Defect diffusion and closed-time distributions for ionic channels in cell membranes

The ionic channels associated with proteins embedded in cell membranes often show a fluctuating behavior between open and closed states. A feature commonly observed is the long-time tail in the distribution f(t) of closed-state durations. A generalization of a defect-diffusion model recently proposed to explain this behavior is solved analytically for a one-dimensional geometry. The analysis involves the solution of a target annihilation problem with a finite annihilation rate for the target hit by a walker. While at short times f(t) may decay exponentially, at long times the solution is dominated either by a power law or a stretched exponential, depending on the initial defect configuration. The predictions of the model are shown to be in agreement with experimental data.