Equilibrium Reaction Rates and the Mechanisms of Bovine Heart and Rabbit Muscle Lactate Dehydrogenases.

Almost all enzyme kinetic studies have been based on measurement of net chemical reaction. Isotopic tracer techniques make possible other types of kinetic measurements, including the rate of interconversion of reactants or interchange of atoms between substrates at equilibrium.1 Only very limited studies have been reported of such equilibrium rate measurements with known concentrations of all reactants (l-5). Studies by Boyer, Mills, and Fromm (4) and by Graves and Boyer (5) of the glutamine synthetase reaction at equilibrium have shown marked inequalities of exchange rates, interpretable in terms of substrate dissociation steps as rate-limiting, and have revealed oxygen transfer patterns which give insight into spatial selectivity among oxygen atoms of bound phosphoryl and carboxyl groups. The studies with glutamine synthetase (4) served as the stimulus ‘for the development by Boyer of theoretical relationships governing equilibrium rates in enzymic reaction systems (6). Alberty et al. (7) and Cleland (8) have subsequently presented other methods for development of such relationships for limiting cases with ordered addition of reactants, and Morales, Horovitz, and Botts (9) have considered transient states affecting isotope distribution when the concentration of enzymebound intermediates is appreciable. More recently, Boyer and Silverstein (10) have extended theoretical treatments to include random or nonlinear as well as linear routes to the formation of two interconvertible ternary complexes in twosubstrate, two-product systems. Fortunately, such complete equations are inherently simpler than initial rate equations because the concentrations of all intermediates in equilibrium reaction rate studies are governed by the respective equilibrium constants. The theoretical considerations suggest that equilibrium rate