Identification of individual channel kinetics from recordings containing many identical channels

Abstract

Given a discrete-time signal consisting of N identical, independent, binary Markov chains observed in white noise, we consider the problem of estimating the non-zero state level, the number of chains and the elementary transition probability matrix. We derive formulae for the central moments, first- and second-order auto-correlation functions and the power spectrum of a first-order, discrete-time Markov chain. We show that the mean, variance, third central moment and power spectrum provide sufficient information for the estimation of the parameters of the signal in question. We demonstrate the estimation procedure with numerical examples for both simulated and real biological data, and describe a method for estimating the non-unity eigenvalue of the transition matrix as well as the noise variance from the power spectrum of the noisy signal. Show more