Power spectrum density equation of fluctuating membrane current based on a discrete-time markov chain model: Application to the analysis of ion channels with two and three states

Abstract

The measured power spectrum density PWSEX of the fluctuating membrane current of neurons often differs from the well known Lorentz curve. Representing the frequency dependence in the high frequency (f) above the corner frequency as f−n, n is less than 2, which indicates that the slope is smaller than in the Lorentz curve f−2. The reason for the rise of the high-frequency side of PWSEX is the aliasing effect produced by application of the FFT to discrete data over a finite interval. In this study, the theoretical expression PWSTH for the power spectrum density obtained from a discrete-line Markov model is used in the analysis of the experimental data. In the practical analysis of experimental data, we assume that the number of states of a single kind of channel on the membrane of the neuron is two or three. Using the discrete-time Markov model, an expression for PWSTH is derived. When the sampling time approaches zero, this expression approximates the known expression for the power spectrum density under the continuous-time Markov model. The plot of PWSTH gave a good fit to the experimental data. The open time that we obtained agreed well with existing values. These results confirm the usefulness of this form of PWSTH when it is applied to processing discrete data sampled at finite intervals.