Full-Scale Mechanistic Gray-Box Modeling

Full-scale mechanistic gray-box modeling is the most common type of modeling currently employed in the systems biology community. The attribute mechanistic is included to denote that the model structure is based on the assumptions of what 

In practice, a gray-box model is developed in steps. One early step is to decide which variables and interactions to include. This is often done by the sketching of an interaction-graph. It must then be decided if a variable should be a state or a dependent variable, and how the interactions should be formulated. In the case of metabolic reactions, the expression forms for the reactions have often been characterized in in-vitro experiments. If this has been done, there are also often in-vitro estimates of the kinetic parameters. For enzymatic networks, however, such in-vitro studies are much more rare, and it is hence typically less known which expression to choose for the reaction rates, and what a good estimate for the kinetic parameters is. In any case, the standard method of combining reaction rates, r,-, and an interaction graph into a set of differential equations is to use the stoichiometric coefficients, Sij 

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