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How would the Hodgkin-Huxley equation change when the geometry of dendrites and axons are introduced?

Also can we model a situation of membrane activity during the corse of evolution, hence the equation would be subject to a periodic function ad it varies with time?

Taking the example of membrane transmission of electronic signals(in humans), can we model the change in conduction of the e-signal through the axon as its speed and geometry changes with evolution?

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  • $\begingroup$ The two processes occur at drastically different time scale. One could clearly model that by assuming the evolutionary state (whichever way you track it) is a constant while the other process reaches its equilibrium conditions. $\endgroup$ – Remi.b Oct 21 '16 at 5:34
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Although you mention evolution, I think what your question is really asking is in your last paragraph: what happens to conduction within dendrites and axons when geometry changes. There might be some evolutionary implications of this question, but you will also find vast variations in geometry among neurons in any one organism, as well.

You might want to look into expansions of Hodgkin-Huxley into compartment models that allow you to test the influences of geometry, see wikipedia for a list of different models at different scales of complexity.

There is a tool available called NEURON that is good for student or curious non-student experimentation, though you will have to read the documentation and hopefully find some examples that are close to what you want and then tweak them.

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