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Moving average filtering with deconvolution (MAD) for hidden Markov model with filtering and correlated noise

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Abstract

Ion channel data recorded using the patch clamp technique are low-pass filtered to remove high-frequency noise. Almanjahie et al. (Eur Biophys J 44:545–556, 2015) based statistical analysis of such data on a hidden Markov model (HMM) with a moving average adjustment for the filter but without correlated noise, and used the EM algorithm for parameter estimation. In this paper, we extend their model to include correlated noise, using signal processing methods and deconvolution to pre-whiten the noise. The resulting data can be modelled as a standard HMM and parameter estimates are again obtained using the EM algorithm. We evaluate this approach using simulated data and also apply it to real data obtained from the mechanosensitive channel of large conductance (MscL) in Escherichia coli. Estimates of mean conductances are comparable to literature values. The key advantages of this method are that it is much simpler and computationally considerably more efficient than currently used HMM methods that include filtering and correlated noise.

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Acknowledgements

The experimental part of the study was supported by the APP1047980 grant from the National Health and Medical Research Council of Australia to Professor B. Martinac. Ibrahim M. Almanjahie thanks the government of Saudi Arabia, King Khalid University and the Cultural Mission of Royal Embassy of Saudi Arabia in Australia for support during his PhD study. We also thank two referees for their comments, which have enabled us to significantly improve the paper.

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Author notes

  1. Ibrahim M. Almanjahie

    Present address: Department of Mathematics, King Khalid University, Abha, 61413, Saudi Arabia

Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Western Australia, Crawley, WA, 6009, Australia

    Ibrahim M. Almanjahie, Ramzan Nazim Khan & Robin K. Milne

  2. Department of Rehabilitation, Kyushu Nutrition Welfare University, Kitakyushu, 800-029, Japan

    Takeshi Nomura

  3. Mechanosensory Biophysics Laboratory, Victor Chang Cardiac Research Institute, Darlinghurst, NSW, 2010, Australia

    Boris Martinac

Authors
  1. Ibrahim M. Almanjahie
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  2. Ramzan Nazim Khan
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  3. Robin K. Milne
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  4. Takeshi Nomura
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  5. Boris Martinac
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Correspondence to Ramzan Nazim Khan.

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Almanjahie, I.M., Khan, R.N., Milne, R.K. et al. Moving average filtering with deconvolution (MAD) for hidden Markov model with filtering and correlated noise. Eur Biophys J 48, 383–393 (2019). https://doi.org/10.1007/s00249-019-01368-1

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  • DOI: https://doi.org/10.1007/s00249-019-01368-1

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