Difference between revisions of "Team:RHIT/Model"

 
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<h1>Background </h1>
 
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<p>Our team designed three separate models to monitor behaviors of the genetics system, enzyme kinetics, and metabolism. Then they were fused into one mechanism predicting P.E.B.B.L.E’s growth.</p>
 
  
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<h4>Background </h4>
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<p>Our team designed three separate models to monitor behaviors of the genetics system, enzyme kinetics, and metabolism. They were fused into one mechanism to predict P.E.B.B.L.E.’s growth.</p>
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<img src="https://static.igem.org/mediawiki/2018/7/72/T--RHIT--TotalModelingPic2.png" style="width:965px;height:766px;" alt="ModelPics" usemap="#modellinks">
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        <area shape="rect" coords="0,0,320,766" href="https://2018.igem.org/Team:RHIT/KineticsModel" title="Kinetics Model" alt="Kinetics Model"/>
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        <area shape="rect" coords="320,0,965,500" href="https://2018.igem.org/Team:RHIT/GeneticsModel" title="Genetics Model" alt="Genetics Model"/>
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        <area shape="rect" coords="320,550,900,766" href="https://2018.igem.org/Team:RHIT/MetabolismModel" title="Metabolism Model" alt="Metabolism Model"/>
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<h3>Kinetics Model </h3>
 
<h3>Kinetics Model </h3>
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<p>The enzyme kinetics model describes the biochemical pathway that our bacteria have to degrade and assimilate PET plastic. Kinetics models in general use differential equations to describe the interactions between the enzymes in the metabolites, chemicals used in metabolism, and they describe the rate of change in the concentration of these metabolites. Click on the biochemical pathway in the picture to see the equations and assumptions used to describe the main metabolites in the PET degradation pathway. </p>
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<p>The enzyme kinetics model describes the biochemical pathway that our bacteria follow to degrade and assimilate PET plastic. In general, kinetics models use differential equations to describe the interactions between the enzymes in the metabolites and the chemicals used in metabolism. They also describe the rate of change in the concentration of these metabolites. Below is a simplified example of how a kinetics model is made. If you would like to see the kinetics model that describes our system's behavior go to the Kinetics Model page by clicking on the biochemical pathway or by going to the model sub-menu. </p>
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<p>Example of the Kinetics
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<p>Example of the Kinetics</p>
 
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<img src = "https://static.igem.org/mediawiki/2018/3/34/T--RHIT--KineticsExample.png">
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<img src = "https://static.igem.org/mediawiki/2018/9/91/T--RHIT--KinExnew.png" style="width:70%">
 
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      <div class="text"> Kinetics Model </div>
 
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<h3>Metabolism Model </h3>
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<p>The final portion of the model used the Flux Balance Analysis (FBA) tool to predict the growth rate of the <em>E. coli </em>cells on the sole carbon source of PET. The original matrix and parameters were downloaded from the CoBRA toolbox iJO1366 model [ ]. The model was then expanded to include the new pathway and genes, and then the system was optimized for biomass growth. The objective value was proportional to the growth rate of the bacteria. FBA uses a stochastic matrix of the all the metabolisms’ chemical reactions and optimizes these various equations to produce a unit of biomass, which is inferred as another metabolite of the system. The general form of the model is shown below. If you want to find out more information about our FBA model go to the Metabolism Model link in the model sub-menu or click on the metabolism portion of the picture above.<br/ >
 
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<h3>Metabolism Model </h3>
 
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<p>The last modeled portion of the project used the Flux Balance Analysis tool to predict the growth rate of the E. coli cells on the sole carbon source of PET. The original matrix and parameters where downloaded from the CoBRA toolbox iJO1366 model [ ]. The model was then expanded to include this new pathway and genes and then the system was optimized for biomass growth and the objective value was proportional to the growth rate of the bacteria.
 
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FBA uses a stochastic matrix of the all the metabolisms’ chemical reactions and optimizes these various equations to produce a unit of biomass, which is inferred as another metabolite of the system. The general form of the model is:<br/ >
 
 
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max { v_g: S v=O} <br />
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<img src = "https://static.igem.org/mediawiki/2018/5/5c/T--RHIT--FBAExampleEq.png" style="width:180px;height:48px;">
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s.t.   L≤v≤U and v≠0 <br />
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<p>The variable column V are fluxes, which are bounded by the upper and lower bounds of U and L. The S matrix is a matrix of stoichiometric coefficients for the metabolites in the reactions. A flux is best described as the number of times the reaction must run forwards or backwards for the entire system to meet the homogenous assumption that the rates of the metabolites changing are zero. The dimensions of the matrix is MxN, where M is number of metabolites and N is number of reactions in the metabolism. The maximized flux, vg, is the flux for the biomass growth equation.
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<p>The variable column V are fluxes, which are bounded by the upper and lower bounds of U and L. The S matrix is a matrix of stoichiometric coefficients for the metabolites in the reactions. A flux is best described as the number of times the reaction must run forwards or backwards for the entire system to meet the homogeneous assumption that the rates of the metabolites changing are zero. The dimensions of the matrix are MxN, where M is the number of metabolites and N is the number of reactions in the metabolism. The maximized flux, vg, is the flux for the biomass growth equation.
 
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<img src="https://static.igem.org/mediawiki/2018/6/68/T--RHIT--FluxModel.png" >
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<img src="https://static.igem.org/mediawiki/2018/6/64/T--RHIT--FluxModel3.png" >
 
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<p>For the fake chemical reaction: 2 [A] ↔ [B] + 3 [C]
 
<p>For the fake chemical reaction: 2 [A] ↔ [B] + 3 [C]
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The reaction is input into the matrix so that metabolite A loses 2 units, while metabolites B and C gain 1 and 3 units respectively.
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The reaction is input into the matrix so that metabolite A loses 2 units, while metabolites B and C gain 1 and 3 units, respectively.
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The dotted column shows the biomass growth reaction with it producing 1 unit of biomass. All the reactions have some bounds on the flux values so that the system will return a real number. <br /><br /><br /><br />
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The dotted column shows the biomass growth reaction producing 1 unit of biomass. All the reactions have some bounds on the flux values so that the system will return a real number. <br /><br /><br /><br /><br /><br /><br /><br /><br /><br />
 
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      <div class="text"> Metabolism Model </div>
 
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<h3>Genetics Model </h3>
 
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<p>The genetics system used in our experiments has the degradation of PET and the assimilation of PET carbons in the cell on two separate plasmids. The relevant amounts of copies of the 6 enzyme genes and their rates of change were described in differential equations. The different promoter interactions of each plasmid were also taken into account and the secretion of mechanisms for PETase and/or MHETase were also included, to help us predict the amount of enzymes breaking down the PET. Click on the plasmid and genetics section to read about our description. </p>
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<p>The genetics system used in our experiments has the degradation of PET and the assimilation of PET carbons in the cell on two separate plasmids. The relevant numbers of copies of the 6 enzyme genes and their rates of change were described in differential equations. The different promoter interactions of each plasmid were also taken into account and the secretion of mechanisms for PETase and/or MHETase were also included to help us predict the amount of enzymes breaking down the PET. Below is a simplified example of how a genetics model is made. If you would like to see the genetics model that describes our system's behavior go to the Genetics Model page by clicking on the plasmid or by going to the model sub-menu.</p>
 
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<p>Example of the Genetics Model</p>
 
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        <img src="https://static.igem.org/mediawiki/2018/thumb/8/8d/T--RHIT--GeneticExampleoffPicture.png/800px-T--RHIT--GeneticExampleoffPicture.png" style="width:500px;height:275px;">
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        <div class="text"> Repressed System </div>
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          <div class="text"> Activated System </div>
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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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<img src="https://static.igem.org/mediawiki/2018/1/16/T--RHIT--GenExampleEq.png" style="width:25%;">
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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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<p>This set of reactions models what is happening in the pictures. The first reaction shows the production of the B protein. The second shows that when B binds to O, it creates an inhibited complex that does not allow the polymerase to bind. The polymerase not being able to bind means that the protein cannot be synthesized. The third reaction describes when the polymerase is able to bind to the operator. When the polymerase does bind, the mRNA is able to be synthesized. The fourth shows the mRNA creating the protein.</p>
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<p>Once assumptions that the rate of creating C_I is at equilibrium and that k_2 and k_3 are grouped into one k ̂_2 are made, a simplified equation can be written to describe what is happening. This equation will be written in the form of:
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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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<p>k ̂_2, Υ , and ρ would be known. The amount of free operator could be determined by the following steps:</p>
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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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<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 14:05, 6 August 2018




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Background


Our team designed three separate models to monitor behaviors of the genetics system, enzyme kinetics, and metabolism. They were fused into one mechanism to predict P.E.B.B.L.E.’s growth.

ModelPics Kinetics Model Genetics Model Metabolism Model

Kinetics Model

The enzyme kinetics model describes the biochemical pathway that our bacteria follow to degrade and assimilate PET plastic. In general, kinetics models use differential equations to describe the interactions between the enzymes in the metabolites and the chemicals used in metabolism. They also describe the rate of change in the concentration of these metabolites. Below is a simplified example of how a kinetics model is made. If you would like to see the kinetics model that describes our system's behavior go to the Kinetics Model page by clicking on the biochemical pathway or by going to the model sub-menu.

Example of the Kinetics

Metabolism Model

The final portion of the model used the Flux Balance Analysis (FBA) tool to predict the growth rate of the E. coli cells on the sole carbon source of PET. The original matrix and parameters were downloaded from the CoBRA toolbox iJO1366 model [ ]. The model was then expanded to include the new pathway and genes, and then the system was optimized for biomass growth. The objective value was proportional to the growth rate of the bacteria. FBA uses a stochastic matrix of the all the metabolisms’ chemical reactions and optimizes these various equations to produce a unit of biomass, which is inferred as another metabolite of the system. The general form of the model is shown below. If you want to find out more information about our FBA model go to the Metabolism Model link in the model sub-menu or click on the metabolism portion of the picture above.

The variable column V are fluxes, which are bounded by the upper and lower bounds of U and L. The S matrix is a matrix of stoichiometric coefficients for the metabolites in the reactions. A flux is best described as the number of times the reaction must run forwards or backwards for the entire system to meet the homogeneous assumption that the rates of the metabolites changing are zero. The dimensions of the matrix are MxN, where M is the number of metabolites and N is the number of reactions in the metabolism. The maximized flux, vg, is the flux for the biomass growth equation.

For the fake chemical reaction: 2 [A] ↔ [B] + 3 [C] The reaction is input into the matrix so that metabolite A loses 2 units, while metabolites B and C gain 1 and 3 units, respectively. The dotted column shows the biomass growth reaction producing 1 unit of biomass. All the reactions have some bounds on the flux values so that the system will return a real number.









Genetics Model

The genetics system used in our experiments has the degradation of PET and the assimilation of PET carbons in the cell on two separate plasmids. The relevant numbers of copies of the 6 enzyme genes and their rates of change were described in differential equations. The different promoter interactions of each plasmid were also taken into account and the secretion of mechanisms for PETase and/or MHETase were also included to help us predict the amount of enzymes breaking down the PET. Below is a simplified example of how a genetics model is made. If you would like to see the genetics model that describes our system's behavior go to the Genetics Model page by clicking on the plasmid or by going to the model sub-menu.

Example of the Genetics Model

Repressed System
Activated System




This set of reactions models what is happening in the pictures. The first reaction shows the production of the B protein. The second shows that when B binds to O, it creates an inhibited complex that does not allow the polymerase to bind. The polymerase not being able to bind means that the protein cannot be synthesized. The third reaction describes when the polymerase is able to bind to the operator. When the polymerase does bind, the mRNA is able to be synthesized. The fourth shows the mRNA creating the protein.

Once assumptions that the rate of creating C_I is at equilibrium and that k_2 and k_3 are grouped into one k ̂_2 are made, a simplified equation can be written to describe what is happening. This equation will be written in the form of:

k ̂_2, Υ , and ρ would be known. The amount of free operator could be determined by the following steps: