The exponential model for a regulatory enzyme: Its extension to describe the binding of two ligands

The exponential model for a regulatory enzyme (Ainsworth, 1977a) is extended to deal explicitly with the presence in solution of a second ligand. This is achieved by introducing exponential interaction coefficients which respectively describe how the affinity of the free and bound forms of the protein for the ligand depend on its fractional saturation by the second ligand. The basic equations, so derived, are applied to binding experiments where the ligands bind independently or competitively and to rate experiments where the ligands represent two substrates or one substrate and a modifier which may be either competitive or non-competitive in type. The conditions required to display linkage between the binding of the two ligands are established and it is also shown that rate data may display a maximum as one ligand concentration is varied at a fixed concentration of the other. The equations that are derived are tested by application to experimental data and the conditions that have to be met to justify such an application are discussed.