  Electrical signaling via voltage-gated ion channels depends upon the function
of a voltage sensor (VS), identified with the S1-S4 domain in voltage-gated K+
channels. Here we investigate some energetic 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 two alternate
S4 configurations, \alpha- and 3(10)-helical. Both forms of VS are found to
have an inherent electrostatic stability. 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. Charge displacement
responds more steeply to voltage in the \alpha-helical than the 3(10)-helical
sensor. This difference is due to differences on the order of 0.1 eV in the
landscapes of electrostatic energy. As a step toward integrating these VS
models into a full-channel model, we include a hypothetical external load in
the Hamiltonian of the system and analyze the energetic in/output relation of
the VS.
