Boundary conditions for- single-ion diffusion

Abstract

We have constructed a theory for diffusion through the pore of a single-ion channel by taking a limit of a random walk around a cycle of states. Similar to Levitt's theory of single-ion diffusion, one obtains boundary conditions for the Nernst-Planck equation that guarantee that the pore is occupied by at most one ion. Two of the terms in the boundary conditions are identical to those given by Levitt. However, the construction gives rise to a third term not found in Levitt's theory. With this term, the channel spends exponentially distributed intervals in the empty state. Ion sample paths have been simulated to help visualize trajectories near the channel entrances, with and without the new term. We use the modified Levitt theory to fit several potential profiles to the conductance data of Russell et al. In particular, we have analyzed the profile for Na+ in gramicidin calculated by Roux and Karplus. The peak-to-peak amplitude of their result must be reduced to at most 35% of its original value to fit the data. But with this reduction, excellent fits are obtained.