The viscosity (eta) dependence of the folding rates for four sequences
(the native state of three sequences is a beta sheet, while the fourt
h forms an alpha helix) is calculated for off-lattice models of protei
ns. Assuming that the dynamics is given by the Langevin equation, we s
how that the folding rates increase linearly at low viscosities eta, d
ecrease as 1/eta at large eta, and have a maximum at intermediate valu
es. The Kramers' theory of barrier crossing provides a quantitative fi
t of the numerical results. By mapping the simulation results to real
proteins we estimate that for optimized sequences the time scale for f
orming a four turn alpha-helix topology is about 500 ns, whereas for b
eta sheet it is about 10 mu s.