Theoretical model of the ionic mechanism of 1/f noise in nerve membrane

Abstract

A model is presented for the ionic mechanism of low frequency 1/f electrical noise which has been observed in axonal membranes. The model consists of narrow channels which open randomly throughout the membrane and remain open for only a short time compared with f-1max where fmax approximately 2 kHz is the maximum frequency for which 1/f noise is observed. The fluctuation in channel formation is coupled to low frequency normal mode vibrations in liquid crystals which have properties similar to nerve membranes. Ionic current flow through the channels is assumed to occur via single file diffusion. The diffusion process is regarded as a non-Markovian random walk on a one-dimensional lattice which is mathematically decomposed into its spatial and temporal components. This technique allows calculation of the mean and variance of the number of ions which flow through any single short-lived channel. The final result for the current noise power spectrum, S, is S(f) = (A + k/I/2)/f, where I is the mean membrane current and A and k are parameters which are independent of membrane voltage. The theoretical result is consistent with observations of 1/f noise in lobster axon by Poussart (1971, Biophys. J. 11:212.) on the dependence of S(f) on the mean steady-state current and the external potassium concentration. We also calculate the mean channel density and the Frank elastic constant of the membrane. This work is an extension of a macroscopic model of Lundström and McQueen (1974, J. Theor. Biol. 45:405.) who obtain a spectral density of the form S approximately /I/2/f.