Bayesian restoration of ion channel records using hidden Markov models.

Hidden Markov models have been used to restore recorded signals of single ion channels buried in background noise. Parameter estimation and signal restoration are usually carried out through likelihood maximization by using variants of the Baum-Welch forward-backward procedures. This paper presents an alternative approach for dealing with this inferential task. The inferences are made by using a combination of the framework provided by Bayesian statistics and numerical methods based on Markov chain Monte Carlo stochastic simulation. The reliability of this approach is tested by using synthetic signals of known characteristics. The expectations of the model parameters estimated here are close to those calculated using the Baum-Welch algorithm, but the present methods also yield estimates of their errors. Comparisons of the results of the Bayesian Markov Chain Monte Carlo approach with those obtained by filtering and thresholding demonstrate clearly the superiority of the new methods.

[1]  J. Besag,et al.  Bayesian Computation and Stochastic Systems , 1995 .

[2]  J. Rice,et al.  Maximum likelihood estimation and identification directly from single-channel recordings , 1992, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[3]  Lain L. MacDonald,et al.  Hidden Markov and Other Models for Discrete- valued Time Series , 1997 .

[4]  Christian P. Robert,et al.  Control by the Central Limit Theorem , 1998 .

[5]  Richard L. Tweedie,et al.  Markov Chains and Stochastic Stability , 1993, Communications and Control Engineering Series.

[6]  R. Kohn,et al.  On Gibbs sampling for state space models , 1994 .

[7]  Alan G. Hawkes,et al.  A Q-Matrix Cookbook , 1995 .

[8]  C. Robert,et al.  Bayesian estimation of hidden Markov chains: a stochastic implementation , 1993 .

[9]  Hoon Kim,et al.  Monte Carlo Statistical Methods , 2000, Technometrics.

[10]  Adrian F. M. Smith,et al.  Sampling-Based Approaches to Calculating Marginal Densities , 1990 .

[11]  F. G. Ball,et al.  Stochastic models for ion channels: introduction and bibliography. , 1992, Mathematical biosciences.

[12]  Roman Kuc,et al.  Identification of hidden Markov models for ion channel currents. I. Colored background noise , 1998, IEEE Trans. Signal Process..

[13]  Ronald L. Wasserstein,et al.  Monte Carlo: Concepts, Algorithms, and Applications , 1997 .

[14]  Peter Green,et al.  Bayesian choice among Markov models of ion channels using Markov chain Monte Carlo , 1999, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[15]  M. E. A. Hodgson.  A Bayesian restoration of an ion channel signal , 1999 .

[16]  S H Chung,et al.  Characterization of single channel currents using digital signal processing techniques based on Hidden Markov Models. , 1990, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[17]  D R Fredkin,et al.  Bayesian restoration of single-channel patch clamp recordings. , 1992, Biometrics.

[18]  C. Robert.  Convergence Control Methods for Markov Chain Monte Carlo Algorithms , 1995 .

[19]  Jens Timmer,et al.  Estimating transition rates in aggregated Markov models of ion channel gating with loops and with nearly equal dwell times , 1999, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[20]  G. C. Tiao,et al.  Bayesian inference in statistical analysis , 1973 .

[21]  K L Magleby,et al.  Dependency plots suggest the kinetic structure of ion channels , 1992, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[22]  E. Nummelin.  General irreducible Markov chains and non-negative operators: List of symbols and notation , 1984 .

[23]  P. Kienker.  Equivalence of aggregated Markov models of ion-channel gating , 1989, Proceedings of the Royal Society of London. B. Biological Sciences.

[24]  L. Tierney.  Markov Chains for Exploring Posterior Distributions , 1994 .

[25]  John G. Kemeny,et al.  Finite Markov Chains. , 1960 .

[26]  J. B. Kadane,et al.  Bayesian inference for ion–channel gating mechanisms directly from single–channel recordings, using Markov chain Monte Carlo , 1999, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[27]  Sue Ball.  Stochastic models of ion channels , 2001 .

[28]  Jun S. Liu,et al.  Covariance Structure and Convergence Rate of the Gibbs Sampler with Various Scans , 1995 .

[29]  J A Stark,et al.  Adjustments for the display of quantized ion channel dwell times in histograms with logarithmic bins. , 2000, Biophysical journal.

[30]  L. Baum,et al.  A Maximization Technique Occurring in the Statistical Analysis of Probabilistic Functions of Markov Chains , 1970 .

[31]  A. Hawkes,et al.  On the stochastic properties of bursts of single ion channel openings and of clusters of bursts. , 1982, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[32]  Peter J. Bickel,et al.  Inference in hidden Markov models I: Local asymptotic normality in the stationary case , 1996 .

[33]  Richard D. Deveaux,et al.  Applied Smoothing Techniques for Data Analysis , 1999, Technometrics.

[34]  F G Ball,et al.  Ion-channel gating mechanisms: model identification and parameter estimation from single channel recordings , 1989, Proceedings of the Royal Society of London. B. Biological Sciences.

[35]  Jens Timmer,et al.  Estimating rate constants in hidden Markov models by the EM algorithm , 1999, IEEE Trans. Signal Process..

[36]  Roman Kuc,et al.  Identification of hidden Markov models for ion channel currents .III. Bandlimited, sampled data , 2000, IEEE Trans. Signal Process..

[37]  P. Bickel,et al.  Asymptotic normality of the maximum-likelihood estimator for general hidden Markov models , 1998 .

[38]  Fred J. Sigworth,et al.  Fitting and Statistical Analysis of Single-Channel Records , 1983 .

[39]  J. Besag.  Spatial Interaction and the Statistical Analysis of Lattice Systems , 1974 .

[40]  C. Robert,et al.  Estimation of Finite Mixture Distributions Through Bayesian Sampling , 1994 .