Ion flow through biomembranes. Physical theory explains its high sensitivity

Numerous biomembranes exhibit a sensitivity to changes in electrical potential greater than predicted as possible from the classical application of the Boltzmann relation, a phenomenon which has long defied explanation, the actual sensitivity of some Na+ channels being many times greater than the classical limit. This paper explains, using a minimum of mathematics, how the very rapid gating effect of adsorbed Ca2+ (or other impermeable divalent cations) can directly affect the conductance of channels, and thus interact with the electric field within the channel to produce a change in the potential across the channel's gate much greater than the change in the membrane potential, with a corresponding change in the fraction of open conformational gates and change in conductance. These results are not in conflict with the Boltzmann relation, the necessary energy being made available from the total potential difference across the membrane by a long unrecognized stochastic process; the full mathematical theory is given in cited references.