Skip to main content
NCBI home page
Biophysical Journal logoLink to Biophysical Journal
. 1999 Apr;76(4):1868–1885. doi: 10.1016/s0006-3495(99)77346-7

Cardiac sodium channel Markov model with temperature dependence and recovery from inactivation.

L A Irvine 1, M S Jafri 1, R L Winslow 1
PMCID: PMC1300163  PMID: 10096885

Abstract

A Markov model of the cardiac sodium channel is presented. The model is similar to the CA1 hippocampal neuron sodium channel model developed by Kuo and Bean (1994. Neuron. 12:819-829) with the following modifications: 1) an additional open state is added; 2) open-inactivated transitions are made voltage-dependent; and 3) channel rate constants are exponential functions of enthalpy, entropy, and voltage and have explicit temperature dependence. Model parameters are determined using a simulated annealing algorithm to minimize the error between model responses and various experimental data sets. The model reproduces a wide range of experimental data including ionic currents, gating currents, tail currents, steady-state inactivation, recovery from inactivation, and open time distributions over a temperature range of 10 degrees C to 25 degrees C. The model also predicts measures of single channel activity such as first latency, probability of a null sweep, and probability of reopening.

Full Text

The Full Text of this article is available as a PDF (226.6 KB).

Selected References

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

  1. Aldrich R. W., Corey D. P., Stevens C. F. A reinterpretation of mammalian sodium channel gating based on single channel recording. Nature. 1983 Dec 1;306(5942):436–441. doi: 10.1038/306436a0. [DOI] [PubMed] [Google Scholar]
  2. 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]
  3. Benndorf K., Koopmann R. Thermodynamic entropy of two conformational transitions of single Na+ channel molecules. Biophys J. 1993 Oct;65(4):1585–1589. doi: 10.1016/S0006-3495(93)81197-4. [DOI] [PMC free article] [PubMed] [Google Scholar]
  4. Benndorf K. Patch clamp analysis of Na channel gating in mammalian myocardium: reconstruction of double pulse inactivation and voltage dependence of Na currents. Gen Physiol Biophys. 1988 Aug;7(4):353–377. [PubMed] [Google Scholar]
  5. Benndorf K. Properties of single cardiac Na channels at 35 degrees C. J Gen Physiol. 1994 Nov;104(5):801–820. doi: 10.1085/jgp.104.5.801. [DOI] [PMC free article] [PubMed] [Google Scholar]
  6. Berman M. F., Camardo J. S., Robinson R. B., Siegelbaum S. A. Single sodium channels from canine ventricular myocytes: voltage dependence and relative rates of activation and inactivation. J Physiol. 1989 Aug;415:503–531. doi: 10.1113/jphysiol.1989.sp017734. [DOI] [PMC free article] [PubMed] [Google Scholar]
  7. Chay T. R. The Hodgkin-Huxley Na+ channel model versus the five-state Markovian model. Biopolymers. 1991 Nov;31(13):1483–1502. doi: 10.1002/bip.360311306. [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. Colatsky T. J. Voltage clamp measurements of sodium channel properties in rabbit cardiac Purkinje fibres. J Physiol. 1980 Aug;305:215–234. doi: 10.1113/jphysiol.1980.sp013359. [DOI] [PMC free article] [PubMed] [Google Scholar]
  10. Correa A. M., Bezanilla F. Gating of the squid sodium channel at positive potentials: II. Single channels reveal two open states. Biophys J. 1994 Jun;66(6):1864–1878. doi: 10.1016/S0006-3495(94)80980-4. [DOI] [PMC free article] [PubMed] [Google Scholar]
  11. Correa A. M., Bezanilla F., Latorre R. Gating kinetics of batrachotoxin-modified Na+ channels in the squid giant axon. Voltage and temperature effects. Biophys J. 1992 May;61(5):1332–1352. doi: 10.1016/S0006-3495(92)81941-0. [DOI] [PMC free article] [PubMed] [Google Scholar]
  12. DiFrancesco D., Noble D. A model of cardiac electrical activity incorporating ionic pumps and concentration changes. Philos Trans R Soc Lond B Biol Sci. 1985 Jan 10;307(1133):353–398. doi: 10.1098/rstb.1985.0001. [DOI] [PubMed] [Google Scholar]
  13. Dubois J. M., Schneider M. F. Kinetics of intramembrane charge movement and sodium current in frog node of Ranvier. J Gen Physiol. 1982 Apr;79(4):571–602. doi: 10.1085/jgp.79.4.571. [DOI] [PMC free article] [PubMed] [Google Scholar]
  14. Ebihara L., Johnson E. A. Fast sodium current in cardiac muscle. A quantitative description. Biophys J. 1980 Nov;32(2):779–790. doi: 10.1016/S0006-3495(80)85016-8. [DOI] [PMC free article] [PubMed] [Google Scholar]
  15. Elinder F., Arhem P. Tail currents in the myelinated axon of Xenopus laevis suggest a two-open-state Na channel. Biophys J. 1997 Jul;73(1):179–185. doi: 10.1016/S0006-3495(97)78058-5. [DOI] [PMC free article] [PubMed] [Google Scholar]
  16. Fozzard H. A., Hanck D. A. Structure and function of voltage-dependent sodium channels: comparison of brain II and cardiac isoforms. Physiol Rev. 1996 Jul;76(3):887–926. doi: 10.1152/physrev.1996.76.3.887. [DOI] [PubMed] [Google Scholar]
  17. Goldman L., Hahin R. Initial conditions and the kinetics of the sodium conductance in Myxicola giant axons. II. Relaxation experiments. J Gen Physiol. 1978 Dec;72(6):879–898. doi: 10.1085/jgp.72.6.879. [DOI] [PMC free article] [PubMed] [Google Scholar]
  18. 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]
  19. HODGKIN A. L., HUXLEY A. F. Currents carried by sodium and potassium ions through the membrane of the giant axon of Loligo. J Physiol. 1952 Apr;116(4):449–472. doi: 10.1113/jphysiol.1952.sp004717. [DOI] [PMC free article] [PubMed] [Google Scholar]
  20. Hanck D. A., Sheets M. F., Fozzard H. A. Gating currents associated with Na channels in canine cardiac Purkinje cells. J Gen Physiol. 1990 Mar;95(3):439–457. doi: 10.1085/jgp.95.3.439. [DOI] [PMC free article] [PubMed] [Google Scholar]
  21. Hanck D. A., Sheets M. F. Modification of inactivation in cardiac sodium channels: ionic current studies with Anthopleurin-A toxin. J Gen Physiol. 1995 Oct;106(4):601–616. doi: 10.1085/jgp.106.4.601. [DOI] [PMC free article] [PubMed] [Google Scholar]
  22. Hirschberg B., Rovner A., Lieberman M., Patlak J. Transfer of twelve charges is needed to open skeletal muscle Na+ channels. J Gen Physiol. 1995 Dec;106(6):1053–1068. doi: 10.1085/jgp.106.6.1053. [DOI] [PMC free article] [PubMed] [Google Scholar]
  23. Hondeghem L. M., Katzung B. G. Time- and voltage-dependent interactions of antiarrhythmic drugs with cardiac sodium channels. Biochim Biophys Acta. 1977 Nov 14;472(3-4):373–398. doi: 10.1016/0304-4157(77)90003-x. [DOI] [PubMed] [Google Scholar]
  24. Horn R., Vandenberg C. A., Lange K. Statistical analysis of single sodium channels. Effects of N-bromoacetamide. Biophys J. 1984 Jan;45(1):323–335. doi: 10.1016/S0006-3495(84)84158-2. [DOI] [PMC free article] [PubMed] [Google Scholar]
  25. 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]
  26. Jonas P. Temperature dependence of gating current in myelinated nerve fibers. J Membr Biol. 1989 Dec;112(3):277–289. doi: 10.1007/BF01870958. [DOI] [PubMed] [Google Scholar]
  27. Josephson I. R., Sperelakis N. Kinetic and steady-state properties of Na+ channel and Ca2+ channel charge movements in ventricular myocytes of embryonic chick heart. J Gen Physiol. 1992 Aug;100(2):195–216. doi: 10.1085/jgp.100.2.195. [DOI] [PMC free article] [PubMed] [Google Scholar]
  28. Kirsch G. E., Brown A. M. Kinetic properties of single sodium channels in rat heart and rat brain. J Gen Physiol. 1989 Jan;93(1):85–99. doi: 10.1085/jgp.93.1.85. [DOI] [PMC free article] [PubMed] [Google Scholar]
  29. Kohlhardt M. Different temperature sensitivity of cardiac Na+ channels in cell-attached and cell-free conditions. Am J Physiol. 1990 Oct;259(4 Pt 1):C599–C604. doi: 10.1152/ajpcell.1990.259.4.C599. [DOI] [PubMed] [Google Scholar]
  30. Kunze D. L., Lacerda A. E., Wilson D. L., Brown A. M. Cardiac Na currents and the inactivating, reopening, and waiting properties of single cardiac Na channels. J Gen Physiol. 1985 Nov;86(5):691–719. doi: 10.1085/jgp.86.5.691. [DOI] [PMC free article] [PubMed] [Google Scholar]
  31. Kuo C. C., Bean B. P. Na+ channels must deactivate to recover from inactivation. Neuron. 1994 Apr;12(4):819–829. doi: 10.1016/0896-6273(94)90335-2. [DOI] [PubMed] [Google Scholar]
  32. Lawrence J. H., Yue D. T., Rose W. C., Marban E. Sodium channel inactivation from resting states in guinea-pig ventricular myocytes. J Physiol. 1991 Nov;443:629–650. doi: 10.1113/jphysiol.1991.sp018855. [DOI] [PMC free article] [PubMed] [Google Scholar]
  33. Liu S., Rasmusson R. L. Hodgkin-Huxley and partially coupled inactivation models yield different voltage dependence of block. Am J Physiol. 1997 Apr;272(4 Pt 2):H2013–H2022. doi: 10.1152/ajpheart.1997.272.4.H2013. [DOI] [PubMed] [Google Scholar]
  34. Luo C. H., Rudy Y. A model of the ventricular cardiac action potential. Depolarization, repolarization, and their interaction. Circ Res. 1991 Jun;68(6):1501–1526. doi: 10.1161/01.res.68.6.1501. [DOI] [PubMed] [Google Scholar]
  35. Milburn T., Saint D. A., Chung S. H. The temperature dependence of conductance of the sodium channel: implications for mechanisms of ion permeation. Receptors Channels. 1995;3(3):201–211. [PubMed] [Google Scholar]
  36. Murray K. T., Anno T., Bennett P. B., Hondeghem L. M. Voltage clamp of the cardiac sodium current at 37 degrees C in physiologic solutions. Biophys J. 1990 Mar;57(3):607–613. doi: 10.1016/S0006-3495(90)82576-5. [DOI] [PMC free article] [PubMed] [Google Scholar]
  37. Nagy K. Evidence for multiple open states of sodium channels in neuroblastoma cells. J Membr Biol. 1987;96(3):251–262. doi: 10.1007/BF01869307. [DOI] [PubMed] [Google Scholar]
  38. Noda M., Ikeda T., Kayano T., Suzuki H., Takeshima H., Kurasaki M., Takahashi H., Numa S. Existence of distinct sodium channel messenger RNAs in rat brain. Nature. 1986 Mar 13;320(6058):188–192. doi: 10.1038/320188a0. [DOI] [PubMed] [Google Scholar]
  39. Noda M., Shimizu S., Tanabe T., Takai T., Kayano T., Ikeda T., Takahashi H., Nakayama H., Kanaoka Y., Minamino N. Primary structure of Electrophorus electricus sodium channel deduced from cDNA sequence. Nature. 1984 Nov 8;312(5990):121–127. doi: 10.1038/312121a0. [DOI] [PubMed] [Google Scholar]
  40. Oxford G. S. Some kinetic and steady-state properties of sodium channels after removal of inactivation. J Gen Physiol. 1981 Jan;77(1):1–22. doi: 10.1085/jgp.77.1.1. [DOI] [PMC free article] [PubMed] [Google Scholar]
  41. Patlak J. B., Ortiz M. Slow currents through single sodium channels of the adult rat heart. J Gen Physiol. 1985 Jul;86(1):89–104. doi: 10.1085/jgp.86.1.89. [DOI] [PMC free article] [PubMed] [Google Scholar]
  42. Patlak J. Molecular kinetics of voltage-dependent Na+ channels. Physiol Rev. 1991 Oct;71(4):1047–1080. doi: 10.1152/physrev.1991.71.4.1047. [DOI] [PubMed] [Google Scholar]
  43. Sakakibara Y., Furukawa T., Singer D. H., Jia H., Backer C. L., Arentzen C. E., Wasserstrom J. A. Sodium current in isolated human ventricular myocytes. Am J Physiol. 1993 Oct;265(4 Pt 2):H1301–H1309. doi: 10.1152/ajpheart.1993.265.4.H1301. [DOI] [PubMed] [Google Scholar]
  44. Scanley B. E., Hanck D. A., Chay T., Fozzard H. A. Kinetic analysis of single sodium channels from canine cardiac Purkinje cells. J Gen Physiol. 1990 Mar;95(3):411–437. doi: 10.1085/jgp.95.3.411. [DOI] [PMC free article] [PubMed] [Google Scholar]
  45. Schreibmayer W., Jeglitsch G. The sodium channel activator Brevetoxin-3 uncovers a multiplicity of different open states of the cardiac sodium channel. Biochim Biophys Acta. 1992 Mar 2;1104(2):233–242. doi: 10.1016/0005-2736(92)90035-k. [DOI] [PubMed] [Google Scholar]
  46. Sheets M. F., Hanck D. A. Voltage-dependent open-state inactivation of cardiac sodium channels: gating current studies with Anthopleurin-A toxin. J Gen Physiol. 1995 Oct;106(4):617–640. doi: 10.1085/jgp.106.4.617. [DOI] [PMC free article] [PubMed] [Google Scholar]
  47. Sheets M. F., Kyle J. W., Krueger S., Hanck D. A. Optimization of a mammalian expression system for the measurement of sodium channel gating currents. Am J Physiol. 1996 Sep;271(3 Pt 1):C1001–C1006. doi: 10.1152/ajpcell.1996.271.3.C1001. [DOI] [PubMed] [Google Scholar]
  48. Starmer C. F., Grant A. O., Strauss H. C. Mechanisms of use-dependent block of sodium channels in excitable membranes by local anesthetics. Biophys J. 1984 Jul;46(1):15–27. doi: 10.1016/S0006-3495(84)83994-6. [DOI] [PMC free article] [PubMed] [Google Scholar]
  49. Vandenberg C. A., Bezanilla F. A sodium channel gating model based on single channel, macroscopic ionic, and gating currents in the squid giant axon. Biophys J. 1991 Dec;60(6):1511–1533. doi: 10.1016/S0006-3495(91)82186-5. [DOI] [PMC free article] [PubMed] [Google Scholar]
  50. Vandenberg C. A., Horn R. Inactivation viewed through single sodium channels. J Gen Physiol. 1984 Oct;84(4):535–564. doi: 10.1085/jgp.84.4.535. [DOI] [PMC free article] [PubMed] [Google Scholar]
  51. Wang D. W., George A. L., Jr, Bennett P. B. Comparison of heterologously expressed human cardiac and skeletal muscle sodium channels. Biophys J. 1996 Jan;70(1):238–245. doi: 10.1016/S0006-3495(96)79566-8. [DOI] [PMC free article] [PubMed] [Google Scholar]
  52. Yue D. T., Lawrence J. H., Marban E. Two molecular transitions influence cardiac sodium channel gating. Science. 1989 Apr 21;244(4902):349–352. doi: 10.1126/science.2540529. [DOI] [PubMed] [Google Scholar]

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

RESOURCES