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[Neuroscience] Re: Hodgkin Huxley equations

r norman via neur-sci%40net.bio.net (by r_s_norman from comcast.net)
Fri Jul 15 10:50:05 EST 2011

On Thu, 14 Jul 2011 12:26:33 -0700 (PDT), "pennsylvaniajake from gmail.com"
<pennsylvaniajake from gmail.com> wrote:

>From what I can gather on the internet, the idea of writing a mathematical program to solve the H-H equations is a waste of time because there are so many software programs that can be used to show this model.   
>I would like to know the opinion of others regarding this issue.  I realize that this model is presented in introductory courses in neuroscience, but beyond this use is it necessary to pursue a detailed mathematical analysis of it?
>I am writing a text book on the mathematics of the neuron and would like to know if I should consider the H-H model or not?  I am going over their paper in detail, but I don't know if I should go into the mathematics of it or not. 

In the past I have written programs to solve the HH equations, both as
a teaching tool and for my own amusement and edification.  Given that
there are now more than enough versions available, there is no good
reason to craft yet another.   The value of the simulations is not to
illustrate the details of the equations but rather to demonstrate the
phenomena of excitability.

In a text on the mathematics of the neuron, it would seem that the HH
model would be extremely useful but only for its historic importance.
It provided absolute and convincing evidence that all the features of
excitability could be explained in terms of voltage/time dependent
ionic conductances.  That continuous mathematical relations -- the
voltage dependence of the alphas and betas for m, n, and h, could
produce a propagated all-or-none action potential was a monumental
achievement.  Now that the "ionic theory" is so unquestionably
established, it is less important and there are better areas to spend
time and effort in coverage.

In particular, the development of patch clamp techniquest that could
directly observe ion channel activity seems to have rendered going
through all the hairy details of HH rather obsolete.   The
demonstration of the key players,  sodium activation and inactivation
and of potassium activation,  ia made clear through patch clamp data.
The qualitative description of how these work to contribute to the
action potential is more than enough for pretty much all modern
neurobiology texts.  

So it depends on what the main purpose of your book is:  To cover the
biophysical basis of neural activity?  How modeling contributed to the
history of the development of our understanding? A presentation of the
principles of neuronal activity?  

How much cable theory are you going into?  How much biophysics of
diffusion and electrochemistry and membrane potential?  What level of
mathematical understanding do you expect of your readers?

All these are important questions to answer before working on how much
HH, if any, to include.

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