Stochastic model for ion shot noise in Hodgkin and Huxley neurons
A stochastic model based on the Monte Carlo technique able to reproduce the steady state and the action potential in neurons in terms of the probabilities for different ions to cross the cell membrane is presented. Gating channels for sodium and potassium cations and leakage channels are considered following the Hodgkin-Huxley equations. Ion shot noise, this is, the noise associated to the random passage of ions across the cell membrane, is naturally accounted for in the model. Shot noise by itself can lead to the excitation and inhibition of action potentials, being of increasing influence the smaller is the area of the membrane patch.