Diffusion-assisted reaction through a fluctuating bottleneck

When a ligand escapes from a heme-pocket of a protein, the migration is geo metrically controlled. A model is proposed by Zwanzig for a rate process th at is controlled by passage through a fluctuating bottleneck. The model pre dicts that the long-time rate constant is inversely proportional to the squ are-root of the solvent viscosity, which is qualitatively consistent with e xperimentally observed rate constants. For a reverse process, namely, ligan d rebinding to the heme from the solvent phase, diffusion motion of ligands in the solvent should be taken into account in addition to bottleneck fluc tuations. In this article, we generalize the Zwanzig model in such a way to include the translational diffusion motion of ligands. The bimolecular reb inding rate is expressed in terms of a continued fraction which converges r apidly. It is shown that in this case the fractional power dependence does not hold for any values of the translational diffusion constant. (C) 2000 A merican Institute of Physics. [S0021-9606(00)52132-1].