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Michaelis Menten kineticsΒΆ

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

\[\begin{aligned} \nu_j = \frac{\mu_{\mathrm{max},j} c_S}{k_{\mathrm{MM},j} + c_S} \cdot \frac{1}{1 + \sum_i c_{Ii}/k_{I,j,i}}. \end{aligned}\]

Here, :math:k_{mathrm{I},j,i} is the inhibition constant with respect to component :math:i in reaction :math:j. If :math:k_{mathrm{I},j,i} leq 0, component :math:i does not act as an inhibitor.

Note: Currently, the model does not allow substrates to function as inhibitors.