Analysis of Hill slopes predicted by the four-ligand exponential model for a regulatory enzyme

The four-ligand exponential model for a regulatory enzyme is described as it is applied to kinetic studies of yeast pyruvate kinase in which the concentrations of four ligands are systematically varied. The Hill slopes predicted by this model are calculated for the two situations in which the fourth ligand is either a substrate or an effector. It is shown that the individual terms that make up the expression for the Hill slope assist the interpretation of the observed behaviour in terms of the constants employed by the model.