Protein Folding Kinetics: Time Scales, Pathways, and Energy Landscapes in Terms of Sequence Dependent Properties

The folding kinetics of a number of sequences for off-lattice continuum model of proteins is studied using Langevin simulations at two values of the friction coefficient. We show that there is a remarkable correlation between folding times, $\tau _{F}$, and $\sigma = (T_{\theta } - T_{F})/T_{\theta } $, where $T_{\theta }$ and $T_{F}$ are the equilibrium collapse and folding transition temperatures, respectively. The microscopic dynamics reveals several scenarios for the refolding kinetics depending on the values of $\sigma $. Proteins with small $\sigma $ reach the native conformation via a nucleation collapse mechanism and their energy landscape is characterized by single dominant native basin of attraction. Proteins with large $\sigma $ get trapped in competing basins of attraction, in which they adopt misfolded structures. In this case only a small fraction of molecules $\Phi $ access the native state rapidly, the majority of them approach the native state by a three stage multipathway mechanism. The partition factor $\Phi $ is determined by $\sigma $: smaller the value of $\sigma $ larger is $\Phi $. The qualitative aspects of our results are found to be independent of the friction coefficient. Estimates for time scales for folding of small proteins via a nucleation collapse mechanism are presented.