Colored noise, folding rates and departure from Kramers' behavior

Recent experiments have shown that, for several proteins, the dependence of folding and unfolding rates on solvent viscosity does not obey Kramers' theory. Such a departure from standard Kramers' behavior is often attributed to the existence of internal friction, related to the structure of a polypeptide chain. In this paper, we propose an entirely different mechanism leading to violation of Kramers' theory. Using the generalized Langevin equation with time-dependent friction and a C α -Go model, we demonstrate that this effect may be caused by the colored Gaussian noise which is characterized by correlation time τ . Surprisingly, the dependence of folding time t f on τ is non-trivial: the plot t f vs τ exhibits two minima at low and intermediate values of τ . The appearance of one more additional minimum is in sharp contrast to one dimensional barrier crossing dynamics. We argue that it is a generic signature of entropy of activation in a multidimensional problem. A first theoretical attempt is made to explain the violation of Kramers' theory for the dependence of protein folding rates on viscosity, using the colored noise theory.