Statistical equilibrium theory
To understand the physical properties of biological ion channels we are working on an equilibrium statistical theory of narrow channels. These are classed as narrow because of the width of the selectivity filter which results in a set of discrete occupancy states. Paradoxically these channels allow conduction at almost the rate of free diffusion whilst maintaining a high selectivity even amongst alike-charged ions.To resolve this conundrum, we have derived statistical properties within the grand canonical ensemble for multiple-species of ions.Our theory describes the coupling between a channels selectivity filter and internal and external bath solutions at arbitrary concentrations. Linear response theory is then used to find the current through the filter for small gradients of electrochemical potential, where the conductivity of the filter being given by the generalized Einstein relation. Importantly we also show that the Eisenman selectivity relation follows directly from the condition of diffusion-limited conductivity through the filter.
