Figure 1. Permeation processes through a single-file pore.

A. A schematic model for a narrow pore that allows passage of ions and water molecules only in single-file. B. A discrete-state Markov model for the channel having two binding sites. The two binding sites are either ion-occupied or not. There are four states, including the double-occupancy state. Tracing transition arrows (violet or blue) leads to cyclic paths (cycle a, b and c), and transitions around cycles generate the net flux (cycle flux). C. A Maxwell's demon stays at the inner pore entrance and takes account of the ion and water molecules in and out of the pore during the net influx. A time series of the random elementary steps (entering or exiting of either an ion or a water molecule) noted by the demon is shown. D. A time series of cycles deduced from a random sequence of ion and water pop-ups. A piece of the random sequence was lumped together and assigned to one of the one-way cycles, and the random sequence of ion-and-water pop-ups was converted to a series of one-way cycles. Detailed trajectories are reproduce by two demons in both sides of the pore. The cyclic sequence provides a more visual image of permeation processes than the simple random sequence. The sum of cycle fluxes gives the net flux.