Difference between revisions of "Team:IISER-Pune-India/Model"

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\[a \xlongrightarrow{\lambda f(X)} \phi \]
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\[a \xrightarrow{\lambda f(X)} \phi \]
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\[r \xlongrightarrow{f(X)} \phi \]
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\[r \xrightarrow{f(X)} \phi \]
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\[m_a \xlongrightarrow{d_a} \phi \]
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\[m_a \xrightarrow{d_a} \phi \]
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\[m_r \xlongrightarrow{d_r} \phi \]
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\[m_r \xrightarrow{d_r} \phi \]
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\[a_{uf}  \xlongrightarrow{{\lambda f(X)}} \phi \]
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\[a_{uf}  \xrightarrow{{\lambda f(X)}} \phi \]
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\[r_{uf} \xlongrightarrow{{f(X)}} \phi \]
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\[r_{uf} \xrightarrow{{f(X)}} \phi \]
  
 
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Revision as of 13:40, 24 October 2017

MathJax TeX Test Page
The Project
Mathematical modelling often gives useful insights into the behaviour of complex systems. The purpose of this project was to model the synthetic gene oscillator circuit made by \cite{Stricker}, where the protein product of the first gene (AraC) activates the expression of both the genes and the protein product of the second gene (LacI) inhibits expression of both the genes. It is expected that such a model would help test what modifications can be done in the mentioned oscillator, to couple it with other genes to achieve oscillations in their protein products, which are essential in the cell cycle. section{The model} The reactions in the lac ara system are as follows- \[P^{a/r}_{0,j} \ + \ a_2 \rightleftharpoons[k_-a]{k_a} \ P^{a/r}_{1,j} \] \[P^{a/r}_{i,0} \ + \ r_4 \rightleftharpoons[k_-r]{2k_r} \ P^{a/r}_{i,1} \] \[P^{a/r}_{i,1} \ + \ r_4 \rightleftharpoons[2k_-r]{k_r} \ P^{a/r}_{i,2} \] where $P^{a/r}_{i,j}$ represent the states of promoters on the (a)ctivator/(r)epressor plasmids with $i \ \ \epsilon \ \ (0, 1)$ AraC dimers $(a_2)$ bound and $ j \ \ \epsilon \ (0, 1, 2) $ LacI tetramers $(r_4)$ bound. Transcription- \[\ \ \ \ \ \ \ P^{a/r}_{0,0} \xrightarrow{b_a} \ P^{a/r}_{0,0} + m_{a/r}\] \[ \ \ \ \ \ \ \ P^{a/r}_{0,1} \xrightarrow{\alpha b_a} \ P^{a/r}_{0,1} + m_{a/r}\] Translation and Protein folding- \[ \ \ \ \ \ \ m_a \xrightarrow{t_a} m_a + a_{uf}\] \[ \ \ \ \ \ \ m_r \xrightarrow{t_r} m_r + r_{uf}\] \[a_{uf} \xrightarrow{k_{fa}} a\] \[r_{uf} \xrightarrow{k_{fa}} r\] where $m_{a/r}$ represents the number of activator/repressor transcripts; $a_{uf}$ and $r_{uf}$ are the unfolded monomeric versions of the activator and repressor; a and r are the folded monomeric versions of activator and repressor; $a_2$ and $r_2$ are the dimeric versions of activator and repressor; and $r_4$ is the tetrameric version of the repressor. Dimerisation and Tetramerisation- \[a \ + \ a \xrightleftharpoons[k_-da]{k_da} \ a_2 \] \[r \ + \ r \xrightleftharpoons[k_-dr]{k_dr} \ r_2 \] \[r_2 \ + \ r_2 \xrightleftharpoons[k_-t]{k_t} \ r_4 \] Degradation- \[a \xrightarrow{\lambda f(X)} \phi \] \[r \xrightarrow{f(X)} \phi \] \[m_a \xrightarrow{d_a} \phi \] \[m_r \xrightarrow{d_r} \phi \] \[a_{uf} \xrightarrow{{\lambda f(X)}} \phi \] \[r_{uf} \xrightarrow{{f(X)}} \phi \]