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Hodgkin-Huxley equations

r norman rsnorman_ at _comcast.net
Sat Apr 12 21:54:20 EST 2003

On Fri, 11 Apr 2003 18:47:27 -0400, Jake <jtrexel at ix.netcom.com>

>How do I parameterize these equations using time as the dependent
>variable ?  v is for voltage, alpha is the alpha symbol and I have 3
>separate equations for alpha (n, h and n).  I also want to be able to
>plot them together.
>alpha(m)(v) = 4*exp(1-0.0556(v+65)
>alpha(h)(v) = 1/(1+exp-0.1(v+35))
>aplah(n)(v) = 0.125*exp(-0.0125*v + 65)
>These are the Hodgkin-Huxley equations.

I think you may not be understanding the H-H equations correctly,
or else or are possibly not asking the question correctly.  Then
again, I may be misunderstanding your question.

The alpha's and beta's in the H-H equations are not functions of time.
They vary with voltage, as you show.  But the alphas and betas are,
in fact, parameters in differential equations for m, n, and h.  That
is where time enters: dm/dt = alpha-m * (1-m) - beta-m * m

It doesn't really mean much to plot the alphas and betas vs time. 
On the other hand, plotting m, n, and h vs time is useful because
they have a physical interpretation in terms of activation and

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