A mesoscopic approach to understanding the mechanisms underlying the ion permeation on the discrete-state diagram

a broad range of per-meation events from femtoseconds to minutes in time scale and sub-angstrom to millimeter in space were discussed. A main message in the Perspectives was to explore each discipline to expand its limitation, such that different levels of knowledge in a hierarchy of ion permeation events are integrated. Here, we propose another approach from a mesoscopic point of view. Electrophysiologists are familiar with single-channel currents, a macroscopic event in terms of ion permeation (Fig. 1 A). They have postulated the underlying mechanisms of ion permeation processes from a top-down point of view. On the other hand, recent progress of the computer simulation enabled visualization of the ion tra-jectories through channel molecules, which provided microscopic views of permeation processes (Bernèche and Roux, 2001). One is eager to understand a whole range of events by integrating microscopic trajectories into macroscopic observables, but it has not been successful because the " reality " and these microscopic trajec-tories have remained far apart. To bridge the gap, electrophysiologists have developed a tool to relate single-channel currents to the discrete state Markov model (DSMM) for permeation. Ion distributions are segregated into a few representative " states, " and connecting these states create a discrete-state diagram (Fig. 1, A→B). A random walk on the diagram leads to the net flux of the reaction (or permeation; Fig. 1 B) (Andersen, 1989; Miller, 1999). Single-channel current recordings under various experimental conditions were collected, and the set of rate constants for the diagram was optimized for the experimental data. These values have been used to draw the free energy profile of ion permeation (Fig. 1, B→C). In this procedure , the ion trajectory in real space is converted to the free energy profile as a function of the electrical distance. Thus, in this line of thinking, the permeation is considered as a simplified motion on linear coordinates of either the real space (Fig. 1 A) or the electrical distance (Fig. 1 C). Abbreviation used in this paper: DSMM, discrete-state Markov model. We present here an alternative way of conceptualizing the permeation processes (Ando et al. The water-ion coupling ratio for ion permeation through the KcsA potassium channel: dependencies on concentration and species of permeating ions. 2009. Biophys. J. Abstr. 927; unpublished data). Our proposal is to trace the processes as cyclic paths on the DSMM (Fig. 1, B→D) rather than linear coordinates. This is a slight modification …