The electrodynamics of the nerve impulse. (English) Zbl 0649.92011
Summary: The electrodynamics of the nerve impulse is described in the quasistatic limit in terms of physically well-differentiated components: the double layer of charge responsible for the action potential, and the ionic current which is invariant under Galilean transformation. The present framework, in which the role of the double layer is prominent, predicts quantitative changes in the ionic current and the rate of rise of the action potentials that are produced by anesthetics which change the capacitance of the membrane. The nonspecific effects produced by changes in the capacitance of the membrane are discriminated from the specific effects which affect only the number of channels. We also calculate in the quasistatic limit the potential in the whole space for a given double layer of charges, obtaining expressions for the intracellular and extracellular potentials in terms of the action potential.
MSC:
| 92Cxx | Physiological, cellular and medical topics |
| 78A70 | Biological applications of optics and electromagnetic theory |
Keywords:
electrodynamics of the nerve impulse; quasistatic limit; double layer of charge; action potential; ionic currentReferences:
| [1] | Armstrong, C. M.; Bezanilla, F., Currents related to movement of gating particles of the sodium channels, Nature (London), 242, 459-461 (1973) |
| [2] | Armstrong, C. M.; Binstock, L., The effects of several alcohols on the properties of the squid giant axon, J. Gen. Physiol., 48, 265-277 (1964) |
| [3] | (blank, M., Electrical Double Layers in Biology (1985), Plenum: Plenum New York) |
| [4] | Burgers, J. M., A mathematical model illustrating the theory of turbulence, Adv. Appl. Mech., 1, 171-199 (1948) |
| [5] | Clark, J.; Plonsey, R., A mathematical evaluation of the core conductor model, Biophys. J., 6, 95-112 (1966) |
| [6] | Clark, J.; Plonsey, R., The extracellular potential field of the single active nerve fiber in a volume conductor, Biophys. J., 8, 842-864 (1968) |
| [7] | del Castillo, J.; Moore, J. W., On increasing the velocity of a nerve impulse, J. Physiol., 148, 665-670 (1959) |
| [8] | FitzHugh, R., Impulses and physiological states in theoretical models of nerve membrane, Biophys. J., 1, 445-466 (1961) |
| [9] | FitzHugh, R., Mathematical models of excitation and propagation in nerve, (Schwan, H. P., Biological Engineering (1969), McGraw-Hill: McGraw-Hill New York), 1-85 |
| [10] | Haydon, D. A., Anesthetic effects on the squid giant axon, Curr. Top. Membr. Transp., 22, 445-482 (1983) |
| [11] | Haydon, D. A.; Kimura, J. E., Some effects of the \(n\)-pentane on the sodium and potassium currents of the squid giant axon, J. Physiol. (London), 312, 57-70 (1981) |
| [12] | Haydon, D. A.; Urban, B. W., The action of hydrocarbons and carbon tetrachloride on the sodium current of the giant squid axon, J. Physiol. (London), 338, 435-450 (1983) |
| [13] | Haydon, D. A.; Urban, B. W., The action of alcohols and other non-ionic surface active substances on the sodium current of the giant squid axom, J. Physiol. (London), 341, 411-427 (1983) |
| [14] | Haydon, D. A.; Requena, J.; Urban, B. W., Some effects of aliphatic hydrocarbons on the electrical capacity and ionic currents of the squid giant axom membrane, J. Physiol. (London), 309, 229-245 (1980) |
| [15] | Hodgkin, A. L., A note on the conduction velocity, J. Physiol. (London), 125, 221-224 (1954) |
| [16] | Hodgkin, A. L.; Huxley, A. F., Currents carried by sodium and potassium ion through the membrane of the giant axon of Loligo, J. Physiol. (London), 116, 449-472 (1952) |
| [17] | Hodgkin, A. L.; Huxley, A. F., The components of membrane conductance in the giant axon of Loligo, J. Physiol. (London), 116, 473-496 (1952) |
| [18] | Hodgkin, A. L.; Huxley, A. F., The dual effect of membrane potential on sodium conductance in the giant axon of Loligo, J. Physiol. (London), 116, 497-506 (1952) |
| [19] | Hodgkin, A. L.; Huxley, A. F., A quantitative description of membrane current and its application to conduction and excitation in nerve, J. Physiol. (London), 117, 500-544 (1952) |
| [20] | Jackson, J. D., Classical Electrodynamics (1962), Wiley: Wiley New York · Zbl 0114.42903 |
| [21] | Jurisic, N., The propagation of the nerve impulse, Biophys. J., 51, 817-823 (1987) |
| [22] | Lorente de No, R., A study of nerve physiology, Rockefeller Inst. Stud., 132, 384-476 (1947) |
| [23] | McLaughlin, S., Electrostatic potentials at membrane solution interfaces, Curr. Top. Membr. Transp., 9, 71-144 (1977) |
| [24] | Nagumo, J.; Arimoto, S.; Yoshigawa, S., An active pulse transmission line simulating nerve axon, Proc. IRE., 50, 2061-2070 (1962) |
| [25] | Plonsey, R., Volume conductor fields of action currents, Biophys. J., 4, 317-328 (1964) |
| [26] | Rosenfalck, P., Volume conducted action potentials and their correlation to the intracellular potentials, Acta Physiol. Scand., 42, 118-119 (1957), (suppl. 145) |
| [27] | Rosenfalck, P., Intra and Extracellular Potential Fields of Active Nerve and Muscle Fibres (1969), Akademisk Forlag: Akademisk Forlag Copenhagen |
| [28] | Seeman, P., The membrane action of anesthetics and tranquilizers, Formacol. Rev., 24, 583-655 (1972) |
| [29] | Scott, A. C., Transmission line equivalent for an unmyelinated nerve axon, Math. Biosci., 13, 47-54 (1972) |
| [30] | Winter, P. M.; Miller, J. N., Anesthesiology, Sci. Amer., 4, 124-131 (1985) |
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