[Neuroscience] Re: membrane voltage equations which one

r norman via neur-sci%40net.bio.net (by r_s_norman from comcast.net)
Mon Sep 6 17:52:13 EST 2010

On Mon, 6 Sep 2010 14:27:23 -0700 (PDT), Bill
<connelly.bill from gmail.com> wrote:

>Or I suppose you could get really nerdy and replace the simple ohmic
>behavior of an ion channel with its true, Goldman-Hoxgkin-Katz
>Flux*area=P.z^2. (V.F^2)/(RT). ([Ion]i - [Ion]o.e^(-z.V.F/RT))/(1-e^(-
>I wonder what happens to the shape of the action potential if you take
>that into account? Probably not a lot seeing as the important fluxes
>take place [not] so far from the reversal potentials.

<snip older stuff>

I am responding here instead of to your correction because this is
more complete.  I did make the correction to your text, above.

Actually, at the initiation of the action potential, Na+ is far from
its reversal potential and, at the beginning of the downsweep at peak
overshoot, K+ is far from its reversal potential.

Certainly Hodgkin and Huxley were aware of the dynamics  you mention
commonly referred to as the GHK equations (Godman, Hodgkin, and Katz)
since Hodgkin and Katz derived that flux term in their 1949 paper on
the role of Na+ in the action potential.  Also, Hodgkin, Huxley, and
Katz were the authors of the first of the series of four
"Hodgkin-Huxley" papers in 1952 describing the mechanism of the action
potential.  Hodgkin and Huxley make explicit reference to the
exponential factors in the equation you describe in at least two of
the four papers (I just skimmed them over looking for them).
Consequently, when they computed the action potential based on their
voltage clamp data and used the simple ohmic relationship, it was not
at all for lack of knowledge.  The finest details of the shape of the
action potential don't really matter:  the H-H computation does not
look exactly like the recorded action potential.  And that is probably
not the only or the most important simplification in the system
necessary to do effective computational work.  Still, the results are
so strikingly similar to reality and all the qualitative features are
reproduced in the equations using ohmic laws that no harm is done.

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