Evaluation of first-order kinetic transients encountered during enzyme assay

Abstract

A method is described for the measurement of the rate parameters which describe first-order kinetic transients often encountered during enzyme assay. This evaluation is accomplished by fitting the data to the general expression describing first-order transients. A method which obviates the need to perform a conventional nonlinear least-squares analysis is described. The partial derivative of the variance of the fit with respect to the transient rate constant has been solved explicity and is shown to be solely a function of the data. The root of this function yields the optimum value for the transient rate constant and can be easily determined by performing a simple, bisectional root finding algorithm. Using this transient rate constant, the remaining rate parameters, i.e., the initial and steady state rate of reaction, are subsequently determined via a straightforward multiple linear regression of the data to the general first-order rate expression. The derivation of this expression as well as the formulas to be used in performing these calculations are presented. Advantages and limitations of evaluating assays in this manner are discussed in relation to existing procedures. Assay in which the steady state cannot be fully achieved before the assay must be terminated are especially appropriate to this procedure. This method saves time and is not as subjective as conventional graphical methods. The calculations described are ideally suited to, though not restricted to, situations where a computer is on line with the measurement device during assay. Limitations on the usefulness of this method occur when the first-order model is an inappropriate description of the transient in question.