Team:UFMG Brazil/Modeling

$M$ is TMAO.

$T$ is TorT.

$TM$ is the complex of T and M.

$S$ is TorS.

$STM$ is the complex of S and TM.

$R$ is TorR.

$R^{ *}$ is TorR Phosophorilated.

Reactions:

$M+T{{k_{1} \atop\displaystyle\longrightarrow} \atop {\displaystyle\longleftarrow \atop k_{-1}}}TM$

$2TM+S{{k_{2} \atop\displaystyle\longrightarrow} \atop {\displaystyle\longleftarrow \atop k_{-2}}}STM$

$STM+R{{k_{3} \atop\displaystyle\longrightarrow} \atop {\displaystyle\longleftarrow \atop k_{-3}}} X {{k_{cat}\atop\longrightarrow} \atop {\quad  \atop \quad }}R^{ *} + STM$

$R^{ *} + P {{\displaystyle\longrightarrow} \atop {\displaystyle\longleftarrow}} PR^{ *}$

\begin{eqnarray}
\begin{cases}
{d M(t)\over d t}&=& -k_1 \cdot  M\cdot T + k_{-1}\cdot TM\\\\
\\\\
{d T(t)\over d t}&=& -k_1 \cdot  M\cdot T + k_{-1}\cdot TM\\\\ 
\\\\
{d TM(t)\over d t}&=& k_1 \cdot  M\cdot T - k_{-1}\cdot TM - k_2\cdot TM^{2} \cdot S + k_{-2} \cdot STM\\\\
\\\\
{d S(t)\over d t}&=& -k_2 \cdot  S\cdot TM^{2} - k_{-1}\cdot TM - k_2\cdot TM^{2} \cdot S + k_{-2} \cdot STM\\\\
\\\\
{d STM(t)\over d t}&=& k_2 \cdot  TM^{2} \cdot S - k_{-2}\cdot STM \\\\
\\\\
{d R^{ *}(t)\over d t}&=& k_{cat}\cdot STM \over{k_m + STM}\\\\
\\\\
{d mRNA(t)\over d t}&=& {\alpha \cdot  R^{ *^{\gamma}} \over{\beta + R^{ *^{\gamma}}}} - \mu \cdot mRNA\\\\
\\
\end{cases}
\end{eqnarray}