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

Line 13: Line 13:
 
<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 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.
 
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.
 
</p>
 
</p>
Line 21: Line 21:
 
<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">
 
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.  
 
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>
Line 31: Line 31:
  
 
<div class="column full_size">
 
<div class="column full_size">
−
<p>
+
<p style="text-align: justify">
 
The first step we did was to convert the pathway into a mathematical form, a matrix \(S\) .
 
The first step we did was to convert the pathway into a mathematical form, a matrix \(S\) .
 
</p>
 
</p>
Line 58: Line 58:
  
 
<div class="column full_size">
 
<div class="column full_size">
−
<p>
+
<p style="text-align: justify">
 
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.
 
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>
 
</p>
Line 69: Line 69:
  
 
<div class="column full_size">
 
<div class="column full_size">
−
<p>
+
<p style="text-align: justify">
 
And we use M-M equation to calculate \( V_{max}\):
 
And we use M-M equation to calculate \( V_{max}\):
 
</p>
 
</p>
Line 76: Line 76:
  
 
<div class="column full_size">
 
<div class="column full_size">
−
<p>
+
<p style="text-align: justify">
 
We found \(k_{cat}\) (Turnover Number) from brenda-enzymes:
 
We found \(k_{cat}\) (Turnover Number) from brenda-enzymes:
 
</p>
 
</p>
Line 82: Line 82:
  
 
<div class="clear"></div>
 
<div class="clear"></div>
−
<div class="column half_size">
+
<div class="column two_thirds_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>
  
Line 89: Line 107:
 
<div class="column full_size">
 
<div class="column full_size">
 
<h2 style="text-align: left">Gradient Descent Method</h2>
 
<h2 style="text-align: left">Gradient Descent Method</h2>
−
<p>
+
<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.
 
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>
 
</p>
Line 96: Line 114:
 
<div class="column full_size">
 
<div class="column full_size">
 
<h2 style="text-align: left">Results</h2>
 
<h2 style="text-align: left">Results</h2>
−
<p>
+
<p style="text-align: justify">
 
This is the result we got after running our model.
 
This is the result we got after running our model.
 
</p>
 
</p>
Line 106: Line 124:
  
 
<div class="column full_size">
 
<div class="column full_size">
−
<p>
+
<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 with ERG13, we finally decided to overexpress HMG1 and ERG12.
 
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 with ERG13, we finally decided to overexpress HMG1 and ERG12.
 
</p>
 
</p>
Line 112: Line 130:
  
  
−
 
+
<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>

Revision as of 18:00, 17 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:

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.

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 with ERG13, we finally decided to overexpress HMG1 and ERG12.