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 + deltat, and t + 2deltat. 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.