One-Dimensional Free Energy Surface Models of Protein Folding: Connecting Theory and Experiments

Abstract

Experimental techniques have now reached the sub-microsecond timescale necessary to study fast events in protein folding. However, analysis of fast folding experiments still commonly rely on conventional procedures that provide an oversimplified picture i.e. an all-or-none transition between the unfolded and native states, which is not valid for all cases. Moreover, due to the presence of discrepancies between theoretical predictions and experimental observations, discerning the correct mechanisms of protein folding becomes difficult. This is true even for the most elementary processes such as a-helix formation. Recent laser-induced temperature jump experiments on a-helical peptides have revealed unprecedented complexity in relaxation kinetics. These observations are suggested to be incompatible with the nucleation-elongation theory for a-helix formation. However, the detailed kinetic model based on nucleation-elongation theory developed in this work quantitatively reproduces all the observed complex kinetics. The results are rationalized using a simple one-dimensional projection of free energy surface. It is concluded that the observed probe-dependent and thermal perturbation size-dependent multiphasic relaxation kinetics are consequences of helix fraying and heterogeneity of peptide sequence. Remarkably, all the kinetic behaviors predicted by the detailed model are successfully reproduced by diffusion on one-dimensional free energy surface. The one-dimensional free energy approach thus validated empirically is then extended for the analysis of protein folding experiments. For this purpose a simple mean field model is formulated that is consistent with the size-scaling properties of thermodynamic parameters as well as with the observation of entropy convergence at high temperatures. The model describes the effects of chemical and thermal denaturation, making it amenable for direct comparison with experimental observables i.e. folding rates and heat capacity changes on a quantitative level. The main advantage of the model is the treatment in which free energy barrier on one-dimensional profile is allowed to modulate by just one parameter, that can be directly related to protein size, structure- and sequence- dependent energetics. Recently the one-dimensional free energy surface model has been applied for analyzing the dependence of rates on temperature and chemical denaturant in fast folding proteins. This analysis has allowed simultaneous investigation of energetic and dynamic factors governing folding kinetics. Unlike traditional methods the model serves as an analytical tool without making any a priori assumptions about the presence of a barrier. With its simplicity and versatility the model provides the foundation for exploring general trends in protein folding as well as prediction of folding properties at the level of individual proteins.