Voltage-dependent gating in K channels: experimental results and quantitative models

Voltage-dependent K channels open and close in response to voltage changes across the cell membrane. This voltage dependence was postulated to depend on the presence of charged particles moving through the membrane in response to voltage changes. Recording of gating currents originating from the movement of these particles fully confirmed this hypothesis, and gave substantial experimental clues useful for the detailed understanding of the process. In the absence of structural information, the voltage-dependent gating was initially investigated using discrete Markov models, an approach only capable of providing a kinetic and thermodynamic comprehension of the process. The elucidation of the crystal structure of the first voltage-dependent channel brought in a dramatic change of pace in the understanding of channel gating, and in modeling the underlying processes. It was now possible to construct quantitative models using molecular dynamics, where all the interactions of each individual atom with the surroundings were taken into account, and its motion predicted by Newton's laws. Unfortunately, this modeling is computationally very demanding, and in spite of the advances in simulation procedures and computer technology, it is still limited in its predictive ability. To overcome these limitations, several groups have developed more macroscopic voltage gating models. Their approaches understandably require a number of approximations, which must however be physically well justified. One of these models, based on the description of the voltage sensor as a Brownian particle, that we have recently developed, is able to simultaneously describe the behavior of a single voltage sensor and to predict the macroscopic gating current originating from a population of sensors. The basics of this model are here described, and a typical application using the Kv1.2/2.1 chimera channel structure is also presented.