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Electrically induced phase transitions via the dipole model in excitable membranes

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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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Literature

  • 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.

    Article  Google Scholar 

  • Blumenthal, R., J. P. Changeux and R. Lefever. 1970. “Membrane Excitability and Dissipative Instabilities.”J. Membrane Biol.,2, 351–374.

    Article  Google Scholar 

  • Changeux, J. P., J. Thiery, Y. Tung and C. Kittel. 1967. “On the Cooperativity of Biological Membranes.”Proc. Nat. Acad. Sci.,57, 335–341.

    Article  Google Scholar 

  • Engelman, D. M. 1970. “X-Ray Diffraction Studies of Phase Transition of Mycoplasma Laidlawii in the Membrane.”J. Mol. Biol.,47, 115–117.

    Article  Google Scholar 

  • 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.

    MATH  Google Scholar 

  • Friedenberg, R. M. 1967.The Electrostatics of Biological Cell Membranes, New York: J. Wiley

    Google Scholar 

  • Frölich, H. 1946. “Dielectric Properties of Dipolar Solids.”Proc. Royal Soc., Ser. A.,185, 399–414.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Hamel, B. B. and I. Zimmerman. 1970. “A Dipole Model for Negative Steady-State Resistance in Excitable Membranes.Biophys. J.,10, 1029–1056.

    Google Scholar 

  • Hill, T. L. 1960.Introduction to Statistical Thermodynamics, Massachusetts: Addison Wesley.

    Google Scholar 

  • — 1967. “Electric Fields and the Cooperativity of Biological Membranes”.Proc. Nat. Acad. Sci.,58, 111–114.

    Article  Google Scholar 

  • — and Y. Chen 1970a. “Cooperative Effects in Models of Steady-State Transport Across Membranes, I”Proc. Nat. Acad. Sci.,65, 1069–1076.

    Article  Google Scholar 

  • — and —. 1970b. “Cooperative Effects in Models of Steady-State Transport Across Membranes, II. Oscillating Phase Transition.” —Ibid.,66, 189–196.

    Article  Google Scholar 

  • — and —. 1970c. “Cooperative Effects in Models of Steady-State Transport Acros membranes, III. Simulation of Potassium Ion Transport in Nerve.” —Ibid.,66, 607–614.

    Article  Google Scholar 

  • — and —. 1971. “On the Theory of Ion Transport Across the Nerve Membrane II. Potassium Ion Kinetics and Cooperative (withx=4)”. —Ibid.,68, 1711–1715.

    Article  Google Scholar 

  • Hodgkin, A. L. 1951. “The Ionic Basis of Electrical Activity in Nerve and Muscle”Biol. Rev. Cambridge Phil. Soc.,26, 339–409.

    Google Scholar 

  • — 1964.The Conduction of the Nervous Impulse. Liverpool: University Press.

    Google Scholar 

  • — and A. F. Huxley. 1939. “Action Potentials Recorded from Inside a Nerve Fiber.”Nature,144, 710–711.

    Google Scholar 

  • — and —. 1952a. “Currents Carried by Sodium and Potassium Ions Through the Membrane of the Giant Axon of Loligo.”J. Physiol. (London.),116, 449–472.

    Google Scholar 

  • — and —. 1952b. “The Components of Membrane Conductance in the Giant Axon of Loligo.” —Ibid.,116, 473–496.

    Google Scholar 

  • — and —. 1952c. “The Dual Effect of Membrane Potential on Sodium Conductance in the Giant Axon of Loligo,” —Ibid.,116, 497–506.

    Google Scholar 

  • Jackson, J. D. 1962.Classical Electrodynamics. New York: J. Wiley.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • — and —. 1952b. “Forces Between Protein Molecules in Solution Arising from Fluctuations in Proton Charge and Configuration.” —Ibid.,38, 863–871.

    Article  Google Scholar 

  • Moore, J. W. 1962.Physical Chemistry. Englewood Cliffs, New Jersey: Prentice-Hall.

    Google Scholar 

  • Ohki, S. 1968. “Dielectric Constant and Refractive Index of Lipid Bilayers.”J. Theor. Biol.,19, 97–115.

    Article  Google Scholar 

  • Reinart, J. C. and J. M. Stein. 1970. “Calorimetric Detection of a membrane-Lipid Phase Transition in Living Cells.”Science,168, 1580–1582.

    Google Scholar 

  • Ruch, T. C. and H. D. Patton. 1966.Physiology and Biophysics. Philadelphia: Saunders.

    Google Scholar 

  • Snell, F. 1970.Physical Principles of Biological Membranes. London: Gordon and Breach.

    Google Scholar 

  • Stein, W. D. 1967.The Movement of Molecules Across Cell Membranes. London: Academic Press.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Stevens, C. F. 1966.Neurophysiology: A Primer. New York: J. Wiley.

    Google Scholar 

  • Tasaki, I. 1968.Nerve Excitation. Springfield: C. C. Thomas.

    Google Scholar 

  • Ward, T. C. and J. D. Bond. 1971. “Comments on the Dipole Model and Membrane Excitation.”Biophys. J.,11, 465–466.

    Google Scholar 

  • Wei, L. Y. 1969. “Molecular Mechanisms of Nerve Excitation and Conduction.”Bull. Math. Biophys.,31, 39–58.

    Google Scholar 

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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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