[Neuroscience] Re: Hodgkin Huxley equations

jonesmat via neur-sci%40net.bio.net (by mathewjones from wisc.edu)
Fri Aug 5 14:21:25 EST 2011

On Jul 14, 2:26 pm, "pennsylvaniaj... from gmail.com"
<pennsylvaniaj... 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.
> Thanks
> Prof. Jake


Sorry if this sounds harsh, but if I picked up a textbook on the
"mathematics of the neuron" and it *didn't* cover HH in substantial
detail, I would be shocked, and would demand my money back.

Several reasons for this opinion. Here are a few:
1) In order to understand HH, you also need to understand the
experiments that lead up to it, namely the fundamentals of current
injections, passive cable properties and voltage responses, voltage-
clamp and current responses to voltage steps, the kinetics of the
currents, how the currents were separated pharmacologically, etc etc
etc. So in teaching HH, you teach all of that stuff. And in my
opinion, the world already has too many mathematician/neuroscientists
who lack a thorough grasp of experimental realities.

2) The HH equations are simple, beautiful and extremely powerful. Of
course, they fall short of accounting for every single detail of our
modern knowledge of the mechanism of the action potential, but every
model falls short of accounting for every single detail. It is
actually amazing how many details they *do* account for. To take just
one example, H and H predicted, based purely on the fitted parameters
that accounted for the V-dependence and kinetics of K-currents, that
there needed to be four separate voltage sensors in the K-conductance
mechanism. This prediction was shown to be correct thirty years later,
only after molecular cloning of K channel genes.

3) Actually writing a program to implement HH is not too difficult,
and doing it is in fact very useful as a learning exercise (as Richard
already mentioned). So this is a great way to teach both programming
and differential equations, which will come in handy for almost every
other area of mathematical neuroscience.

4) Alternative models of the action potential, for example based on
stochastic ion channel gating (i.e., Markov chains) are much more
complicated that HH. So teaching HH first would allow students to gain
an intuition for how the voltage interacts with the channels, and how
the channel activity shapes the voltage. After they have such an
intuition, then refining the description of, say, Na channel gating to
include the stochastic noisiness, and thereby introducing Markov
chains, would not be as jarring to the student.

Ok, I'll get off my soapbox now.



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