Identification of hidden Markov models for ion channel currents. II. State-dependent excess noise

Hidden Markov modeling (HMM) techniques have been applied in the past few years to characterize single ion channel current events at low signal-to-noise ratios (SNR’s). In this paper, an adaptation of the forward-backward procedure and Baum–Welch algorithm is presented to model ion channel kinetics under conditions of correlated and state-dependent excess noise like that observed in patch-clamp recordings. An autoregressive with additive nonstationary (ARANS) noise model is introduced to model the experimentally observed noise, and an algorithm called the Baum–Welch weighted least squares (BW-WLS) procedure is presented to re-estimate the noise model parameters along with the parameters of the underlying HMM. The performance of the algorithm is demonstrated with simulated data.