Difference between revisions of "Team:SCUT-ChinaA/Model"

 
(40 intermediate revisions by the same user not shown)
Line 1: Line 1:
 
{{SCUT-ChinaA/CSS}}
 
{{SCUT-ChinaA/CSS}}
{{SCUT-ChinaA/Nav}}
+
{{SCUT-ChinaA/T3}}
 
{{SCUT-ChinaA}}
 
{{SCUT-ChinaA}}
  
Line 8: Line 8:
 
<div class="clear"></div>
 
<div class="clear"></div>
 
<div class="igem_content_wrapper">
 
<div class="igem_content_wrapper">
 
+
<img class="full_size_image" style="margin-top:-360px" src="https://static.igem.org/mediawiki/2018/8/88/T--SCUT-ChinaA--title3-1.png">
 
+
<img class="full_size_image" style="margin-top:-250px" src="https://static.igem.org/mediawiki/2018/3/3f/T--SCUT-ChinaA--mo.png">
+
  
 
<div class="column full_size">
 
<div class="column full_size">
 
<h2 style="text-align: left">Abstract</h2>
 
<h2 style="text-align: left">Abstract</h2>
  
<p>
+
<p style="text-align: justify">
To improve the efficiency of producing limonene, we build a model to help us design our genetic machine. We use flux balance analysis to set up a relationship of input ( substrate ) and output (the produce rate of limonene), with the matrix of the pathway and the \(V_{max}\) (calculated by \(k_{cat}\) and \(E_t\) ) of each reactions. After we get the relationship we optimize the output by finding the best solution of \(E_t\) , using Newton method.
+
To improve the efficiency of producing limonene, we build a model to help us design our genetic machine. We use flux balance analysis to simulate our system, with the matrix of the pathway and the \(V_{max}\) (calculated by \(k_{cat}\) and \(E_t\) ) of each reactions. And, inspired of machine learning algorithms, we established an algorithm using gradient descent method to search for the optimal solution of \(E_t\). Finally, we got results that were close to the results on some published articles we read, and hence we decided to design our experiment based on the model. Also, while building our model, we have developed a <a href="https://2018.igem.org/Team:SCUT-ChinaA/Software">software tool
 +
</a> which may be helpful for those who need to optimize a pathway.
 
</p>
 
</p>
 
 
</div>
 
</div>
  
 
<div class="column full_size">
 
<div class="column full_size">
 
<h2 style="text-align: left">Flux Balance Analysis</h2>
 
<h2 style="text-align: left">Flux Balance Analysis</h2>
<p>
+
<p style="text-align: justify">
To improve the efficiency of producing limonene, we build a model to help us design our genetic machine. We use flux balance analysis to set up a relationship of input ( substrate ) and output (the produce rate of limonene), with the matrix of the pathway and the \(V_{max}\) (calculated by \(k_{cat}\) and \(E_t\) ) of each reactions. After we get the relationship we optimize the output by finding the best solution of \(E_t\) , using Newton method.
+
Flux balance analysis is a method to calculate the flow of metabolites through a metabolic network. It assumes that under steady state, the concentration of each metabolite remains unchanged, and the reaction rate satisfies a certain distribution.  
 
</p>
 
</p>
 
</div>
 
</div>
 
 
  
 
<div class="column full_size">
 
<div class="column full_size">
Line 35: Line 31:
  
 
<div class="column full_size">
 
<div class="column full_size">
<p>
+
<p style="text-align: justify">
To improve the efficiency of producing limonene, we build a model to help us design our genetic machine. We use flux balance analysis to set up a relationship of input ( substrate ) and output (the produce rate of limonene), with the matrix of the pathway and the \(V_{max}\) (calculated by \(k_{cat}\) and \(E_t\) ) of each reactions. After we get the relationship we optimize the output by finding the best solution of \(E_t\) , using Newton method.
+
The first step we did was to convert the pathway into a mathematical form, a matrix \(S\) .
 
</p>
 
</p>
 
</div>
 
</div>
 
 
\[maximize \quad f=c*v\]
 
\[s.t. \quad A*v=0\]
 
\[\qquad \qquad 0 \leq v \leq V_{max} \]
 
 
 
 
<div class="column full_size">
 
<p>
 
To improve the efficiency of producing limonene, we build a model to help us design our genetic machine. We use flux balance analysis to set up a relationship of input ( substrate ) and output (the produce rate of limonene), with the matrix of the pathway and the \(V_{max}\) (calculated by \(k_{cat}\) and \(E_t\) ) of each reactions. After we get the relationship we optimize the output by finding the best solution of \(E_t\) , using Newton method.
 
</p>
 
</div>
 
 
  
 
<div class="column full_size">
 
<div class="column full_size">
Line 76: Line 58:
  
 
<div class="column full_size">
 
<div class="column full_size">
<p>
+
<p style="text-align: justify">
To improve the efficiency of producing limonene, we build a model to help us design our genetic machine. We use flux balance analysis to set up a relationship of input ( substrate ) }\) (calculated by \(k_{cat}\) and \(E_t\) ) of each reactions. After we get the relationship we optimize the output by finding the best solution of \(E_t\) , using Newton method.
+
Then we use flux balance analysis to maximize \( f=c^t v\) with constrains, where \(f\) is our objective function, and \(c\) is a vector of zeros with a one at the last reaction, \(b2\) , and \(v\) represents for the flux through all of the reactions.
 +
</p>
 +
</div>
 +
 
 +
\[maximize \quad f=c^t \cdot v\]
 +
\[subject \quad to \quad S \cdot v=0\]
 +
\[\qquad \qquad \qquad \quad 0 \leq v \leq V_{max} \]
 +
 
 +
 
 +
<div class="column full_size">
 +
<p style="text-align: justify">
 +
And we use M-M equation to calculate \( V_{max}\):
 +
</p>
 +
</div>
 +
\[ V_{max} = k_{cat} \cdot E_t\]
 +
 
 +
<div class="column full_size">
 +
<p style="text-align: justify">
 +
We found \(k_{cat}\) (Turnover Number) from brenda-enzymes and assumed all initial \(E_t\) are the same:
 
</p>
 
</p>
 
</div>
 
</div>
  
 
<div class="clear"></div>
 
<div class="clear"></div>
<div class="column half_size">
+
<div class="column jiadefull_size">
<img  src="https://static.igem.org/mediawiki/2018/9/93/T--SCUT-ChinaA--enzymeC.png">
+
<table>
 +
<tr>
 +
<th> enzyme </th> <th> Substrate </th> <th> Turnover Number [1/s] </th> <th> KM Value [mM] </th>
 +
</tr>
 +
<tr>
 +
<td> ERG10</td> <td>acetyl-CoA</td> <td>2.1</td> <td>0.33</td> </tr>
 +
<tr>
 +
<td> ERG13</td> <td>acetoacetyl-CoA, acetyl-CoA</td> <td>4.6</td> <td>acetoacetyl-CoA:0.0014, acetyl-CoA:0.05</td> </tr>
 +
<tr>
 +
<td> HMG1</td> <td>hydroxymethylglutaryl-CoA</td> <td>0.023</td> <td>0.045</td> </tr>
 +
<tr>
 +
<td>ERG12</td> <td>mevalonate</td> <td>2.36</td> <td>0.012</td> </tr>
 +
<tr>
 +
<td> ERG8</td> <td>phosphomevalonate</td> <td>3.4</td> <td>0.0042</td> </tr>
 +
<tr>
 +
<td>ERG19</td> <td>(R,S)-5-diphosphomevalonate</td> <td>5.9</td> <td>0.0091</td> </tr>
 +
<tr>
 +
<td> NDPS1</td> <td>isopentenyl diphosphate</td> <td>0.14</td> <td>0.047</td> </tr>
 +
</table>
 
</div>
 
</div>
 +
  
 
<div class="column full_size">
 
<div class="column full_size">
<p>
+
<h2 style="text-align: left">Gradient Descent Method</h2>
To improve the efficiency of producing limonene, we build a model to help us design our genetic machine. We use flux balance analysis to set up a relationship of input ( substrate ) and output (the produce rate of limonene), with the matrix of the pathway and the \(V_{max}\) (calculated by \(k_{cat}\) and \(E_t\) ) of each reactions. After we get the relationship we optimize the output by finding the best solution of \(E_t\) , using Newton method.
+
<p style="text-align: justify">
 +
Inspired by some machine learning methods, we established an algorithm using gradient descent method and innovatively combined it with flux balance analysis. We calculated the gradients of \(f\) on \(E_t\), and searched for the best length of step on the gradient, to improve \(f\). And we have repeat for 10 times to get the results.
 +
</p>
 +
</div>
  
To improve the efficiency of producing limonene, we build a model to help us design our genetic machine. We use flux balance analysis to set up a relationship of input ( substrate ) and output (the produce rate of limonene), with the matrix of the pathway and the \(V_{max}\) (calculated by \(k_{cat}\) and \(E_t\) ) of each reactions. After we get the relationship we optimize the output by finding the best solution of \(E_t\) , using Newton method.
+
<div class="column full_size">
 +
<h2 style="text-align: left">Results</h2>
 +
<p style="text-align: justify">
 +
This is the result we got after running our model. The ordinate indicates the multiple of the predicted product generation rate of the model, and the sequence below the abscissa indicates the priority of the enzymes (the left is the highest).
 +
</p>
 +
</div>
 +
<div class="column half_size">
 +
<img  src="https://static.igem.org/mediawiki/2018/5/56/T--SCUT-ChinaA--modelresult.jpg">
 +
</div>
  
To improve the efficiency of producing limonene, we build a model to help us design our genetic machine. We use flux balance analysis to set up a relationship of input ( substrate ) and output (the produce rate of limonene), with the matrix of the pathway and the \(V_{max}\) (calculated by \(k_{cat}\) and \(E_t\) ) of each reactions. After we get the relationship we optimize the output by finding the best solution of \(E_t\) , using Newton method.
+
 
 +
<div class="column full_size">
 +
<p style="text-align: justify">
 +
From the figure we can see that the priority of enzymes are: HMG1->NDPS1->ERG10->ERG12->..... For NDPS1 is the enzyme which will be put into the <em>Y. lipolytica</em> and ERG10 shares the substrate (Acetyl-CoA) with ERG13, we finally decided to overexpress HMG1 and ERG12.
 
</p>
 
</p>
 
</div>
 
</div>
  
 +
<div class="column full_size">
 +
<h2 style="text-align: left">References</h2>
 +
<ul>
 +
<li>Klipp E. etc. Systems Biology: A Textbook, Wiley-VCH, 2009.</li>
 +
<li>Orth JD, Thiele I, Palsson BØ. What is flux balance analysis? Nat Biotechnol [Internet]. 2010;28:245–248. doi: 10.1038/nbt.1614.</li>
 +
</ul>
 +
</div>
  
  
  
 +
<div class="column full_size">
 +
<img class="full_size_image" style="margin-top:200px" src="https://static.igem.org/mediawiki/2018/0/0e/T--SCUT-ChinaA--bottom.png">
 +
</div>
 
</html>
 
</html>

Latest revision as of 01:57, 18 October 2018

SCUT-ChinaA

Abstract

To improve the efficiency of producing limonene, we build a model to help us design our genetic machine. We use flux balance analysis to simulate our system, with the matrix of the pathway and the \(V_{max}\) (calculated by \(k_{cat}\) and \(E_t\) ) of each reactions. And, inspired of machine learning algorithms, we established an algorithm using gradient descent method to search for the optimal solution of \(E_t\). Finally, we got results that were close to the results on some published articles we read, and hence we decided to design our experiment based on the model. Also, while building our model, we have developed a software tool which may be helpful for those who need to optimize a pathway.

Flux Balance Analysis

Flux balance analysis is a method to calculate the flow of metabolites through a metabolic network. It assumes that under steady state, the concentration of each metabolite remains unchanged, and the reaction rate satisfies a certain distribution.

The first step we did was to convert the pathway into a mathematical form, a matrix \(S\) .

$$S= \left[ \begin{matrix} & v1 & v2 & v3 & v4 & v5 & v6 & v7 & v8 & v9 & b1 & b2 \\ Acetyl-CoA & -1 & -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\ Acetoacetyl-CoA & 1 & -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ HMG-CoA & 0 & 1 & -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ Mevalonate & 0 & 0 & 1 & -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ Mevalonate-5-phosphate & 0 & 0 & 0 & 1 & -1 & 0 & 0 & 0 & 0 & 0 & 0 \\ Mevalonate-diphosphate & 0 & 0 & 0 & 0 & 1 & -1 & 0 & 0 & 0 & 0 & 0 \\ IPP & 0 & 0 & 0 & 0 & 0 & 1 & 1 & -1 & -1 & 0 & 0 \\ DMAPP & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 1 & 0 & 0 & 0 \\ NPP & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & -1 \\ \end{matrix} \right]\tag{001} $$

Then we use flux balance analysis to maximize \( f=c^t v\) with constrains, where \(f\) is our objective function, and \(c\) is a vector of zeros with a one at the last reaction, \(b2\) , and \(v\) represents for the flux through all of the reactions.

\[maximize \quad f=c^t \cdot v\] \[subject \quad to \quad S \cdot v=0\] \[\qquad \qquad \qquad \quad 0 \leq v \leq V_{max} \]

And we use M-M equation to calculate \( V_{max}\):

\[ V_{max} = k_{cat} \cdot E_t\]

We found \(k_{cat}\) (Turnover Number) from brenda-enzymes and assumed all initial \(E_t\) are the same:

enzyme Substrate Turnover Number [1/s] KM Value [mM]
ERG10 acetyl-CoA 2.1 0.33
ERG13 acetoacetyl-CoA, acetyl-CoA 4.6 acetoacetyl-CoA:0.0014, acetyl-CoA:0.05
HMG1 hydroxymethylglutaryl-CoA 0.023 0.045
ERG12 mevalonate 2.36 0.012
ERG8 phosphomevalonate 3.4 0.0042
ERG19 (R,S)-5-diphosphomevalonate 5.9 0.0091
NDPS1 isopentenyl diphosphate 0.14 0.047

Gradient Descent Method

Inspired by some machine learning methods, we established an algorithm using gradient descent method and innovatively combined it with flux balance analysis. We calculated the gradients of \(f\) on \(E_t\), and searched for the best length of step on the gradient, to improve \(f\). And we have repeat for 10 times to get the results.

Results

This is the result we got after running our model. The ordinate indicates the multiple of the predicted product generation rate of the model, and the sequence below the abscissa indicates the priority of the enzymes (the left is the highest).

From the figure we can see that the priority of enzymes are: HMG1->NDPS1->ERG10->ERG12->..... For NDPS1 is the enzyme which will be put into the Y. lipolytica and ERG10 shares the substrate (Acetyl-CoA) with ERG13, we finally decided to overexpress HMG1 and ERG12.

References

  • Klipp E. etc. Systems Biology: A Textbook, Wiley-VCH, 2009.
  • Orth JD, Thiele I, Palsson BØ. What is flux balance analysis? Nat Biotechnol [Internet]. 2010;28:245–248. doi: 10.1038/nbt.1614.