FitSpace Explorer: An algorithm to evaluate multidimensional parameter space in fitting kinetic data

Fitting several sets of kinetic data directly to a model based on numerical integration provides the best method to extract kinetic parameters without relying on the simplifying assumptions required to achieve analytical solutions of rate equations. However, modern computer programs make it too easy to enter an overly complex model, and standard error analysis grossly underestimates errors when a system is underconstrained and fails to reveal the full degree to which multiple parameters are linked through the complex relationships common in kinetic data. Here we describe the application of confidence contour analysis obtained by measuring the dependence of the sum square error on each pair of parameters while allowing all remaining parameters to be adjusted in seeking the best fit. The confidence contours reveal complex relationships between parameters and clearly outline the space over which parameters can vary (the “FitSpace”). The utility of the method is illustrated by examples of well-constrained fits to published data on tryptophan synthase and the kinetics of oligonucleotide binding to a ribozyme. In contrast, analysis of alanine racemase clearly refutes claims that global analysis of progress curves can be used to extract the free energy profiles of enzyme-catalyzed reactions.