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I was playing around with a simulation of the Hodgkin-Huxley model using their original parameters for the squid giant axon.

By applying a constant stimulation current to the model in resting state, an infinite train of action potentials is triggered, which seems reasonable. However, if the current exceeds a threshold, these APs die off very quickly as both the membrane potential and the ion conductances reach a steady state.

What is this phenomenon called? Is it a real phenomenon, or just an artefact of the Hodgkin-Huxley model?

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  • $\begingroup$ Just for my own ability to reproduce your results, did you use one of the online simulators or did you code your own? $\endgroup$
    – jonsca
    Commented Jan 2, 2012 at 1:10
  • $\begingroup$ @jonsca: It's based on one from a university course. I shouldn't share it publicly, but could email you the Matlab code ([email protected]). It's a naïve DE solver that directly approximates the differentials in time steps of 1e-3 ms. $\endgroup$
    – user24
    Commented Jan 2, 2012 at 9:20

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This phenomenon is called depolarization block and it occurs in real membranes in current-clamp experiments.

The key mechanism is that the membrane has not been allowed to repolarize sufficiently to relieve the inactivation of sodium channels. The Hodgkin-Huxley model reflects this in the "inverted" voltage-dependence of the h gate (sodium inactivation gate)--inactivation is greater at higher voltages. This means that sodium channels cannot open again, or trigger another action potential, until the membrane is repolarized. Canonically, the need to relieve inactivation of sodium channels is the reason for the afterhyperpolarization phase of an action potential where the AP downstroke becomes transiently more negative than the resting potential.

The relevance of depolarization block in in vivo physiological conditions is not well studied. It is not likely that depolarization block occurs in well-behaved neurons under physiological conditions. However, it's possible that it does occur during pathological states.

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(I probably ought to have a pat answer to this on the tip of my mind, but since I don't I'm going to wing it. This is probably just an opportunity to make an utter fool of myself. Please treat everything that follows with extreme suspicion.)

I think this is effectively an artefact of the model. That may not be true in the strictest sense -- it is possible such behaviour could be produced in real experimental preparations -- but it would require driving them in drastically non-physiological ways. I am not aware of this having been done, but I'm sure that's just my ignorance -- I would be surprised if nobody has tried.

In physiological terms, though: where would such a large constant current come from in a real cell? Where would the charges go? How would that be sustained with realistic boundary conditions?

While it is possible that such an effect can come into play very transiently in living systems, it seems unlikely that a true steady state of this kind could ever be reached.

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  • $\begingroup$ Thanks for your input. I'm interested in what would happen to a real membrane, though, not whether the situation is likely to occur naturally. $\endgroup$
    – user24
    Commented Jan 2, 2012 at 9:55
  • $\begingroup$ @Tim In which case you probably need to be more specific about the experiment you're proposing. Your question seems to boil down to how fully the H-H model describes the behaviour of an actual axon membrane propagating APs. (There's an auxiliary issue of how well your sim implements the model, but let's shelve that for now.) Not having done the experiment, I can only guess. My intuition is that it would be possible to drive a real membrane to steady state if you're sufficiently aggressive about it, but that doing so would not demonstrate anything meaningful. $\endgroup$
    – walkytalky
    Commented Jan 2, 2012 at 22:58
  • $\begingroup$ The question is rather how well the model describes reality in one specific aspect. A way to check would be to clamp a squid giant axon the way Hodgkin and Huxley did, apply a constant current of sufficient amplitude, and measure the membrane potential. $\endgroup$
    – user24
    Commented Jan 2, 2012 at 23:02
  • $\begingroup$ I don't find it improbable that this could be a known problem with the model or a known behaviour of the real membrane. $\endgroup$
    – user24
    Commented Jan 2, 2012 at 23:04
  • $\begingroup$ @Tim For that experiment, I broadly stand by my guess. With sufficient current injection you could overwhelm the oscillatory behaviours of the channel population. It would, however, be interesting to see how closely the real current needed for that matched the model prediction. $\endgroup$
    – walkytalky
    Commented Jan 2, 2012 at 23:10

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