Theory of threshold fluctuations in nerves. I. Relationships between electrical noise and fluctuations in axon firing.

Relations describing threshold fluctuation phenomena in nerves are derived by calculating the approximate response of the Hodgkin-Huxley (HH) axon to electrical noise. We use FitzHugh's reduced phase space approximation and describe the dynamics of a noisy nerve by a two-dimensional brownian motion. The theory predicts the functional form and parametric dependence of the relation between probability of firing and stimulus strength. Expressions are also obtained for the firing probability as a function of stimulus duration and for the distribution of latency times as a function of stimulus strength.