Analysis of progress curves in enzyme kinetics.

Since Michaelis & Menten (1913) demonstrated that many of the problems encountered by earlier workers in enzyme kinetics could be avoided by measuring initial rates and using kinetic equations in their differential forms, most biochemists have been reluctant to use integrated rate equations. However, confining analysis to the initial linear part of a progress curve wastes much of the available information , and also wastes materials and time, because more experiments are needed to obtain estimates of the kinetic parameters. Balcom & Fitch (1970) have proposed a method of analysing progress curves in which the kinetic equations are used in their familiar differential forms, by estimating the velocities at different times in the experiment from the differences between adjacent points on the curve. For a set of observations of substrate concentrations, so, s1, (1) for values of i from 1 to n-1. From this set of velocities and substrate concentrations they obtain estimates of the kinetic parameters by means of the computer programs of Cleland (1963). The method of Balcom & Fitch (1970) would, if valid, be an extremely valuable one, because it would permit the highly developed techniques for analysing rate equations to be applied to progress curves. This would permit much more information to be obtained from each experiment, and it would remove the subjective element inherent in most estimates of initial rates. Unfortunately the method is not valid, because most of the observations are given very little weight in the analysis. It has long been recognized (Roseveare, 1931) that methods similar to that of Balcom & Fitch (1970) are unsuitable for estimating the slopes of straight-line plots, because all points except the first two and last two cancel out in the calculations. The analysis is less simple for enzyme kinetic equations, but the conclusions to be drawn are similar. Intuitively, one would expect that an error in any point other than the first two or the last two would produce equal and opposite errors in two velocity estimates, which would approximately cancel Vol. 130 one another out in the estimates of the kinetic parameters. More detailed examination supports this expectation. Balcom & Fitch (1970) discussed their method in connexion with a mechanism involving a significant back reaction and product inhibition, and proposed that it could be used generally for complex rate equations. However, any general method ought to be valid for the simplest cases, and the Michaelis-Menten …