Michaelis Menten kinetics

Implements liquid phase Michaelis-Menten reaction kinetics of the form

\[\begin{aligned} f_\text{react} = S \mathbf{\nu}, \end{aligned}\]

where \(S\) is the stoichiometric matrix and the fluxes are given by

\[\begin{aligned} \nu_j = \frac{\mu_{\mathrm{max},j} \, c_S}{k_{\mathrm{MM},j} + c_S}, \end{aligned}\]

where

• \(j\) is the reaction index,

• \(c_S\) is the substrate component,

• \(\mu_{\mathrm{max},j}\), is the limiting rate approached by the system at saturation,

• \(k_{\mathrm{MM},j}\) is the Michaelis constant, which is defined as the concentration of substrate at which the reaction rate is half ov \(\mu_{\mathrm{max},j}\).

In addition, the reaction might be inhibited by other components. In this case, the flux has the form

\[\begin{aligned} \nu_j = \frac{\mu_{\mathrm{max},j} \, c_S}{k_{\mathrm{MM},j} + c_S} \prod_i \frac{k_{\mathrm{I},j,i}}{k_{\mathrm{I},j,i} + c_{\mathrm{I},i}}. \end{aligned}\]

Here, \(k_{\mathrm{I},j,i}\) is the inhibition constant w.r.t component \(i\) and reaction \(j\). If \(k_{\mathrm{I},j,i} <= 0\), component \(i\) does not inhibit the reaction.