Ion-channel gating mechanisms: model identification and parameter estimation from single channel recordings

Patch-clamp data may be analysed in terms of Markov process models of channel gating mechanisms. We present a maximum likelihood algorithm for estimation of gating parameters from records where only a single channel is present. Computer simulated data for three different models of agonist receptor gated channels are used to demonstrate the performance of the procedure. Full details of the implementation of the algorithm are given for an example gating mechanism. The effects of omission of brief openings and closings from the single-channel data on parameter estimation are explored. A strategy for discriminating between alternative possible gating models, based upon use of the Schwarz criterion, is described. Omission of brief events is shown not to lead to incorrect model identification, except in extreme circumstances. Finally, the algorithm is extended to include channel gating models exhibiting multiple conductance levels.

[1]  Frank Ball,et al.  Aggregated Markov processes incorporating time interval omission , 1988, Advances in Applied Probability.

[2]  J. Rice,et al.  On aggregated Markov processes , 1986 .

[3]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[4]  Edward Moczydlowski,et al.  Single-Channel Enzymology , 1986 .

[5]  R E Oswald,et al.  Relationships of agonist properties to the single channel kinetics of nicotinic acetylcholine receptors. , 1988, Biophysical journal.

[6]  R Horn,et al.  Estimating kinetic constants from single channel data. , 1983, Biophysical journal.

[7]  Frank Ball,et al.  Aggregated Markov processes incorporating time interval omission , 1987 .

[8]  C. Loan,et al.  Nineteen Dubious Ways to Compute the Exponential of a Matrix , 1978 .

[9]  F. G. Ball,et al.  Analysis of post-perturbation gating kinetics of single ion channels , 1989, Proceedings of the Royal Society of London. B. Biological Sciences.

[10]  A. Hawkes,et al.  On the stochastic properties of single ion channels , 1981, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[11]  Richard Bellman,et al.  Introduction to Matrix Analysis , 1972 .

[12]  J. R. Clay,et al.  Relationship between membrane excitability and single channel open-close kinetics. , 1983, Biophysical journal.

[13]  R Horn,et al.  Statistical properties of single sodium channels , 1984, The Journal of general physiology.

[14]  C. Stevens,et al.  Glutamate activates multiple single channel conductances in hippocampal neurons , 1987, Nature.

[15]  F G Ball,et al.  The use of dwell time cross-correlation functions to study single-ion channel gating kinetics. , 1988, Biophysical journal.

[16]  R O Edeson,et al.  Statistical inference from single channel records: two-state Markov model with limited time resolution , 1988, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[17]  Richard Horn,et al.  Gating of Channels in Nerve and Muscie: A Stochastic Approach , 1984 .

[18]  B. Roux,et al.  A general solution to the time interval omission problem applied to single channel analysis. , 1985, Biophysical journal.

[19]  D Colquhoun.  Single channel analysis costs time. , 1988, Trends in pharmacological sciences.

[20]  R J Bauer,et al.  Theory of the kinetic analysis of patch-clamp data. , 1987, Biophysical journal.

[21]  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.

[22]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[23]  M Montal,et al.  Kinetic analysis of channel gating. Application to the cholinergic receptor channel and the chloride channel from Torpedo californica. , 1985, Biophysical journal.

[24]  Claudio Cobelli,et al.  Identifiability results on some constrained compartmental systems , 1979 .

[25]  H. D. Miller,et al.  The Theory Of Stochastic Processes , 1977, The Mathematical Gazette.

[26]  D Colquhoun,et al.  Activation of ion channels in the frog end‐plate by high concentrations of acetylcholine. , 1988, The Journal of physiology.

[27]  S. Cull-Candy,et al.  Multiple-conductance channels activated by excitatory amino acids in cerebellar neurons , 1987, Nature.

[28]  Curtis F. Gerald.  Applied numerical analysis , 1970 .

[29]  A G Hawkes,et al.  Relaxation and fluctuations of membrane currents that flow through drug-operated channels , 1977, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[30]  F G Ball,et al.  Single-channel autocorrelation functions: the effects of time interval omission. , 1988, Biophysical journal.

[31]  R Horn,et al.  Statistical methods for model discrimination. Applications to gating kinetics and permeation of the acetylcholine receptor channel. , 1987, Biophysical journal.

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

[33]  B Sakmann,et al.  Fast events in single‐channel currents activated by acetylcholine and its analogues at the frog muscle end‐plate. , 1985, The Journal of physiology.

[34]  H. Akaike.  A new look at the statistical model identification , 1974 .

[35]  M S Sansom,et al.  Glutamate receptor channel kinetics: the effect of glutamate concentration. , 1988, Biophysical journal.

[36]  A G Hawkes,et al.  A note on correlations in single ion channel records , 1987, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[37]  T R Chay.  Kinetic modeling for the channel gating process from single channel patch clamp data. , 1988, Journal of theoretical biology.