Team:Imperial College/Modelling PLAdeg

From 2013.igem.org

(Difference between revisions)
 
(22 intermediate revisions not shown)
Line 1: Line 1:
{{:Team:Imperial_College/Templates:header}}  
{{:Team:Imperial_College/Templates:header}}  
-
<h1>Polylactic acid (PLA) Degradation Module </h1>
+
<h1>Polyhydroxybutyrate (P(3HB)) Synthesis Module </h1>
-
<h2>Introduction</h2>  
+
<h2>Metabolic modelling</h2>
 +
<h3>Introduction of the metabolic model</h3>
<p align="justify">
<p align="justify">
-
The efficiency of Polylactic acid is important for the performance of MAPLE. Therefore, we chose a strong enzyme Proteinase K which is suggested by many literature as an efficient PLA degrading enzyme. We performed several assays in order to determine the kinetic properties of Proteinase K. The PLA degradation model was then built based on the experimental results. </p>
+
The metabolic model predicts the interaction of our pathway with endogenous pathways. In synthetic biology, an ideal system is fully orthogonal. However, if the synthetic pathway uses some metabolites from the metabolism pathways, the metabolic fluxes (the rate of conversion between metabolites) will be affected. If the cell is overloaded by losing too much metabolites, it would either reject the synthetic pathway or burn out. As for the optimization of PHB production in our MAPLE system, metabolic analysis need to be carried out to estimate the effects on the cell metabolism from increases in the PHB production. </p>
-
<h2>Objective and Design</h2>
+
<h3>Methods</h3>
-
<p>1. With the defined kinetic properties of Proteinase K. The model can predict the time needed to degrade a certain amount of PLA. The information is important as it estimates the efficiency of the MAPLE system when degrading the large amount of plastic.Therefore, further improvements can be made if the system is not efficient.</p>  
+
<p align="justify">We altered the metabolic model by Angela Dixon in her paper “Predictive Mathematical Model for Polyhydroxybutyrate Synthesis in Escherichia coli”. [http://digitalcommons.usu.edu/engineering_datasets/1/] The metabolic model is built in Simbiology, which is an extension in MATLAB especially for biological system analysis. The model consists two metabolic pathways: Glycolysis and TCA cycle. The reactions in the metabolic pathways are defined by ordinary differential equations and kinetic parameters. The model also contains a synthetic pathway that produce P(3HB) from acetyl-coA. The pathway consists three enzymes which are PhaA, PhaB and PhaC.  
-
<p>2. The model also involves the gene expression model of the Proteinase K with an inducible promoter. Therefore, gene expression can be regulated by adjusting the inducer concentration. The overall plastic degradation can be regulated by the gene expression. </p>
+
The reasons we chose this model:</p>
-
<p>3. The secretion model is also contained in the model which assumes the efficiency of enzyme secretion to the culture. </p>
+
<p>1. The model is based on ODEs instead of FBA (flux balance analysis) method, which is a common methods of metabolic analysis. However, FBA cannot determine the real time concentration of the metabolites whereas it can be done by models of ODEs.</p>
-
<h2>Specifications of the model</h2>
+
<p>2. Only single gene deletion or addition can be performed in FBA. More than that, the metabolic model here can perform modification on any single or multiple genes and reactions through Simbiology. </p>
-
<p align="justify">Polylactic acid (PLA) degradation involves proteinase K:</p>
+
<p>3. The FBA model is static, it cannot analyze the dynamic interactions between our synthetic pathways with the metabolic pathways. As both our P(3HB) synthesis model and the metabolic model are in the same platform. It was really easy to integrate our pathway into the metabolic model.</p>
-
<table border="2" bgcolor="#efefef">
+
<p><b>In our project, we have a different pathway:</b></p>
-
<tr>
+
<p>1. We use 3HB as one of the input.</p>
-
<th width="150">enzyme</th>
+
<p>2. Existence of ato system in the E.coli MG1655 strain. </p>
-
<th>source organism</th>
+
<p>3. We removed phaA in our case because we use 3HB as the major source to produce P(3HB) to avoid too much acetyl-coA be taken from the metabolic pathways.</p>
-
<th>biobrick</th>
+
<p align="justify">Therefore, we substitute the original pathway with our synthetic pathway. Moreover, we added our gene expression models for the enzymes into the metabolic model as well. In terms of the consistency of the model, we changed the units of our synthetic pathway into micro molar and seconds. </p>
-
<th>reference</th>
+
<p>Here is the combination of our model with the metabolic model</p>
-
</tr>
+
[[File:MetaSyn.png|800px|centre]]
-
<tr>
+
<p align="justify">We also carried out a parameter estimations of the initial concentrations of several substrates in our synthetic pathway. The reason is we have single-cell scaled magnitude for them originally (fM level), but there are much higher magnitudes in any of the species in the metabolic pathways (mM level). Therefore, we scaled up the pathway in order to maintain the consistency of the model. As for the metabolites which are involved in our pathway, we cloned the blocks of them from the metabolic pathway in Simbiology and deliberately put them into our pathway. That means our pathway dynamically interact with the metabolic pathways. </p>
-
<th>Proteinase K</th>
+
<p>Here is the table for the updated initial concentrations for the species in our synthetic pathway:
-
<td>Engyodontium album</td>
+
All the kinetic data and initial concentrations of the metabolites in the metabolic pathways are referenced in the paper[http://digitalcommons.usu.edu/engineering_datasets/1/]: </p>
-
<td>[http://parts.igem.org/Part:BBa_K1149002 BBa_K1149002] </td>
+
 
-
<td>[http://www.ncbi.nlm.nih.gov/nuccore/X14689.1] </td>
+
-
</tr>
+
-
</table>
+
-
<p>The overall PLA degradation model is shown as below:</p>
+
-
[[File:PKPLA.png]]
+
-
<p>There are two compartments which represents cells and the culture from left to right. The "cell" compartment contains the gene expression module whereas the "culture" compartment contains the degradation module. The "secretion" block that connects two compartments is the secretion module.</p>
+
-
<h3>Parameters and assumptions </h3>
+
-
<h4>Gene expression module of Proteinase K</h4>
+
<table border="2" bgcolor="#efefef">
<table border="2" bgcolor="#efefef">
       <tr>
       <tr>
-
         <th>Parameter</th>
+
         <th>Substrates</th>
-
         <th>Description</th>
+
         <th>Concentration</th>
-
        <th>Value</th>
+
         <th>Units</th>
         <th>Units</th>
         <th>Sources</th>
         <th>Sources</th>
Line 40: Line 33:
       </tr>
       </tr>
       <tr>
       <tr>
-
         <th>β</th>
+
         <th>3HB</th>
-
        <td>maximum rate of transcription</td>
+
     
-
         <td>0.032</td>
+
         <td>5000</td>
-
         <td>mM/min</td>
+
         <td>uM</td>
-
         <td>Please see derivation 1 below.</td>
+
         <td>-</td>
-
         <td>Please see derivation 1 below.</td>
+
         <td>The initial input to the system</td>
       </tr>
       </tr>
        
        
       <tr>
       <tr>
-
         <th>K</th>
+
         <th>Acetoacetate</th>
-
         <td>Activation coefficient</td>
+
     
-
         <td>0.0031</td>
+
         <td>1000</td>
-
         <td>mM</td>
+
         <td>uM</td>
-
         <td>[http://parts.igem.org/Part:BBa_K206000:Characterization]</td>
+
         <td>-</td>
-
        <td>Taking the "switch point" as the activation coefficient</td>
+
         <td>The ato system in E.coli suggest a favourable conversion from acetoacetyl-coA to acetoacetate. Therefore, the concentration of acetoacetate is 10 times larger than acetoacetyl-coA[http://www.sciencedirect.com/science/article/pii/0003986177904969]</td>
       </tr>
       </tr>
       <tr>
       <tr>
-
         <th>d<sub>mRNA</sub></th>
+
         <th>Acetoacetyl-coA</th>
-
         <td>mRNA degradation rate</td>
+
          
-
         <td>0.10</td>
+
         <td>100</td>
-
         <td>1/min</td>
+
         <td>uM</td>
-
         <td>[http://www.ncbi.nlm.nih.gov/pmc/articles/PMC420366/pdf/07X.pdf]</td>
+
         <td>[http://www.ncbi.nlm.nih.gov/pubmed/1103741]</td>
-
         <td>Taking the value of mRNA half-life in E.coli strain MG1655 as 6.8min.  rate = ln2/half-life = ln2/6.8 = 0.10</td>
+
         <td>The ato system in E.coli suggest a favourable conversion from acetoacetyl-coA to acetoacetate. [http://www.sciencedirect.com/science/article/pii/0003986177904969]</td>
       </tr>
       </tr>
       <tr>
       <tr>
-
         <th>d<sub>protein</sub></th>
+
         <th>NADH</th>
-
        <td>Protein degradation rate</td>
+
     
-
         <td>0.050</td>
+
         <td>200</td>
-
         <td>1/min</td>
+
         <td>uM</td>
-
         <td>[http://jb.asm.org/content/189/23/8746.full]</td>
+
         <td>[http://digitalcommons.usu.edu/engineering_datasets/1/]</td>
-
         <td>There is no active degradation pathway and that dilution is the dominant way by which the protein level decreases in a cell.  Rate = 1/doubling time, where doubling time = 20min.  Assuming steady-state growth in LB broth as presented in paper.</td>
+
         <td>-</td>
       </tr>
       </tr>
       <tr>
       <tr>
-
         <th>k<sub>2</sub></th>
+
         <th>NAD+</th>
-
         <td>Protein production rate (Proteinase K)</td>
+
     
-
         <td>4.7</td>
+
         <td>1200</td>
-
         <td>1/min</td>
+
         <td>uM</td>
-
        <td>Please see derivation 2 below.</td>
+
         <td>[http://digitalcommons.usu.edu/engineering_datasets/1/]</td>
-
         <td>Please see derivation 2 below.</td>
+
         <td>-</td>
       </tr>
       </tr>
        
        
       <tr>
       <tr>
-
         <th>[Arabinose]</th>
+
         <th>Acetyl-coA</th>
-
         <td>Concentration of arabinose</td>
+
          
-
         <td>Initial: 0.008</td>
+
         <td>5000</td>
-
         <td>mM</td>
+
         <td>uM</td>
-
         <td></td>
+
         <td>[http://digitalcommons.usu.edu/engineering_datasets/1/]</td>
-
         <td></td>
+
         <td>-</td>
       </tr>
       </tr>
       <tr>
       <tr>
-
         <th>[mRNA]</th>
+
         <th>Coenzyme A</th>
-
         <td>Concentration of mRNA</td>
+
          
-
         <td>-</td>
+
         <td>250</td>
-
         <td>mM</td>
+
         <td>uM</td>
-
         <td>-</td>
+
         <td>[http://digitalcommons.usu.edu/engineering_datasets/1/]</td>
         <td>-</td>
         <td>-</td>
       </tr>
       </tr>
       <tr>
       <tr>
-
         <th>[Proteinase K]</th>
+
         <th>Acetate</th>
-
         <td>Concentration of Proteinase K</td>
+
       
 +
        <td>40000</td>
 +
        <td>uM</td>
 +
        <td>[http://www.ncbi.nlm.nih.gov/pubmed/1103741]</td>
 +
        <td>Assay data from the literature which the ato system efficiency was measured</td>
 +
      </tr>
 +
      <tr>
 +
        <th>3HB-coA</th>
 +
       
 +
        <td>0</td>
 +
         <td>uM</td>
         <td>-</td>
         <td>-</td>
-
         <td>mM</td>
+
         <td>One of the intermediate product of the pathway</td>
 +
      </tr>
 +
<tr>
 +
        <th>NADPH</th>
 +
       
 +
        <td>200</td>
 +
        <td>uM</td>
 +
        <td>[http://digitalcommons.usu.edu/engineering_datasets/1/]</td>
         <td>-</td>
         <td>-</td>
 +
      </tr>
 +
<tr>
 +
        <th>NADP+</th>
 +
       
 +
        <td>1200</td>
 +
        <td>uM</td>
 +
        <td>[http://digitalcommons.usu.edu/engineering_datasets/1/]</td>
         <td>-</td>
         <td>-</td>
       </tr>
       </tr>
-
        
+
 
 +
    <tr>
 +
        <th>PHB</th>
 +
       
 +
        <td>0</td>
 +
        <td>uM</td>
 +
        <td>-</td>
 +
        <td>The final product of the pathway</td>
 +
       </tr>
 +
   
      
      
       </table>
       </table>
-
<p>'''1.Derivation of the maximal expression rate,β'''
+
<h3>ATP analysis:</h3>
-
*Average molecular weight (Mw) of a base pair = 660g/mol[http://www.geneinfinity.org/sp/sp_dnaprop.html][http://www.lifetechnologies.com/uk/en/home/references/ambion-tech-support/rna-tools-and-calculators/dna-and-rna-molecular-weights-and-conversions.html]
+
<p>In our optimization of P(3HB) production module, we discovered that increasing in the PhaB expression can efficiently increase the yield of P(3HB). It’s important to see whether increase in the PhaB expression would dramatically change the fluxes in the metabolic pathways or not. As ATP is the essential energy carriers in the cell, we carried a parameter scan for the variation in ATP concentrations levels under different concentration of PhaB.</p>
-
*Average mass of a base pair = 660g/mol x 1.66x10<sup>-24</sup> = 1.1x10<sup>-21</sup>g
+
[[File:ATPPHAB.png|600px|centre]]
-
*Volume of an E.coli cell = 1µm<sup>3</sup>[http://kirschner.med.harvard.edu/files/bionumbers/fundamentalBioNumbersHandout.pdf] = 1x10<sup>-15</sup>L
+
<p>There is an approximately 5.3% drop in the concentration of ATP when increasing the phaB concentration from 50uM to 200uM. It suggests that increasing the efficiency in our pathway will reduce the efficiency of energy transports in the cell. However, it’s still unsure about  the effect of 5.3% drop in ATP concentration on the cell growth.</p>
-
**∴Mass concentration = [[File:Imperial College Mass conc cal beta.JPG|200px]]
+
<h3>Large scale PHB production and implementation in MAPLE</h3>
-
**∴Molar concentration of 1 base pair in the volume of E.coli = [[File:Imperial College Molar conc cal beta.JPG|300px]] = 1.66x10<sup>-6</sup> mM
+
<p>In our MAPLE system, the bioplastic Polyhydroxybutyrate P(3HB) is produced from both 3HB monomers and glucose. 3HB is the degradation product from the wasted P(3HB）plastic and glucose is the product from the degradation of mixed waste in Module 1. Therefore, the overall PHB production rates need to be defined by considering different situations:</p>
-
*BioBrick assembly plasmid pSB1C3 is a high copy number plasmid (100-300 copies per cell)[http://parts.igem.org/Part:pSB1C3?title=Part:pSB1C3]
+
<p>1. In module 1, we have glucose as the only source to produce PHB.</p>
-
**assume 200 copies per cell
+
<p>2. In module 2, we have both glucose and 3HB as resources. </p>
-
*∴ concentration of the gene per cell = N x 200 x 1.66x10<sup>-6</sup>mM, where N = number of base pairs
+
-
**∴ concentration of the gene BDH2 (N = 768) in the volume of an E.coli cell is = 0.25mM
+
-
*Transcription rate in E.coli = 80bp/s[http://kirschner.med.harvard.edu/files/bionumbers/fundamentalBioNumbersHandout.pdf] = 80 x 1.66x10<sup>-6</sup>mM/s = 80 x 1.66x10<sup>-6</sup> x 60mM/min = 7.97x10<sup>-3</sup>mM/min
+
-
*∴ Rate of mRNA_Proteinase K production under the control of pBAD = 7.97x10<sup>-3</sup> ÷ 0.25 = '''0.032/min'''
+
-
 
+
-
'''2.Protein production rate of Proteinase K, k<sub>2</sub>'''
+
-
*Average molecular weight(Mw) of an amino acid(aa)= 110g/mol[http://www.genscript.com/conversion.html][http://www.promega.com/~/media/Files/Resources/Technical%20References/Amino%20Acid%20Abbreviations%20and%20Molecular%20Weights.pdf]
+
-
*Average mass of an amino acid = 110g/mol x 1.66x10<sup>-24</sup>=1.83x10<sup>-22</sup>g/L
+
-
**∴Mass concentration of one aa in the volume of an E.coli = [[File:Imperial College Mass conc cal beta aa.JPG|130px]] = 1.83x10<sup>-6</sup>g/L
+
-
**∴Molar concentration of one aa = [[File:Imperial College Molar conc cal aa.JPG|150px]] = 1.66x10<sup>-5</sup>mM
+
-
*Translation rate = 20aa/s = (20 x 1.66x10<sup>-5</sup> x 60)mM/min = 0.020mM/min
+
-
*BDH2 comprises of 256aa[http://www.uniprot.org/uniprot/Q2PEN2&format=html]
+
-
**∴concentration of BDH2's aa in the volume of an E.coli = 1.66x10<sup>-5</sup>mM x 256 = 4.25x10<sup>-3</sup>mM
+
-
*∴ Rate of protein production = 0.020 ÷ 4.25x10<sup>-3</sup> = '''4.7/min'''
+
-
</p>
+
-
<h4>Degradation</h4>
+
-
<p>The reaction equation of the PLA degradation is:</p>
+
-
[Polylactic acid]+[Proteinase K]= 5 [lactic acid] + [Proteinase K]
+
-
<p><b>Assumptions:</b></p>
+
-
<p>We assumed 1 mole of polylactic acid  can produce 5 moles of lactic acid. </p>
+
-
<p>The molecular weight of a single polylactic acid monomer is 470 g/mol whereas the molecular weight of the solid polylactic acid is around 2000 g/mol.[]
+
-
<p>We also assumed a simple Michaelis-Menten mechanism for PudA</p>
+
-
[[File:MMPLA.png]]
+
{{:Team:Imperial_College/Templates:footer}}
{{:Team:Imperial_College/Templates:footer}}

Latest revision as of 13:41, 4 October 2013

Contents

Polyhydroxybutyrate (P(3HB)) Synthesis Module

Metabolic modelling

Introduction of the metabolic model

The metabolic model predicts the interaction of our pathway with endogenous pathways. In synthetic biology, an ideal system is fully orthogonal. However, if the synthetic pathway uses some metabolites from the metabolism pathways, the metabolic fluxes (the rate of conversion between metabolites) will be affected. If the cell is overloaded by losing too much metabolites, it would either reject the synthetic pathway or burn out. As for the optimization of PHB production in our MAPLE system, metabolic analysis need to be carried out to estimate the effects on the cell metabolism from increases in the PHB production.

Methods

We altered the metabolic model by Angela Dixon in her paper “Predictive Mathematical Model for Polyhydroxybutyrate Synthesis in Escherichia coli”. [http://digitalcommons.usu.edu/engineering_datasets/1/] The metabolic model is built in Simbiology, which is an extension in MATLAB especially for biological system analysis. The model consists two metabolic pathways: Glycolysis and TCA cycle. The reactions in the metabolic pathways are defined by ordinary differential equations and kinetic parameters. The model also contains a synthetic pathway that produce P(3HB) from acetyl-coA. The pathway consists three enzymes which are PhaA, PhaB and PhaC. The reasons we chose this model:

1. The model is based on ODEs instead of FBA (flux balance analysis) method, which is a common methods of metabolic analysis. However, FBA cannot determine the real time concentration of the metabolites whereas it can be done by models of ODEs.

2. Only single gene deletion or addition can be performed in FBA. More than that, the metabolic model here can perform modification on any single or multiple genes and reactions through Simbiology.

3. The FBA model is static, it cannot analyze the dynamic interactions between our synthetic pathways with the metabolic pathways. As both our P(3HB) synthesis model and the metabolic model are in the same platform. It was really easy to integrate our pathway into the metabolic model.

In our project, we have a different pathway:

1. We use 3HB as one of the input.

2. Existence of ato system in the E.coli MG1655 strain.

3. We removed phaA in our case because we use 3HB as the major source to produce P(3HB) to avoid too much acetyl-coA be taken from the metabolic pathways.

Therefore, we substitute the original pathway with our synthetic pathway. Moreover, we added our gene expression models for the enzymes into the metabolic model as well. In terms of the consistency of the model, we changed the units of our synthetic pathway into micro molar and seconds.

Here is the combination of our model with the metabolic model

MetaSyn.png

We also carried out a parameter estimations of the initial concentrations of several substrates in our synthetic pathway. The reason is we have single-cell scaled magnitude for them originally (fM level), but there are much higher magnitudes in any of the species in the metabolic pathways (mM level). Therefore, we scaled up the pathway in order to maintain the consistency of the model. As for the metabolites which are involved in our pathway, we cloned the blocks of them from the metabolic pathway in Simbiology and deliberately put them into our pathway. That means our pathway dynamically interact with the metabolic pathways.

Here is the table for the updated initial concentrations for the species in our synthetic pathway: All the kinetic data and initial concentrations of the metabolites in the metabolic pathways are referenced in the paper[http://digitalcommons.usu.edu/engineering_datasets/1/]:

Substrates Concentration Units Sources Assumptions
3HB 5000 uM - The initial input to the system
Acetoacetate 1000 uM - The ato system in E.coli suggest a favourable conversion from acetoacetyl-coA to acetoacetate. Therefore, the concentration of acetoacetate is 10 times larger than acetoacetyl-coA[http://www.sciencedirect.com/science/article/pii/0003986177904969]
Acetoacetyl-coA 100 uM [http://www.ncbi.nlm.nih.gov/pubmed/1103741] The ato system in E.coli suggest a favourable conversion from acetoacetyl-coA to acetoacetate. [http://www.sciencedirect.com/science/article/pii/0003986177904969]
NADH 200 uM [http://digitalcommons.usu.edu/engineering_datasets/1/] -
NAD+ 1200 uM [http://digitalcommons.usu.edu/engineering_datasets/1/] -
Acetyl-coA 5000 uM [http://digitalcommons.usu.edu/engineering_datasets/1/] -
Coenzyme A 250 uM [http://digitalcommons.usu.edu/engineering_datasets/1/] -
Acetate 40000 uM [http://www.ncbi.nlm.nih.gov/pubmed/1103741] Assay data from the literature which the ato system efficiency was measured
3HB-coA 0 uM - One of the intermediate product of the pathway
NADPH 200 uM [http://digitalcommons.usu.edu/engineering_datasets/1/] -
NADP+ 1200 uM [http://digitalcommons.usu.edu/engineering_datasets/1/] -
PHB 0 uM - The final product of the pathway

ATP analysis:

In our optimization of P(3HB) production module, we discovered that increasing in the PhaB expression can efficiently increase the yield of P(3HB). It’s important to see whether increase in the PhaB expression would dramatically change the fluxes in the metabolic pathways or not. As ATP is the essential energy carriers in the cell, we carried a parameter scan for the variation in ATP concentrations levels under different concentration of PhaB.

ATPPHAB.png

There is an approximately 5.3% drop in the concentration of ATP when increasing the phaB concentration from 50uM to 200uM. It suggests that increasing the efficiency in our pathway will reduce the efficiency of energy transports in the cell. However, it’s still unsure about the effect of 5.3% drop in ATP concentration on the cell growth.

Large scale PHB production and implementation in MAPLE

In our MAPLE system, the bioplastic Polyhydroxybutyrate P(3HB) is produced from both 3HB monomers and glucose. 3HB is the degradation product from the wasted P(3HB）plastic and glucose is the product from the degradation of mixed waste in Module 1. Therefore, the overall PHB production rates need to be defined by considering different situations:

1. In module 1, we have glucose as the only source to produce PHB.

2. In module 2, we have both glucose and 3HB as resources.

Our Sponsors

TueSponsorsEppendorf.png 125px Invitrogen.jpg Geneart.jpg CSynBI.JPG

Retrieved from "http://2013.igem.org/Team:Imperial_College/Modelling_PLAdeg"