Viscosity dependence of passage through a fluctuating bottleneck

We generalize the model of a rate process involving the passage of an object through a fluctuating bottleneck. The rate of passage is considered to be proportional to a power function of the radius of the bottleneck with exponent alpha > 0. The fluctuations of the bottleneck are coupled to the motion of the surrounding medium and governed by Langevin dynamics. We show numerically and also explain analytically that for slow bottleneck fluctuations the long time decay rate of the process has a fractional power law dependence on the solvent viscosity with exponent alpha/(alpha + 2). The results are consistent with the experimental data on ligand binding to myoglobin, and might also be relevant to other reactions for which exponents between 0 and 1 were reported. (C) 2014 AIP Publishing LLC.