Identification of hidden Markov models for ion channel currents - Part I: Colored background noise

Signal processing based on hidden Markov models (HMM's) has been applied recently to the characterization of single ion channel currents as recorded with the patch clamp technique from living cells. The estimation of HMM parameters using the traditional forward-backward and Baum-Welch algorithms can be performed at signal-to-noise ratios (SNR's) that are too low for conventional analysis; however, the application of these algorithms relies on the assumption that the background noise is white. In this paper, the observed single channel current is modeled as a vector hidden Markov process. An extension of the forward-backward and Baum-Welch algorithms is described to model ion channel kinetics under conditions of colored noise like that seen in patch clamp recordings. Using simulated data, we demonstrate that the traditional algorithms result in biased estimates and that the vector HMM approach provides unbiased estimates of the parameters of the underlying hidden Markov scheme.