  Electrical signaling via voltage-gated ion channels depends upon the function
of the voltage sensor (VS), identified with the S1-S4 domain of voltage-gated K
channels. Here we investigate some physical aspects of the sliding-helix model
of the VS using simulations based on VS charges, linear dielectrics and
whole-body motion. Model electrostatics in voltage-clamped boundary conditions
are solved using a boundary element method. The statistical mechanical
consequences of the electrostatic configurational energy are computed to gain
insight into the sliding-helix mechanism and to predict experimentally measured
ensemble properties such as gating charge displaced by an applied voltage.
Those consequences and ensemble properties are investigated for variations of:
S4 configuration ({\alpha}- and 3(10)-helical), intrinsic counter-charges,
protein polarizability, geometry of the gating canal, screening of S4 charges
by the baths, and protein charges located at the bath interfaces. We find that
the sliding helix VS has an inherent electrostatic stability and its function
as a VS is robust in the parameter space explored. Maximal charge displacement
is limited by geometry, specifically the range of movement where S4 charges and
counter-charges overlap in the region of weak dielectric. The steepness of
charge rearrangement in the physiological voltage range is sensitive to the
landscape of electrostatic energy: energy differences of <2 kT have substantial
consequences. Such variations of energy landscape are produced by all
variations of model features tested. The amount of free energy per unit voltage
that a sliding-helix VS can deliver to other parts of the channel (conductance
voltage sensitivity) is limited by both the maximal displaced charge and the
steepness of charge redistribution by voltage (sensor voltage sensitivity).
