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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.
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Flux balance analysis is a mathematical approach for analyzing the flow of metabolites through a metabolic network.[1]
 
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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.
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We use a stoichiometric matrix to represent metabolic reactions:
 
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\[maximize \quad f=c^t v\]
 
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\[s.t. \quad S v=0\]
 
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\[\qquad \quad \qquad 0 \leq v \leq V_{max} \]
 
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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.
 
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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.
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\[maximize \quad f=c^t v\]
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\[s.t. \quad S v=0\]
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\[\qquad \quad \qquad 0 \leq v \leq V_{max} \]
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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.
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Revision as of 08:46, 10 October 2018

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 mathematical approach for analyzing the flow of metabolites through a metabolic network.[1]

We use a stoichiometric matrix to represent metabolic reactions:

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

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.

\[maximize \quad f=c^t v\] \[s.t. \quad S v=0\] \[\qquad \quad \qquad 0 \leq v \leq V_{max} \]

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 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.

We have converted the design of our project to a optimization problem, and build up a model to find out the optimal solution (which enzyme to be over expressed in the pathway.). At first, we used dynamics system, which is always been used by iGEM teams, to simulate our project. However, we found it took a lot of time calculating, and what's worse, the dynamics system was in bad robustness and always gave different results. Then we tried flux balance analysis. We found it time-saving and in good robustness. So we decided to search for the optimal solution based on flux balance analysis. Inspired by some machine learning methods, we established an algorithm using gradient descent method and innovatively combined it with flux balance analysis. We used python to run the model we built and got really clear results. What's more, the results we got were close to the results on some published articles we read, which makes us believe that our model is reliable.