A graphical method for extracting rate constants from some enzyme-catalyzed reactions not monitored to completion

A large number of enzyme-catalyzed reactions can be described by the equation y = At−B(1−e−kt) where y is the amount of product formed, A is the slope of the linear portion of the curve, and B is a constant dependent on the mechanism of the reaction. The methods which are generally used to extract the rate constant, k, from absorbance–time data described by this equation require that the reaction be monitored for some 10 to 15 half-lives. We show herein that the rate constant k is readily obtained from a plot of (y″−y′) vs. (y′−y0) where y0, y′, and y″ are the values of y at times t, t + Δt, and t + 2Δt. This graphical method is simple, reliable, and requires that the reaction be monitored for only three to five half-lives of the exponential phase of the reaction.We have used this method to measure the rate of activation of a mixed disulfide of papain and 2-nitro-5-mercaptobenzoic acid in the presence of substrate.