BOUNDARY-CONDITIONS FOR SINGLE-ION DIFFUSION

We have constructed a theory for diffusion through the pore of a singl e-ion channel by taking a limit of a random walk around a cycle of sta tes. Similar to Levitt's theory of single-ion diffusion, one obtains b oundary conditions for the Nernst-Planck equation that guarantee that the pore is occupied by at most one ion. Two of the terms in the bound ary conditions are identical to those given by Levitt. However, the co nstruction gives rise to a third term not found in Levitt's theory. Wi th this term, the channel spends exponentially distributed intervals i n the empty state. ion sample paths have been simulated to help visual ize trajectories near the channel entrances, with and without the new term. We use the modified Levitt theory to fit several potential profi les to the conductance data of Russell et al. In particular, we have a nalyzed the profile for Na+ in gramicidin calculated by Roux and Karpl us. The peak-to-peak amplitude of their result must be reduced to at m ost 35% of its original value to fit the data, But with this reduction , excellent fits are obtained.