Skip to main content
Biophysical Journal logoLink to Biophysical Journal
. 1990 Dec;58(6):1411–1426. doi: 10.1016/S0006-3495(90)82487-5

Estimating kinetic parameters for single channels with simulation. A general method that resolves the missed event problem and accounts for noise.

K L Magleby 1, D S Weiss 1
PMCID: PMC1281094  PMID: 1703449

Abstract

Analysis of currents recorded from single channels is complicated by the limited time resolution (filtering) of the data which can prevent the detection of brief intervals. Although a number of approaches have been used to correct for the undetected intervals (missed events) when identifying kinetic models and estimating parameters, none of them provide a general method which takes into account the true effects of noise and limited time resolution. This paper presents such a method. The approach is to use simulated single-channel currents to incorporate the true effects of filtering and noise on missed events and interval durations. The simulated currents are then analyzed in a manner identical to that used to analyze the experimental currents. An iterative search process using likelihood comparison of two-dimensional dwell-time distributions obtained from the simulated and experimental single-channel currents then allows the most likely rate constants to be determined. The large errors and false solutions that can result from the more typically applied assumptions of no noise and an absolute dead time (idealized filtering) are excluded by the iterative simulation method, and the correlation information contained in the two-dimensional distributions should increase the ability to distinguish among different gating mechanisms. The iterative simulation method is generally applicable to channels which typically open to a single conductance level. For these channels the method places no restrictions on the proposed gating mechanism or the form of the predicted dwell-time distributions.

Full text

PDF
1411

Selected References

These references are in PubMed. This may not be the complete list of references from this article.

  1. Ball F. G., Kerry C. J., Ramsey R. L., Sansom M. S., Usherwood P. N. The use of dwell time cross-correlation functions to study single-ion channel gating kinetics. Biophys J. 1988 Aug;54(2):309–320. doi: 10.1016/S0006-3495(88)82961-8. [DOI] [PMC free article] [PubMed] [Google Scholar]
  2. 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]
  3. Bauer R. J., Bowman B. F., Kenyon J. L. Theory of the kinetic analysis of patch-clamp data. Biophys J. 1987 Dec;52(6):961–978. doi: 10.1016/S0006-3495(87)83289-7. [DOI] [PMC free article] [PubMed] [Google Scholar]
  4. Blatz A. L., Magleby K. L. Adjacent interval analysis distinguishes among gating mechanisms for the fast chloride channel from rat skeletal muscle. J Physiol. 1989 Mar;410:561–585. doi: 10.1113/jphysiol.1989.sp017549. [DOI] [PMC free article] [PubMed] [Google Scholar]
  5. Blatz A. L., Magleby K. L. Correcting single channel data for missed events. Biophys J. 1986 May;49(5):967–980. doi: 10.1016/S0006-3495(86)83725-0. [DOI] [PMC free article] [PubMed] [Google Scholar]
  6. Blatz A. L., Magleby K. L. Quantitative description of three modes of activity of fast chloride channels from rat skeletal muscle. J Physiol. 1986 Sep;378:141–174. doi: 10.1113/jphysiol.1986.sp016212. [DOI] [PMC free article] [PubMed] [Google Scholar]
  7. Blatz A. L., Magleby K. L. Single apamin-blocked Ca-activated K+ channels of small conductance in cultured rat skeletal muscle. Nature. 1986 Oct 23;323(6090):718–720. doi: 10.1038/323718a0. [DOI] [PubMed] [Google Scholar]
  8. Clay J. R., DeFelice L. J. Relationship between membrane excitability and single channel open-close kinetics. Biophys J. 1983 May;42(2):151–157. doi: 10.1016/S0006-3495(83)84381-1. [DOI] [PMC free article] [PubMed] [Google Scholar]
  9. Colquhoun D., Hawkes A. G. A note on correlations in single ion channel records. Proc R Soc Lond B Biol Sci. 1987 Feb 23;230(1258):15–52. doi: 10.1098/rspb.1987.0008. [DOI] [PubMed] [Google Scholar]
  10. Colquhoun D., Hawkes A. G. On the stochastic properties of bursts of single ion channel openings and of clusters of bursts. Philos Trans R Soc Lond B Biol Sci. 1982 Dec 24;300(1098):1–59. doi: 10.1098/rstb.1982.0156. [DOI] [PubMed] [Google Scholar]
  11. Colquhoun D., Hawkes A. G. On the stochastic properties of single ion channels. Proc R Soc Lond B Biol Sci. 1981 Mar 6;211(1183):205–235. doi: 10.1098/rspb.1981.0003. [DOI] [PubMed] [Google Scholar]
  12. Colquhoun D., Hawkes A. G. Relaxation and fluctuations of membrane currents that flow through drug-operated channels. Proc R Soc Lond B Biol Sci. 1977 Nov 14;199(1135):231–262. doi: 10.1098/rspb.1977.0137. [DOI] [PubMed] [Google Scholar]
  13. Colquhoun D., Sakmann B. Fast events in single-channel currents activated by acetylcholine and its analogues at the frog muscle end-plate. J Physiol. 1985 Dec;369:501–557. doi: 10.1113/jphysiol.1985.sp015912. [DOI] [PMC free article] [PubMed] [Google Scholar]
  14. 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]
  15. Horn R. Statistical methods for model discrimination. Applications to gating kinetics and permeation of the acetylcholine receptor channel. Biophys J. 1987 Feb;51(2):255–263. doi: 10.1016/S0006-3495(87)83331-3. [DOI] [PMC free article] [PubMed] [Google Scholar]
  16. Horn R., Vandenberg C. A. Statistical properties of single sodium channels. J Gen Physiol. 1984 Oct;84(4):505–534. doi: 10.1085/jgp.84.4.505. [DOI] [PMC free article] [PubMed] [Google Scholar]
  17. Jackson M. B., Wong B. S., Morris C. E., Lecar H., Christian C. N. Successive openings of the same acetylcholine receptor channel are correlated in open time. Biophys J. 1983 Apr;42(1):109–114. doi: 10.1016/S0006-3495(83)84375-6. [DOI] [PMC free article] [PubMed] [Google Scholar]
  18. Kerry C. J., Ramsey R. L., Sansom M. S., Usherwood P. N. Glutamate receptor channel kinetics: the effect of glutamate concentration. Biophys J. 1988 Jan;53(1):39–52. doi: 10.1016/S0006-3495(88)83064-9. [DOI] [PMC free article] [PubMed] [Google Scholar]
  19. Kienker P. Equivalence of aggregated Markov models of ion-channel gating. Proc R Soc Lond B Biol Sci. 1989 Apr 22;236(1284):269–309. doi: 10.1098/rspb.1989.0024. [DOI] [PubMed] [Google Scholar]
  20. Labarca P., Rice J. A., Fredkin D. R., Montal M. Kinetic analysis of channel gating. Application to the cholinergic receptor channel and the chloride channel from Torpedo californica. Biophys J. 1985 Apr;47(4):469–478. doi: 10.1016/S0006-3495(85)83939-4. [DOI] [PMC free article] [PubMed] [Google Scholar]
  21. 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]
  22. McManus O. B., Blatz A. L., Magleby K. L. Inverse relationship of the durations of adjacent open and shut intervals for C1 and K channels. Nature. 1985 Oct 17;317(6038):625–627. doi: 10.1038/317625a0. [DOI] [PubMed] [Google Scholar]
  23. McManus O. B., Blatz A. L., Magleby K. L. Sampling, log binning, fitting, and plotting durations of open and shut intervals from single channels and the effects of noise. Pflugers Arch. 1987 Nov;410(4-5):530–553. doi: 10.1007/BF00586537. [DOI] [PubMed] [Google Scholar]
  24. McManus O. B., Magleby K. L. Kinetic states and modes of single large-conductance calcium-activated potassium channels in cultured rat skeletal muscle. J Physiol. 1988 Aug;402:79–120. doi: 10.1113/jphysiol.1988.sp017195. [DOI] [PMC free article] [PubMed] [Google Scholar]
  25. McManus O. B., Weiss D. S., Spivak C. E., Blatz A. L., Magleby K. L. Fractal models are inadequate for the kinetics of four different ion channels. Biophys J. 1988 Nov;54(5):859–870. doi: 10.1016/S0006-3495(88)83022-4. [DOI] [PMC free article] [PubMed] [Google Scholar]
  26. Milne R. K., Yeo G. F., Edeson R. O., Madsen B. W. Stochastic modelling of a single ion channel: an alternating renewal approach with application to limited time resolution. Proc R Soc Lond B Biol Sci. 1988 Apr 22;233(1272):247–292. doi: 10.1098/rspb.1988.0022. [DOI] [PubMed] [Google Scholar]
  27. Milne R. K., Yeo G. F., Madsen B. W., Edeson R. O. Estimation of single channel kinetic parameters from data subject to limited time resolution. Biophys J. 1989 Apr;55(4):673–676. doi: 10.1016/S0006-3495(89)82865-6. [DOI] [PMC free article] [PubMed] [Google Scholar]
  28. Moczydlowski E., Latorre R. Gating kinetics of Ca2+-activated K+ channels from rat muscle incorporated into planar lipid bilayers. Evidence for two voltage-dependent Ca2+ binding reactions. J Gen Physiol. 1983 Oct;82(4):511–542. doi: 10.1085/jgp.82.4.511. [DOI] [PMC free article] [PubMed] [Google Scholar]
  29. Pietrobon D., Prod'hom B., Hess P. Interactions of protons with single open L-type calcium channels. pH dependence of proton-induced current fluctuations with Cs+, K+, and Na+ as permeant ions. J Gen Physiol. 1989 Jul;94(1):1–21. doi: 10.1085/jgp.94.1.1. [DOI] [PMC free article] [PubMed] [Google Scholar]
  30. Roux B., Sauvé R. A general solution to the time interval omission problem applied to single channel analysis. Biophys J. 1985 Jul;48(1):149–158. doi: 10.1016/S0006-3495(85)83768-1. [DOI] [PMC free article] [PubMed] [Google Scholar]
  31. Sachs F., Neil J., Barkakati N. The automated analysis of data from single ionic channels. Pflugers Arch. 1982 Dec;395(4):331–340. doi: 10.1007/BF00580798. [DOI] [PubMed] [Google Scholar]
  32. Sigworth F. J., Sine S. M. Data transformations for improved display and fitting of single-channel dwell time histograms. Biophys J. 1987 Dec;52(6):1047–1054. doi: 10.1016/S0006-3495(87)83298-8. [DOI] [PMC free article] [PubMed] [Google Scholar]
  33. Wilson D. L., Brown A. M. Effect of limited interval resolution on single channel measurements with application to Ca channels. IEEE Trans Biomed Eng. 1985 Oct;32(10):786–797. doi: 10.1109/TBME.1985.325494. [DOI] [PubMed] [Google Scholar]
  34. Yellen G. Ionic permeation and blockade in Ca2+-activated K+ channels of bovine chromaffin cells. J Gen Physiol. 1984 Aug;84(2):157–186. doi: 10.1085/jgp.84.2.157. [DOI] [PMC free article] [PubMed] [Google Scholar]
  35. Yeo G. F., Milne R. K., Edeson R. O., Madsen B. W. Statistical inference from single channel records: two-state Markov model with limited time resolution. Proc R Soc Lond B Biol Sci. 1988 Oct 22;235(1278):63–94. doi: 10.1098/rspb.1988.0063. [DOI] [PubMed] [Google Scholar]

Articles from Biophysical Journal are provided here courtesy of The Biophysical Society

RESOURCES