Network Library

This page presents a list of sensitivity equations for a selection of network motifs.

Linear Chains

Two step pathway:

    \[X_o \stackrel{v_1}{\longrightarrow} S_1 \stackrel{v_2}{\longrightarrow} X_1\]

    \begin{align*} C^{S_1}_{E_1} &= \frac{1}{\varepsilon^2_1 - \varepsilon^1_1} \\[5pt] C^{S_1}_{E_2} &= -\frac{1}{\varepsilon^2_1 - \varepsilon^1_1} \\[5pt] C^J_{E_1} &= \frac{\varepsilon^2_1}{\varepsilon^2_1 - \varepsilon^1_1} \\[5pt] C^J_{E_2} &= -\frac{\varepsilon^1_1}{\varepsilon^2_1 - \varepsilon^1_1} \end{align*}

Three step pathway:

    \[X_o \stackrel{v_1}{\longrightarrow}S_1 \stackrel{v_2}{\longrightarrow} S_2 \stackrel{v_3}{\longrightarrow} X_1\]

    \begin{align*} C^J_{E_1} &= \varepsilon^{2}_1 \varepsilon^{3}_2 / D \\[5pt] C^J_{E_2} &= -\varepsilon^{1}_1 \varepsilon^{3}_2 / D \\[5pt] C^J_{E_3} &= \varepsilon^{1}_1 \varepsilon^{2}_2 / D \end{align*}

where D the denominator is given by:

    \[D = \varepsilon^{2}_1 \varepsilon^{3}_2 -\varepsilon^{1}_1 \varepsilon^{3}_2 + \varepsilon^{1}_1 \varepsilon^{2}_2\]

    \begin{align*} C^{S_1}_{E_1} &= (\varepsilon^{3}_2 - \varepsilon^{2}_2) / D \\[5pt] C^{S_1}_{E_2} &= - \varepsilon^{3}_2 / D \\[5pt] C^{S_1}_{E_3} &= \varepsilon^{2}_2 / D \\ \end{align*}

And for S_2

    \begin{align*} C^{S_2}_{E_1} &= \varepsilon^{2}_1 / D \\[5pt] C^{S_2}_{E_2} &= -\varepsilon^{1}_1 / D \\[5pt] C^{S_2}_{E_3} &= (\varepsilon^{1}_1 - \varepsilon^{2}_1) / D \end{align*}

Negative Feedback

Branches

Cycles

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