Interplay between channel and shot noise at the onset of spiking activity in neural membranes

The role played by ion channel noise and ion shot noise around the threshold conditions for spiking activity in biological membranes is studied by means of a stochastic model based on the Hodgkin–Huxley equations, considering membrane voltage-dependent gating channels for sodium and potassium cations, and leakage channels. Ion channel noise, that is, the noise linked to the random opening and closing of the ion channels, is included by means of Langevin sources. Ion shot noise, associated with the random passage of ions through the cell membrane, is considered by using the Gillespie’s method, in terms of the probabilities for different ions to cross the membrane. The threshold for spiking activity is reached by applying increasing values of an external excitation I app in a large membrane patch S , for which the strength of channel noise is insufficient for the onset of spikes in the absence of I app . On the other hand, since by decreasing S the strength of both noise sources increases, spiking activity is also achieved for small enough values of S when I app = 0. The noise behavior of this biological system is analyzed in terms of the autocorrelation function and the spectral density of the membrane voltage fluctuations. Even if ion shot noise is typically considered as negligible when other electrical sources of neural noise are taken into account, the results indicate that, particularly around the onset of instabilities, the signature of shot noise, by the interplay with channel noise, is evident in the spectral density of the membrane voltage fluctuations.