Counting charges

Voltage-gated ion channels of excitable tissue have evolved an exquisite sensitivity to membrane potential. The open probability of a typical potassium or sodium channel, for example, may be increased by two orders of magnitude in response to a depolarization of less than 10 mV (Zagotta et al., 1994; Hirschberg et al., 1995). As recognized by Hodgkin and Huxley (1952), this responsiveness to changes of membrane potential is a consequence of the movement of charges during the conformational changes known as gating (see arguments in Sigworth, 1994). Charge transfer must occur across the membrane electric field during gating, and, in principal, it is possible to estimate the total number of elementary electronic charges (e0) completely transferred across the electric field to account for the voltage dependence of gating observed experimentally. We now know that ion channels are t ransmembrane proteins and that the charges which move during gating are likely to be comprised mainly of the amino acids of the so-called e~ subunits of sodium, potassium, and calcium channels. The usual assumption is that charge movement during gating is due to a rearrangement of the sidechains of highly charged amino acids, such as arginine, lysine, aspartate, or glutamate. However, it is worth considering that significant charge also resides in the atoms of neutral amino acids (Creighton, 1993). As a first step in understanding the molecular basis of voltage dependence and at identifying the important players in voltage sensitivity, it is necessary to know just how many charges move through the electric field as a channel undergoes a transformation from a resting closed state to an open configuration. This turns out to be a relatively trivial task for a channel with exactly two gating states: closed and open. For this two-state channel gating is de termined by two voltage-dependent rate constants: one for opening and the other for closing the channel. If these rate constants each depend exponentially on membrane potential, the relationship between steady-state open probability (Po) and voltage (V) will have the form of a Boltzmann function with a midpoint on the voltage axis of Vmi,t and a voltagedependen t equilibrium constant K(V),