The analysis of enzyme progress curves by numerical differentiation, including competitive product inhibition and enzyme reactivation

Abstract

A new method for analyzing steady-state enzyme kinetic data is presented. The technique, which is based on the numerical differentiation of the complete reaction curve, has several advantages over initial velocity and integrated Michaelis-Menten equation methods. The differentiated data are fit to the differential equation describing the appropriate kinetic scheme. This approach is particularly valuable in cases of strong competitive product inhibition and of changing concentrations of active enzyme. The method assumes a reversible reaction and is applicable to a very wide variety of steady-state kinetic schemes. A particular advantage of this approach over integrated methods is that it is independent of [S 0] and hence of errors in [S 0]. The combination of complete progress curve and computer analysis makes this approach very efficient with respect to both time and materials. Running on an IBM PC XT or equivalent microcomputer with an 8087 coprocessor, the analyses are very fast, the complete process usually being complete in a minute or two. The utility of the technique is demonstrated by application to both simulated and real data. We show that the differentiation of the progress curve for the ribonuclease-catalyzed hydrolysis of 2′, 3′-cyclic cytidine monophosphate reveals strong product inhibition by 3′-CMP, and this product inhibition accounts for the large discrepancies reported in the literature for the value of K m for this substrate. The method was also applied to determine the rate of reactivation of β-lactamase which had been reversibly inactivated by cloxacillin. Since large numbers of data points are required for the numerical differentiation the method has become practical only with the advent of computer-acquired data systems.