Estimation of ion channel kinetics from fluctuations of macroscopic currents.

For single channel recordings, the maximum likelihood estimation (MLE) of kinetic rates and conductance is well established. A direct extrapolation of this method to macroscopic currents is computationally prohibitive: it scales as a power of the number of channels. An approximated MLE that ignored the local time correlation of the data has been shown to provide estimates of the kinetic parameters. In this article, an improved approximated MLE that takes into account the local time correlation is proposed. This method estimates the channel kinetics using both the time course and the random fluctuations of the macroscopic current generated by a homogeneous population of ion channels under white noise. It allows arbitrary kinetic models and stimulation protocols. The application of the proposed algorithm to simulated data from a simple three-state model on nonstationary conditions showed reliable estimates of all the kinetic constants, the conductance and the number of channels, and reliable values for the standard error of those estimates. Compared to the previous approximated MLE, it reduces by a factor of 10 the amount of data needed to secure a given accuracy and it can even determine the kinetic rates in macroscopic stationary conditions.

[1]  A G Hawkes,et al.  Asymptotic distributions of apparent open times and shut times in a single channel record allowing for the omission of brief events. , 1992, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[2]  R O Edeson,et al.  Estimation of single channel kinetic parameters from data subject to limited time resolution. , 1989, Biophysical journal.

[3]  J. J. Celentano,et al.  Use of the covariance matrix in directly fitting kinetic parameters: application to GABAA receptors. , 2004, Biophysical journal.

[4]  U. Fröbe,et al.  Analysing ion channels with hidden Markov models , 2004, Pflügers Archiv.

[5]  F. Qin,et al.  Estimating single-channel kinetic parameters from idealized patch-clamp data containing missed events. , 1996, Biophysical journal.

[6]  B. Hille.  Ionic channels of excitable membranes , 2001 .

[7]  F. Sigworth.  Interpreting power spectra from nonstationary membrane current fluctuations. , 1981, Biophysical journal.

[8]  F J Sigworth,et al.  Applying hidden Markov models to the analysis of single ion channel activity. , 2002, Biophysical journal.

[9]  Frederick Sachs,et al.  Maximum likelihood estimation of ion channel kinetics from macroscopic currents. , 2005, Biophysical journal.

[10]  F G Ball,et al.  Single-channel data and missed events , 1990, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[11]  L. Baum,et al.  Statistical Inference for Probabilistic Functions of Finite State Markov Chains , 1966 .

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

[13]  Robert C. Cannon,et al.  The Ion Channel Inverse Problem: Neuroinformatics Meets Biophysics , 2006, PLoS Comput. Biol..

[14]  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.

[15]  B. Sakmann,et al.  Fluctuations in the microsecond time range of the current through single acetylcholine receptor ion channels , 1981, Nature.

[16]  F. Sigworth,et al.  Data transformations for improved display and fitting of single-channel dwell time histograms. , 1987, Biophysical journal.

[17]  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.

[18]  D. Shanno.  Conditioning of Quasi-Newton Methods for Function Minimization , 1970 .

[19]  A G Hawkes,et al.  The quality of maximum likelihood estimates of ion channel rate constants , 2003, The Journal of physiology.

[20]  F Sachs,et al.  A direct optimization approach to hidden Markov modeling for single channel kinetics. , 2000, Biophysical journal.

[21]  K L Magleby,et al.  Estimating kinetic parameters for single channels with simulation. A general method that resolves the missed event problem and accounts for noise. , 1990, Biophysical journal.

[22]  F Sachs,et al.  Hidden Markov modeling for single channel kinetics with filtering and correlated noise. , 2000, Biophysical journal.

[23]  Lawrence R. Rabiner,et al.  A tutorial on hidden Markov models and selected applications in speech recognition , 1989, Proc. IEEE.

[24]  K L Magleby,et al.  Correcting single channel data for missed events. , 1986, Biophysical journal.

[25]  A. Hodgkin,et al.  A quantitative description of membrane current and its application to conduction and excitation in nerve , 1952, The Journal of physiology.

[26]  B. Sakmann,et al.  Improved patch-clamp techniques for high-resolution current recording from cells and cell-free membrane patches , 1981, Pflügers Archiv.

[27]  A. Auerbach,et al.  Maximum likelihood estimation of aggregated Markov processes , 1997, Proceedings of the Royal Society of London. Series B: Biological Sciences.

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

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

[30]  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.

[31]  E Neher,et al.  Conductance fluctuations and ionic pores in membranes. , 1977, Annual review of biophysics and bioengineering.

[32]  F. Sigworth,et al.  Yet another approach to the dwell-time omission problem of single-channel analysis. , 1990, Biophysical journal.