Skip to main content
NCBI home page
Biophysical Journal logoLink to Biophysical Journal
. 1980 May;30(2):327–345. doi: 10.1016/S0006-3495(80)85098-3

Influence of intercellular clefts on potential and current distribution in a multifiber preparation.

H G Haas, G Brommundt
PMCID: PMC1328738  PMID: 7260279

Abstract

A theoretical model is presented for current and voltage clamp of multifiber bundles in a double sucrose gap. Attention is focused on methodological errors introduced by the intercellular cleft resistance. The bundle is approximated by a continuous geometry. Voltage distribution, as a function of radial distance and time, is defined by a parabolic partial differential equation which is specified for different membrane characteristics. Assuming a linear membrane, analytical solutions are given for current step and voltage step conditions. The theoretical relations (based on Bessel functions) may be used to calculate membrane conductance and capacity from experimental clamp data. The case of a nonlinear membrane with standard Hodgkin-Huxley kinetics for excitatory Na current is treated assuming maximum Na conductances (gNa) of 120, 10, and 1 mmho/cm2. Numerical simulations are presented for potential and current distribution in a bundle of 60 microns diameter during depolarizing voltage steps. Adequate voltage control is restricted to the peripheral fibers of the bundle whereas the membrane potential of the inner fibers deviates from the command level during early inward current, tending to the Na equilibrium potential. In the peak current-voltage diagram the loss of voltage control is reflected by an increased steepness of the negative region and a decreased slope conductance of the positive region. With gNa = 120 mmho/cm2, the positive slope conductance is approximately 25% of the slope expected from ideal space clamping. With the lower values of gNa, the slope conductance ratio is in the order of 50%. Implications of the results for an experimental voltage clamp analysis of early inward current on multifiber preparations are discussed.

Full text

PDF
327

Selected References

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

  1. ANTONI H., DELIUS W. NACHWEIS VON ZWEI KOMPONENTEN IN DER ANSTIEGSPHASE DES AKTIONSPONTENTIALS VON FROSCHMYOKARDFASERN. Pflugers Arch Gesamte Physiol Menschen Tiere. 1965 Apr 6;283:187–202. [PubMed] [Google Scholar]
  2. Adrian R. H., Chandler W. K., Hodgkin A. L. The kinetics of mechanical activation in frog muscle. J Physiol. 1969 Sep;204(1):207–230. doi: 10.1113/jphysiol.1969.sp008909. [DOI] [PMC free article] [PubMed] [Google Scholar]
  3. Attwell D., Cohen I. The voltage clamp of multicellular preparations. Prog Biophys Mol Biol. 1977;31(3):201–245. doi: 10.1016/0079-6107(78)90009-3. [DOI] [PubMed] [Google Scholar]
  4. BARR L., DEWEY M. M., BERGER W. PROPAGATION OF ACTION POTENTIALS AND THE STRUCTURE OF THE NEXUS IN CARDIAC MUSCLE. J Gen Physiol. 1965 May;48:797–823. doi: 10.1085/jgp.48.5.797. [DOI] [PMC free article] [PubMed] [Google Scholar]
  5. Baldwin K. M. The fine structure and electrophysiology of heart muscle cell injury. J Cell Biol. 1970 Sep;46(3):455–476. doi: 10.1083/jcb.46.3.455. [DOI] [PMC free article] [PubMed] [Google Scholar]
  6. Beeler G. W., Reuter H. Reconstruction of the action potential of ventricular myocardial fibres. J Physiol. 1977 Jun;268(1):177–210. doi: 10.1113/jphysiol.1977.sp011853. [DOI] [PMC free article] [PubMed] [Google Scholar]
  7. Connor J., Barr L., Jakobsson E. Electrical characteristics of frog atrial trabeculae in the double sucrose gap. Biophys J. 1975 Oct;15(10):1047–1067. doi: 10.1016/S0006-3495(75)85882-6. [DOI] [PMC free article] [PubMed] [Google Scholar]
  8. Eisenberg R. S., Barcilon V., Mathias R. T. Electrical properties of spherical syncytia. Biophys J. 1979 Jan;25(1):151–180. doi: 10.1016/S0006-3495(79)85283-2. [DOI] [PMC free article] [PubMed] [Google Scholar]
  9. FITZHUGH R. Thresholds and plateaus in the Hodgkin-Huxley nerve equations. J Gen Physiol. 1960 May;43:867–896. doi: 10.1085/jgp.43.5.867. [DOI] [PMC free article] [PubMed] [Google Scholar]
  10. HODGKIN A. L., HUXLEY A. F. A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol. 1952 Aug;117(4):500–544. doi: 10.1113/jphysiol.1952.sp004764. [DOI] [PMC free article] [PubMed] [Google Scholar]
  11. HODGKIN A. L., HUXLEY A. F. The dual effect of membrane potential on sodium conductance in the giant axon of Loligo. J Physiol. 1952 Apr;116(4):497–506. doi: 10.1113/jphysiol.1952.sp004719. [DOI] [PMC free article] [PubMed] [Google Scholar]
  12. JULIAN F. J., MOORE J. W., GOLDMAN D. E. Current-voltage relations in the lobster giant axon membrane under voltage clamp conditions. J Gen Physiol. 1962 Jul;45:1217–1238. doi: 10.1085/jgp.45.6.1217. [DOI] [PMC free article] [PubMed] [Google Scholar]
  13. JULIAN F. J., MOORE J. W., GOLDMAN D. E. Membrane potentials of the lobster giant axon obtained by use of the sucrose-gap technique. J Gen Physiol. 1962 Jul;45:1195–1216. doi: 10.1085/jgp.45.6.1195. [DOI] [PMC free article] [PubMed] [Google Scholar]
  14. Jakobsson E., Barr L., Connor J. A. An equivalent circuit for small atrial trabeculae of frog. Biophys J. 1975 Oct;15(10):1069–1085. doi: 10.1016/S0006-3495(75)85883-8. [DOI] [PMC free article] [PubMed] [Google Scholar]
  15. Johnson E. A., Lieberman M. Heart: excitation and contraction. Annu Rev Physiol. 1971;33:479–532. doi: 10.1146/annurev.ph.33.030171.002403. [DOI] [PubMed] [Google Scholar]
  16. Kern R., Einwächter H. M., Haas H. G., Lack E. G. Cardiac membrane currents as affected by an neuroleptic agent: droperidol. Pflugers Arch. 1971;325(3):262–278. doi: 10.1007/BF00588359. [DOI] [PubMed] [Google Scholar]
  17. Kootsey J. M., Johnson E. A. Voltage clamp of cardiac muscle. A theoretical analysis of early currents in the single sucrose gap. Biophys J. 1972 Nov;12(11):1496–1508. doi: 10.1016/S0006-3495(72)86177-0. [DOI] [PMC free article] [PubMed] [Google Scholar]
  18. McAllister R. E., Noble D., Tsien R. W. Reconstruction of the electrical activity of cardiac Purkinje fibres. J Physiol. 1975 Sep;251(1):1–59. doi: 10.1113/jphysiol.1975.sp011080. [DOI] [PMC free article] [PubMed] [Google Scholar]
  19. McGuigan J. A. Some limitations of the double sucrose gap, and its use in a study of the slow outward current in mammalian ventricular muscle. J Physiol. 1974 Aug;240(3):775–806. doi: 10.1113/jphysiol.1974.sp010634. [DOI] [PMC free article] [PubMed] [Google Scholar]
  20. Niedergerke R., Orkand R. K. The dual effect of calcium on the action potential of the frog's heart. J Physiol. 1966 May;184(2):291–311. doi: 10.1113/jphysiol.1966.sp007916. [DOI] [PMC free article] [PubMed] [Google Scholar]
  21. Noble D. Applications of Hodgkin-Huxley equations to excitable tissues. Physiol Rev. 1966 Jan;46(1):1–50. doi: 10.1152/physrev.1966.46.1.1. [DOI] [PubMed] [Google Scholar]
  22. Page S. G., Niedergerke R. Structures of physiological interest in the frog heart ventricle. J Cell Sci. 1972 Jul;11(1):179–203. doi: 10.1242/jcs.11.1.179. [DOI] [PubMed] [Google Scholar]
  23. Peskoff A. Electric potential in cylindrical syncytia and muscle fibers. Bull Math Biol. 1979;41(2):183–192. doi: 10.1007/BF02460877. [DOI] [PubMed] [Google Scholar]
  24. Peskoff A. Electric potential in three-dimensional electrically syncytial tissues. Bull Math Biol. 1979;41(2):163–181. doi: 10.1007/BF02460876. [DOI] [PubMed] [Google Scholar]
  25. Ramón F., Anderson N., Joyner R. W., Moore J. W. Axon voltage-clamp simulations. A multicellular preparation. Biophys J. 1975 Jan;15(1):55–69. doi: 10.1016/S0006-3495(75)85791-2. [DOI] [PMC free article] [PubMed] [Google Scholar]
  26. SHANES A. M. Electrochemical aspects of physiological and pharmacological action in excitable cells. II. The action potential and excitation. Pharmacol Rev. 1958 Jun;10(2):165–273. [PubMed] [Google Scholar]
  27. Schoenberg M., Fozzard H. A. The influence of intercellular clefts on the electrical properties of sheep cardiac Purkinje fibers. Biophys J. 1979 Feb;25(2 Pt 1):217–234. doi: 10.1016/s0006-3495(79)85287-x. [DOI] [PMC free article] [PubMed] [Google Scholar]
  28. Sommer J. R., Johnson E. A. Cardiac muscle. A comparative study of Purkinje fibers and ventricular fibers. J Cell Biol. 1968 Mar;36(3):497–526. doi: 10.1083/jcb.36.3.497. [DOI] [PMC free article] [PubMed] [Google Scholar]
  29. Tarr M., Trank J. W. An assessment of the double sucrose-gap voltage clamp technique as applied to frog atrial muscle. Biophys J. 1974 Sep;14(9):627–643. doi: 10.1016/S0006-3495(74)85940-0. [DOI] [PMC free article] [PubMed] [Google Scholar]
  30. Tarr M., Trank J. W. Limitations of the double sucrose gap voltage clamp technique in tension-voltage determinations on frog atrial muscle. Circ Res. 1976 Jul;39(1):106–112. doi: 10.1161/01.res.39.1.106. [DOI] [PubMed] [Google Scholar]
  31. de Hemptinne A. Voltage clamp analysis in isolated cardiac fibres as performed with two different perfusion chambres for double sucrose gap. Pflugers Arch. 1976 May 6;363(1):87–95. doi: 10.1007/BF00587407. [DOI] [PubMed] [Google Scholar]

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

RESOURCES