Abstract
The dipole models for steady-state currents in excitable membranes of Arndt, Bond and Roper and of Hamel and Zimmerman are compared by fitting the equations to the data of Gilbert and Ehrenstein. The more complex Hammel and Zimmerman model does not fit the data as well as does the simpler Arndt, Bond and Reper model. When fitting the data, the Hammel and Zimmerman current equation reduces to the Arndt, Bond and Roper current equation because of the values assumed by the parameters. An interpretation is given for the parameter values obtained with the Arndt, Bond and Roper model.
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Literature
Arndt, R. A., J. D. Bond and L. D. Roper. 1970a. “Nerve Radiation and the Dipole Model.”Biophys. J.,10, 1125.
——— and ——. 1970b. “An Exact Constant-Field Solution for a Simple Membrane.”—Ibid.,,10, 1149–1153.
——— and ——. 1972. “A Fit to Nerve Rectification Curves with a Double-Dipole-Layer Membrane Model.”Bull. Math. Biophysics,34, 151–172.
Cole, K. S. 1968.Membranes, Ions and Impulses, p. 192. Berkeley: Univ. of Calif. Press.
Fraser, A. and A. H. Frey. 1968. “Electromagnetic Emission at Micron Wavelength from Active Nerves,”Biophys. J.,8, 731–734.
Gilbert, D. L. and G. Ehrenstein. 1969. “Elect of Divalent Cations on Potassium Conductance of Squid Axons: Determination of Surface Charge.”Biophys. J.,9, 447–463.
Hamel, B. B. and I. D. Zimmerman. 1970. “A Dipole Model for Negative Steady-State Resistance in Excitable Membranes.”—Ibid.,,10, 1029–1056.
—— and——. 1971. “Cooperative Dipole Model for Excitable Membranes.” —Ibid.,,11, 240a.
Hodgkin, A. L., A. F. Huxley and B. Katz, 1952. “Measurement of Current-Voltage Relations in the Membrane of the Giant Axon of Loligo”J. Physiol. 116, 424–447.
Robertson, J. D. 1964.Cellular Membranes in Development, pp. 1–80. Ed. by M. Locke, New York: Academic Press.
Sears, F. W. 1953.An Introduction to Thermodynamics, The Kinetic Theory of Gases, and Statistical Mechanics, 2nd Ed., p. 235. Reading, Mass.: Addison-Wesley Pub. Co.
Stein, W. D. 1967.The Movement of Molecules Across Cell Membranes, chapter 1. New York: Academic Press.
Vandenheuval, F. A. 1963. “The Study of Biological Structure at the Molecular Level with Stereomodel Projections I. The Lipids in the Myelin Sheath of Nerve.”J. Amer. Oil Chem. Soc.,40, 455–471.
Vanderkooi, G. and D. E. Green. 1970. “Biological Membranes Structure, I. The Protein Crystal Model for Membranes.”Proc. Nat. Acad. Sci. 66, 615–621.
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Arndt, R.A., Roper, L.D. Quantitative comparison of dipole models for steady-state currents in excitable membranes. Bulletin of Mathematical Biophysics 34, 305–324 (1972). https://doi.org/10.1007/BF02476444
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DOI: https://doi.org/10.1007/BF02476444