  The physical mechanism underlying the voltage-dependent gating of K channels
is usually addressed theoretically using molecular dynamics
simulations.However, besides being computationally very expensive, this
approach is presently unable to fully predict the behavior of fundamental
variables of channel gating, such as the macroscopic gating current.To fill
this gap here we propose a voltage gating model that treats the S4 segment as a
Brownian particle moving through a gating channel pore and adjacent internal
and external vestibules.In our model charges on the S4 segment are screened by
charged residues localized on the other segments of the channel protein, and by
ions present in the vestibules, whose dynamics is assessed using a flux
conservation equation. The electrostatic voltage spatial profile is
consistently assessed by applying the Poisson equation to all the charges
present in the system. The treatment of the S4 segment as a Brownian particle
allows to alternatively describe the dynamics of a single S4 segment, using the
Langevin stochastic differential equation, or the behavior of a population of
S4 segments, useful to assess the macroscopic gating current, using the
Fokker-Planck equation. The proposed model confirms the gating charge transfer
hypothesis, with the movement of the S4 segment among 5 different stable
positions where the gating charges differently interact with the negatively
charged residues on the channel protein. This behavior results in macroscopic
gating currents displaying properties quite similar to those experimentally
found, including a very fast component followed by a slower one with an evident
rising phase at high depolarizing voltages.
