Abstract
Hidden Markov modeling (HMM) can be applied to extract single channel kinetics at signal-to-noise ratios that are too low for conventional analysis. There are two general HMM approaches: traditional Baum's reestimation and direct optimization. The optimization approach has the advantage that it optimizes the rate constants directly. This allows setting constraints on the rate constants, fitting multiple data sets across different experimental conditions, and handling nonstationary channels where the starting probability of the channel depends on the unknown kinetics. We present here an extension of this approach that addresses the additional issues of low-pass filtering and correlated noise. The filtering is modeled using a finite impulse response (FIR) filter applied to the underlying signal, and the noise correlation is accounted for using an autoregressive (AR) process. In addition to correlated background noise, the algorithm allows for excess open channel noise that can be white or correlated. To maximize the efficiency of the algorithm, we derive the analytical derivatives of the likelihood function with respect to all unknown model parameters. The search of the likelihood space is performed using a variable metric method. Extension of the algorithm to data containing multiple channels is described. Examples are presented that demonstrate the applicability and effectiveness of the algorithm. Practical issues such as the selection of appropriate noise AR orders are also discussed through examples.
Full Text
The Full Text of this article is available as a PDF (145.3 KB).
Selected References
These references are in PubMed. This may not be the complete list of references from this article.
- Ball F. G., Sansom M. S. Ion-channel gating mechanisms: model identification and parameter estimation from single channel recordings. Proc R Soc Lond B Biol Sci. 1989 May 22;236(1285):385–416. doi: 10.1098/rspb.1989.0029. [DOI] [PubMed] [Google Scholar]
- Chay T. R. Kinetic modeling for the channel gating process from single channel patch clamp data. J Theor Biol. 1988 Jun 22;132(4):449–468. doi: 10.1016/s0022-5193(88)80084-5. [DOI] [PubMed] [Google Scholar]
- Chung S. H., Moore J. B., Xia L. G., Premkumar L. S., Gage P. W. Characterization of single channel currents using digital signal processing techniques based on Hidden Markov Models. Philos Trans R Soc Lond B Biol Sci. 1990 Sep 29;329(1254):265–285. doi: 10.1098/rstb.1990.0170. [DOI] [PubMed] [Google Scholar]
- Fredkin D. R., Rice J. A. Bayesian restoration of single-channel patch clamp recordings. Biometrics. 1992 Jun;48(2):427–448. [PubMed] [Google Scholar]
- Horn R., Lange K. Estimating kinetic constants from single channel data. Biophys J. 1983 Aug;43(2):207–223. doi: 10.1016/S0006-3495(83)84341-0. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Magleby K. L., Pallotta B. S. Calcium dependence of open and shut interval distributions from calcium-activated potassium channels in cultured rat muscle. J Physiol. 1983 Nov;344:585–604. doi: 10.1113/jphysiol.1983.sp014957. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Magleby K. L., Weiss D. S. Estimating kinetic parameters for single channels with simulation. A general method that resolves the missed event problem and accounts for noise. Biophys J. 1990 Dec;58(6):1411–1426. doi: 10.1016/S0006-3495(90)82487-5. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Magleby K. L., Weiss D. S. Identifying kinetic gating mechanisms for ion channels by using two-dimensional distributions of simulated dwell times. Proc Biol Sci. 1990 Sep 22;241(1302):220–228. doi: 10.1098/rspb.1990.0089. [DOI] [PubMed] [Google Scholar]
- Premkumar L. S., Auerbach A. Identification of a high affinity divalent cation binding site near the entrance of the NMDA receptor channel. Neuron. 1996 Apr;16(4):869–880. doi: 10.1016/s0896-6273(00)80107-5. [DOI] [PubMed] [Google Scholar]
- Qin F., Auerbach A., Sachs F. A direct optimization approach to hidden Markov modeling for single channel kinetics. Biophys J. 2000 Oct;79(4):1915–1927. doi: 10.1016/S0006-3495(00)76441-1. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Qin F., Auerbach A., Sachs F. Estimating single-channel kinetic parameters from idealized patch-clamp data containing missed events. Biophys J. 1996 Jan;70(1):264–280. doi: 10.1016/S0006-3495(96)79568-1. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Qin F., Auerbach A., Sachs F. Maximum likelihood estimation of aggregated Markov processes. Proc Biol Sci. 1997 Mar 22;264(1380):375–383. doi: 10.1098/rspb.1997.0054. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Sine S. M., Claudio T., Sigworth F. J. Activation of Torpedo acetylcholine receptors expressed in mouse fibroblasts. Single channel current kinetics reveal distinct agonist binding affinities. J Gen Physiol. 1990 Aug;96(2):395–437. doi: 10.1085/jgp.96.2.395. [DOI] [PMC free article] [PubMed] [Google Scholar]