Download e-book for kindle: Biomathematics in 1980Papers presented at a workshop on by Luigi Ricciardi and Alwyn Scott (Eds.)

By Luigi Ricciardi and Alwyn Scott (Eds.)

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J. ~,87-104. Math. A critical test. Bezanilla, F. M. (1975): Kinetic properties and inactivation of the gating currents of sodium channels in squid axon. Phil. Trans. R. Soc. Lond. B ~, 459-482. R. R. (1980): Analysis of the effects of changes in rate and rhythm upon the electrical activity in the heart. Progr. Biophys. Mo 1ec. Bi 01. l,§" 1- 52 . R. and Kerr, D. B. (1974): Potassium conductance models related to an interactive subunit membrane. J. Membrane Biol. ~,363-380. 41 THE MATHEMA TICS OF EXCITA TlON Canneliet, E.

Small smalr' I 2 ", -, -----. - 11 '1 o I 'f u I of lOb? u 1100 mV 20 s Figure 10. Bifurcation diagram for FitzHugh's equation. The large amplitude so 1ut ions found between II and 12 correspond to the repet i t i ve action potentials, illustrated by records obtained from a molluscan neurone (VV 1/2 of Lymnaea). As the current increases, the rate increases and the steady-state amplitude of the action potentials decreases. system is sketched in Fi gure 10, together with ill ustrat ions of the types of behaviour actually found in an isopotential neurone.

Three voltage sensitive ionic currents were described, INa IK and Ip a delayed sodium current found in Xenopus but not Rana (Dodge, 1963). The currents were controlled by activation m, n, p, and inactivation variables h: INa 2 - = m h INa' IK 2 = n i K, 2 Ip a pIp, where m, n, h, P obey firs t order k i net i c s with vo lt age-dependent rate coeff icients ct , B . The empirical equations describing the voltage dependence of the i i rate coefficients were all of the form ct, B = a(V - b)/(l - exp (b - Vic)) (17) with a, b, c constants.

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