ZONE BEHAVIOR OF ENZYMES

Abstract

1. The kinetics of the reversible combination of one enzyme center with one molecule of a substrate or inhibitor is treated as a true bimolecular instead of a pseudomonomolecular reaction. The general equations describing such a reaction are presented and analyzed algebraically and graphically. 2. A new term, "specific concentration," is introduced to denote the concentration of reactants in units equal to the dissociation constant. Its use makes the kinetic equations universally applicable to all reversible systems of the given type. 3. It is shown that such a system exhibits three "zones" of behavior. Each zone is characterized and shown to exhibit significant differences in the function relating the concentrations of the components of the system at equilibrium. The zone boundaries are rigorously defined in terms of the specific enzyme concentration, for the mathematical error tolerable with a given experimental accuracy; and approximate boundaries for practical use are proposed. 4. The classical treatment of enzyme kinetics is shown to be a limiting case valid only for low specific enzyme concentrations (zone A) and to be inapplicable in a number of systems whose dissociation constants are very small or whose molar enzyme concentrations are very great, and in which, therefore, the specific enzyme concentrations are large. See Table I for a summary of zone differences. 5. In an enzyme system containing substrate or inhibitor, dilution before determination of reaction velocities is shown to be a crucial operation, entailing large changes in the fraction of enzyme in the form of a complex. The changes in fractional activity or inhibition with dilution are shown to be a function of specific enzyme concentration, the dilution factor, and the fraction of enzyme initially in the form of complex. Equations are given permitting the calculation of the state of the system at any concentration. The errors introduced into physiological work by failure to take the dilution effect into account are pointed out. 6. Experimental data are presented showing that the system composed of serum cholinesterase and physostigmine behaves as predicted by the dilution effect equations. 7. Two other conclusions of practical pharmacological importance are drawn from the theory of zone behavior: (a) The finding that a biological response is a linear function of the dose of a drug does not necessarily mean that the reaction is irreversible, but only that if reversible, the reactant with which the drug combines has a high specific concentration. (b) If a tissue enzyme has a high specific concentration, all reversible inhibitors will be equally potent in combining with it, regardless of their relative potency in dilute systems; provided only that their dissociation constants are within certain broad limits. 8. It is shown how the type of analysis here applied to bimolecular reactions can be applied in toto to systems of the type E + nX ⇋ EXn, where n molecules of substrate or inhibitor unite with one enzyme center. The zone boundaries and the magnitude of the dilution effect change with n, but the general characteristics of the zones are the same for all values of n. 9. Since the analysis is based only on mass law assumptions, it is applicable to any system that is formally analogous to the one here treated.