THE REVERSIBLE HILL EQUATION - HOW TO INCORPORATE COOPERATIVE ENZYMESINTO METABOLIC MODELS

Motivation: Realistic simulation of the kinetic properties of metaboli c pathways requires rate equations to be expressed in reversible form, because substrate and product elasticities are drastically different in reversible and irreversible reactions. This presents no special pro blem for reactions that follow reversible Michaelis-Menten kinetics, b ut for enzymes showing cooperative kinetics the full reversible rare e quations are extremely complicated, and anyway in virtually all cases the fill equations are unknown because sufficiently complete kinetic s tudies have not been carried out. There is a need, therefore, for appr oximate reversible equations that allow convenient simulation without violating thermodynamic constraints. Results: We show how the irrevers ible Hill equation can be generalized to a reversible form, including effects of modifiers, The proposed equation leads to behaviour virtual ly indistinguishable from that predicted by a kinetic form of the Adai r equation, despite the fact that the latter is a far more complicated equation. By contrast, a reversible form of the Monod-Wyman-Changeux equation that has sometimes been used lends to predictions for the eff ects of modifiers at high substrate concentration that differ qualitat ively from those given by the Adair equation.