Migration of a finite size ligand through a fluctuating bottleneck

A model for ligand migration within a protein, where the migration is controlled by an escape through a fluctuating bottleneck, has been introduced by Zwanzig (J. Chem. Phys. 97 (1992) 3587) for point ligands. We concentrate on the case where the ligand size is finite and larger than the characteristic thermal width of the bottleneck. An analytical solution for the escape rate of the ligand is derived and the dependence of the rate on the solvent viscosity is predicted. The prediction is confirmed by a numerical solution of the eigenvalue problem for the Smoluchowski equation with the sink term.