Resonant multi-ion conduction in a simple model of calcium channels

The ionic permeation of a biological ion channel is a multi-particle, non-equilibrium, stochastic process. Brownian dynamics simulations for a simple electrostatic model of the calcium channel reveal regular structure in the conductance and selectivity as functions of the negative fixed charge Q
_f
on the protein wall at the selectivity filter. This structure consists of distinct high conductance regions (conduction bands) separated by regions of near non-conductance (stop-bands). We report self-consistent electrostatic calculations of single-file, double-ion, stochastic optimal trajectories, and of the energy profiles along these trajectories, for different Q
_f
. We show that the energy difference ΔE along the optimal path exhibits a pronounced minimum near Q
_f
= 3e corresponding to an almost barrier-less (ΔE ~ k
_B
T) resonance-like form of conduction. We demonstrate explicitly that the sharply-defined conduction/selectivity peak of the L-type calcium channel is attributable to the barrier-less knock-on motion of a pair of calcium ions that can occur when their mutual electrostatic repulsion balances their electrostatic attraction to the charge at the selectivity filter. The electrostatics calculations agree well with the results of Brownian dynamics simulations. These results clarify the longstanding puzzle of how the L-type calcium channel exhibits, simultaneously, both high calcium selectivity and conduction at almost the rate of free diffusion.