THRESHOLDS AND SUPEREXCITABILITY

[Lyle J. Borg-Graham]

>Can Raymond's threshold results be accounted for via current models?

We have modelled the time course of K+ currents which could in principle reduce
'threshold' in hippocampal cells (MIT AI Lab Technical Report 1161)
(see also "Simulations suggest information processing roles for the
diverse currents in hippocampal neurons", NIPS 1987 Proceedings, ed.
D.Z. Anderson). 

>I haven't seen any models where the afterpotentials have amplitudes
>sufficient to reduce the effective threshold by 50-70%

Again, as I mentioned in a previous message, it might be useful to be
more precise in the definition of 'threshold'. From the statement
above, I assume you mean that the voltage difference between the
afterpotential and the normal action potential (voltage) threshold is
50-70% smaller than that between the resting potential and threshold,
thus reducing the threshold *current* by the same amount (assuming
that the input impedance doesn't change, which it does). I am not
familiar with the cited results, but I would also expect (as mentioned
earlier) that the normal voltage threshold would be increased after
the spike because of (a) incomplete re-activation of Na+ channels
(which I believe is the classic mechanism cited for the refactory
period) and (b) decreased input impedance due to activation of various
channels (which means that a larger Na+ current is needed to start up
the positive feedback underlying the upstroke of the spike). My
suggestion as to role of K+ currents underlying a super-excitable
phase was that *inactivation* of these currents by depolarization
might both reduce the decrease in impedance (b) *and* increase the
"resting potential".

Why is this minutia important? Well for one thing in real neurons
inputs and intrinsic properties are mediated by conductance changes,
which, in turn, interact non-linearly (as analyzed by Poggio, Torre, and Koch,
among others). Whether or not these non-linear interactions are
relevant depends on the model, but at least we should know enough
about their general properties so that we can scope out the right
context of the problem at the beginning.

>    In defense of simple models, they are often useful in developing the
>broader functional implications of a style of information processing. If
>most neurons have (potentially) complex temporal characteristics, then
>we'd better work on our coupled oscillator models and maybe some
>adaptively tuned oscillator models if we are going to make any sense 
>of it all.   

Absolutely.

- Lyle