We introduce a statistical and linear response theory of selective conduction in biological ion channels with multiple binding sites and possible point mutation. 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