Viscosity dependence of the folding rates of proteins

The viscosity (eta) dependence of the folding rates for four sequences (the native state of three sequences is a beta sheet, while the fourth forms an alpha helix) is calculated for off-lattice models of proteins. Assuming that the dynamics is given by the Langevin equation, we show that the folding rates increase linearly at low viscosities eta, decrease as 1/eta at large eta, and have a maximum at intermediate values. The Kramers' theory of barrier crossing provides a quantitative fit of the numerical results. By mapping the simulation results to real proteins we estimate that for optimized sequences the time scale for forming a four turn alpha-helix topology is about 500 ns, whereas for beta sheet it is about 10 mu s.