Team:SDU-Denmark/Tour32

From 2013.igem.org

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<h2>Modelling</h2>
<h2>Modelling</h2>
<h4>Revealing the bits behind the simulation</h4>
<h4>Revealing the bits behind the simulation</h4>
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<p>
<p>
<span class="intro">An introduction</span><br>
<span class="intro">An introduction</span><br>
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The projects aims to optimize the conditions present in our cells to maximize the production of rubber. Two pathways aid the conversion of glucose to the substrates of the prenyltransferase: the glycolysis and the MEP pathway. The glycolysis is heavily regulated and changes to this pathway will be diminished and overridden by the cell. However, overexpressing rate-limiting steps in the MEP pathway should allow for a faster conversion of substrates; thereby pulling the pyruvate out of the glycolysis and speeding up the overall rate of conversion.
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We aim to optimize the conditions already present in the cell to optimize the overall production of rubber. We’ve been looking at two quite different ways of optimizing the rubber production, which should be applicable to a real-life production. These two are:
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</p><p>
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The obvious questions that follow upon such a deduction are: Which steps in the MEP pathway are rate limiting? And what will happen to overall production economy if we speed up the pathway?
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</p><p>
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The answers to these questions indicate which steps in the MEP pathway would be most effective to manipulate.
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</p><p>
</p><p>
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<h4>The model</h4>
 
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The model consists of four different velocity terms, depending on the reaction. The four terms are:<br>
 
<ul>
<ul>
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<li>Ordinary uni-uni reaction</li>
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<li>Optimization of each cell</li>
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<li>Ordinary bi-bi reaction</li>
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<li>Optimization of the number of cells</li>
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<li>Reversible bi-bi reaction</li>
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<li>Substrate inhibitory bi-bi reaction</li>
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</ul>
</ul>
</p><p>
</p><p>
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All of the terms are given by their respective Michaelis-Menten velocity term.<br>
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The optimization of each cell identifies rate-limiting steps in the pathways related to the production of the polyisoprene. Where the optimization of the number of cells is to make in vitro tests of how a cell responds to different changes in environment, and find the environment with the best influence.
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Change in the concentration is given by the the ingoing terms subtracted the outgoing terms:<br>
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<center><span class="intro">dc/dt = (Ingoing terms) - (Outgoing terms)</span></center>
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</p><p>
</p><p>
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This allows a system of equations to be build with one differential equation for each step in the pathway.
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<span class="intro">Optimization of each cell</span><br>
 +
In the production of rubber, there are three primary pathways: the glycolysis, the MEP-pathway, and the rubber transferase itself. We decided to focus on the MEP-pathway.
</p><p>
</p><p>
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The solution to the system is found using K<sub>cat</sub> and K<sub>m</sub>, which are constants related directly to a given enzyme and to substrate and product concentrations, respectively. Both can be established experimentally, and we found them in the literature. From these equations and constants, the maximum speed of each enzyme relative to the substrate(s) concentration, can then be determined.  
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Since no one had modelled the entire pathway before, we build the model from the ground up. We based the model on Michaelis Menten kinetics, and the kinetic terms entering the model are: ordinary uni-uni reaction, ordinary bi-bi reaction, reversible bi-bi reaction and substrate inhibitory bi-bi reaction.
</p><p>
</p><p>
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<h4>Results</h4>
<h4>Results</h4>
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<span class="intro">Rate limiting steps</span><br>
<span class="intro">Rate limiting steps</span><br>
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Articles have shown the reaction catalysed by dxs to be the rate limiting step, and we asked the question: If we were to manipulate this step, which step would then be rate limiting? Simulating reaction kinetics often leads to stiff systems, and this is no exception. Traditional methods of solving differential equations therefore did not suffice, and MATLAB’s ODE15s, which is an L-stable solver, was used.  
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Articles have shown the reaction catalysed by Dxs to be the  
 +
 
 +
<span class="sourceReference">rate limiting step,</span>
 +
<span class="tooltip">
 +
  <span class="tooltipHeader">Source:</span>
 +
  Sprenger GA, Schorken U, Wiegert T, Grolle S, De Graaf AA, Taylor
 +
SV, Begley TP, Bringer-Meyer S, Sahm H (1997) Identification
 +
of a thiamin-dependent synthase in Escherichia coli required for
 +
the formation of the 1-deoxy-D-xylulose 5-phosphate precursor to
 +
isoprenoids, thiamin, and pyridoxol. Proc Natl Acad Sci USA
 +
94:12857–12862 <a href="http://www.ncbi.nlm.nih.gov/pubmed/9371765" target="_blank">(Link)</a>
 +
</span>
 +
 
 +
 
 +
and we asked the question: If we were to manipulate this step, which step would then be rate limiting? Simulating reaction kinetics often leads to stiff systems, and this is no exception. Traditional methods of solving differential equations therefore did not suffice, and MATLAB’s ODE15s, which is an L-stable solver, was used.  
 +
 
 +
 
</p><p>
</p><p>
-
Simulations showed that the next rate limiting step would occur after an improvement in rate of conversion of 12 percent, and that this new rate limiting step was the reaction catalysed by IspG, as seen below. This result is worth keeping in mind when deciding on the design of the plasmids. Namely, if there was time to spare, then cloning IspG into the system might have further enhanced its functionality.  
+
Simulations showed that the next rate limiting step would occur after an improvement in rate of conversion of 12 percent, and that this new rate limiting step was the reaction catalysed by IspG, as seen below. This result is worth keeping in mind when deciding on the design of the plasmids. Namely, if there is time to spare, then cloning <span class="specialWord">ispG</span> into the system might further enhance functionality.  
</p><p>
</p><p>
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<span class="intro">Economy</span><br>
<span class="intro">Economy</span><br>
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<a class="popupImg alignRight" style="width:300px" target="_blank" href="https://static.igem.org/mediawiki/2013/4/42/SDU2013_Modelling_2.png" title="Figure 2 - Here we see how much dxs reacts to B<sub>1</sub> vitamin. As it's reversible, it stops producing B<sub>1</sub> vitamin faster, than the cell can use it, which is indicated by the horizontal line. But still what we throw exponentially more and more out as a function of the speed of the pathway.">
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<a class="popupImg alignRight" style="width:300px" target="_blank" href="https://static.igem.org/mediawiki/2013/4/42/SDU2013_Modelling_2.png" title="Figure 2 - Here we see how much DXP reacts to B<sub>1</sub> vitamin. As it's reversible, it stops producing B<sub>1</sub> vitamin faster, than the cell can use it, which is indicated by the horizontal line. But still what we throw exponentially more and more out as a function of the speed of the pathway.">
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  <img src="https://static.igem.org/mediawiki/2013/4/42/SDU2013_Modelling_2.png" style="width:300px" />Figure 2 - Here we see how much dxs reacts to B<sub>1</sub> vitamin. As it's reversible, it stops producing B<sub>1</sub> vitamin faster, than the cell can use it, which is indicated by the horizontal line. But still what we throw exponentially more and more out as a function of the speed of the pathway.
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  <img src="https://static.igem.org/mediawiki/2013/4/42/SDU2013_Modelling_2.png" style="width:300px" />Figure 2 - Here we see how much DXP reacts to B<sub>1</sub> vitamin. As it's reversible, it stops producing B<sub>1</sub> vitamin faster, than the cell can use it, which is indicated by the horizontal line. But still what we throw exponentially more and more out as a function of the speed of the pathway.
</a>
</a>
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The second question posed concerned the economy of the system. That is, does the increase in velocity through the pathway result in increased product, or does the substrates exit the pathway at an unintended point. Based on the literature, intermediates after the reaction catalysed by IspD pass directly through the pathway, while there exists a reversible exit to vitamin B<sub>1</sub> from DXP.
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The second question posed concerned the economy of the system. That is, does the increase in velocity through the pathway result in increased product, or does the substrates exit the pathway at an unintended point. Based on the literature, intermediates after the reaction catalysed by IspD pass directly through the pathway, while there exists a reversible exit to vitamin B<sub>1</sub> from <span class="tooltipLink">DXP.</span><span class="tooltip"><span class="tooltipHeader">DXP</span>1-deoxy-D-xylulose-5-phosphate</span>
</p><p>
</p><p>
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</p><p>
</p><p>
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In conclusion, the simulations showed the rate limiting steps to be the reactions catalysed by Dxs, IspG, and IspF. We chose to concentrate our efforts on overexpressing Dxs and IspG. The choice not to clone IspF was made in the light of the fact that an increase in speed through the pathway of more than 100 % was futile in terms of economy.  
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In conclusion, the simulations showed the rate limiting steps to be the reactions catalysed by Dxs, IspG, and IspF. We chose to concentrate our efforts on overexpressing the genes of <span class="specialWord">dxs</span> and <span class="specialWord">ispG</span>. The choice not to clone <span class="specialWord">ispF</span> was made in the light of the fact that an increase in speed through the pathway of more than 100 % was futile in terms of economy.  
 +
</p><p>
 +
 +
For a simpler approach on what we actually did in our model you can visit our off-iGEM-server <a class="dialogLink" href="http://lrm.dk/igem/beregner.html">interaktiv model</a>, made to give a simplified glimpse of the mehanism of the model.
</p>
</p>
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<h4>Modelling together with the team of Edinburgh</h4>
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<p>
 +
<span class="intro">Sources for enzyme kinetic details of MEP pathway</span>
 +
<ul><li>
-
<span class="intro">We wanted to model the bacterial growth</span> as a natural consequence of the influx of resources into the cell and the consumption of these resources by the synthesis of proteins, ribosomes, and DNA. The model we uses was created by Tobias Bollenbach and incorporates Cooper and Helmstetter’s classical results about chromosome replication and the cell division cycle of <span class="specialWord">Escherichia coli</span> as well as Donachie’s “initiation mass” mechanism that couples protein synthesis to DNA replication and <span class="sourceReference">cell division.</span>
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<b>Dxs:</b>
 +
 
 +
Sprenger GA, Schorken U, Wiegert T, Grolle S, De Graaf AA, Taylor
 +
SV, Begley TP, Bringer-Meyer S, Sahm H (1997) Identification
 +
of a thiamin-dependent synthase in Escherichia coli required for
 +
the formation of the 1-deoxy-D-xylulose 5-phosphate precursor to
 +
isoprenoids, thiamin, and pyridoxol. Proc Natl Acad Sci USA
 +
94:12857–12862
 +
<a href="http://www.ncbi.nlm.nih.gov/pubmed/9371765" target="_blank">(Link)</a>
 +
 
 +
 
 +
</li><li>
 +
 
 +
<b>Dxs:</b>
 +
 
 +
Miller B, Heuser T, Zimmer W (2000) Functional involvement of a
 +
deoxy-xylulose 5-phosphate reductoisomerase gene harboring
 +
locus of Synechococcus leopoliensis in isoprenoid biosynthesis.
 +
FEBS Lett 481:221–226
 +
 
 +
<a href="http://www.ncbi.nlm.nih.gov/pubmed/11007968" target="_blank">(Link)</a>
 +
 
 +
</li><li>
 +
 
 +
<b>Dxr:</b> 
 +
Koppisch AT, Fox DT, Blagg BS, Poulter CD. E. coli MEP synthase: steady-state kinetic analysis and substrate binding. Biochemistry. 2002 Jan 8;41(1):236-43.
 +
 
 +
<a href="http://www.ncbi.nlm.nih.gov/pubmed/11772021" target="_blank">(Link)</a>
 +
 
 +
</li><li>
 +
 
 +
<b>IspD:</b>
 +
Richard SB, Lillo AM, Tetzlaff CN, Bowman ME, Noel JP, Cane DE. Kinetic analysis of Escherichia coli 2-C-methyl-D-erythritol-4-phosphate cytidyltransferase, wild type and mutants, reveals roles of active site amino acids. Biochemistry. 2004 Sep 28;43(38):12189-97.
 +
 
 +
<a href="http://www.ncbi.nlm.nih.gov/pubmed/15379557" target="_blank">(Link)</a>
 +
 
 +
</li><li>
 +
 
 +
<b>IspE:</b>
 +
 
 +
Bernal C, Mendez E, Terencio J, Boronat A, Imperial S. A spectrophotometric assay for the determination of 4-diphosphocytidyl-2-C-methyl-D-erythritol kinase activity. Anal Biochem. 2005 May 15;340(2):245-51.
 +
 
 +
<a href="http://www.ncbi.nlm.nih.gov/pubmed/15840497" target="_blank">(Link)</a>
 +
 
 +
 
 +
</li><li>
 +
 
 +
<b>IspF:</b>
 +
Geist JG, Lauw S, Illarionova V, Illarionov B, Fischer M, Gräwert T, Rohdich F, Eisenreich W, Kaiser J, Groll M, Scheurer C, Wittlin S, Alonso-Gómez JL, Schweizer WB, Bacher A, Diederich F. Thiazolopyrimidine inhibitors of 2-methylerythritol 2,4-cyclodiphosphate synthase (IspF) from Mycobacterium tuberculosis and Plasmodium falciparum.
 +
 
 +
<a href="http://www.ncbi.nlm.nih.gov/pubmed/20480490" target="_blank">(Link)</a>
 +
 
 +
 
 +
 
 +
</li><li>
 +
 
 +
<b>IspG:</b>
 +
 
 +
Zepeck F, Gräwert T, Kaiser J, Schramek N, Eisenreich W, Bacher A, Rohdich F. Biosynthesis of isoprenoids. purification and properties of IspG protein from Escherichia coli. J Org Chem. 2005 Nov 11;70(23):9168-74.
 +
<a href="http://www.ncbi.nlm.nih.gov/pubmed/16268586" target="_blank">(Link)</a>
 +
 
 +
</li><li>
 +
 
 +
<b>B<sub>1</sub> and B<sub>6</sub>:</b>
 +
 
 +
Yeh JI, Du S, Pohl E, Cane DE. Multistate binding in pyridoxine 5'-phosphate synthase: 1.96 A crystal structure in complex with 1-deoxy-D-xylulose phosphate. Biochemistry. 2002 Oct 1;41(39):11649-57.
 +
 
 +
<a href="http://www.ncbi.nlm.nih.gov/pubmed/12269807" target="_blank">(Link)</a>
 +
 
 +
</li><li>
 +
 
 +
<b>B<sub>1</sub> and B<sub>6</sub>:</b>
 +
 
 +
D. E. Cane, S. C. Du, J. K. Robinson, Y. J. Hsiung, I. D. Spenser. Biosynthesis of Vitamin B<sub>6</sub>: Enzymatic Conversion of 1-Deoxy-D-xylulose-5-phosphate to Pyridoxol Phosphate J. Am. Chem. Soc. 121,
 +
7722–7723 (1999).
 +
 
 +
<a href="http://pubs.acs.org/doi/pdf/10.1021/ja9914947" target="_blank">(Link)</a>
 +
 
 +
 
 +
</li></ul>
 +
 
 +
 
 +
</p>
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 +
 
 +
 
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<p>
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<h4>Modelling with the team of Edinburgh</h4>
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<span class="intro">Optimization of the number of cells</span><br>
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Together with the team of Edinburgh, we implemented and ran a model created by
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<span class="sourceReference">Tobias Bollenbach (2009),</span>
<span class="tooltip">
<span class="tooltip">
   <span class="tooltipHeader">Source:</span>
   <span class="tooltipHeader">Source:</span>
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   Bollenbach, T. et al. Non-optimal microbial response to antibiotics underlies suppressive drug interactions; Cell. 2009 November 13; 139(4): P. 707–718. <a href="http://download.cell.com/pdf/PIIS0092867409013154.pdf?intermediate=true" target="_blank")</a>
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   Bollenbach, T. et al. Non-optimal microbial response to antibiotics underlies suppressive drug interactions; Cell. 2009 November 13; 139(4): P. 707–718. <a href="http://download.cell.com/pdf/PIIS0092867409013154.pdf?intermediate=true" target="_blank")>(Link)</a>
</span>
</span>
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</p>
 
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<p>
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using measurements done by the team of Edinburgh on their system. We’re using a whole cell model, aiming to predict an entire cell's behavior and growth. The model has to restrict itself at some point, so in our model, we include the most essential features of the metabolism of the cell; resource availability, growth rate, and intracellular protein levels. Most important is growth rate, as this allows us to test different environments and see their influence on the rate. As mentioned earlier, we simulated the system created by Edinburgh using their measurements. The resulting simulation can be found on Edinburgh’s <a class="dialogLink" href="https://2013.igem.org/Team:Edinburgh/Modeling">wiki page</a> as can the results. Though we haven’t implemented our own measurements, Edinburg's data proves the concept and demonstrates the possibility of enhancing rubber production through the whole cell model.  
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<span class="intro">The following dynamical system</span> <b>(Fig. 3)</b> describes the population averages of the amount of protein (p) , DNA (c) , ribosomes (r), and resources (a) per cell in an exponentially growing bacterial culture. The variable p describes all protein in the cell except for ribosomal protein. Proteins, DNA, and ribosomes are synthesized by the cells and are diluted as a result of cell divisions. In addition, resources are consumed in the synthesis of these cell constituents, where the s-values are synthetic rates of their corresponding subscripts. These are given by new functions. p, c, r and a, are the concentration of protein, DNA, ribosomes and resources. To fully determine the rest of the variables we have a system of nonlinear equations.
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 +
 
</p>
</p>
<p>
<p>
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<a class="popupImg alignRight" style="width:400px" href="https://static.igem.org/mediawiki/2013/f/f5/SDU2013_Modelling_Edinburgh_1.png" title="Figure 3 - The four main differential equations in Tobias Bollenbach's model">
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<a class="popupImg alignRight" style="width:400px" href="https://static.igem.org/mediawiki/2013/f/f5/SDU2013_Modelling_Edinburgh_1.png" title="Figure 3 - The four main differential equations in Tobias Bollenbach's model.">
   <img src="https://static.igem.org/mediawiki/2013/f/f5/SDU2013_Modelling_Edinburgh_1.png" style="width:400px">
   <img src="https://static.igem.org/mediawiki/2013/f/f5/SDU2013_Modelling_Edinburgh_1.png" style="width:400px">
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Figure 3.  
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Figure 3 - The four main differential equations in Tobias Bollenbach's model.
</a>
</a>
</p>
</p>
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<p>
<p>
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<span class="intro">So far, it has only been possible</span> to solve these equations by solving the dynamics, even though we’re only interested in the steady state. So it should be possible to equate the differential equations to zero (steady state), and “just” solve that system. But so far only solving the dynamics have showed to be the only option which worked.  
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<span class="intro">So far, it has only been possible</span> to solve the equations by solving the dynamics, even though we’re interested in the steady state. Equating the differential equations to zero (steady state) should provide a solution to the system. However, dynamics proved to be the only option that worked.  
</p>
</p>
<p>
<p>
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<span class="intro">We solved the dynamics</span> by first using a preprogrammed function solver in python to solve the nonlinear equations. To solve the dynamics itself we first used the implicit euler, which is a Radau IIA method of order one. As a prove of concept, implicit methods were necessary because of stiffness. Using such easy method we were able to prove the concept, but it has the same structure as the SDIRK method, which is of order maximum three. So if necessary we can improve the error by easily change the solver method.
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<span class="intro">We solved the dynamics</span> first by using a preprogrammed function solver in python to solve the nonlinear equations. Then - to solve the dynamics itself - we used the implicit euler, which is a Radau IIA method of order one. As a proof of concept, implicit methods were necessary because of stiffness. The method enabled us to prove the concept, but it has the same structure as the SDIRK method, which is of order maximum three. So if necessary we can improve the error by easily changing the solver method.
</p>
</p>
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Latest revision as of 01:07, 29 October 2013

Modelling

Revealing the bits behind the simulation

An introduction
We aim to optimize the conditions already present in the cell to optimize the overall production of rubber. We’ve been looking at two quite different ways of optimizing the rubber production, which should be applicable to a real-life production. These two are:

  • Optimization of each cell
  • Optimization of the number of cells

The optimization of each cell identifies rate-limiting steps in the pathways related to the production of the polyisoprene. Where the optimization of the number of cells is to make in vitro tests of how a cell responds to different changes in environment, and find the environment with the best influence.

Optimization of each cell
In the production of rubber, there are three primary pathways: the glycolysis, the MEP-pathway, and the rubber transferase itself. We decided to focus on the MEP-pathway.

Since no one had modelled the entire pathway before, we build the model from the ground up. We based the model on Michaelis Menten kinetics, and the kinetic terms entering the model are: ordinary uni-uni reaction, ordinary bi-bi reaction, reversible bi-bi reaction and substrate inhibitory bi-bi reaction.

Results

Figure 1 - We're interested in the largest slope (velocity) of the curve, here we see that the increase in slope stops after a certain increase in the starting velocity. A rate limiting step! Rate limiting steps
Articles have shown the reaction catalysed by Dxs to be the rate limiting step, Source: Sprenger GA, Schorken U, Wiegert T, Grolle S, De Graaf AA, Taylor SV, Begley TP, Bringer-Meyer S, Sahm H (1997) Identification of a thiamin-dependent synthase in Escherichia coli required for the formation of the 1-deoxy-D-xylulose 5-phosphate precursor to isoprenoids, thiamin, and pyridoxol. Proc Natl Acad Sci USA 94:12857–12862 (Link) and we asked the question: If we were to manipulate this step, which step would then be rate limiting? Simulating reaction kinetics often leads to stiff systems, and this is no exception. Traditional methods of solving differential equations therefore did not suffice, and MATLAB’s ODE15s, which is an L-stable solver, was used.

Simulations showed that the next rate limiting step would occur after an improvement in rate of conversion of 12 percent, and that this new rate limiting step was the reaction catalysed by IspG, as seen below. This result is worth keeping in mind when deciding on the design of the plasmids. Namely, if there is time to spare, then cloning ispG into the system might further enhance functionality.

Repeating the simulation with the increased velocities (i.e. post-modifying of Dxs and IspG), it is seen that IspF catalysed the third rate limiting step. IspF would thus be an enzyme of interest, if the system was to be further improved.

Economy
Figure 2 - Here we see how much DXP reacts to B1 vitamin. As it's reversible, it stops producing B1 vitamin faster, than the cell can use it, which is indicated by the horizontal line. But still what we throw exponentially more and more out as a function of the speed of the pathway. The second question posed concerned the economy of the system. That is, does the increase in velocity through the pathway result in increased product, or does the substrates exit the pathway at an unintended point. Based on the literature, intermediates after the reaction catalysed by IspD pass directly through the pathway, while there exists a reversible exit to vitamin B1 from DXP.DXP1-deoxy-D-xylulose-5-phosphate

It has been implicitly established that the increase in velocity through the pathway does not exclusively represent an increased exit to vitamin B1. Otherwise, there would be no increase in product, at all. So, the question is (in plain English) how much, exactly, can we increase the speed of the pathway before it starts leaking - before the amount diverted to the exit surpasses the increase in amount of product. This can be seen on the plot below.

It is noticeable that the increase in speed leads to an increase in the B1 vitamin producing term. At increases up to 100 percent, the exit term is unproblematic, while it seems at increases above 200% that the reaction would become uneconomical, as growth of this term is exponential. However, this is not of concern, as such increases in speed through the pathway are far higher than what we hope to achieve.

In conclusion, the simulations showed the rate limiting steps to be the reactions catalysed by Dxs, IspG, and IspF. We chose to concentrate our efforts on overexpressing the genes of dxs and ispG. The choice not to clone ispF was made in the light of the fact that an increase in speed through the pathway of more than 100 % was futile in terms of economy.

For a simpler approach on what we actually did in our model you can visit our off-iGEM-server interaktiv model, made to give a simplified glimpse of the mehanism of the model.

Sources for enzyme kinetic details of MEP pathway

  • Dxs: Sprenger GA, Schorken U, Wiegert T, Grolle S, De Graaf AA, Taylor SV, Begley TP, Bringer-Meyer S, Sahm H (1997) Identification of a thiamin-dependent synthase in Escherichia coli required for the formation of the 1-deoxy-D-xylulose 5-phosphate precursor to isoprenoids, thiamin, and pyridoxol. Proc Natl Acad Sci USA 94:12857–12862 (Link)
  • Dxs: Miller B, Heuser T, Zimmer W (2000) Functional involvement of a deoxy-xylulose 5-phosphate reductoisomerase gene harboring locus of Synechococcus leopoliensis in isoprenoid biosynthesis. FEBS Lett 481:221–226 (Link)
  • Dxr: Koppisch AT, Fox DT, Blagg BS, Poulter CD. E. coli MEP synthase: steady-state kinetic analysis and substrate binding. Biochemistry. 2002 Jan 8;41(1):236-43. (Link)
  • IspD: Richard SB, Lillo AM, Tetzlaff CN, Bowman ME, Noel JP, Cane DE. Kinetic analysis of Escherichia coli 2-C-methyl-D-erythritol-4-phosphate cytidyltransferase, wild type and mutants, reveals roles of active site amino acids. Biochemistry. 2004 Sep 28;43(38):12189-97. (Link)
  • IspE: Bernal C, Mendez E, Terencio J, Boronat A, Imperial S. A spectrophotometric assay for the determination of 4-diphosphocytidyl-2-C-methyl-D-erythritol kinase activity. Anal Biochem. 2005 May 15;340(2):245-51. (Link)
  • IspF: Geist JG, Lauw S, Illarionova V, Illarionov B, Fischer M, Gräwert T, Rohdich F, Eisenreich W, Kaiser J, Groll M, Scheurer C, Wittlin S, Alonso-Gómez JL, Schweizer WB, Bacher A, Diederich F. Thiazolopyrimidine inhibitors of 2-methylerythritol 2,4-cyclodiphosphate synthase (IspF) from Mycobacterium tuberculosis and Plasmodium falciparum. (Link)
  • IspG: Zepeck F, Gräwert T, Kaiser J, Schramek N, Eisenreich W, Bacher A, Rohdich F. Biosynthesis of isoprenoids. purification and properties of IspG protein from Escherichia coli. J Org Chem. 2005 Nov 11;70(23):9168-74. (Link)
  • B1 and B6: Yeh JI, Du S, Pohl E, Cane DE. Multistate binding in pyridoxine 5'-phosphate synthase: 1.96 A crystal structure in complex with 1-deoxy-D-xylulose phosphate. Biochemistry. 2002 Oct 1;41(39):11649-57. (Link)
  • B1 and B6: D. E. Cane, S. C. Du, J. K. Robinson, Y. J. Hsiung, I. D. Spenser. Biosynthesis of Vitamin B6: Enzymatic Conversion of 1-Deoxy-D-xylulose-5-phosphate to Pyridoxol Phosphate J. Am. Chem. Soc. 121, 7722–7723 (1999). (Link)

Modelling with the team of Edinburgh

Optimization of the number of cells
Together with the team of Edinburgh, we implemented and ran a model created by Tobias Bollenbach (2009), Source: Bollenbach, T. et al. Non-optimal microbial response to antibiotics underlies suppressive drug interactions; Cell. 2009 November 13; 139(4): P. 707–718. (Link) using measurements done by the team of Edinburgh on their system. We’re using a whole cell model, aiming to predict an entire cell's behavior and growth. The model has to restrict itself at some point, so in our model, we include the most essential features of the metabolism of the cell; resource availability, growth rate, and intracellular protein levels. Most important is growth rate, as this allows us to test different environments and see their influence on the rate. As mentioned earlier, we simulated the system created by Edinburgh using their measurements. The resulting simulation can be found on Edinburgh’s wiki page as can the results. Though we haven’t implemented our own measurements, Edinburg's data proves the concept and demonstrates the possibility of enhancing rubber production through the whole cell model.

Figure 3 - The four main differential equations in Tobias Bollenbach's model.

So far, it has only been possible to solve the equations by solving the dynamics, even though we’re interested in the steady state. Equating the differential equations to zero (steady state) should provide a solution to the system. However, dynamics proved to be the only option that worked.

We solved the dynamics first by using a preprogrammed function solver in python to solve the nonlinear equations. Then - to solve the dynamics itself - we used the implicit euler, which is a Radau IIA method of order one. As a proof of concept, implicit methods were necessary because of stiffness. The method enabled us to prove the concept, but it has the same structure as the SDIRK method, which is of order maximum three. So if necessary we can improve the error by easily changing the solver method.