Relating microscopic charge movement to macroscopic currents: The Ramo-Shockley theorem applied to ion channels

Since the discovery of gating current, electrophysiologists have studied the movement of charged groups within channel proteins by changing potential and measuring the resulting capacitive current. The relation of atomic-scale movements of charged groups to the gating current measured in an external circuit, however, is not obvious. We report here that a general solution to this problem exists in the form of the Ramo-Shockley theorem. For systems with different amounts of atomic detail, we use the theorem to calculate the gating charge produced by movements of protein charges. Even without calculation or simulation, the Ramo-Shockley theorem eliminates a class of interpretations of experimental results. The theorem may also be used at each time step of simulations to compute external current.