Figure 3. A kinetic model for ion and water permeation through the KcsA potassium channel.

A. A DSMM for the KcsA channel. The dark blue arrows indicate the transitions for efflux, and the violet for influx. B. Two examples of the expanded diagram. For the left diagram, transitions started from state 3 to state 1a (red line), and a trajectory of the branching tree is indicated by the white arrows. At each sub-state, returning paths for completing cycles were found. For each cycle, stoichiometric numbers were calculated. Among them, a cycle 4a → 5a → 7a → 4a gave the stoichiometry of zero for both ion and water flux, and thus it was not named. C. The expanded diagram. This diagram was constructed by setting the starting state as 3, from which the red lines were drawn for the initial transitions. The numbers indicate the state number followed by the sub-state alphabetical character. The arrows indicate the last transitions for completing a cycle. The solid arrows indicate the completing transitions for non-zero cycles, and they are labeled with the cycle names. The broken arrows are the completing transitions for cycles generating no net flux. There are six sub-cycles for cycle a+ and a−, but the rest of the cycles have only one. D. The cycles contributing to the non-zero net flux. The arrows indicate the direction of net efflux. The water-ion coupling ratios were assigned for each cycle. The green numbers represent the stoichiometric number for the ions and the red represent the water molecules.