Advertisement

Ion Channel Kinetics: A Fractal Time Sequence of Conformational States

  • James B. Bassingthwaighte
  • Larry S. Liebovitch
  • Bruce J. West
Part of the Methods in Physiology Series book series (METHPHYS)

Abstract

Ions such as sodium, potassium, and chloride can move freely through water but cannot cross the hydrophobic lipids that form the cell membrane. However, these ions can interact with proteins in the cell membrane that transport them across the cell membrane. Three types of proteins are involved in ion transport: 1) Pumps, such as the sodium-potassium ATPase, bind tightly to a few ions at a time and use energy from ATP to move these ions against their electrochemical gradient. 2) Carriers, such as the sodium-potassium-chloride cotransporter, bind tightly to a few ions at a time and help them move down their electrochemical gradient. 3) Channels, such as the sodium channel, bind weakly to many ions at a time and allow them to move down their electrochemical gradient.

Keywords

Energy Barrier Fractal Model Conformational State Closed Time Potential Energy Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Background references

  1. Sakmann, B., and E. Neher. Single-Channel Recording. New York: Plenum Press, 1983, 503 pp.Google Scholar
  2. Hille, B. Ionic Channels of Excitable Membranes. Sunderland, Mass.: Sinauer Associates, 1984, 426 pp.Google Scholar
  3. Liebovitch, L. S., J. Fischbarg, and J. P. Koniarek. Ion channel kinetics: a model based on fractal scaling rather than multistate Markov processes. Math. Biosci. 84: 37 - 68, 1987a.CrossRefGoogle Scholar
  4. Liebovitch, L. S., and J. M. Sullivan. Fractal analysis of a voltage-dependent potassium channel from cultured mouse hippocampal neurons. Biophys. J. 52: 979 - 988, 1987.PubMedCrossRefGoogle Scholar
  5. Liebovitch, L. S., and T. I. Tóth. Fractal activity in cell membrane ion channels. Ann. NYAcad. Sci. 591: 375 - 391, 1990a.Google Scholar
  6. Liebovitch, L. S., and T. I. Tóth. Using fractals to understand the opening and closing of ion channels. Ann. Biomed. Eng. 18: 177 - 194, 1990b.PubMedCrossRefGoogle Scholar
  7. Liebovitch, L. S. Analysis of fractal ion channel gating kinetics: kinetic rates, energy levels, and activation energies. Math. Biosci. 93:97-115, 1989a. Liebovitch, L. S. Testing fractal and Markov models of ion channel kinetics. Biophys. J. 55: 373 - 377, 1989b.PubMedCrossRefGoogle Scholar
  8. Liebovitch, L. S., and T. I. T6th. The Akaike information criterion (AIC) is not a sufficient condition to determine the number of ion channel states from single channel recordings. Synapse 5: 134 - 138, 1990c.PubMedCrossRefGoogle Scholar
  9. French, A. S., and L. L. Stockbridge. Fractal and Markov behavior in ion channel kinetics. Can. J. Physiol. Pharmacol. 66: 967 - 970, 1988.PubMedCrossRefGoogle Scholar
  10. Stockbridge, L. L., and A. S. French. Characterization of a calcium-activated potassium channel in human fibroblasts. Can. J. Physiol. Pharmacol. 67: 1300 - 1307, 1989.PubMedCrossRefGoogle Scholar
  11. McManus, O. B., D. S. Weiss, C. E. Spivak, A. L. Blatz, and K. L. Magleby. Fractal models are inadequate for the kinetics of four different ion channels. Biophys. J. 54: 859 - 870, 1988.PubMedCrossRefGoogle Scholar
  12. Korn, S. J., and R. Horn. Statistical discrimination of fractal and Markov models of single-channel gating. Biophys. J. 54: 871 - 877, 1988.PubMedCrossRefGoogle Scholar
  13. Sansom, M. S. P., F. G. Ball, C. J. Kerry, R. McGee, R. L. Ramsey, and P. N. R. Usherwood. Markov, fractal, diffusion, and related models of ion channel gating. Biophys. J. 56: 1229 - 1243, 1989.PubMedCrossRefGoogle Scholar

Copyright information

© American Physiological Society 1994

Authors and Affiliations

  • James B. Bassingthwaighte
    • 1
  • Larry S. Liebovitch
    • 2
  • Bruce J. West
    • 3
  1. 1.Center for BioengineeringUniversity of WashingtonSeattleUSA
  2. 2.Center for Complex SystemsFlorida Atlantic UniversityBoca RatonUSA
  3. 3.Physics DepartmentUniversity of North TexasDentonUSA

Personalised recommendations