Apparent first-order behavior under second-order kinetic conditions: A general concept illustrated by the reversible binding of hydrogen peroxide to cytochrome c oxidase

Abstract

The theory of the second-order reversible reaction, A + B<-->A.B, has been extensively discussed. Apparent first-order behavior is observed when, for example, [B] >> [A]. If the reaction exhibits second-order behavior then it is presumed that the concentrations of A and B were initially equal and that they remain equal during the reaction. However, in the case of hydrogen peroxide binding to cytochrome c oxidase, Weng & Baker (1991, Biochemistry 30, 5727-5733) showed that the observed rate was rigorously first order over a broad concentration range of ligand, including the stoichiometric case. It was further shown that kobs increased linearly with [H2O2], precluding the possibility of a rate-limiting, unimolecular pre-step. The current work examines the theoretical rate equation for the bimolecular, reversible reaction when [A] = [B]. Simulations show that this equimolar condition resulted in rigorous exponential binding as kd, the equilibrium dissociation constant for the A.B complex, approached the initial concentration of A (or B). In particular, the second-order simulation was rigorously exponential when [A]o/Kd = 0.5, and showed only minor deviations when the ratio was increased to 25. These results demonstrate that a reversible, bimolecular reaction can appear first order even under second order conditions, without the need for more complicated mechanisms.