question related to Hodgkin-Huxley model

r norman rsn_ at _comcast.net
Mon Dec 22 18:43:03 EST 2003


On Mon, 22 Dec 2003 15:26:25 +0000, Xiaoshen Li <xli6 at gmu.edu> wrote:

>Hi Everybody:
>
>I am studying Hodgkin-huxley mechanism and action potentials. I get lost 
>in a few *basic*, *simple* questions:
>
>What really is the Action Potential definition? In my work I saw many 
>soma spikes. Some peak at
>+35mV, some peak at 0mV and some peak at -10mV. They
>all have Na channel opens then inactivates, K channel
>with a delay opens and closes. The different peaks
>they reach I think is due to different percentage of
>Na channel be activated and opened. In some conditions
>a big portion of Na channel are still in inactivated
>status so they cannot be employed in that spike and
>they have a lower peak. I am wondering those spikes
>with peak at -10mV can be called action potential. If
>not, what is the fine line to divide them, since they
>all go through the similar AP mechanism.
>
>How to explicitly calculate/predict the threshold of membrane potential 
>  which determines to fire an action potential or not? What are the 
>factors related to threshold?
>
>Thank you very much for your help. I greatly appreciate it.
>

Under "normal" circumstances, the action potential is all-or-none. You
either get one (by stimulating past threshold) or you don't.  Many
people think that means all action potentials are the same, but as you
found out, they are not.  You can have different size action
potentials depending on a lot of factors -- the percentage of sodium
channels available for activation is the main one.  If there is a lot
of capacitance, the rate of change of the potential can be so slow so
that the sodium channels inactivate before the potential has had a
chance to really get very far.

If you are simulating a complex cell with some membrane electrically
excitable and some membrane (the dendrites) not, then you have another
problem.  You can record the action potential as it spreads by
decrement back into the dendrites.  These potentials will be smaller
than the "normal" action potential.  By the same token, if you use
extracellular electrodes, you can record the electrical potentials
produced by the local current loops and these will be very small,
perhaps only on the order of microvolts in amplitude and will look
nothing at all like the "real" action potential.  Still, you usually
still call them "action potentials" or "spikes" even though they are
not even membrane potentials. 

The key is the response to stimulation.  For a true action potential,
there is a discontinuity in the relation between stimulus and
response.  As you increase the stimulus, suddenly you reach a point
where the respond is distinctly different.  That different response is
an action potential, no matter how big or small it is, and the
stimulus amplitude were the discontinuity occurs is threshold.  It is
possible to degrade the axon so much -- gradually start killing or
inactivating sodium channels or make them so few on the membrane --
that you get an "active" response but not a true action potential.
That is, the relation between stimulus and response is non-linear but
continuous.

I don't really know of any way to calculate the threshold, even
knowing the Hodgkin-Huxley equations.  It is usually just found by
trial and error in a simulation or an experiment.




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