Theoretical Studies of Structure-Function Relationships in Kv Channels: Electrostatics of the Voltage Sensor

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 and S2 & S3 negatively charged counter-charges; 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 (Jiang et al., 2003) is rejected on electrostatic grounds, owing to unfavorable energetics, insufficient charge displacement and excessive Maxwell stress. On the other hand, a ‘sliding helix’ model (Catterall, 1986) with three local counter-charges, a protein dielectric coefficient of 4 and a 2/3 interval of counter-charge positioning relative to the S4 α-helix period of positive residues is electrostatically reasonable, comparing well with Shaker (Seoh et al., 1996). Lack of countercharges 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 (S2, S3 & S4) constrains the height of energy maxima relative to the energy troughs. These ‘sliding helix’ models compare favorably with experimental results for single & double mutant charge experiments on Shaker by Seoh et al. (1996). Single S4 positive charge mutants are predicted quite well by this model; single S2 or S3 negative counter-charge mutants are predicted less well; and double mutants for both an S4 charge and an S2 or S3 counter-charge are characterized least well by these electrostatic models (which do not include gating load, unlike their biological analogs). Further computational and experimental investigation of S2 & S3 counter-charge structure for voltage-gated ion channels is warranted. 1 ar X iv :1 11 2. 30 82 v1 [ qbi o. B M ] 1 4 D ec 2 01 1