Escape through a system of fluctuating bottlenecks

Environmental effects on rate processes in complex dynamical systems, such as biomolecules, have drawn much interest in recent years, with emphasis 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 several geometric 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. A power law dependence K_eff ∼ η^-α, 1/2 ≤ α ≤ 1 is obtained.