An error analysis for two-state protein-folding kinetic parameters and θ-values: Progress toward precision by exploring pH dependencies on leffler plots

Abstract

The interpretation of θ-values has led to an understanding of the folding transition state ensemble of a variety of proteins. Although the main guidelines and equations for calculating θ are well established, there remains some controversy about the quality of the numerical values obtained. By analyzing a complete set of results from kinetic experiments with the SH3 domain of α-spectrin (Spc-SH3) and applying classical error methods and error-propagation formulas, we evaluated the uncertainties involved in two-state-folding kinetic experimental parameters and the corresponding calculated θ-values. We show that kinetic constants in water and m values can be properly estimated from a judicious weighting of fitting errors and describe some procedures to calculate the errors in Gibbs energies and θ-values from a traditional two-point Leffler analysis. Furthermore, on the basis of general assumptions made with the protein engineering method, we show how to generate multipoint Leffler plots via the analysis of pH dependencies of kinetic parameters. We calculated the definitive θ-values for a collection of single mutations previously designed to characterize the folding transition state of the α-spectrin SH3 domain. The effectiveness of the pH-scanning procedure is also discussed in the context of error analysis. Judging from the magnitudes of the error bars obtained from two-point and multipoint Leffler plots, we conclude that the precision obtained for θ-values should be ∼25%, a reasonable limit that takes into account the propagation of experimental errors. © 2008 by the Biophysical Society.