We present an equilibrium statistical-mechanical theory of selectivity in biological ion channels. In doing so, we introduce a grand canonical ensemble for ions in a channels selectivity filter coupled to internal and external bath solutions for a mi
xture of ions at arbitrary concentrations, we use linear response theory to find the current through the filter for small gradients of electrochemical potential, and we show that the conductivity of the filter is given by the generalized Einstein relation. We apply the theory to the permeation of ions through the potassium selectivity filter, and are thereby able to resolve the long-standing paradox of why the high selectivity of the filter brings no associated delay in permeation. We show that the Eisenman selectivity relation follows directly from the condition of diffusion-limited conductivity through the filter. We also discuss the effect of wall fluctuations on the filter conductivity.
Electrostatic interaction between ions in an ionic channel and the charge fluctuations in the channel mouth are considered. It is shown that the charge fluctuations can be enhanced in the channels with low dielectric constant and result in strong mod
ulation of the potential barrier at the selectivity site. The effect of charge fluctuational on transition probabilities in other molecular dynamical systems is briefly discussed.
