Studies On The Mechanism Of Two-state And One-state Protein Folding

Protein folding is one of the most advanced topics in biology. To quantitatively explain the facts observed in experiments and co-explain the mechanism of both downhill protein and two-state protein folding, a general protein-folding model is proposed at the amino acid level in this paper.Considering the different effects of the "stochastic interactions" of solvent molecules and the "order interactions" among atoms in polypeptide in different folding stages, we divide the folding process of protein into two successive phases: the rate-determining step, dominated by the "stochastic interactions" of solvent molecules, and the rapid phase, dominated by the "order interactions" among atoms in polypeptide. Suppose that the total number of native contacts is N, from the beginning of folding to the formation of the Nth native contact is the first stage, while conformational changes between forming all N native contacts to final folded state is the second stage. The second phase goes downhill in free energy, and is regarded as an almost instantaneous process. Hence the first phase is approximately considered as the protein-folding time here. The master equation approach is used to investigate the folding kinetics in the theory, and an analytical treatment of the master equation yields a simple three-parameter expression for folding time (or folding rate). Further analysis shows that, both two-state and downhill protein folding can be described by a unifying model, depending on different folding conditions, and therefore the different parameter values in the model.A set of 66 small two-state proteins are selected in the study, where all the folding rates and native structures were measured by experiment. We write a program to calculate the number of native contacts of these proteins. It is found that the relationship between the natural logarithm of folding rate and the number of native contacts is nearly linear, which is consistent with the results predicted by the theoretical model. Due to the controversy surrounding the experiments and the lack of accepted experimental data, it is difficult at present to directly verify the theoretical predict by a set of valid downhill folding proteins. However, the folding speed limit that experimental and theoretical approaches predict is close.On the one hand, the established unifying model of protein folding makes up the defect that the popular folding models can not explain some experimental phenomena quantitatively; on the other hand, it can be used to describe both two-state protein folding and one-state protein folding. Hope our work can provide useful inspiration to the further study of protein folding mechanism.