Domain and Interdomain Energetics Underlying Gating in Shaker-Type Kv Channels

To understand gating events with a time-base many orders-of-magnitude slower than that of atomic motion in voltage-gated ion channels such as the Shaker-type K-v channels, a multiscale physical model is constructed from the experimentally well-characterized voltage-sensor (VS) domains coupled to a hydrophobic gate. The four VS domains are described by a continuum electrostatic model under voltage-clamp conditions, the control of ion flow by the gate domain is described by a vapor-lock mechanism, and the simple coupling principle is informed by known experimental results and trial-and-error. The configurational energy computed for each element is used to produce a total Hamiltonian that is a function of applied voltage, VS positions, and gate radius. We compute statistical-mechanical expectation values of macroscopic laboratory observables. This approach stands in contrast with molecular-dynamic models which are challenged by increasing scale, and kinetic models which assume a probability distribution rather than derive it from the underlying physics. This generic model predicts well the Shaker charge/voltage and conductance/voltage relations; the tight constraints underlying these results allow us to quantitatively assess the underlying physical mechanisms. The total electrical work picked up by the VS domains is an order-of-magnitude larger than the work required to actuate the gate itself, suggesting an energetic basis for the evolutionary flexibility of the voltage-gating mechanism. The cooperative slide-and-interlock behavior of the VS domains described by the VS-gate coupling relation leads to the experimentally observed bistable gating. This engineering approach should prove useful in the investigation of various elements underlying gating characteristics and degraded behavior due to mutation.