A new approach to understanding kinetic cooperativity when the Hill coefficients are less than 2

Abstract

The simple enzyme kinetic equation, V ̄ v = 1 + K [ S] + D (A + [ S]) , allows one to obtain more information than does the Michaelis-Menten equation, from many nonlinear Lineweaver-Burk double-reciprocal plots in terms of four useful empirical parameters V ̄ , K, D, and A . Thus, in the absence of substrate inhibition, maximum or minimum Hill coefficients ( H) from 0 to 2 are given by the expression H 2 (1 − H) = 4K D . Only the parameter D can be negative and this is associated either with positive kinetic cooperativity (1 < H < 2) or substrate inhibition (( K + D) ≤, 0). By assuming that dissociation of the product is an exchange reaction coupled with either binding of the substrate or a surrogate ligand (competitive inhibitor), a minimal model was obtained that defines these four empirical parameters in terms of only five specific chemical reaction rate constants that can, in fact, be evaluated experimentally. In this model negative kinetic cooperativity (0 < H < 1) results when the substrate displaces the modifier more easily than the product and positive kinetic cooperativity (1 < H < 2) when the converse is true, whether this occurs by a direct displacement or through allosteric interactions. This simple minimal model successfully predicts how the parameters vàry with the concentration of surrogate ligand (competitive inhibitor) in several instances. In particular a new equation [ 1 (H − 1) = α + β[ modifier]] that relates the Hill coefficient ( H) to the modifier concentration was derived and shown to be empirically valid for both Eschericia coli phosphofructokinase and yeast pyruvate kinase even though they have Hill coefficients up to 4.