Abstract
Calculations based upon the membrane dipole model have been carried out and indicate the possibility of cooperative behavior during the membrane excitation process. An explicit expression is obtained for the critical electric field,E, which must be present to initiate the cooperative structural transition assumed to occur during membrane excitation. An hypothesis concerning the occurrence of two distinct phase transitions in the membrane resulting in the rapid influx of sodium ions and sodium ion inactivation, respectively, is presented.
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Almeida, S. P., J. D. Bond and T. C. Ward. 1971. “The Dipole Model and Phase Transitions in Biological Membranes.”Biophys. J.,11, 995–1001.
Blumenthal, R., J. P. Changeux and R. Lefever. 1970. “Membrane Excitability and Dissipative Instabilities.”J. Membrane Biol.,2, 351–374.
Changeux, J. P., J. Thiery, Y. Tung and C. Kittel. 1967. “On the Cooperativity of Biological Membranes.”Proc. Nat. Acad. Sci.,57, 335–341.
Engelman, D. M. 1970. “X-Ray Diffraction Studies of Phase Transition of Mycoplasma Laidlawii in the Membrane.”J. Mol. Biol.,47, 115–117.
Fowler, R. H. 1935. “A Theory of the Rotations of Molecules in Solids and of the Dielectric Constant of Solids and Liquids”Proc. Royal Soc., Ser. A., Math. Phys. Sci.,149, 1–28.
Friedenberg, R. M. 1967.The Electrostatics of Biological Cell Membranes, New York: J. Wiley
Frölich, H. 1946. “Dielectric Properties of Dipolar Solids.”Proc. Royal Soc., Ser. A.,185, 399–414.
Hanai, T., D. A. Haydon and J. Taylor 1965. “Polar Group Orientation and the Electrical Propertie of Lecithin Bimolecular Leaflets.”J. Theory. Biol.,9, 278–296.
Hamel, B. B. and I. Zimmerman. 1970. “A Dipole Model for Negative Steady-State Resistance in Excitable Membranes.Biophys. J.,10, 1029–1056.
Hill, T. L. 1960.Introduction to Statistical Thermodynamics, Massachusetts: Addison Wesley.
— 1967. “Electric Fields and the Cooperativity of Biological Membranes”.Proc. Nat. Acad. Sci.,58, 111–114.
— and Y. Chen 1970a. “Cooperative Effects in Models of Steady-State Transport Across Membranes, I”Proc. Nat. Acad. Sci.,65, 1069–1076.
— and —. 1970b. “Cooperative Effects in Models of Steady-State Transport Across Membranes, II. Oscillating Phase Transition.” —Ibid.,66, 189–196.
— and —. 1970c. “Cooperative Effects in Models of Steady-State Transport Acros membranes, III. Simulation of Potassium Ion Transport in Nerve.” —Ibid.,66, 607–614.
— and —. 1971. “On the Theory of Ion Transport Across the Nerve Membrane II. Potassium Ion Kinetics and Cooperative (withx=4)”. —Ibid.,68, 1711–1715.
Hodgkin, A. L. 1951. “The Ionic Basis of Electrical Activity in Nerve and Muscle”Biol. Rev. Cambridge Phil. Soc.,26, 339–409.
— 1964.The Conduction of the Nervous Impulse. Liverpool: University Press.
— and A. F. Huxley. 1939. “Action Potentials Recorded from Inside a Nerve Fiber.”Nature,144, 710–711.
— and —. 1952a. “Currents Carried by Sodium and Potassium Ions Through the Membrane of the Giant Axon of Loligo.”J. Physiol. (London.),116, 449–472.
— and —. 1952b. “The Components of Membrane Conductance in the Giant Axon of Loligo.” —Ibid.,116, 473–496.
— and —. 1952c. “The Dual Effect of Membrane Potential on Sodium Conductance in the Giant Axon of Loligo,” —Ibid.,116, 497–506.
Jackson, J. D. 1962.Classical Electrodynamics. New York: J. Wiley.
Kirkwood, J. G. and J. B. Shumaker. 1952a. “The Influence of Dipole Moment fluctuations on the Dielectric Increment of Proteins in solution.”Proc. Nat. Acad. Sci.,38, 855–862.
— and —. 1952b. “Forces Between Protein Molecules in Solution Arising from Fluctuations in Proton Charge and Configuration.” —Ibid.,38, 863–871.
Moore, J. W. 1962.Physical Chemistry. Englewood Cliffs, New Jersey: Prentice-Hall.
Ohki, S. 1968. “Dielectric Constant and Refractive Index of Lipid Bilayers.”J. Theor. Biol.,19, 97–115.
Reinart, J. C. and J. M. Stein. 1970. “Calorimetric Detection of a membrane-Lipid Phase Transition in Living Cells.”Science,168, 1580–1582.
Ruch, T. C. and H. D. Patton. 1966.Physiology and Biophysics. Philadelphia: Saunders.
Snell, F. 1970.Physical Principles of Biological Membranes. London: Gordon and Breach.
Stein, W. D. 1967.The Movement of Molecules Across Cell Membranes. London: Academic Press.
Stein, W. D., M. E. Tourtellotte, J. C. Reinert, R. N. McElhaney and R. L. Rader. 1969. “Calorimetric Evidence for the Liquid-Crystalline State of Lipids in a Biomebrane.”Proc. Nat. Acad. Sci.,63, 104–109.
Stevens, C. F. 1966.Neurophysiology: A Primer. New York: J. Wiley.
Tasaki, I. 1968.Nerve Excitation. Springfield: C. C. Thomas.
Ward, T. C. and J. D. Bond. 1971. “Comments on the Dipole Model and Membrane Excitation.”Biophys. J.,11, 465–466.
Wei, L. Y. 1969. “Molecular Mechanisms of Nerve Excitation and Conduction.”Bull. Math. Biophys.,31, 39–58.
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Almeida, S.P., Bond, J.D. & Ward, T.C. Electrically induced phase transitions via the dipole model in excitable membranes. Bltn Mathcal Biology 36, 17–28 (1974). https://doi.org/10.1007/BF02461187
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DOI: https://doi.org/10.1007/BF02461187