Transition paths, diffusive processes, and preequilibria of protein folding.

Fundamental relationships between the thermodynamics and kinetics of protein folding were investigated using chain models of natural proteins with diverse folding rates by extensive comparisons between the distribution of conformations in thermodynamic equilibrium and the distribution of conformations sampled along folding trajectories. Consistent with theory and single-molecule experiment, duration of the folding transition paths exhibits only a weak correlation with overall folding time. Conformational distributions of folding trajectories near the overall thermodynamic folding/unfolding barrier show significant deviations from preequilibrium. These deviations, the distribution of transition path times, and the variation of mean transition path time for different proteins can all be rationalized by a diffusive process that we modeled using simple Monte Carlo algorithms with an effective coordinate-independent diffusion coefficient. Conformations in the initial stages of transition paths tend to form more nonlocal contacts than typical conformations with the same number of native contacts. This statistical bias, which is indicative of preferred folding pathways, should be amenable to future single-molecule measurements. We found that the preexponential factor defined in the transition state theory of folding varies from protein to protein and that this variation can be rationalized by our Monte Carlo diffusion model. Thus, protein folding physics is different in certain fundamental respects from the physics envisioned by a simple transition-state picture. Nonetheless, transition state theory can be a useful approximate predictor of cooperative folding speed, because the height of the overall folding barrier is apparently a proxy for related rate-determining physical properties.