1Physiology 472/572 - 2011 - Quantitative modeling of biological systems Lecture 7: Nerve impulse propagation - Part I Neurons • cells responsible for generation, transmission and processing of nervous impulses • diverse in form, but normally consist of a cell body, one or more axons, and dendrites • dendrites receive input from other neurons • signals travel from dendrites to axons • axons carry impulses a large distance without decay • a nerve is a bundle of axons • signals travel from axon terminal to other neurons at synapses, by release of chemicals (neurotransmitters) Action potential • rapid change in membrane potential, propagates along nerve axon as a traveling wave2Hodgkin-Huxley model • A quantitative description of membrane current and its application to conduction and excitation in nerve. A.L. Hodgkin and A.F. Huxley. J. Physiol. 1952;117;500-544. • Applications of Hodgkin-Huxley equations to excitable tissues. D. Noble. Physiol. Rev. 1966:46;1-50. Membrane current • two components - ionic and capacitive: im = ii + ic • ionic: ii = gNa(Em - ENa) + gK(Em - EK) + gL(Em - EL) • L stands for leakage - includes Cl- current • capacitive: dtdECimc= , C = capacitance per length Determination of membrane ion conductances - voltage clamp experiments - potassium • experiments on giant axon of squid Loligo • a wire was inserted in the axon, such that the membrane potential could be controlled • variations in conductance: A: depolarized by 25 mV. B: repolarized • can describe by gK = gKmax n4 where 0 ≤ n ≤ 1 and nβ)n1(αdtdnnn−−= • equilibrium value of n: nnnβααn+=∞3• αn and βn depend on the membrane potential - as membrane depolarizes, gK tends to increase Determination of membrane ion conductances - voltage clamp experiments - sodium • can describe by gNa = gNamax m3h where 0 ≤ m ≤ 1, 0 ≤ h ≤ 1 • mβ)m1(αdtdmmm−−= and hβ)h1(αdtdhhh−−= • as membrane depolarizes, αm increases and βm decreases so m tends to increase, but αh decreases and βh increases so h tends to decrease • when depolarized, αm >> αh, so m increases fast and h decreases slowly, resulting in a transient increase in gNa4Example - response to square wave of membrane potential • gNa > gK in the initial phase, but then gK overtakes
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