  Voltage-gated ion channels mediate electrical excitability of cellular
membranes. Reduced models of the voltage sensor (VS) of Kv channels produce
insight into the electrostatic physics underlying the response of the highly
positively charged S4 transmembrane domain to changes in membrane potential and
other electrostatic parameters. By calculating the partition function computed
from the electrostatic energy over translational and/or rotational degrees of
freedom, I compute expectations of charge displacement, energetics, probability
distributions of translation & rotation and Maxwell stress for arrangements of
S4 positively charged residues; these computations can then be compared with
experimental results to elucidate the role of various putative atomic level
features of the VS. A `paddle' model is rejected on electrostatic grounds,
owing to unfavorable energetics, insufficient charge displacement and excessive
Maxwell stress. On the other hand, a `sliding helix' model with three local
counter-charges, a protein dielectric coefficient of 4 and a 2/3 interval of
counter-charge positioning relative to the S4-helix period of positive residues
is electrostatically reasonable, comparing well with Shaker (Seoh et al.,
1996). Lack of counter-charges destabilizes the S4 in the membrane;
counter-charge interval helps determine the number and shape of energy barriers
and troughs over the range of motion of the S4; and the local dielectric
coefficient of the protein constrains the height of energy maxima. These
`sliding helix' models compare favorably with experimental results for single &
double mutant charge experiments on Shaker. Single S4 positive charge mutants
are predicted quite well by this model; single counter-charge mutants are
predicted less well; and double mutants for both an S4 charge and a
counter-charge are characterized least well.

Biomolecules;Biological Physics;Quantitative Methods