Skip to main content
PMC home page
Biophysical Journal logoLink to Biophysical Journal
. 1994 Aug;67(2):634–640. doi: 10.1016/S0006-3495(94)80523-5

Superposition properties of interacting ion channels.

A M Keleshian 1, G F Yeo 1, R O Edeson 1, B W Madsen 1
PMCID: PMC1225405  PMID: 7524711

Abstract

Quantitative analysis of patch clamp data is widely based on stochastic models of single-channel kinetics. Membrane patches often contain more than one active channel of a given type, and it is usually assumed that these behave independently in order to interpret the record and infer individual channel properties. However, recent studies suggest there are significant channel interactions in some systems. We examine a model of dependence in a system of two identical channels, each modeled by a continuous-time Markov chain in which specified transition rates are dependent on the conductance state of the other channel, changing instantaneously when the other channel opens or closes. Each channel then has, e.g., a closed time density that is conditional on the other channel being open or closed, these being identical under independence. We relate the two densities by a convolution function that embodies information about, and serves to quantify, dependence in the closed class. Distributions of observable (superposition) sojourn times are given in terms of these conditional densities. The behavior of two channel systems based on two- and three-state Markov models is examined by simulation. Optimized fitting of simulated data using reasonable parameters values and sample size indicates that both positive and negative cooperativity can be distinguished from independence.

Full text

PDF
639

Selected References

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

  1. Chen Y. H., DeHaan R. L. Multiple-channel conductance states and voltage regulation of embryonic chick cardiac gap junctions. J Membr Biol. 1992 Apr;127(2):95–111. doi: 10.1007/BF00233282. [DOI] [PubMed] [Google Scholar]
  2. Colquhoun D., Hawkes A. G. Stochastic properties of ion channel openings and bursts in a membrane patch that contains two channels: evidence concerning the number of channels present when a record containing only single openings is observed. Proc R Soc Lond B Biol Sci. 1990 Jun 22;240(1299):453–477. doi: 10.1098/rspb.1990.0048. [DOI] [PubMed] [Google Scholar]
  3. DeFelice L. J. Molecular and biophysical view of the Ca channel: a hypothesis regarding oligomeric structure, channel clustering, and macroscopic current. J Membr Biol. 1993 May;133(3):191–202. doi: 10.1007/BF00232019. [DOI] [PubMed] [Google Scholar]
  4. Draber S., Schultze R., Hansen U. P. Cooperative behavior of K+ channels in the tonoplast of Chara corallina. Biophys J. 1993 Oct;65(4):1553–1559. doi: 10.1016/S0006-3495(93)81194-9. [DOI] [PMC free article] [PubMed] [Google Scholar]
  5. Fox J. A. Ion channel subconductance states. J Membr Biol. 1987;97(1):1–8. doi: 10.1007/BF01869609. [DOI] [PubMed] [Google Scholar]
  6. Fredkin D. R., Rice J. A. On the superposition of currents from ion channels. Philos Trans R Soc Lond B Biol Sci. 1991 Dec 30;334(1271):347–356. doi: 10.1098/rstb.1991.0121. [DOI] [PubMed] [Google Scholar]
  7. Hill T. L., Chen Y. D. On the theory of ion transport across the nerve membrane. 3. Potassium ion kinetics and cooperativity (with x=4,6,9). Proc Natl Acad Sci U S A. 1971 Oct;68(10):2488–2492. doi: 10.1073/pnas.68.10.2488. [DOI] [PMC free article] [PubMed] [Google Scholar]
  8. Hill T. L., Chen Y. D. On the theory of ion transport across the nerve membrane. II. Potassium ion kinetics and cooperativity (with x = 4). Proc Natl Acad Sci U S A. 1971 Aug;68(8):1711–1715. doi: 10.1073/pnas.68.8.1711. [DOI] [PMC free article] [PubMed] [Google Scholar]
  9. Hunter M., Giebisch G. Multi-barrelled K channels in renal tubules. Nature. 1987 Jun 11;327(6122):522–524. doi: 10.1038/327522a0. [DOI] [PubMed] [Google Scholar]
  10. Kijima S., Kijima H. Statistical analysis of channel current from a membrane patch. I. Some stochastic properties of ion channels or molecular systems in equilibrium. J Theor Biol. 1987 Oct 21;128(4):423–434. doi: 10.1016/s0022-5193(87)80188-1. [DOI] [PubMed] [Google Scholar]
  11. Krouse M. E., Schneider G. T., Gage P. W. A large anion-selective channel has seven conductance levels. Nature. 1986 Jan 2;319(6048):58–60. doi: 10.1038/319058a0. [DOI] [PubMed] [Google Scholar]
  12. Neher E., Sakmann B., Steinbach J. H. The extracellular patch clamp: a method for resolving currents through individual open channels in biological membranes. Pflugers Arch. 1978 Jul 18;375(2):219–228. doi: 10.1007/BF00584247. [DOI] [PubMed] [Google Scholar]
  13. Sigworth F. J. The conductance of sodium channels under conditions of reduced current at the node of Ranvier. J Physiol. 1980 Oct;307:131–142. doi: 10.1113/jphysiol.1980.sp013427. [DOI] [PMC free article] [PubMed] [Google Scholar]
  14. Yeo G. F., Edeson R. O., Milne R. K., Madsen B. W. Superposition properties of independent ion channels. Proc R Soc Lond B Biol Sci. 1989 Nov 22;238(1291):155–170. doi: 10.1098/rspb.1989.0073. [DOI] [PubMed] [Google Scholar]

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

RESOURCES