Difference between revisions of "Team:British Columbia/Model"

 
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<h3>★  ALERT! </h3>
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<p>This page is used by the judges to evaluate your team for the <a href="https://2018.igem.org/Judging/Medals">medal criterion</a> or <a href="https://2018.igem.org/Judging/Awards"> award listed below</a>. </p>
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<p> Delete this box in order to be evaluated for this medal criterion and/or award. See more information at <a href="https://2018.igem.org/Judging/Pages_for_Awards"> Instructions for Pages for awards</a>.</p>
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<h1> Modeling</h1>
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<p>Mathematical models and computer simulations provide a great way to describe the function and operation of BioBrick Parts and Devices. Synthetic Biology is an engineering discipline, and part of engineering is simulation and modeling to determine the behavior of your design before you build it. Designing and simulating can be iterated many times in a computer before moving to the lab. This award is for teams who build a model of their system and use it to inform system design or simulate expected behavior in conjunction with experiments in the wetlab.</p>
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<h3> Gold Medal Criterion #3</h3>
 
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Convince the judges that your project's design and/or implementation is based on insight you have gained from modeling. This could be either a new model you develop or the implementation of a model from a previous team. You must thoroughly document your model's contribution to your project on your team's wiki, including assumptions, relevant data, model results, and a clear explanation of your model that anyone can understand.
 
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The model should impact your project design in a meaningful way. Modeling may include, but is not limited to, deterministic, exploratory, molecular dynamic, and stochastic models. Teams may also explore the physical modeling of a single component within a system or utilize mathematical modeling for predicting function of a more complex device.
 
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Please see the <a href="https://2018.igem.org/Judging/Medals"> 2018
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Medals Page</a> for more information.  
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            A model was developed to understand the dynamics of a co-culture of DH5a and BL21 E. coli strains engineered for kaempferol production. This model had to capture both the kinetics of relevant substrates in our engineered pathways, as well as commensal dynamics between the two strains. Specifically, we used the model to predict the ideal sensitivity of the biosensor, and additionally predict kaempferol production yields based on different co-culture ratios. This enables us to determine the ideal ratio of bacterial strains for optimal kaempferol production, theoretically outperforming what would be possible in a single synthetically engineered strain.
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This was accomplished by constructing a system of five Ordinary Differential Equations (ODEs), addressing the concentration dynamics of each E. coli strain (DH5a and BL21), media substrate consumption (glucose), and changes in concentration of both the naringenin intermediate and kaempferol product. The model was implemented in MATLAB and solved using the ode45 algorithm—a numerical 1st order ODE solver. In order to have the model reflect our actual experimental setup, several constants needed to be obtained. These quantify the growth rates of the two E. coli strains, the dependency of naringenin production on glucose concentration, and the secondary production constants of both naringenin and kaempferol. To model substrate limited growth, we relied on Monod kinetics to provide a relationship between substrate concentration and strain growth. Two constants, maximum specific growth rate and the saturation constant, are required to utilize this relationship. The maximum specific growth rate of a culture (μmax) is obtained when it is grown in an excess of substrate; the saturation constant (Ks) is the concentration at which the specific growth rate is half the maximum specific growth rate.
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We performed a series of experiments to populate data points on a Lineaweaver-Burke plot, recovering the maximum specific growth rate of the E. coli strains. These experiments consisted of growing a single strain of E. coli on various concentrations of glucose substrate and recording the growth of the bacteria over time. In logarithmic space, the bacterial growth rate during the linear growth phase (i.e. growth prior to media glucose depletion) was determined for each assessed glucose concentration. By plotting these data points on a double-reciprocal plot of substrate concentration and growth rate, we performed a linear least-squares regression to construct a Lineaweaver-Burke plot. From this, values for Ks and μmax could be obtained: the slope of this plot is equal to Ks/μmax, while the intercept is equal to 1/μmax.
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The developed differential equations were combined with these experimental constants and then solved using the ode45 function in MATLAB. Our model consisted of two codes: consortium.m was created to specify the aforementioned constants and the relationships between quantities in the form of ordinary differential equations. A second code, variables.m, was constructed to specify initial conditions, link the ODEs described in consortium.m to the ode45 function, and plot the resulting predictions. These plots showed the species and substrate concentration as a function of time.<br>
 
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<h3>Best Model Special Prize</h3>
 
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To compete for the <a href="https://2018.igem.org/Judging/Awards">Best Model prize</a>, please describe your work on this page  and also fill out the description on the <a href="https://2018.igem.org/Judging/Judging_Form">judging form</a>. Please note you can compete for both the gold medal criterion #3 and the best model prize with this page.
 
 
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You must also delete the message box on the top of this page to be eligible for the Best Model Prize.
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<h3> Inspiration </h3>
 
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Here are a few examples from previous teams:
 
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<li><a href="https://2016.igem.org/Team:Manchester/Model">2016 Manchester</a></li>
 
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<li><a href="https://2016.igem.org/Team:TU_Delft/Model">2016 TU Delft</li>
 
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<li><a href="https://2014.igem.org/Team:ETH_Zurich/modeling/overview">2014 ETH Zurich</a></li>
 
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<li><a href="https://2014.igem.org/Team:Waterloo/Math_Book">2014 Waterloo</a></li>
 
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Latest revision as of 00:37, 11 November 2018



A model was developed to understand the dynamics of a co-culture of DH5a and BL21 E. coli strains engineered for kaempferol production. This model had to capture both the kinetics of relevant substrates in our engineered pathways, as well as commensal dynamics between the two strains. Specifically, we used the model to predict the ideal sensitivity of the biosensor, and additionally predict kaempferol production yields based on different co-culture ratios. This enables us to determine the ideal ratio of bacterial strains for optimal kaempferol production, theoretically outperforming what would be possible in a single synthetically engineered strain.


This was accomplished by constructing a system of five Ordinary Differential Equations (ODEs), addressing the concentration dynamics of each E. coli strain (DH5a and BL21), media substrate consumption (glucose), and changes in concentration of both the naringenin intermediate and kaempferol product. The model was implemented in MATLAB and solved using the ode45 algorithm—a numerical 1st order ODE solver. In order to have the model reflect our actual experimental setup, several constants needed to be obtained. These quantify the growth rates of the two E. coli strains, the dependency of naringenin production on glucose concentration, and the secondary production constants of both naringenin and kaempferol. To model substrate limited growth, we relied on Monod kinetics to provide a relationship between substrate concentration and strain growth. Two constants, maximum specific growth rate and the saturation constant, are required to utilize this relationship. The maximum specific growth rate of a culture (μmax) is obtained when it is grown in an excess of substrate; the saturation constant (Ks) is the concentration at which the specific growth rate is half the maximum specific growth rate.


We performed a series of experiments to populate data points on a Lineaweaver-Burke plot, recovering the maximum specific growth rate of the E. coli strains. These experiments consisted of growing a single strain of E. coli on various concentrations of glucose substrate and recording the growth of the bacteria over time. In logarithmic space, the bacterial growth rate during the linear growth phase (i.e. growth prior to media glucose depletion) was determined for each assessed glucose concentration. By plotting these data points on a double-reciprocal plot of substrate concentration and growth rate, we performed a linear least-squares regression to construct a Lineaweaver-Burke plot. From this, values for Ks and μmax could be obtained: the slope of this plot is equal to Ks/μmax, while the intercept is equal to 1/μmax.


The developed differential equations were combined with these experimental constants and then solved using the ode45 function in MATLAB. Our model consisted of two codes: consortium.m was created to specify the aforementioned constants and the relationships between quantities in the form of ordinary differential equations. A second code, variables.m, was constructed to specify initial conditions, link the ODEs described in consortium.m to the ode45 function, and plot the resulting predictions. These plots showed the species and substrate concentration as a function of time.