Abstract
In this work an attempt is made to develop a new physical theory for physiological excitation. The theory is based on the concept of cooperative specific adsorption, an offshoot of the association-induction hypothesis originated by G. N. Ling (1962).
The basic ideas of this work are the following:
-
1)
the specificity for the cooperative adsorption of potassium in exchange for sodium at certain (lipo-)protein sites, called regular sites in this work, are controlled by the cooperative adsorption of calcium in exchange for sodium at certain strategically located sites called cardinal sites by Ling (1962);
-
2)
the desorption energy of potassium from the regular sites is higher when more cardinal sites have adsorbed calcium, or in other words the specificity of those sites for potassium as compared with sodium is then higher;
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3)
cathode electric stimulation withdraws calcium from the cardinal sites.
It is shown that a threshold for cathodic electric stimulation exists such that if the latter is above that threshold a phase transition occurs leading to inward sodium movement. The importance of cooperative phenomena and of the role of cardinal sites as well as that of calcium as a cardinal adsorbant in this physical theory of physiological excitation is emphasized.
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Literature
Ackerman, E. 1962.Biophysical Science. Englewood Cliffs, N.J.: Prentice Hall, Inc.
Adam, G. 1967. “Nervenerregung als kooperativer Kationenaustausch in einem zweidimensionalen Gitter.”Ber. Bunsenges. Phys. Chem.,71, 829–831.
— 1968. “Theorie der Nervenerregung als kooperativer Kationenaustausch in einem zweidimensionalen Gitter I. Ionenstrom nach einem depolarisierenden Sprung in Membranpotential.”Zeitschr f. Naturf.,236, 181–197.
— 1970. “Theory of nerve excitation as a cooperative cation exchange in a two-dimensional lattice” inPhysical Principles of Biological Membranes, pp. 35–67. Eds. F. Snellet al. New York: Gordon and Breach Science Publishers.
— 1971.A Molecular Mechanism for Regulation of the K + current Through the Axon Membrane. First Eur. Biophys. Congr. Eds. E. Brodaet al. E. 9/2, pp. 193–197. Wien: Verlag Wiener Mediz. Akad.
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.
Arvanitaki, A. 1939. “Recherches sur la réponse oscillatoire locale de l'axone géant isolé de Sepia.”Arch. Internat. Physiol.,49, 209–236.
Bianchi, C. P. 1968.Cell Calcium. New York: Appleton-Century Crofts, Division of Merewith Corporation; London: Butterworths.
Blair, H. A. 1932a. “On the Intensity-Time Relations for Stimulation by Electric Currents. I.”J. Gen. Physiol.,15, 709–729.
— 1932b. “On the Intensity-Time Relations for Stimulation by Electric Currents. II.” ——Ibid.,15, 731–755.
Blumenthal, R., J. P. Changeux and R. Lefever. 1970. “Membrane Excitability and Dissipative Instabilities.”J. Membrane Biol.,2, 351–374.
Bragg, W. L. and E. J. Williams. 1934. “The Effect of Thermal Agitation on Atomic Arrangements in Alloys.”Proc. Roy. Soc. A,145, 699–730.
Changeux, J. P., J. Thiery, Y. Tung and C. Kittel. 1967. “On the Cooperativity of Biological Membranes.”Proc. Nat. Acad. Sci. 57, 335–341.
Cole, K. S. 1968.Membranes, Ions and Impulses. A Chapter of Classical Biophysics. Berkeley: University of California Press.
Falk, G. and R. W. Gerard. 1954. “Effect of Micro-Injected Salts and ATP on the Membrane Potential and Mechanical Response of Muscle.”J. Cell. and Comp. Physiol.,43, 393–403.
Grundfest, H., C. Y. Kao and M. Altamirano. 1955. “Bioelectric Effects of Ions Microinjected into the Giant Axon of Loligo.”J. Gen. Physiol.,38, 245–282.
Hamel, B. B. and I. Zimmerman. 1970. “A Dipole Model for Negative Steady-State Resistance in Excitable Membranes.”Biophys. J.,10, 1029–1056.
Heibrunn, L. V. 1943.An Outline of Physiology. Philadelphia and London: Saunders Co.
Hill, A. V. 1936a. “Excitation and Accommodation in Nerve.”Proc. Roy. Soc. London,B119, 305–355.
— 1936b. “The Strength-Duration Relation for Electric Excitation of Medullated Nerve.” ——Ibid.,B119, 440–453.
Hill, T. L. 1960.Introduction to Statistical Thermodynamics. Reading, Mass.: Addison-Wesley Publ. Co. Inc.
— and Yi-der 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.
Hill, T. L. and Yi-der Chen. 1970c. “Cooperative Effects in Models of Steady-State Transport across Membranes, III. Simulation of Potassium Ion Transport in Nerve.” ——Ibid.,66, 607–614.
— and —. 1971a. “On the Theory of Ion Transport Across the Nerve Membrane, II. Potassium Ion Kinetics and Cooperativity (withx=4).” ——Ibid.,68, 1711–1715.
— and —. 1971b. “Cooperative Effects in Models of Steady-State Transport Across Membranes, IV. One-Site, Two-Site, and Multisite Models.”Biophys. J.,11, 685–710.
— and —. 1971c. “On the Theory of Ion Transport Across the Nerve Membranes. III. Potassium Ion Kinetics and Cooperativity (withx=4, 6, 9).”Proc. Nat. Acad. Sci.,68, 2488–2492.
Hodgkin, A. L., A. F. Huxley and B. Katz. 1952. “Measurement of Current-Voltage Relations in Membrane of Giant Axon of Loligo.”J. Physiol.,116, 424–448.
— and —. 1952a. “Currents Carried by Sodium and Potassium Ions through Membrane of Giant Axon of Loligo.” ——Ibid.,116, 449–472.
— and —. 1952b. “Components of Membrane Conductance in Giant Axon of Loligo.” ——Ibid.,116, 473–496.
— and —. 1952c. “Dual Effect of Membrane Potential on Sodium Conductance in Giant Axon of Loligo.” ——Ibid.,116, 497–506.
— and —. 1952d. “A Quantitative Description of Membrane Current and its Application to Conductance and Excitation in Nerve.” ——Ibid.,117, 500–544.
— and —. 1952e. “Properties of Nerve Axons (I). Movement of Sodium and Potassium Ions during Nervous Activity.”Cold Spring Harbor Symp. Quant. Biol., XVII, 43–52.
Jones, A. W. 1972. “Control of Cooperative K-Accumulation in Smooth Muscle by Divalent Ions.”Ann. New York Acad. Sci. In press.
— and G. Karreman. 1969a. “Ion Exchange Properties of the Canine Carotid Artery.”Biophys. J.,9, 884–909.
— and —. 1969b. “Potassium Accumulation and Permeation in the Canine Carotid Artery.”-——Ibid.,9, 910–924.
Karreman, G.. 1951. “Contributions to the Mathematical Biology of Excitation with Particular Emphasis on Changes in Membrane Permeability and on Threshold Phenomena.”Bull. Math. Biophysics,13, 189–243.
—. 1964. “Adsorption of Ions at Charged Sites and Phase Boundary Potentials.” ——Ibid.,26, 275–290.
—. 1965. “Cooperative Specific Adsorption of Ions at Charged Sites in an Electric Field.” ——Ibid.,27, Special Issue, 91–104.
—. 1971. “Stochastic Treatment of Cooperative Specific Adsorption.” ——Ibid.,33, 483–495.
Karreman, G. 1972. “Cooperative Specific Adsorption.”Ann. New York Acad. Sci. In press.
— and H. D. Landahl. 1952. “On the Mathematical Biology of Excitation Phenomena.”Cold Spring Harbor Symp. on Quant. Biol., XVII, 293–297.
Katchalski, E. L., Bichowski-Slomnitzki, E. L. and B. E. Volcani. 1953. “The Action of Some Water-Soluble Poly-α-Amino-Acids on Bacteria.”Biochem. J.,55, 671–680.
Ling, G. N.. 1962.A Physical Theory of the Living State: The Association Induction Hypothesis. New York: Blaisdell Pub. Co., a Div. of Random House, Inc.
—. 1964a. “The Association-Induction Hypothesis.”Texas Rep. on Biol. and Med.,22, 244–265.
—. 1964b. “The Role of Inductive Effect in Cooperative Phenomena of Proteins.”Biopolym. Symp.,1, 91–116.
Ling, G. N.. 1965. “The Membrane View and Other Views for Solute Permeability, Distribution and Transport in Living Cells.”Perspect. in Biol. and Med.,9, 87–106.
—. 1966. “All-or-none Adsorption by Living Cells and Model Protein-water Systems: Discussion of the Problem of ‘Permease-Induction’ and Determination of Secondary and Tertiary Structures of Proteins.”Fed. Proc.,25, 958–970.
—. 1970. “The Physical State of Water in Living Cells and its Physiological Significance.”Intern. J. Neurosci.,1, 129–152.
—, S. Will and P. Shannon. 1969. “Studies on Insulin Action. IV. Cooperative Transition in Adsorption: A Theoretical Interpretation of the Priming Action of Glucose Treatment by 25°C on the Subsequent Accumulation of Labelled Glucose by Insulinized Frog Muscle at 0°C with a Discussion of Bacterial Permease Induction.”Physiol. Chem. & Phys.,1, 355–367.
— and G. Bohr. 1970. “Studies on Ion Distribution in Living Cells. II. Cooperative Interaction between Intracellular Potassium and Sodium Ions.”Biophys. J.,10, 519–538.
Luettgau, H. C. and R. Niedergerke. 1958. “The Antagonism between Ca and Na Ions on the Frog's Heart.”J. Physiol.,143, 486–505.
Offner, F. 1937. “Excitation Theories of Rashevsky and Hill.”J. Gen. Physiol.,21, 89–105.
Rashevsky, N. 1933. “Outline of a Physico-Mathematical Theory of Excitation and Inhibition.”Protoplasma,20, 42–56.
—. 1948.Mathematical Biophysics. Chicago: University of Chicago Press.
Rosen, R. 1968. “Turing's Morphogens, Two-Factor Systems and Active Transport.”Bull. Math. Biophysics,30, 493–499.
Segal, J. R. 1968. “Surface Charge on Giant Axons of Squid and Lobster.”Biophys. J.,8, 470–499.
Tasaki, I. 1968.Nerve Excitation. Springfield, Ill.: C. C. Thomas.
—, T. Teorell and C. S. Spyropoulos. 1961. “Movement of Radioactive Tracers Across Squid Membranes.”Am. J. Physiol.,200, 11–22.
— and T. Takenaka. 1963. “Resting and Action Potential of Squid Giant Axons Intracellularly Perfused with Sodium-rich Solutions.”Proc. Nat. Acad. Sci.,50, 619–626.
— and —. 1964. “Effects of Various Potassium Salts and Proteases upon Excitability of Intracellularly Perfused Squid Giant Axons.” ——Ibid.,52, 804–810.
— and M. Luxoro. 1964. “Intracellular Perfusion of Chilean Giant Squid Axon.”Science,145, 1313–1315.
Tasaki, I., A. Watanabe and I. Singer. 1966. “Excitability of Squid Giant Axons in the Absence of Univalent Cations in the External Medium.”Proc. Nat. Acad. Sci.,56, 1116–1122.
Tasaki, I., W. Barry and L. Carnay. 1970. “Optical and Electrophysiological Evidence for Conformational Changes in Membrane Macromolecules during Nerve Excitation.” InPhysical Principles of Biological Membranes. Eds. F. Snellet al. New York: Gordon and Breach Science Publ.
Wei, L. Y. 1969. “Molecular Mechanisms of Nerve Excitation and Conduction.”Bull. Math. Biophysics,31, 39–58.
—. 1971. “Quantum Theory of Nerve Excitation.” ——Ibid.,33, 187–193.
Wobschall, D. 1968. “An Electret Model of the Nerve Membrane.”J. Theor. Biol.,21, 439–448.
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Karreman, G. Towards a physical understanding of physiological excitation as a cooperative specific adsorption phenomenon. Bltn Mathcal Biology 35, 149–171 (1973). https://doi.org/10.1007/BF02558803
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DOI: https://doi.org/10.1007/BF02558803