Transient-phase kinetics of α-chymotrypsin and other enzyme systems

Abstract

A transient-phase method is described for obtaining values for the individual rate constants of a single-substrate two-intermediate enzyme mechanism. In principle, values of k 1, k −1 and k 3 can be obtained from such studies, as can values of inhibition constants k q and k −q from studies of a competitively-inhibited reaction. An experimental stopped-flow study is made for the α-chymotrypsin-catalyzed hydrolysis of p- nitrophenyl acetate, in the absence and presence of the inhibitor indole, and the results are consistent with the theoretical predictions. Values of k 1, k −1, k 2 and k 3 were obtained. The transient-phase equations for many enzyme systems, at limiting enzyme concentration, are in all cases of the form. x = vt + β + ∑ i=1 n β ie − λ i i where n, the number of exponential terms, is equal to the number of enzyme-containing intermediates in the mechanism (not counting the free enzyme). The sum of the exponents λ, i.e. ∑ i=1 n , is equal to the sum of all of the first-order rate constants, plus the sum of all the second-order rate constants each multiplied by the corresponding substrate or modifier concentration: ∑ i=1 n λ i = ∑ i k ic i + ∑ j k j where k i is a second-order rate constant and k j a first-order constant. This suggests general procedures for obtaining rate constants. Published results on α-chymotrypsin and alkaline phosphatase are reinterpreted in the light of the theory.