Coordinate and time-dependent diffusion dynamics in protein folding

We developed both analytical and simulation methods to explore the diffusion dynamics in protein folding. We found the diffusion as a quantitative measure of escape from local traps along the protein folding funnel with chosen reaction coordinates has two remarkable effects on kinetics. At a fixed coordinate, local escape time depends on the distribution of barriers around it, therefore the diffusion is often time distributed. On the other hand, the environments (local escape barriers) change along the coordinates, therefore diffusion is coordinate dependent. The effects of time-dependent diffusion on folding can lead to non-exponential kinetics and non-Poisson statistics of folding time distribution. The effects of coordinate dependent diffusion on folding can lead to the change of the kinetic barrier height as well as the position of the corresponding transition state and therefore modify the folding kinetic rates as well as the kinetic routes. Our analytical models for folding are based on a generalized Fokker-Planck diffusion equation with diffusion coefficient both dependent on coordinate and time. Our simulation for folding are based on structure-based folding models with a specific fast folding protein CspTm studied experimentally on diffusion and folding with single molecules. The coordinate and time-dependent diffusion are especially important to be considered in fast folding and single molecule studies, when there is a small or no free energy barrier and kinetics is controlled by diffusion while underlying statistics of kinetics become important. Including the coordinate dependence of diffusion will challenge the transition state theory of protein folding. The classical transition state theory will have to be modified to be consistent. The more detailed folding mechanistic studies involving phi value analysis based on the classical transition state theory will also have to be quantitatively modified. Complex kinetics with multiple time scales may allow us not only to explore the folding kinetics but also probe the local landscape and barrier height distribution with single-molecule experiments.