The Michaelis-Menten reaction may be used to model enzyme kinetics where the enzyme $\mathcal{E}^{e}$ triggers the conversion of the substrate $\mathcal{E}^{s}$ into the product $\mathcal{E}^{p}$ . The product molar supply is given by $$\hat{c}^{p}=\begin{cases} \frac{V_{\max}c^{s}}{K_{m}+c^{s}} & c^{s}\geqslant c_{0}\\ 0 & c^{s}<c_{0} \end{cases}\,,$$ where $c^{s}$ is the substrate concentration. The default value of $c_{0}$ is 0. This relation may be derived, with some simplifying assumptions, by applying the law of mass action to the combination of two reactions, $$\mathcal{E}^{e}+\mathcal{E}^{s}\rightleftharpoons\mathcal{E}^{es}\to\mathcal{E}^{e}+\mathcal{E}^{p}$$ Since the enzyme is not modeled explicitly in the Michaelis-Menten approximation to these two reactions, this reaction model is effectively equivalent to $$\mathcal{E}^{s}\to\mathcal{E}^{p}.$$ Therefore, this reaction accepts only one reactant tag <vR> and one product tag <vP>. For consistency with the formulation of this reaction, the stoichiometric coefficients should be set to $\nu_{R}^{s}=\nu_{P}^{p}=1$ , so that $\hat{c}^{p}=\hat{\zeta}$ .

The constitutive form of the specific forward reaction rate $V_{\max}$ must be selected from the list of materials given in Section 4.11.4↓.

Example:

<reaction name="enzyme kinetics" type="Michaelis-Menten">
  <Vbar>0</Vbar>
  <vR sol="1">1</vR>
  <vP sol="2">1</vP>
  <forward_rate type="constant">
    <k>1.0</k>
  </forward_rate>
  <Km>5.0</Km>
</reaction>