12.2. Simplified mechanism of the action potential[[Student version, January 17, 2003]] 455
force. Let the total retarding force beγθ,whereγis some constant. Find the rate at which
mechanical work gets converted to thermal form.
c. What sets the speedθof the traveling wave?Finally, let’s begin again with the chain entirely in the upper channel. This time we grasp it in
the middle, pull it over the hump, and let go (Figure 12.5b). If we pull too little over the hump,
as shown in the figure, then both gravity and the applied tension act to pull it back to its initial
state: No traveling wave appears, though the disturbance will spread before settling down. But if
wedrape a large enough segment over the hump initially, upon releasing the chain we’ll seetwo
propagating waves begin to spread from the center point, one moving in each direction.
Our thought experiment has displayed most of the qualitative features of the action potential, as
described in Section 12.1.1! The chain’s height roughly represents the deviation of concentrations
from their equilibrium values; the viscous dissipation represents electrical resistance. We saw how
adynamical system with continuously distributed stored potential energy, and dissipation, can
behave as anexcitable medium,ready to release its energy in a controlled way as a propagating
waveof excitation:
- The wave requires a threshold stimulus.
- Forsubthreshold stimuli the system gives a spreading, but rapidly decaying, response,
like electrotonus. - Similarly, stimuli of any strength but the “wrong” sign give decaying responses (imag-
ine lifting the rope up the far side of the higher trough in Figure 12.5b). - Above-threshold stimuli create a travelingwave ofexcitation. The strength of the
distant response does not depend on the stimulus strength. Though we did not
prove this, it should be reasonable to you that itsformwill also be stereotyped
(independent of the stimulus type). - The traveling wave moves at constant speed. You found in Your Turn 12b that
this speed is determined by a tradeoff between the stored energy density and the
dissipation (friction).
There will be numerous technical details before we have a mathematical model of the action
potential rooted in verifiable facts about membrane physiology (Sections 12.2–12.3). In the end,
though, the mechanism discovered by Hodgkin and Huxley boils down to the one depicted in
Figure 12.5:
Each segment of axon membrane goes in succession from resisting change (like
chain segments to the left of the kink in Figure 12.5a) to amplifying it (like
segments immediately to the right of the kink) when pulled over a threshold by
its neighboring segment.(12.12)
Though it’s suggestive, our mechanical model has one very big difference from the action po-
tential: It predicts one-shot behavior. We cannot pass a second wave along our chain. Action
potentials, in contrast, areself-limiting:The passing nerve impulse stops itself before exhausting
the available free energy, leaving behind it a state that is able to carry more impulses (after a short
refractory period). Even after we kill a nerve cell, or temporarily suspend its metabolism, its axon
can conduct thousands of action potentials before running out of stored free energy. This property
is needed when a nerve cell is called upon to transmit rapid bursts of impulses in between quiescent
periods of trickle charging by the ion pumps.