A mixed block diagram bond graph approach for biochemical models with mass action and rate law kinetics

Abstract

The use of a pseudo bond graph coupled with an algebraic block control structure is proposed to model biochemical systems with reactions defined by mass action and rate laws kinetics. The name “pseudo” refers to the assumption that the reactions are modelled by mass action kinetics with stoichiometric coefficients in power form. It is shown that the resulting model displays the topology of the stoichiometric reactions and of their enzymatic controls much more clearly than graphical methods used in chemistry. To illustrate the approach, several examples are presented: elementary enzymatic mechanisms, end product inhibition, enzymatic amplificatory cascade, simplified glycolysis. Finally, some “kinetic-like” models are presented: autocatalytic networks, Volterra systems, Goodwyn models of cellular controls.