European Biophysics Journal

, Volume 34, Issue 4, pp 306–313 | Cite as

Estimating rate constants from single ion channel currents when the initial distribution is known

  • Yu-Kai TheEmail author
  • Jacqueline Fernandez
  • M. Oana Popa
  • Holger Lerche
  • Jens Timmer


Single ion channel currents can be analysed by hidden or aggregated Markov models. A classical result from Fredkin et al. (Proceedings of the Berkeley conference in honor of Jerzy Neyman and Jack Kiefer, vol I, pp 269–289, 1985) states that the maximum number of identifiable parameters is bounded by 2nonc, where no and nc denote the number of open and closed states, respectively. We show that this bound can be overcome when the probabilities of the initial distribution are known and the data consist of several sweeps.


Hidden Markov models Aggregated Markov models Identifiability Maximum likelihood estimation Sodium channel 



We thank Steffen Michalek for providing his implementation of algorithms for the ARMA-filtered hidden Markov models. This work was supported by the Deutsche Forschungsgemeinschaft (Le1030/5-2). H.L. is a Heisenberg fellow of the Deutsche Forschungsgemeinschaft.


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Copyright information

© EBSA 2005

Authors and Affiliations

  • Yu-Kai The
    • 1
    • 2
    Email author
  • Jacqueline Fernandez
    • 3
  • M. Oana Popa
    • 3
  • Holger Lerche
    • 3
  • Jens Timmer
    • 1
    • 2
  1. 1.Institut für PhysikAlbert-Ludwigs-UniversitätFreiburgGermany
  2. 2.Freiburger Zentrum für Datenanalyse und ModellbildungAlbert-Ludwigs-UniversitätFreiburgGermany
  3. 3.Abteilung für Angewandte Physiologie und Neurologische KlinikUniversität UlmUlmGermany

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