Molecular motion through correlated fluctuating bottlenecks

Environmental effects on rate processes in complex dynamical systems, such as biomolecules, have drawn much interest in recent years. Emphasis has been put on studies of escape over fluctuating barriers, which can generally be either energetic or geometric in character. Here we concentrate on the geometrical aspect, investigating the motion of molecules in a time-dependent environment that involves crossing of two correlated geometrical barriers which act as bottlenecks. We assume that the rate of passage through a bottleneck is proportional to its cross-sectional area. Fluctuations that may be solvent induced, and therefore viscosity dependent, change the cross-sectional area and thus affect the rate of passage. We calculate the dependence of the escape rate K_eff on the solvent viscosity η and on the correlation between the bottlenecks.