore models for association (Fig1.), cleavage (Fig.2) and |
| + | dissociation (Fig.3) of the different Fok domains, Fok_i and Fok_a, are |
| + | introduced. With the help of ODEs (Ordinary differential equations) |
| + | simulations |
| + | were done, even though a limited set of data is given. <o:p></o:p></span></p> |
| + | <p><span style="font-size: 14pt; line-height: 115%;"><o:p> </o:p></span></p> |
| + | <span style="font-size: 14pt; line-height: 115%;">1.</span><span |
| + | style="font-size: 10pt; line-height: 115%;"></span> While |
| + | each complex is bound to the DNA double |
| + | strand, the protein parts can come together to form a heterodimer, |
| + | which is the assumption to activate the enzyme. |
| + | <p style=""><span style=""><br /> |
| + | </span></p> |
| + | <p style=""><span style=""><img |
| + | alt="" |
| + | src="https://static.igem.org/mediawiki/2009/6/68/Freiburg09_anika001association.png" /></span></p> |
| + | <p><span style=""><o:p> </o:p></span></p> |
| + | <p><span style="font-size: 10pt; line-height: 115%;">Figure |
| + | 1:<span style=""> |
| + | </span>Association of linker FluA and Dig with DNA and Fok_a and |
| + | Fok_i monomers.<o:p></o:p></span></p> |
| + | <p><span style="font-size: 10pt; line-height: 115%;"><o:p> </o:p></span></p> |
| + | <p style="margin-left: 177pt; text-indent: -177pt;"><span |
| + | style="font-size: 14pt; line-height: 115%;">2.</span><span |
| + | style="font-size: 10pt; line-height: 115%;"> |
| + | </span><span style="">After the |
| + | accomplishment <span style="">of the<b> </b></span>heterodimer, |
| + | the |
| + | cleavage domain is prepared to cut the DNA.<span style=""> |
| + | </span></span><span |
| + | style="font-size: 12pt; line-height: 115%;"><span style=""> </span></span><span |
| + | style=""><o:p></o:p></span></p> |
| + | <p><span style="display:block; overflow:hidden;"><img alt="" |
| + | src="https://static.igem.org/mediawiki/2009/7/79/Freiburg09_anika002cleavage.png" /></span><span |
| + | style="font-size: 12pt; line-height: 115%;"><o:p></o:p></span></p> |
| + | <p><span style="font-size: 12pt; line-height: 115%;"><o:p> </o:p></span></p> |
| + | <p><span style="font-size: 10pt; line-height: 115%;">Figure |
| + | 2: <span style=""> </span>Cleavage of DNA |
| + | double strand<o:p></o:p></span></p> |
| + | <p><span style="font-size: 10pt; line-height: 115%;"><o:p> </o:p></span></p> |
| + | <p><span style="font-size: 14pt; line-height: 115%;">3.</span><span |
| + | style=""> Because the unidirectional |
| + | cutting process took place, the two DNA |
| + | fragments and the restriction enzyme dissociate. <o:p></o:p></span></p> |
| + | <p><span style=""><o:p> </o:p></span></p> |
| + | <p><span style="display:block; overflow:hidden;"><img alt="" |
| + | src="https://static.igem.org/mediawiki/2009/3/35/Freiburg09_anika003dissociation.png" /></span><span |
| + | style="line-height: 115%;"><o:p></o:p></span></p> |
| + | <p><span style="line-height: 115%;"><o:p> </o:p></span></p> |
| + | <p><span style="font-size: 10pt; line-height: 115%;">Figure |
| + | 3: Dissociation of construct after cleavage <o:p></o:p></span></p> |
| + | <p><span style="font-size: 10pt; line-height: 115%;"><o:p> </o:p></span></p> |
| + | <span |
| + | style="font-size: 20pt; line-height: 115%; font-family: "Calibri","sans-serif";"><br |
| + | style="page-break-before: always;" clear="all" /> |
| + | </span> |
| + | <p><b style=""><span |
| + | style="font-size: 20pt; line-height: 115%;">2. |
| + | Model 1, |
| + | ‘Ready’-‘Steady’-cut</span></b><b |
| + | style=""><span |
| + | style="font-size: 20pt; line-height: 115%; font-family: "Times New Roman","serif";"><o:p></o:p></span></b></p> |
| + | <p><span style="">One |
| + | part to |
| + | activate the enzyme is the dimerization of the two cutting domains |
| + | Fok_i and |
| + | Fok_a. Fok_i is linked to FluA (the anticalin binding fluorescein) |
| + | compared to |
| + | Fok_a, which is linked DigA (the anticalin binding digoxigenin). Here, |
| + | we |
| + | assume Fok_a and Fok_i dimerize only when the adapter bound to the |
| + | tagged DNA |
| + | and both DigA and FluA are connected with the linker specific tags |
| + | hybrid by |
| + | the DNA strand.<o:p></o:p></span></p> |
| + | <p><span style="">As |
| + | the two |
| + | adapter domains, DigA and FluA, are bound and Fok_i and Fok_a are close |
| + | enough |
| + | to each other, they can dimerize. In order to get an active enzyme the |
| + | Fok_a |
| + | /Fok_i heterodimer has to shift into an active state, which is in our |
| + | model |
| + | called ‘Steady’. But before the enzyme reaches the |
| + | active state ‘Steady’, it |
| + | takes time to change its conformation. For this reason the enzymes |
| + | reach a |
| + | condition, which is not yet activated. This step is called |
| + | ‘Ready’. An enzyme passed |
| + | through the step ‘Ready’ and arrived in |
| + | ‘Steady’ is able to cut a double |
| + | stranded DNA. <o:p></o:p></span></p> |
| + | <p><span style="">A |
| + | schematized pathway (Fig 4.) shows the sequence of enzyme activation.<o:p></o:p></span></p> |
| + | <p><span style="display:block; overflow:hidden;"><img alt="" |
| + | src="https://static.igem.org/mediawiki/2009/c/cb/Freiburg09_anika004flussdiagrammmodel1.png" /></span><span |
| + | style="font-size: 12pt; line-height: 115%;"><o:p></o:p></span></p> |
| + | <p style="margin-left: 35.4pt;"><span |
| + | style="font-size: 10pt; line-height: 115%;">Fig.4: Flowchart |
| + | model 1<o:p></o:p></span></p> |
| + | <p style="margin-left: 35.4pt;"><span |
| + | style="font-size: 14pt; line-height: 115%;"><o:p> </o:p></span></p> |
| + | <p style="margin-left: 35.4pt;"><span |
| + | style="font-size: 16pt; line-height: 115%;">2.1 |
| + | Reaction |
| + | kinetics<o:p></o:p></span></p> |
| + | <p><span style="">The |
| + | parts |
| + | Fok_i and Fok_a bind DNA at the same time and with the reaction rate <b |
| + | style="">k1on</b> and change to the state |
| + | ‘Ready’, |
| + | whereas they dissociate with the rate <b style="">k1off.<o:p></o:p></b></span></p> |
| + | <p><span style="font-size: 12pt; line-height: 115%;"><o:p> </o:p></span></p> |
| + | <p><span style="display:block; overflow:hidden;"><img alt="" |
| + | src="https://static.igem.org/mediawiki/2009/1/13/Freiburg09_anika005kinetik_1-1.png" /></span><span |
| + | style="font-size: 12pt; line-height: 115%;"><o:p></o:p></span></p> |
| + | <p><span style="font-size: 12pt; line-height: 115%;"><o:p> </o:p></span></p> |
| + | <p style="text-align: right;" align="right"><span |
| + | style="font-size: 12pt; line-height: 115%;"><o:p> </o:p></span></p> |
| + | <p style="text-align: right;" align="right"><span |
| + | style="font-size: 12pt; line-height: 115%;"><o:p> </o:p></span></p> |
| + | <p><span style="">The |
| + | enzyme |
| + | becomes activated with rate <b style="">k2_on</b> |
| + | and dissociates with the reaction rate <b style="">k2_off</b>:<o:p></o:p></span></p> |
| + | <p><span style="display:block; overflow:hidden;"><img style="height:50%; width:50%;" alt="" |
| + | src="https://static.igem.org/mediawiki/2009/c/cf/Freiburg09_anika006kinetik_1-2.png" /></span><span |
| + | style="font-size: 12pt; line-height: 115%;"><o:p></o:p></span></p> |
| + | <p><span style="font-size: 12pt; line-height: 115%;"><o:p> </o:p></span></p> |
| + | <p><span style="">After |
| + | activation, the enzyme cuts with the rate <b style="">k3</b>:</span><span |
| + | style="font-size: 12pt; line-height: 115%;"><o:p></o:p></span></p> |
| + | <p><span style="display:block; overflow:hidden;"><img alt="" |
| + | src="https://static.igem.org/mediawiki/2009/7/76/Freiburg09_anika007kinetik_1-3.png" /></span><span |
| + | style="font-size: 12pt; line-height: 115%;"><o:p></o:p></span></p> |
| + | <p><span style="font-size: 12pt; line-height: 115%;"><o:p> </o:p></span></p> |
| + | <p><span style="font-size: 12pt; line-height: 115%;"><o:p> </o:p></span></p> |
| + | <p style="text-indent: 35.4pt;"><span |
| + | style="font-size: 14pt; line-height: 115%;"><o:p> </o:p></span></p> |
| + | <p style="text-indent: 35.4pt;"><span |
| + | style="font-size: 16pt; line-height: 115%;">2.2 |
| + | ODEs<o:p></o:p></span></p> |
| + | <p><span style="">All |
| + | ODE’s |
| + | are derived from the reaction kinetics. The association and |
| + | dissociation |
| + | constants are analog to the constants in the flow chart above (Fig. 4).<a |
| + | name="OLE_LINK1"><o:p></o:p></a></span></p> |
| + | <p style="text-indent: 35.4pt;"><span style=""><span |
| + | style=""><o:p> </o:p></span></span></p> |
| + | <span style=""></span> |
| + | <p><span style="display:block; overflow:hidden;"><img alt="" |
| + | src="https://static.igem.org/mediawiki/2009/a/ac/Freiburg09_anika008AzPresentation1.png" /></span><span |
| + | style="font-size: 14pt; line-height: 115%;"><o:p></o:p></span></p> |
| + | <p><span style="font-size: 14pt; line-height: 115%;"><o:p> </o:p></span></p> |
| + | <p><span style="font-size: 14pt; line-height: 115%;"><o:p> </o:p></span></p> |
| + | <p><span style="font-size: 16pt; line-height: 115%;">2.3 |
| + | Simulating temperature dependence for a set of |
| + | parameters<o:p></o:p></span></p> |
| + | <p><span style="">Temperature |
| + | plays an important role concerning biochemical reactions. It has a high |
| + | influence |
| + | on the reaction rate. The collision frequency is increased and |
| + | molecules have |
| + | more thermal energy at higher temperatures.<o:p></o:p></span></p> |
| + | <p><span style="">We |
| + | simulate |
| + | increased temperature by increased rate constants of enzymes and we |
| + | provide |
| + | increased dissociation rates. For this reason it is interesting to test |
| + | how the |
| + | model behaves under different temperatures. Three different cases are |
| + | introduced: temperature around optimum, higher temperature than optimum |
| + | and |
| + | lower temperature than optimum. <span style=""> </span><o:p></o:p></span></p> |
| + | <p><span style="">The |
| + | ODE’s |
| + | above are solved numerically; the chosen set of parameters test the |
| + | model |
| + | corresponding to the above-mentioned circumstances. Later on the |
| + | results will |
| + | be discussed.<span style=""> </span><o:p></o:p></span></p> |
| + | <p><span style=""><o:p> </o:p></span></p> |
| + | <p><span style="display:block; overflow:hidden;"><img alt="" |
| + | src="https://static.igem.org/mediawiki/2009/7/79/Freiburg09_anika008graph1model1.png" /></span><span |
| + | style=""><o:p></o:p></span></p> |
| + | <p><span style="font-size: 10pt; line-height: 115%;">Fig.5: |
| + | Temperature around optimum, Model 1<o:p></o:p></span></p> |
| + | <p><span style="display:block; overflow:hidden;"><img alt="" style="height:50%; width:50%;" |
| + | src="https://static.igem.org/mediawiki/2009/c/ce/Freiburg09_anika009tabelle1model1.png" /></span><span |
| + | style="line-height: 115%;"><o:p></o:p></span></p> |
| + | <p><span style="font-size: 10pt; line-height: 115%;">Table1: |
| + | <st1:place w:st="on">Chosen</st1:place> set of |
| + | parameters<o:p></o:p></span></p> |
| + | <p><span style="font-size: 10pt; line-height: 115%;"><o:p> </o:p></span></p> |
| + | <p><span style="display:block; overflow:hidden;"><img alt="" |
| + | src="https://static.igem.org/mediawiki/2009/3/35/Freiburg09_anika010graph2model1.png" /></span><span |
| + | style="line-height: 115%;"><o:p></o:p></span></p> |
| + | <p><span style="font-size: 10pt; line-height: 115%;">Fig.6: |
| + | Higher temperature than optimum, Model 1<o:p></o:p></span></p> |
| + | <p><span style="display:block; overflow:hidden;"><img alt=""style="height:50%; width:50%;" |
| + | src="https://static.igem.org/mediawiki/2009/d/d6/Freiburg09_anika011tabelle2model1.png" /></span><span |
| + | style="line-height: 115%;"><o:p></o:p></span></p> |
| + | <p><span style="line-height: 115%;"><o:p> </o:p></span></p> |
| + | <p><span style="font-size: 10pt; line-height: 115%;">Table2: |
| + | <st1:place w:st="on">Chosen</st1:place> set of |
| + | parameters<o:p></o:p></span></p> |
| + | <p><span style="display:block; overflow:hidden;"><img alt="" |
| + | src="https://static.igem.org/mediawiki/2009/6/6e/Freiburg09_anika012graph3model1.png" /></span><span |
| + | style="font-size: 10pt; line-height: 115%;"><o:p></o:p></span></p> |
| + | <p><span style="font-size: 20pt; line-height: 115%;"><o:p> </o:p></span></p> |
| + | <p><span style="font-size: 10pt; line-height: 115%;">Fig.7: |
| + | Lower temperature than optimum, Model 1<o:p></o:p></span></p> |
| + | <p><span style="display:block; overflow:hidden;"><img alt="" style="height:50%; width:50%;" |
| + | src="https://static.igem.org/mediawiki/2009/f/f4/Freiburg09_anika013tabelle3model1.png" /></span><span |
| + | style="font-size: 10pt; line-height: 115%;"><o:p></o:p></span></p> |
| + | <p><span style="line-height: 115%;"><o:p> </o:p></span></p> |
| + | <p><span style="font-size: 10pt; line-height: 115%;"><span |
| + | style=""> </span>Table3: |
| + | <st1:place w:st="on">Chosen</st1:place> set of |
| + | parameters<o:p></o:p></span></p> |
| + | <p><span style="font-size: 10pt; line-height: 115%;"><o:p> </o:p></span></p> |
| + | <p><span style="font-size: 16pt; line-height: 115%;">2.4 |
| + | Discussion<o:p></o:p></span></p> |
| + | <p><span style="">We |
| + | generated ODEs modeling both complex formation and DNA cleavage.<span |
| + | style=""> </span><o:p></o:p></span></p> |
| + | <p><span style="">This |
| + | process |
| + | clearly depends on the temperature of the reaction environment. A |
| + | process |
| + | mimicking the higher temperature (which leads i.e. to an increased k3 ) |
| + | is |
| + | characterized by faster increasing of the DNA fragments curve and |
| + | because of |
| + | this, </span><span>intermediate |
| + | product</span><span></span>s<span> </span><span>exist |
| + | for a shorter time period.<span style=""> </span>In |
| + | contrast a process |
| + | mimicking lower |
| + | temperature, intermediate products are more stable.<o:p></o:p></span></p> |
| + | <p><span style="">At |
| + | this |
| + | point one has to remark that model 1 is in a manner too much |
| + | simplified. To render |
| + | the model more realistic, this simulation should consider a limited |
| + | temperature |
| + | range. Even experiments are done <i style="">in vitro</i>, |
| + | every enzyme cannot work at temperatures too high or too low.<o:p></o:p></span></p> |
| + | <p><span style="font-size: 20pt; line-height: 115%;">3. |
| + | Model 2, bind - ‘Ready’- |
| + | ‘Steady’- cut<o:p></o:p></span></p> |
| + | <p><span style="">Similar |
| + | to |
| + | model 1, we developed an extended second model sharing the same basic |
| + | concept. In |
| + | the second model we additionally considered the formation of Fok |
| + | monomer/ DNA |
| + | intermediate states.<o:p></o:p></span></p> |
| + | <p><span style=""><o:p> </o:p></span></p> |
| + | <p><span style="">The |
| + | significant difference between both models is the assumption that the |
| + | whole |
| + | process works slightly more complicated than considered in model 1. <o:p></o:p></span></p> |
| + | <p><span style="">By |
| + | enzyme |
| + | reactions chemical equations show which educts have to react with each |
| + | other to |
| + | generate a certain number of products. In our case Fok_a, Fok_i and DNA |
| + | represent |
| + | educts, whereas the active heterodimer is the final product coming out |
| + | of the |
| + | reaction. On the way from educts to product interstage products appear |
| + | such as DNAFok_a, |
| + | DNAFok_i Ready and Steady. However, the likelihood of three parts |
| + | colliding |
| + | with each other at the same time is quite low. In a first step, two |
| + | parts associate |
| + | and form an interstage product. In a second or third step the final |
| + | product is |
| + | formed when distinct interstage products collide with each other. At |
| + | this point |
| + | one has to remark that the anticalins of the Fok- Monomers are attached |
| + | to the |
| + | DNA, so that Fok_a has to bind next to Fok_i and vice versa. Other |
| + | binding combinations |
| + | do not allow dimerization. Hence the central point of this model is the |
| + | formation and interaction of all generated interstate products.<o:p></o:p></span></p> |
| + | <p><span style="">As |
| + | a |
| + | consequence of these considerations, we now consolidated the |
| + | assumptions for |
| + | our second model. <o:p></o:p></span></p> |
| + | <p><span style="">The |
| + | flowchart below shows a schematic presentation of model 2 (Fig. 8).<o:p></o:p></span></p> |
| + | <p><span style="font-size: 12pt; line-height: 115%;"><o:p> </o:p></span></p> |
| + | <p><span style="display:block; overflow:hidden;"><img alt="" |
| + | src="https://static.igem.org/mediawiki/2009/7/78/Freiburg09_anika014flussdiagrammmodel2.png" /></span><span |
| + | style="font-size: 12pt; line-height: 115%;"><o:p></o:p></span></p> |
| + | <p><span style="font-size: 20pt; line-height: 115%;"><o:p> </o:p></span></p> |
| + | <p><span style="font-size: 10pt; line-height: 115%;">Fig.8: |
| + | Flowchart of model 2<o:p></o:p></span></p> |
| + | <p><span style="font-size: 12pt; line-height: 115%;"><o:p> </o:p></span></p> |
| + | <p style="text-indent: 35.4pt;"><span |
| + | style="font-size: 16pt; line-height: 115%;"><span style=""> </span>3.1 |
| + | Reaction kinetics<o:p></o:p></span></p> |
| + | <p><span style="">The |
| + | process |
| + | of binding Fok_a, Fok_i and DNA is of dynamic nature. Fok_a binds to |
| + | the DNA |
| + | with the reaction rate <b style="">k1a_on</b> or a |
| + | DNAFok_a complex dissociates with the reaction rate <b style="">k1a_off</b>. |
| + | <o:p></o:p></span></p> |
| + | <p><span style="">Likewise |
| + | Fok_i binds to the DNA with the reaction rate <b style="">k1i_on</b> |
| + | and the DNAFok_i complex dissociates with the reaction rate <b |
| + | style="">k1i_off:<o:p></o:p></b></span></p> |
| + | <p><b style=""><span style=""><o:p> </o:p></span></b></p> |
| + | <p><span style="display:block; overflow:hidden;"><img alt="" |
| + | src="https://static.igem.org/mediawiki/2009/2/22/Freiburg09_anika015kinetik1model2.png" /></span><span |
| + | style="font-size: 12pt; line-height: 115%;"><o:p></o:p></span></p> |
| + | <p><span style="display:block; overflow:hidden;"><img alt="" |
| + | src="https://static.igem.org/mediawiki/2009/2/29/Freiburg09_anika016kinetik2model2.png" /></span><span |
| + | style="font-size: 12pt; line-height: 115%;"><o:p></o:p></span></p> |
| + | <p><b style=""><span |
| + | style="font-size: 12pt; line-height: 115%;"><o:p> </o:p></span></b></p> |
| + | <p><span style="font-size: 12pt; line-height: 115%;"><o:p> </o:p></span></p> |
| + | <p><span style="">The |
| + | complex |
| + | DNAFok_a binds Fok_i with reaction rate <b style="">k2a_on |
| + | </b>forming a trimetric complex which dissociates with reaction |
| + | rate <b style="">k2a_off</b>. In a similar fashion, |
| + | DNAFok_i |
| + | binds Fok_a with the rate <b style="">k2i_on</b> |
| + | and |
| + | dissociates with the rate <b style="">k2i_off</b>. |
| + | We |
| + | call these states ‘Ready’: <o:p></o:p></span></p> |
| + | <p><span style="font-size: 12pt; line-height: 115%;"><o:p> </o:p></span></p> |
| + | <p><span style="font-size: 12pt; line-height: 115%;"><o:p> </o:p></span></p> |
| + | <p><span style="font-size: 12pt; line-height: 115%;"><o:p> </o:p></span></p> |
| + | <p><span style="display:block; overflow:hidden;"><img alt="" |
| + | src="https://static.igem.org/mediawiki/2009/a/ae/Freiburg09_anika017kinetik3model2.png" /></span><span |
| + | style="font-size: 12pt; line-height: 115%;"><o:p></o:p></span></p> |
| + | <p><span style="display:block; overflow:hidden;"><img alt="" |
| + | src="https://static.igem.org/mediawiki/2009/9/9e/Freiburg09_anika018kinetik4model2.png" /></span><span |
| + | style="font-size: 12pt; line-height: 115%;"><o:p></o:p></span></p> |
| + | <p><span style="font-size: 12pt; line-height: 115%;"><o:p> </o:p></span></p> |
| + | <p><span style="font-size: 12pt; line-height: 115%;"><o:p> </o:p></span></p> |
| + | <p><span style="">We |
| + | now assume |
| + | that the Fok_a and Fok_i complexes are initially in the inactive |
| + | ‘Ready’ state, |
| + | which is subsequently converted to the ‘Steady ‘ |
| + | state. It is activated with |
| + | rate <b style="">k3_on</b> and becomes inactive |
| + | with |
| + | rate <b style="">k3_off</b>:<o:p></o:p></span></p> |
| + | <p><span style="display:block; overflow:hidden;"><img alt="" |
| + | src="https://static.igem.org/mediawiki/2009/5/52/Freiburg09_anika019kinetik5model2.png" /></span><span |
| + | style="font-size: 12pt; line-height: 115%;"><o:p></o:p></span></p> |
| + | <p><span style="font-size: 12pt; line-height: 115%;"><o:p> </o:p></span></p> |
| + | <p><span style="">After |
| + | activation, the enzyme cuts the DNA substrate with the rate <b |
| + | style="">k4. </b>In contrast to the proceeding |
| + | steps, this is a unidirectional reaction: <o:p></o:p></span></p> |
| + | <p><span style="display:block; overflow:hidden;"><img alt="" |
| + | src="https://static.igem.org/mediawiki/2009/e/ed/Freiburg09_anika020kinetik6model2.png" /></span><span |
| + | style="font-size: 12pt; line-height: 115%;"><o:p></o:p></span></p> |
| + | <p><span style="font-size: 12pt; line-height: 115%;"><o:p> </o:p></span></p> |
| + | <p><span style="font-size: 12pt; line-height: 115%;"><o:p> </o:p></span></p> |
| + | <p style="text-indent: 35.4pt;"><span |
| + | style="font-size: 16pt; line-height: 115%;">3.2 |
| + | ODE’s<o:p></o:p></span></p> |
| + | <p><span style="">The |
| + | ODE’s |
| + | can again be derived from the reaction kinetics and are as follows: <o:p></o:p></span></p> |
| + | <p><span style="font-size: 14pt; line-height: 115%;"><o:p> </o:p></span></p> |
| + | <p><span style="font-size: 14pt; line-height: 115%;"><o:p> </o:p></span></p> |
| + | <p><span style="font-size: 14pt; line-height: 115%;"><o:p> </o:p></span></p> |
| + | <p><span style="font-size: 14pt; line-height: 115%;"><o:p> </o:p></span></p> |
| + | <p><span style="font-size: 12pt; line-height: 115%;"><o:p> </o:p></span></p> |
| + | <p><span style="display:block; overflow:hidden;"><img alt="" |
| + | src="https://static.igem.org/mediawiki/2009/4/45/Freiburg09_anika026A_zzPresentation1.png" /></span><span |
| + | style="font-size: 12pt; line-height: 115%;"><o:p></o:p></span></p> |
| + | <p><span style="font-size: 12pt; line-height: 115%;"><o:p> </o:p></span></p> |
| + | <p><span style="display:block; overflow:hidden;"><img alt="" |
| + | src="https://static.igem.org/mediawiki/2009/8/86/Freiburg09_anika026ABzzzPresentation1.png" /></span><span |
| + | style="font-size: 12pt; line-height: 115%;"><o:p></o:p></span></p> |
| + | <p><span style="font-size: 12pt; line-height: 115%;"><o:p> </o:p></span></p> |
| + | <p><span style="font-size: 12pt; line-height: 115%;"><o:p> </o:p></span></p> |
| + | <p><span style="font-size: 14pt; line-height: 115%;"><o:p> </o:p></span></p> |
| + | <p><span style="font-size: 16pt; line-height: 115%;">3.3 |
| + | Different Concentrations of Fok_a and Fok_i<o:p></o:p></span></p> |
| + | <p><span style="">According |
| + | to the collision theory, the concentrations of the different reactants |
| + | play an |
| + | important role for their interactions and also in our special case of |
| + | the |
| + | formation of an active complex. <span style=""> </span>To |
| + | react |
| + | with each other, single parts have to collide and the likelihood of |
| + | collision |
| + | increases with the concentration of every single reactant. <o:p></o:p></span></p> |
| + | <p><span style="">On |
| + | the |
| + | other hand if the concentrations differ, a </span><span |
| + | style="color: windowtext; text-decoration: none;">disequilibrium</span><span |
| + | style=""> arises and the balance of the |
| + | reaction is shifted |
| + | to one side of the reaction. <o:p></o:p></span></p> |
| + | <p><span style="">The |
| + | use of |
| + | different amounts of reactants may represent the most important impact |
| + | on our |
| + | model. As the Parts Fok_a and Fok_i are the basis to start the cleavage |
| + | process, |
| + | their amounts strongly determine the number of active enzymes. <o:p></o:p></span></p> |
| + | <p><span style="">In |
| + | the |
| + | following simulation we tested how the process would react if Fok_a |
| + | would be in |
| + | excess of Fok_i. The increased concentration is simulated by elevated |
| + | association |
| + | rates. Again, the ODEs are solved for a set of parameters and the |
| + | concentrations of the different reaction partners are revealed amongst |
| + | the time |
| + | course.<o:p></o:p></span></p> |
| + | <p><span style=""><o:p> </o:p></span></p> |
| + | <p><span style="display:block; overflow:hidden;"><img alt="" |
| + | src="https://static.igem.org/mediawiki/2009/7/76/Freiburg09_anika026Z_253.png" /></span><span |
| + | style="font-size: 14pt; line-height: 115%;"><o:p></o:p></span></p> |
| + | <p><span style="font-size: 14pt; line-height: 115%;"><o:p> </o:p></span></p> |
| + | <p><span style="font-size: 12pt; line-height: 115%;"><o:p> </o:p></span></p> |
| + | <p><span style="font-size: 10pt; line-height: 115%;">Fig. |
| + | 9: Fok_a and Fok_i in equilibrium, Model 2<o:p></o:p></span></p> |
| + | <p><span style="font-size: 10pt; line-height: 115%;"><o:p> </o:p></span></p> |
| + | <p><span style="display:block; overflow:hidden;"><img alt="" style="height:70%; width:70%;" |
| + | src="https://static.igem.org/mediawiki/2009/d/da/Freiburg09_anika027_264tabelle.png" /></span><span |
| + | style="font-size: 10pt; line-height: 115%;"><o:p></o:p></span></p> |
| + | <p><span style="font-size: 10pt; line-height: 115%;"><o:p> </o:p></span></p> |
| + | <p><span style="font-size: 10pt; line-height: 115%;">Table4: |
| + | Chosen set of parameters<o:p></o:p></span></p> |
| + | <p><span style="display:block; overflow:hidden;"><img alt="" |
| + | src="https://static.igem.org/mediawiki/2009/f/fc/Freiburg09_anika028._27.png" /></span><span |
| + | style="font-size: 10pt; line-height: 115%;"><o:p></o:p></span></p> |
| + | <p><span style="font-size: 10pt; line-height: 115%;"><o:p> </o:p></span></p> |
| + | <p><span style="font-size: 12pt; line-height: 115%;"><o:p> </o:p></span></p> |
| + | <p><span style="font-size: 10pt; line-height: 115%;">Fig. |
| + | 10: More Fok_a than Fok_i, Model 2<o:p></o:p></span></p> |
| + | <p><span style="display:block; overflow:hidden;"><img alt="" style="height:70%; width:70%;" |
| + | src="https://static.igem.org/mediawiki/2009/9/9d/Freiburg09_anika029_286.png" /></span><span |
| + | style="font-size: 10pt; line-height: 115%;"><o:p></o:p></span></p> |
| + | <p><span style="font-size: 10pt; line-height: 115%;"><o:p> </o:p></span></p> |
| + | <p><span style="font-size: 10pt; line-height: 115%;">Table5: |
| + | Chosen set of parameters<o:p></o:p></span></p> |
| + | <p><span style=""><o:p> </o:p></span></p> |
| + | <p><span style=""><o:p> </o:p></span></p> |
| + | <p><span style=""><o:p> </o:p></span></p> |
| + | <p><span style=""><o:p> </o:p></span></p> |
| + | <p><span style=""><o:p> </o:p></span></p> |
| + | <p><span style=""><o:p> </o:p></span></p> |
| + | <p><span style="">The |
| + | following diagram nicely represents the relation between the |
| + | concentration of |
| + | Fok_a and Fok_i and how the amount of active protein complexes changes |
| + | along the |
| + | time course. As expected, at a ratio of Fok_a/Fok_i = 1 the highest |
| + | concentration of active protein can be observed. Whenever the |
| + | concentration equilibrium |
| + | shifts to either Fok_a or Fok_i, the amount of active protein |
| + | decreases. <i style="">In vivo</i>, this would |
| + | occur if one part is |
| + | higher expressed compared to the other part. <o:p></o:p></span></p> |
| + | <p><span style="">. |
| + | <o:p></o:p></span></p> |
| + | <p><span style=""><o:p> </o:p></span></p> |
| + | <p><span style="display:block; overflow:hidden;"><img alt="" |
| + | src="https://static.igem.org/mediawiki/2009/3/3c/Freiburg09_anika030_297.png" /></span><span |
| + | style="font-size: 12pt; line-height: 115%;"><o:p></o:p></span></p> |
| + | <p><span style="font-size: 12pt; line-height: 115%;"><o:p> </o:p></span></p> |
| + | <p><span style="font-size: 12pt; line-height: 115%;"><o:p> </o:p></span></p> |
| + | <p><span style="font-size: 10pt; line-height: 115%;">Fig. |
| + | 11:<span style=""> </span>Fok_a/Fok_i |
| + | Ratio, Model 2<o:p></o:p></span></p> |
| + | <p><span style="display:block; overflow:hidden;"><img alt="" style="height:70%; width:70%;" |
| + | src="https://static.igem.org/mediawiki/2009/d/da/Freiburg09_anika027_264tabelle.png" /></span><span |
| + | style="font-size: 10pt; line-height: 115%;"><o:p></o:p></span></p> |
| + | <p><span style="font-size: 12pt; line-height: 115%;"><o:p> </o:p></span></p> |
| + | <p><span style="font-size: 10pt; line-height: 115%;">Table6: |
| + | Chosen set of parameters<o:p></o:p></span></p> |
| + | <p><span style="font-size: 14pt; line-height: 115%;">5. |
| + | Results<o:p></o:p></span></p> |
| + | <p><span style="font-size: 12pt; line-height: 115%;">In |
| + | addition, it would be interesting to enhance our model |
| + | 2 with the assumption that Fok_a and Fok_i could also dimerize before |
| + | one of |
| + | the parts is bound to the DNA via its anticalin. <o:p></o:p></span></p> |
| + | <p><span style="font-size: 12pt; line-height: 115%;">Based |
| + | on the assumption that dimerization of Fok_i/ |
| + | Fok_a is possible without the need of preceding DNA-binding of DigA or |
| + | FluA the |
| + | possibility arises that one of the tags necessary to create an active |
| + | complex |
| + | on the DNA is already occupied by another monomer. This would prevent |
| + | cleavage |
| + | activity of the preassembled heterodimer because it is not able to bind |
| + | both |
| + | tags of the target DNA sequence. Eventually, this would lead to an |
| + | overall decreased |
| + | rate of DNA cleavage. <o:p></o:p></span></p> |
| + | <p><span style="font-size: 12pt; line-height: 115%;">Based |
| + | our considerations, the following equation has |
| + | to be added to the reaction kinetics of our model 2 and represents the |
| + | dimerization process of Fok_a and Fok_i.<o:p></o:p></span></p> |
| + | <p><span style="font-size: 12pt; line-height: 115%;"><o:p> </o:p></span></p> |
| + | <p><span style="display:block; overflow:hidden;"><img alt="" |
| + | src="https://static.igem.org/mediawiki/2009/1/18/Freiburg09_anika031_01schemamodel3.png" /></span><span |
| + | style="font-size: 12pt; line-height: 115%;"><o:p></o:p></span></p> |
| + | <p><span style="font-size: 12pt; line-height: 115%;"><o:p> </o:p></span></p> |
| + | <p><span style="font-size: 12pt; line-height: 115%;"><o:p> </o:p></span></p> |
| + | <p><span style="font-size: 12pt; line-height: 115%;"><o:p> </o:p></span></p> |
| + | <p><span style="font-size: 12pt; line-height: 115%;"><o:p> </o:p></span></p> |
| + | <p><span style="font-size: 12pt; line-height: 115%;">One |
| + | has to keep in mind that all the models above are |
| + | simplified and do not include all variables influencing the |
| + | interactions. Models |
| + | always have to be tested if they are close enough to reality and |
| + | therefore it |
| + | is a necessity to feed a model with realistic data. <o:p></o:p></span></p> |
| + | <p><span style="font-size: 12pt; line-height: 115%;">Simulations |
| + | able to represent <i style="">in vitro</i> |
| + | conditions would have to include tremendous numbers of |
| + | physicochemical factors such as solvent properties, salt concentrations |
| + | and |
| + | structural diversities of the involved molecules. This would require |
| + | setup and |
| + | computation of enormous equation. <o:p></o:p></span></p> |
| + | <p><span style="font-size: 12pt; line-height: 115%;">However, |
| + | predictions made on the basis of models like |
| + | ours can often be used to optimize conditions for simple experimental |
| + | setups. For |
| + | example, the effects of the lower expression rates of our Fok_a |
| + | constructs can |
| + | be visualized before the actual experiment is performed.<o:p></o:p></span></p> |
| + | <p><span style="font-size: 12pt; line-height: 115%;" |
| + | lang="EN-GB"><o:p> </o:p></span></p> |
| + | <p><span style="font-size: 12pt; line-height: 115%;">5. |
| + | Literature: <o:p></o:p></span></p> |
| + | <ol style="margin-top: 0cm; color: rgb(0, 0, 0);" start="1" |
| + | type="1"> |
| + | <li><span style="" lang="EN-GB">1. Gerald |
| + | Beste, Frank Schmidt, Thomas Stibora |
| + | and Arne Skerra: “Small antibody-like proteins with |
| + | prescribed ligand specificities derived from the lipocalin |
| + | fold“, Proc. Natl. Acad. Sci. USA, Vol 96, pp. 1898 |
| + | – 1903, March 1999, Biochemistry<o:p></o:p></span></li> |
| + | <li>2. David Wah, Joel Hirsch, Lydia |
| + | Dorner, Ira Schildkraut and Aneel Aggarwal: “Structure of the |
| + | multimodular endonuclease FokI bound to DNA”, Nature, VOL |
| + | 388, July 1997<span style="" lang="EN-GB"><o:p></o:p></span></li> |
| + | <li style="">3. Peter Atkins, |
| + | ‘Physikalische Chemie’, Wiley-VCH, Third Edition, |
| + | January 2002<span style="font-size: 10pt; line-height: 115%;"><o:p></o:p></span></li> |
| + | </ol> |
| + | <div class="cleared"></div> |
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| + | </div> |
| + | <br /> |
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| + | <p>contact: <a |
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https://2009.igem.org/wiki/index.php?title=Team:Freiburg_bioware/Modeling&action=edit