A simple model for a regulatory enzyme

A simple model for a regulatory enzyme is described which leads to relationships between the initial velocity of the catalysed reaction and the varied concentration of a substrate that are of the non-inflected or sigmoidal varieties without a maximum. The model assumes that the most relevant measure of protein configuration (itself determining the kinetic behaviour of the enzyme) is the apparent association constant, α_i, measured for the given fractional saturation of the ligand under investigation. It is further assumed that the original state of the protein in solution, α₀, is destabilized by an increment of energy, ΔG_p⁰, that is proportional to the fractional saturation of the enzyme by ligand so that the formation of a new configurational state, a,, can be represented by ?ΔG_p⁰ = RT ln $\text{α}{}_1\text{α}{}_0$. The rate or fractional saturation equation that can be derived from this model predicts both positive and negative cooperativity. Either equation can be transformed for linear representation, provided the maximum velocity or its equivalent maximum saturation is known, and estimates of α₀ and α_i (the apparent association constants at zero and complete saturation) can be obtained thereby. A procedure is also described by which an initial estimate of the maximum velocity or saturation can be improved. The model is tested by application to a range of data in the literature and it is shown to give fits to the data comparable in quality to those provided by the model of Monod, Wyman &; Changeux (1965).