Extended Michaelis Menten Model Implementation in CADET-Core

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Dear CADET Community,

an extension of the implemented reaction modul Michaelis-Menten in CADET-Core has been done by including the influence of a non-substrate component (i.e. biomass) in form of a multiplication factor to the Michaelis-Menten kinetics of a reaction.

\begin{aligned} f_\text{react} = S \nu, \end{aligned} \newline \text{where } S \text{ is the stoichiometric matrix and } \nu \text{ a flux vector with } \newline \begin{aligned} \nu_{j} = \prod_{q = 1}^{N_{q,j}} K_{q,j} c_{q,j} \cdot v_{\mathrm{max},j} \prod_{i = 1}^{N_{sub,j}} \frac{ c_{i,j}}{K_{\mathrm{M}_{i,j}} + c_{i,j}} \end{aligned} \newline \text{for reaction $j$ and where}: \newline -c_{q,j} \text{ is biomass concentration (or any other component that has a prefactorial effect on the reaction rate)} \newline -K_{q,j} \text{ is the prefactorial constant (if no prefactorial effect it is set as false (integer value 0)} ) \newline -N_{q,j} \text{ components in }S \text{ that are not in } N_{sub,j} \text{ but have a prefactorial effect on the reaction rate}

The implementation includes the addition of an initialization parameter called MM_PRE_K which has the dimension [ \# reactions \times \# components ]. If a component has a prefactorial influence to the reaction, the parameter has to have a non-zero entry which is also used as a factor to the component concentration. The component can be used as an inhibition as well for the same reaction but not as a substrate.

By adding this functionality, the implementation of Monod kinetic and modeling of cell cultivations can be made possible with CADET.

A case study has been implemented for a reduced form of the model Kontoravdi et. al (2005) doi.org/10.1016/S1570-7946(05)80173-7 describing cell population kinetics and cell metabolism. Equation 1-16 are included in this case study without consideration of the hill kinetics and without the influence of m_{GLC}.

ResultsCADETvsAnalytical
ResultsCADETvsAnalytical1200×500 78.6 KB

Cadet_KontoravdiModel.zip (3.5 KB)

The detailed implementation and interface documentation can be found in the feature branch feature/extendMichaelisMenten

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