PH-dependence of the steady-state rate of a two-step enzymic reaction

Abstract

The pH-dependence is considered of a reaction between E and S that proceeds through an intermediate ES under Briggs-Haldane conditions, i.e., there is a steady state in ES and [S]0 .mchgt. [E]T, where [S]0 is the initial concentration of S and [E]T is the total concentration of all forms of E. Reactants and intermediates are assumed to interconvert in 3 protonic states (E .dblarw. ES; EH .dblarw. EHS; EH2 .dblarw. EH2S), but only EHS provides products by an irreversible reaction whose rate constant is ~kcat.. Protonations are assumed to be so fast that they are all at equilibrium. The rate equation for this model is shown to be v = d[P]/dt = (~kcat.[E]T[S]0/A)/[(~KmBC/DA)+[S]0], where ~Km is the usual assembly of rate constants around EHS and A-D are functions of the form (1+[H]/K1+K2/[H]), in which K1 and K2 are in A, the molecular ionization constants of ES; in B, the analogous constants of E; and in C and D, apparent ionization constants composed of molecular ionization constants (of E or ES) and assemblies of rate constants. As in earlier treatments of this type of reaction which involve either the assumption that the reactants and intermediate are in equilibrium or the assumption of Peller and Alberty that only EH and EHS interconvert directly, the pH-dependence of kcat. is determined only by A. The pH-dependence of Km is determined in general by B.cntdot.C/A.cntdot.D, but when reactants and intermediate are in equilibrium, C .tbd. D and this expression simplifies to B/A. The pH-dependence of kcat./Km, i.e., of the rate when [S]0 .mchlt. Km, is not necessarily a simple bell-shaped curve characterized only by the ionization constants of B, but is a complex curve characterized by D/B.cntdot.C. Various situations are discussed in which the pH-dependence of kcat./Km is determined by assemblies simpler than D/B.cntdot.C. The special situation in which a kcat./Km-pH profile provides the molecular pKa values of the intermediate ES complex is delineated.