Protein folding kinetics: timescales, pathways and energy landscapes in terms of sequence-dependent properties

Recent experimental and theoretical studies have revealed that protein folding kinetics can be quite complex and diverse depending on various factors such as size of the protein sequence and external conditions. For example, some proteins fold apparently in a kinetically two-state manner, whereas others follow complex routes to the native state. We have set out to provide a theoretical basis for understanding the diverse behavior seen in the refolding kinetics of proteins in terms of properties that are intrinsic to the sequence.

The folding kinetics of a number of sequences for off-lattice continuum models of proteins is studied using Langevin simulations at two different values of the friction coefficient. We show for these models that there is a remarkable correlation between folding time, tau F, and sigma = (T theta - TF)/T theta, where T theta and TF are the equilibrium collapse and folding transition temperatures, respectively. The microscopic dynamics reveals that several scenarios for the kinetics of refolding arise depending on the range of values of sigma. For relatively small sigma, the chain reaches the native conformation by a direct native conformation nucleation collapse (NCNC) mechanism without being trapped in any detectable intermediates. For moderate and large values of sigma, the kinetics is described by the kinetic partitioning mechanism, according to which a fraction of molecules phi (kinetic partition factor) reach the native conformation via the NCNC mechanism. The remaining fraction attains the native state by off-pathway processes that involve trapping in several misfolded structures. The rate-determining step in the off-pathway processes is the transition from the misfolded structures to the native state. The partition factor phi is also determined by sigma: the smaller the value of sigma, the larger is phi. The qualitative aspects of our results are found to be independent of the friction coefficient. The simulation results and theoretical arguments are used to obtain estimates for timescales for folding via the NCNC mechanism in small proteins, those with less than about 70 amino acid residues.

We have shown that the various scenarios for folding of proteins, and possibly other biomolecules, can be classified solely in terms of sigma. Proteins with small values of sigma reach the native conformation via a nucleation collapse mechanism and their energy landscape is characterized by having one dominant native basin of attraction (NBA). On the other hand, proteins with large sigma get trapped in competing basins of attraction (CBAs) in which they adopt misfolded structures. Only a small fraction of molecules access the native state rapidly when sigma is large. For these sequences, the majority of the molecules approach the native state by a three-stage multipathway mechanism in which the rate-determining step involves a transition from one of the CBAs to the NBA.