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

Abstract

1. 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]o greater than [E]T, where [S]o 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 three protonic states (E equilibrium ES; EH equilibrium EHS; EH2 equilibrium 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. 2. The rate equation for this model is shown to be v = d[P]/dt = (kcat.[E]T[S]o/A)/[(KmBC/DA) + [S]o], 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; in C and D, apparent ionization constants composed of molecular ionization constants (of E or ES) and assemblies of rate constants. 3. 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 & Alberty [(1959) J. Am. Chem. Soc. 81, 5907-5914] that only EH and EHS interconvert directly, the pH-dependence of kcat. is determined only by A. 4. The pH-dependence of Km is determined in general by B-C/A-D, but when reactants and intermediate are in equilibrium, C identical to D and this expression simplifies to B/A. 5. The pH-dependence of kcat./Km, i.e. of the rate when [S]o less than 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-C. 6. Various situations are discussed in which the pH-dependence of kcat./Km is determined by assemblies simpler than D/B-C. The special situation in which a kcat./Km-pH profile provides the molecular pKa values of the intermediate ES complex is delineated.

A convenient method of preparation of high-activity urease from Canavalia ensiformis by covalent chromatography and an investigation of its thiol groups with 2,2'-dipyridyl disulphide as a thiol titrant and reactivity probe

“…Thus ifthese reactions proceed through the intermediacy of an adsorptive complex, they were studied at reagent concentrations much less than the dissociation constant of the enzyme-reagent complex. The pHdependence of these apparent second-order rate constants, therefore, could provide information about native urease, although, if such complexes exist in non-equilibrium steady states, complications can exist (see Brocklehurst & Dixon, 1976).…”

The equilibrium assumption is valid for the kinetic treatment of most time-dependent protein-modification reactions

“…'= k-llk+l (4) The simplification that is introduced into the mechanistic interpretation of pH-k data by this assumption was discussed by Brocklehurst & Dixon (1976).…”

“…Even when saturation of enzyme by reagent cannot be detected, it may be dangerous to ignore complex-formation before covalency change, as has been demonstrated in connection with pH-rate studies (Brocklehurst & Dixon, 1976;Knowles, 1976b).…”

Benzofuroxan as a thiol-specific reactivity probe. Kinetics of its reactions with papain, ficin, bromelain and low-molecular-weight thiols

“…Reactions that are thus controlled include acylation by substrate during the catalytic act (see, e.g., Glazer & Smith, 1971), alkylation by both anionic alkylating agents such as chloroacetate (see, e.g., Chaiken & Smith, 1969) and uncharged alkylating agents such as chloroacetamide and methyl iodide (Polgar, 1973;Halasz & Polgar, 1976) and thiol-disulphide interchange with 2,2'-dipyridyl disulphide [see, e.g., Brocklehurst (1974) and Shipton et al (1975)]. Although all these reactions were studied under conditions that might reveal pKa values of ionizing groups in the enzyme molecule, the difficulties inherent in inferring such group pKa values from observed molecular pKa values are considerable (see Brocklehurst & Dixon, 1976;Knowles, 1976). Accordingly it is difficult to be sure that, for any one reaction, molecular pKa values reflected by profiles of pH against second-order rate constant approximate closely to pKa values characteristic of ionizing groups in the enzyme molecule.…”