[Neuroscience] Re: Alpha & Beta equations in the Hodgkin-Huxley
Model
rays
via neur-sci%40net.bio.net
(by ray.subhasis from gmail.com)
Tue Nov 2 09:59:55 EST 2010
On Nov 2, 12:59 am, "pennsylvaniaj... from gmail.com"
<pennsylvaniaj... from gmail.com> wrote:
> I am trying to solve the Hodgkin-Huxley Model and I keep going around
> in circles. I have seen on the net and in my books so many different
> ways to write the alpha and beta equations that I am dizzy. Since
> this is not field of expertise, I get lost with what I call
> biophysics. The math is no problem.
>
> One I just ran into on the internet used a different voltage for each
> and every one. I thought you just used membrane voltage such as V or
> for a value 65 mV.
>
> In the book "From Computer to Brain", by W. W. Lytton, pg 332 they use
> V.
> In the book "Biophysics of Computation" by C. Koch, he uses V, but
> they are different equations. Also he through in Tau equations, page
> 146.
>
> And each and every book, and program such as the Neuron, SNAP, and so
> on all have there own.
>
> Also if you don't mind what other equation should I use, such as C dV/
> dt = -Im(t), where Im(t)= gNa(t) [V(t)-ENa] + gK(t) [V(t)-EK] + gleak
> [V(t) - Eleak], or what
>
> Thanks
> Jake
The GENESIS simulator book has detailed discussion of the original
Hodgkin-Huxley model :
http://www.genesis-sim.org/GENESIS/iBoG/iBoGpdf/chapt4.pdf
m_inf/tau_m and alpha/beta are different forms of the same equations.
The same book chapter can resolve your second doubt. You can always
check out the classic paper by Hodgkin and Huxley.
My impression is that NEURON uses the equations for m' and h' with
m_inf, tau_m, h_inf, tau_h for Na+ channels.
Best,
Subha
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