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

The case where third-order cumulants of stationary ionic-channel current fluctuations (SICFs) are nonzero, and where SICFs are corrupted by an unobservable additive colored Gaussian noise that is independent of SICFs is considered. First, a virtual synthesizer that yields an output whose third-order cumulants are equivalent to those of SICFs on a specific slice is constructed. The synthesizer output is expressed by the sum of N _s-1 first-order differential equation systems, where N _s denotes the number of states of single ionic channels. Next, discretizing the synthesizer output, a discrete autoregressive (AR(N _s-1)) process driven by the sum of N _s-1 moving average (MA(N _s-2)) processes is derived. 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 autoregressive moving-average 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.