Noise and stochastic resonance in voltage-gated ion channels.

Using Monte Carlo techniques, I calculate the effects of internally generated noise on information transfer through the passage of action potential spikes along unmyelinated axons in a simple nervous system. I take the Hodgkin-Huxley (HH) description of Na and K channels in squid giant axons as the basis of the calculations and find that most signal transmission noise is generated by fluctuations in the channel open and closed populations. To bring the model closer to conventional descriptions in terms of thermal noise energy, kT, and to determine gating currents, I express the HH equations in the form of simple relations from statistical mechanics where the states are separated by a Gibbs energy that is modified by the action of the transmembrane potential on dipole moments held by the domains. Using the HH equations, I find that the output response (in the probability of action potential spikes) from small input potential pulses across the cell membrane is increased by added noise but falls off when the input noise becomes large, as in stochastic resonance models. That output noise response is sharply reduced by a small increase in the membrane polarization potential or a moderate increase in the channel densities. Because any reduction of noise incurs metabolic and developmental costs to an animal, the natural noise level is probably optimal and any increase in noise is likely to be harmful. Although these results are specific to signal transmission in unmyelinated axons, I suggest that the conclusions are likely to be general.