Team:IIT Bombay India/DDM

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== '''Introduction''' ==
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== '''Detailed Deterministic Model''' ==
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| Established in 1958, [http://www.iitb.ac.in IIT Bombay] is one of the most recognized centers of academic excellence in the country today. The excellence of its academic programs, a robust  research and development program with  parallel improvement in facilities and infrastructure have kept it at par with the best institutions in the world. The ideas on which such institutes are built evolve and change with national aspirations, national perspectives, and global trends. At IIT Bombay we are continuously seeking to extend the boundaries of our research in a sustained manner with clear cut executable goals, grounded solidly in national realities.
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Detailed Deterministic Model
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'''Objective'''
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This is our first year of participation and as such, we are pretty excited about the prospects. We are a group of chemical engineering and bioschool students. The most exciting aspect that we found about this competition was the interdisciplinary learning. A chemical reactor system invariably involves the design of control structures, and it is the design of these structures in a biological system that we wish to attain via our project.
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Here we wish to show how the dynamics of the cellular material (proteins and plasmids) changes with time and IPTG and also how the specific growth rate of the four constructs on lactose is controlled and maximized by use of multiple feedbacks.  In this model quantification by simulation was done and later results were verified by experimental data. A concept of burden on cells and normalized growth rate is introduced to show that in multiple feedback loops helps in optimizing growth rate.
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'''Primary Kinetics and Equations'''
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In our system we have the key components being plasmid copy number, fusion protein, yfp, lactose, IPTG and growth associated enzyme β-galactosidase. The E. coli genome inherently consists of β gal gene which has plac promoter. LacI interacts with lactose and IPTG and also with plac promoter.
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[[Image:abhinav1.jpg]]
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Assuming these 3 equilibrium reactions, we can now write differential equations for the components relating their concentrations with time. The total amount of plac promoter present in any strain could be given by the equation:
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[[Image:abhinav2.jpg]]
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Where ‘a’ is an integer which depends on the strain for which differential equation has been used to describe.(Total plac promoter, is the sum of concentration of free plac(fp) promoter and plac-LacI complex.
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[[Image:abhinav3.jpg]]
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LacI total equals cfp (because they are a fusion protein). LacI refers to unbounded free lacI in the medium.
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[[Image:abhinav4.jpg]]
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Note: here plac1, plac2, plac3 are the free plac associated with β-gal production, plasmid number and cfp-LacI protein.  
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The differential equations are solved for two different conditions. Equations were first solved for 24 hours on other medium with different IPTG and no lactose.  After 24 hours the equations were solved for the same value of IPTG but on different values of lactose.
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Equations for growth on no Lactose:
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[[Image:abhinav5.jpg]]
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Equations for growth on Lactose:
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[[Image:abhinav6.jpg]]
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[[Image:abhinav7.jpg]]
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'''Results'''
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We now define the cost that cell has to pay for growing in the Open loop and MIMO strains. In open loop, cell overproduces plasmid, LacI, Yfp and β-gal.
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In MIMO, it optimizes this load to as low as possible and is able to grow at higher specific growth rate. We define the burden on the cell by 2 different definitions:
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Definition 1:
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[[Image:pr5.jpg]]
   
   
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Here all maximum values are the maximum amount of the protein or plasmid produced by mutant strain. Other definition used for Burden is
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Definition 2
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[[Image:pr6.jpg]]
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The Normalized growth rate is
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[[Image:pr7.jpg]]
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Plots of Burden and Normalized growth rate at various Lactose show, that the strain 4 has been able to successfully reduce its burden and optimize its growth, whereas in strain 1 the overproduction occurs at the cost of reduced growth rate. At higher IPTG when MIMO strain behaves like Open loop it could be seen that burden on the cell increases.
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For cells growth, cell has to produce the β-gal. In order to produce β-gal, our mutant strains have been forced to produce LacI and YFP protein. Due to this, cells now have only a part of machinery working for cell division. This is the burden that cells have to pay for growing at a particular specific growth rate.
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[[Image:pr1.jpg]]
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[[Image:pr2.jpg]]
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[[Image:pr3.jpg]]
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[[Image:pr4.jpg]]
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'''Conclusions'''
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1. The detailed model was developed to generate the dynamic profiles of the plasmid copy number, LacI, Yfp, β-gal, Lactose and biomass. Using the above model, we are able to correlate the simulation results with the experimentally obtained values. 
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2. We also see that growth on lactose for strain 4 is highest among the 4 strains with lesser burden on the cell to produce the unnecessarily higher amount of protein for growth.
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3. We observe that as lactose concentration is increased within our simulation range, burden of the cell does not change. For strain 4, as lactose concentration increases, the normalized growth rate crosses the burden, indicating that cell has now optimized its growth for the corresponding burden. For strain 1, the increase in lactose does not have any such effect and burden is always above the normalized growth rate. As IPTG increases, burden on strain 4 increases, the growth rate now crosses the burden at an higher value of lactose. Also as IPTG increases growth rate of strain 1 also increases.
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The detailed methodology, system equations, results and discussion can be seen [[Media:Deterministic modelling.pdf|here]].
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A major objective of synthetic biology is to unveil the inherent design principles prevailing in biological circuits. Multiple feedback loops (having both positive and negative regulation) are highly prevalent in biological systems. The relevance of such a design in biological systems is unclear. Our team will use synthetic biology approaches to answer these questions. Our team comprises of nine undergraduates, 3 graduate students as student mentor and two faculty mentors, one each from biology and engineering background. The project specifically deals with the analysis of effect of single and multiple feedback loops on gene expression. This project will involve theoretical and experimental studies. We have designed synthetic constructs to mimic multiple feedbacks. The focus of our experimental work will be to visualize the effect of multiple feedback loops on the synthetic construct using single cell analysis. The project will provide insights into the roles of multiple feedback loops in biological systems.
 
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Latest revision as of 02:30, 22 October 2009

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Detailed Deterministic Model

Detailed Deterministic Model

Objective

Here we wish to show how the dynamics of the cellular material (proteins and plasmids) changes with time and IPTG and also how the specific growth rate of the four constructs on lactose is controlled and maximized by use of multiple feedbacks. In this model quantification by simulation was done and later results were verified by experimental data. A concept of burden on cells and normalized growth rate is introduced to show that in multiple feedback loops helps in optimizing growth rate.


Primary Kinetics and Equations

In our system we have the key components being plasmid copy number, fusion protein, yfp, lactose, IPTG and growth associated enzyme β-galactosidase. The E. coli genome inherently consists of β gal gene which has plac promoter. LacI interacts with lactose and IPTG and also with plac promoter.


Abhinav1.jpg

Assuming these 3 equilibrium reactions, we can now write differential equations for the components relating their concentrations with time. The total amount of plac promoter present in any strain could be given by the equation:

Abhinav2.jpg

Where ‘a’ is an integer which depends on the strain for which differential equation has been used to describe.(Total plac promoter, is the sum of concentration of free plac(fp) promoter and plac-LacI complex.

Abhinav3.jpg

LacI total equals cfp (because they are a fusion protein). LacI refers to unbounded free lacI in the medium.

Abhinav4.jpg

Note: here plac1, plac2, plac3 are the free plac associated with β-gal production, plasmid number and cfp-LacI protein.

The differential equations are solved for two different conditions. Equations were first solved for 24 hours on other medium with different IPTG and no lactose. After 24 hours the equations were solved for the same value of IPTG but on different values of lactose.

Equations for growth on no Lactose:

Abhinav5.jpg

Equations for growth on Lactose:

Abhinav6.jpg

Abhinav7.jpg


Results

We now define the cost that cell has to pay for growing in the Open loop and MIMO strains. In open loop, cell overproduces plasmid, LacI, Yfp and β-gal. In MIMO, it optimizes this load to as low as possible and is able to grow at higher specific growth rate. We define the burden on the cell by 2 different definitions: Definition 1:

Pr5.jpg

Here all maximum values are the maximum amount of the protein or plasmid produced by mutant strain. Other definition used for Burden is Definition 2

Pr6.jpg

The Normalized growth rate is

Pr7.jpg

Plots of Burden and Normalized growth rate at various Lactose show, that the strain 4 has been able to successfully reduce its burden and optimize its growth, whereas in strain 1 the overproduction occurs at the cost of reduced growth rate. At higher IPTG when MIMO strain behaves like Open loop it could be seen that burden on the cell increases. For cells growth, cell has to produce the β-gal. In order to produce β-gal, our mutant strains have been forced to produce LacI and YFP protein. Due to this, cells now have only a part of machinery working for cell division. This is the burden that cells have to pay for growing at a particular specific growth rate.

Pr1.jpg

Pr2.jpg

Pr3.jpg

Pr4.jpg


Conclusions

1. The detailed model was developed to generate the dynamic profiles of the plasmid copy number, LacI, Yfp, β-gal, Lactose and biomass. Using the above model, we are able to correlate the simulation results with the experimentally obtained values.

2. We also see that growth on lactose for strain 4 is highest among the 4 strains with lesser burden on the cell to produce the unnecessarily higher amount of protein for growth.

3. We observe that as lactose concentration is increased within our simulation range, burden of the cell does not change. For strain 4, as lactose concentration increases, the normalized growth rate crosses the burden, indicating that cell has now optimized its growth for the corresponding burden. For strain 1, the increase in lactose does not have any such effect and burden is always above the normalized growth rate. As IPTG increases, burden on strain 4 increases, the growth rate now crosses the burden at an higher value of lactose. Also as IPTG increases growth rate of strain 1 also increases.


The detailed methodology, system equations, results and discussion can be seen here.