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. 1990 Mar;57(3):433–444. doi: 10.1016/S0006-3495(90)82560-1

Global parameter optimization for cardiac potassium channel gating models.

J R Balser 1, D M Roden 1, P B Bennett 1
PMCID: PMC1280738  PMID: 2306494

Abstract

Quantitative ion channel model evaluation requires the estimation of voltage dependent rate constants. We have tested whether a unique set of rate constants can be reliably extracted from nonstationary macroscopic voltage clamp potassium current data. For many models, the rate constants derived independently at different membrane potentials are not unique. Therefore, our approach has been to use the exponential voltage dependence predicted from reaction rate theory (Stevens, C. F. 1978. Biophys. J. 22:295-306; Eyring, H., S. H. Lin, and S. M. Lin. 1980. Basic Chemical Kinetics. Wiley and Sons, New York) to couple the rate constants derived at different membrane potentials. This constrained the solution set of rate constants to only those that also obeyed this additional set of equations, which was sufficient to obtain a unique solution. We have tested this approach with data obtained from macroscopic delayed rectifier potassium channel currents in voltage-clamped guinea pig ventricular myocyte membranes. This potassium channel has relatively simple kinetics without an inactivation process and provided a convenient system to determine a globally optimized set of voltage-dependent rate constants for a Markov kinetic model. The ability of the fitting algorithm to extract rate constants from the macroscopic current data was tested using "data" synthesized from known rate constants. The simulated data sets were analyzed with the global fitting procedure and the fitted rate constants were compared with the rate constants used to generate the data. Monte Carlo methods were used to examine the accuracy of the estimated kinetic parameters. This global fitting approach provided a useful and convenient method for reliably extracting Markov rate constants from macroscopic voltage clamp data over a broad range of membrane potentials. The limitations of the method and the dependence on initial guesses are described.

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Selected References

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

  1. Armstrong C. M. Sodium channels and gating currents. Physiol Rev. 1981 Jul;61(3):644–683. doi: 10.1152/physrev.1981.61.3.644. [DOI] [PubMed] [Google Scholar]
  2. 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]
  3. Bennett P. B., McKinney L. C., Kass R. S., Begenisich T. Delayed rectification in the calf cardiac Purkinje fiber. Evidence for multiple state kinetics. Biophys J. 1985 Oct;48(4):553–567. doi: 10.1016/S0006-3495(85)83813-3. [DOI] [PMC free article] [PubMed] [Google Scholar]
  4. Bennett P., McKinney L., Begenisich T., Kass R. S. Adrenergic modulation of the delayed rectifier potassium channel in calf cardiac Purkinje fibers. Biophys J. 1986 Apr;49(4):839–848. doi: 10.1016/S0006-3495(86)83713-4. [DOI] [PMC free article] [PubMed] [Google Scholar]
  5. Clapham D. E., Defelice L. J. Voltage-activated k channels in embryonic chick heart. Biophys J. 1984 Jan;45(1):40–42. doi: 10.1016/S0006-3495(84)84099-0. [DOI] [PMC free article] [PubMed] [Google Scholar]
  6. Gintant G. A., Datyner N. B., Cohen I. S. Gating of delayed rectification in acutely isolated canine cardiac Purkinje myocytes. Evidence for a single voltage-gated conductance. Biophys J. 1985 Dec;48(6):1059–1064. doi: 10.1016/S0006-3495(85)83869-8. [DOI] [PMC free article] [PubMed] [Google Scholar]
  7. 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]
  8. Hamill O. P., Marty A., Neher E., Sakmann B., Sigworth F. J. Improved patch-clamp techniques for high-resolution current recording from cells and cell-free membrane patches. Pflugers Arch. 1981 Aug;391(2):85–100. doi: 10.1007/BF00656997. [DOI] [PubMed] [Google Scholar]
  9. Hille B. Local anesthetics: hydrophilic and hydrophobic pathways for the drug-receptor reaction. J Gen Physiol. 1977 Apr;69(4):497–515. doi: 10.1085/jgp.69.4.497. [DOI] [PMC free article] [PubMed] [Google Scholar]
  10. 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]
  11. 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]
  12. 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]
  13. Korn S. J., Horn R. Statistical discrimination of fractal and Markov models of single-channel gating. Biophys J. 1988 Nov;54(5):871–877. doi: 10.1016/S0006-3495(88)83023-6. [DOI] [PMC free article] [PubMed] [Google Scholar]
  14. 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]
  15. Liebovitch L. S., Sullivan J. M. Fractal analysis of a voltage-dependent potassium channel from cultured mouse hippocampal neurons. Biophys J. 1987 Dec;52(6):979–988. doi: 10.1016/S0006-3495(87)83290-3. [DOI] [PMC free article] [PubMed] [Google Scholar]
  16. 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]
  17. Mitra R., Morad M. A uniform enzymatic method for dissociation of myocytes from hearts and stomachs of vertebrates. Am J Physiol. 1985 Nov;249(5 Pt 2):H1056–H1060. doi: 10.1152/ajpheart.1985.249.5.H1056. [DOI] [PubMed] [Google Scholar]
  18. Motulsky H. J., Ransnas L. A. Fitting curves to data using nonlinear regression: a practical and nonmathematical review. FASEB J. 1987 Nov;1(5):365–374. [PubMed] [Google Scholar]
  19. Roden D. M., Bennett P. B., Snyders D. J., Balser J. R., Hondeghem L. M. Quinidine delays IK activation in guinea pig ventricular myocytes. Circ Res. 1988 May;62(5):1055–1058. doi: 10.1161/01.res.62.5.1055. [DOI] [PubMed] [Google Scholar]
  20. 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]
  21. Stevens C. F. Interactions between intrinsic membrane protein and electric field. An approach to studying nerve excitability. Biophys J. 1978 May;22(2):295–306. doi: 10.1016/S0006-3495(78)85490-3. [DOI] [PMC free article] [PubMed] [Google Scholar]
  22. Stühmer W., Conti F., Suzuki H., Wang X. D., Noda M., Yahagi N., Kubo H., Numa S. Structural parts involved in activation and inactivation of the sodium channel. Nature. 1989 Jun 22;339(6226):597–603. doi: 10.1038/339597a0. [DOI] [PubMed] [Google Scholar]

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