Progress Curves in Enzyme Kinetics: Design and Analysis of Experiments

Abstract

Three shortcomings in progress curve analysis are discussed, and solutions or at least optimal strategies to overcome these problems are presented. (i) Systematic deviations in the progress curve data due to errors in the initial concentrations are taken into account in a linear approach by a proper weighting matrix in the parameter optimization. A transformation matrix, derived from the weighting matrix, leads to uncorrelated errors when applied to the data. The statistical tools developed for independent measurements can thus be applied to the transformed data. (ii) Model development by progress curve analysis is very cumbersome, since a progress curve does not reflect clearly the properties of the kinetics by visual inspection. Furthermore, the integration of the rate law leads to long computation times. These problems can be alleviated by determining the rates from the derivatives of a functional approximation of the progress curves. After developing a model using the rates, parameter refinement can be performed by fitting the original progress curve data. This procedure has the further advantage that optimization using the rate data is much less sensitive to the initial parameter estimates. (iii) The lack of inference from the visual inspection of progress curves also affects their experimental design. Methods mentioned in the literature that are applicable to the design of initial rate experiments, are extended for progress curves. The best results are obtained with a discrimination function that includes the statistical expectations of the minimum sum of squares.