Continuum model of voltage-dependent gating. Macroscopic conductance, gating current, and single-channel behavior

It is assumed that the conformational change of the voltage-gated channel is continuous, characterized by movement along a generalized one-dimensional reaction coordinate, x, varying from 0 to 1. This large conformational change is coupled to the movement of most of the gating charge. Superimposed on this large movement is a smaller, very fast conformational change that opens or closes the channel. The large conformational change perturbs the channel so that opening is favored near x = 1 and closing is favored near x = 0. The movement along the x axis is described by a generalized Nernst-Planck equation, whereas the open-close transition is modeled as a discrete reaction-rate process. The macroscopic conductance, gating current, and single-channel behavior of a simple, linearized version of the model is described. Although the model has only seven adjustable constants (about the same as would be required for a conventional three-state model), it can mimic the behavior of the delayed rectified K+ channel with 12 or more closed states. The single-channel behavior of the model can have bursts of rapid openings and closings, separated by long closed times. If the conformational change is assumed to correspond to the rotation and translation of charged helices, then this model can be used to estimate the effective rotational diffusion coefficient of the helix. Such calculations for the delayed rectifier K+ channel indicate that the motion must be very restricted.