Role of a Stochastic Friction Coefficient in Open Channel Noise

The electric current noise through an open channel in a membrane is analyzed with the aid of a stochastic differential equation to describe the process of ionic permeation along the channel. Unlike the Langevin theory, the effective friction constant of the channel is given by a deterministic quantity plus a multiplicative noise. The Brownian or additive noise is taken as white. Two models for the multiplicative noise are considered, a dichotomous Markov process and white noise. In both models, the correlation function decays exponentially and, therefore, the spectral density of the noise is a Lorentzian with a corner frequency proportional to the effective friction coefficient. The relaxation time of the fluctuations is modulated by the strength of the multiplicative noise. We conclude that these models characterize only those dynamical processes that occur on the rapid time scale of diffusion and cannot be used to describe slow conformational changes of a protein channel.