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== Simplification and construction of ODEs == | == Simplification and construction of ODEs == | ||
The general reaction scheme is | The general reaction scheme is | ||
| + | \begin{align} | ||
| + | \color{blue} m + \color{red}s &\mathop{\rightleftharpoons}_{k_{-1,s}}^{k_{1,s}} c_{ms} \mathop{\rightarrow}^{k_{2,s}} (1 - p_s) \color{red} s \\ | ||
| + | \color{red} s + \color{green} r &\mathop{\rightleftharpoons}_{k_{-1,r}}^{k_{1,r}} c_{sr} \mathop{\rightarrow}^{k_{2,r}} (1-p_r) \color{green} r | ||
| + | \end{align} | ||
| + | |||
| + | \begin{align} | ||
| + | \color{blue} m + \color{red}s &\mathop{\rightleftharpoons}_{k_{-1,s}}^{k_{1,s}} c_{ms} \mathop{\rightarrow}^{k_{2,s}} (1 - p_s) \color{red} s \\ | ||
| + | \color{red} s + \color{green} r &\mathop{\rightleftharpoons}_{k_{-1,r}}^{k_{1,r}} c_{sr} \mathop{\rightarrow}^{k_{2,r}} (1-p_r) \color{green} r | ||
| + | \end{align} | ||
| + | |||
| + | |||
| + | \begin{align} | ||
| + | \color{blue} m + \color{red}s &\mathop{\rightleftharpoons}_{k_{-1,s}}^{k_{1,s}} c_{ms} \mathop{\rightarrow}^{k_{2,s}} (1 - p_s) \color{red} s \\ | ||
| + | \color{red} s + \color{green} r &\mathop{\rightleftharpoons}_{k_{-1,r}}^{k_{1,r}} c_{sr} \mathop{\rightarrow}^{k_{2,r}} (1-p_r) \color{green} r | ||
| + | \end{align} | ||
| + | |||
| + | |||
| + | \begin{align} | ||
| + | \color{blue} m + \color{red}s &\mathop{\rightleftharpoons}_{k_{-1,s}}^{k_{1,s}} c_{ms} \mathop{\rightarrow}^{k_{2,s}} (1 - p_s) \color{red} s \\ | ||
| + | \color{red} s + \color{green} r &\mathop{\rightleftharpoons}_{k_{-1,r}}^{k_{1,r}} c_{sr} \mathop{\rightarrow}^{k_{2,r}} (1-p_r) \color{green} r | ||
| + | \end{align} | ||
| + | |||
| + | |||
| + | \begin{align} | ||
| + | \color{blue} m + \color{red}s &\mathop{\rightleftharpoons}_{k_{-1,s}}^{k_{1,s}} c_{ms} \mathop{\rightarrow}^{k_{2,s}} (1 - p_s) \color{red} s \\ | ||
| + | \color{red} s + \color{green} r &\mathop{\rightleftharpoons}_{k_{-1,r}}^{k_{1,r}} c_{sr} \mathop{\rightarrow}^{k_{2,r}} (1-p_r) \color{green} r | ||
| + | \end{align} | ||
| + | |||
| + | |||
\begin{align} | \begin{align} | ||
\color{blue} m + \color{red}s &\mathop{\rightleftharpoons}_{k_{-1,s}}^{k_{1,s}} c_{ms} \mathop{\rightarrow}^{k_{2,s}} (1 - p_s) \color{red} s \\ | \color{blue} m + \color{red}s &\mathop{\rightleftharpoons}_{k_{-1,s}}^{k_{1,s}} c_{ms} \mathop{\rightarrow}^{k_{2,s}} (1 - p_s) \color{red} s \\ | ||
\color{red} s + \color{green} r &\mathop{\rightleftharpoons}_{k_{-1,r}}^{k_{1,r}} c_{sr} \mathop{\rightarrow}^{k_{2,r}} (1-p_r) \color{green} r | \color{red} s + \color{green} r &\mathop{\rightleftharpoons}_{k_{-1,r}}^{k_{1,r}} c_{sr} \mathop{\rightarrow}^{k_{2,r}} (1-p_r) \color{green} r | ||
\end{align} | \end{align} | ||
Latest revision as of 16:27, 24 September 2012
{{{1}}}
Simplification and construction of ODEs
The general reaction scheme is \begin{align} \color{blue} m + \color{red}s &\mathop{\rightleftharpoons}_{k_{-1,s}}^{k_{1,s}} c_{ms} \mathop{\rightarrow}^{k_{2,s}} (1 - p_s) \color{red} s \\ \color{red} s + \color{green} r &\mathop{\rightleftharpoons}_{k_{-1,r}}^{k_{1,r}} c_{sr} \mathop{\rightarrow}^{k_{2,r}} (1-p_r) \color{green} r \end{align}
\begin{align} \color{blue} m + \color{red}s &\mathop{\rightleftharpoons}_{k_{-1,s}}^{k_{1,s}} c_{ms} \mathop{\rightarrow}^{k_{2,s}} (1 - p_s) \color{red} s \\ \color{red} s + \color{green} r &\mathop{\rightleftharpoons}_{k_{-1,r}}^{k_{1,r}} c_{sr} \mathop{\rightarrow}^{k_{2,r}} (1-p_r) \color{green} r \end{align}
\begin{align}
\color{blue} m + \color{red}s &\mathop{\rightleftharpoons}_{k_{-1,s}}^{k_{1,s}} c_{ms} \mathop{\rightarrow}^{k_{2,s}} (1 - p_s) \color{red} s \\
\color{red} s + \color{green} r &\mathop{\rightleftharpoons}_{k_{-1,r}}^{k_{1,r}} c_{sr} \mathop{\rightarrow}^{k_{2,r}} (1-p_r) \color{green} r
\end{align}
\begin{align}
\color{blue} m + \color{red}s &\mathop{\rightleftharpoons}_{k_{-1,s}}^{k_{1,s}} c_{ms} \mathop{\rightarrow}^{k_{2,s}} (1 - p_s) \color{red} s \\
\color{red} s + \color{green} r &\mathop{\rightleftharpoons}_{k_{-1,r}}^{k_{1,r}} c_{sr} \mathop{\rightarrow}^{k_{2,r}} (1-p_r) \color{green} r
\end{align}
\begin{align}
\color{blue} m + \color{red}s &\mathop{\rightleftharpoons}_{k_{-1,s}}^{k_{1,s}} c_{ms} \mathop{\rightarrow}^{k_{2,s}} (1 - p_s) \color{red} s \\
\color{red} s + \color{green} r &\mathop{\rightleftharpoons}_{k_{-1,r}}^{k_{1,r}} c_{sr} \mathop{\rightarrow}^{k_{2,r}} (1-p_r) \color{green} r
\end{align}
\begin{align}
\color{blue} m + \color{red}s &\mathop{\rightleftharpoons}_{k_{-1,s}}^{k_{1,s}} c_{ms} \mathop{\rightarrow}^{k_{2,s}} (1 - p_s) \color{red} s \\
\color{red} s + \color{green} r &\mathop{\rightleftharpoons}_{k_{-1,r}}^{k_{1,r}} c_{sr} \mathop{\rightarrow}^{k_{2,r}} (1-p_r) \color{green} r
\end{align}
