A parametric modeling of ionic channel current fluctuations using third-order statistics and its application to estimation of the kinetic parameters of single ionic channels

Abstract

A parametric modeling of stationary ionic-channel current fluctuations (SICF's) using third-order cumulants is presented and its application to estimation of the kinetic parameters of single ionic channels is discussed. We consider the case where third-order cumulants of SICF's are nonzero, and where SICF's are corrupted by an unobservable additive colored Gaussian noise that is independent of SICF's. First, we construct a virtual synthesizer that yields an output whose third-order cumulants are equivalent to those of SICF's on a specific slice. The synthesizer output is expressed by the sum of N5 - 1 first-order differential equation systems, where N8 denotes the number of states of single ionic channels. Next, discretizing the synthesizer output, we derive a discrete autoregressive (AR(N8 - 1)) process driven by the sum of N8 - 1 moving average (MA(N9 - 2)) processes. Then the AR coefficients are explicitly related to the kinetic parameters of single ionic channels, implying that the kinetic parameters can be estimated by identifying the ARMA coefficients using the third-order cumulants. In order to assess the validity of the proposed modeling and the accuracy of parameter estimates, Monte Carlo simulation is carried out in which the closed-open and closed-open-blocked schemes are treated as specific examples.