Diffusion-assisted reaction through a fluctuating bottleneck

When a ligand escapes from a heme-pocket of a protein, the migration is geometrically controlled. A model is proposed by Zwanzig for a rate process that is controlled by passage through a fluctuating bottleneck. The model predicts that the long-time rate constant is inversely proportional to the square-root of the solvent viscosity, which is qualitatively consistent with experimentally observed rate constants. For a reverse process, namely, ligand rebinding to the heme from the solvent phase, diffusion motion of ligands in the solvent should be taken into account in addition to bottleneck fluctuations. In this article, we generalize the Zwanzig model in such a way to include the translational diffusion motion of ligands. The bimolecular rebinding rate is expressed in terms of a continued fraction which converges rapidly. It is shown that in this case the fractional power dependence does not hold for any values of the translational diffusion constant. (C) 2000 American Institute of Physics. [S0021-9606(00)52132-1].