  We introduce a statistical and linear response theory of selective conduction
in biological ion channels with multiple binding sites and possible point
mutations. We derive an effective grand-canonical ensemble and generalised
Einstein relations for the selectivity filter, assuming strongly coordinated
ionic motion, and allowing for ionic Coulomb blockade. The theory agrees well
with data from the KcsA K$^+$ channel and a mutant. We show that the Eisenman
relations for thermodynamic selectivity follow from the condition for fast
conduction and find that maximum conduction requires the binding sites to be
nearly identical.
