cable model voltage clamp propagation of an action potential

EE-515 Bioelectricity & Biomagnetism 2002 Fall Murat Eyuboglu

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Cable ModelVoltage Clamp

Propagation of an Action Potential

Illustrations are taken from:J. Malmivuo, R. Plonsey, Bioelectromagnetism, Oxford Press, 1995http://butler.cc.tut.fi/~malmivuo/bem/book/


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Cable Model of Axon


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Steady-State Response


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Propagation of Activation


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Uniform Current Injection


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Step Excitation


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Voltage Clamp Experiment


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Membrane Current


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Membrane Current


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Ionic Membrane Currents


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Selective measurement of sodium and potassium currents by selective blocking of Na and K

channels

Control measurement without pharmacological agents.

After tetrodotoxin (TTX). After tetraethylammonium (TEA).


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Potassium Conductance


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Rate Constants & noo


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The potassium ions cross the membrane only through channels that are specific for potassium. Hodgkin and Huxley supposed that the opening and closing of these channels are controlled by electrically charged particles called n-particles.

These may stay in a permissive (i.e., open) position (for instance inside the membrane) or in a nonpermissive (i.e., closed) position (for instance outside the membrane), and they move between these states (or positions) with first-order kinetics.

The probability of an n-particle being in the open position is described by the parameter n, and in the closed position by (1 - n), where 0 n 1. Thus, when the membrane potential is changed, the changing distribution of the n-particles is described by the probability of n relaxing exponentially toward a new value.


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The process determining the variation of K

conductance with depolarization

and repolarization


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Sodium Conductance


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Rate Constants for Na


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The behavior of sodium conductance is initially similar to that of potassium conductance, except that the speed of the conductance increase during depolarization is about 10 times faster. The rise in sodium conductance occurs well before the rise in potassium conductance becomes appreciable.

Hodgkin and Huxley assumed again that at the sodium channels certain electrically charged particles called m-particles exist whose position control the opening of the channel.

Thus they have two states, open (permissive) and closed (nonpermissive); the proportion m expresses the fraction of these particles in the open state (for instance inside the membrane) and (1 - m) the fraction in the closed state (for instance outside the membrane), where 0 m 1.


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The process determining the variation of K conductance

with depolarization

and repolarization


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Voltages in the Squid Axon


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In addition to the variables discussed above, the constants of the Hodgkin-Huxley model are as shown:

Cm = 1 µF/cm²Vr - VNa = -115 mVVr - VK= +12 mVVr - VL= -10.613 mVGNa max = 120 mS/cm²GK max = 36 mS/cm²GL = 0.3 mS/cm²


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H-H Model for Propagation


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During a Propagating Nerve Impulse


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Propagating Nerve Impulse


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End of the Lecture

cable model voltage clamp propagation of an action potential

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