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Spike-accomodation in the hippocampus

bruce raoul parnas brp at neuron.arc.nasa.gov
Thu Feb 24 14:01:13 EST 1994

In article <kisley.762106808 at rintintin.Colorado.EDU>, kisley at rintintin.Colorado.EDU (Michael Kisley) writes:
|> On the matter of my definition of accommodation:  I have a seen a very
|> convincing explanation of a possible mechanism underlying spike-reduction,
|> namely threshold accommodation.  For instance, Ron MacGregor, using a
|> simplified but realistic model of a neuron shows how an accommodating
|> threshold can produce an "on-response" to a constant stimulus ("Neural
|> and Brain Modeling", MacGregor, 1987, Academic Press).  In other words,
|> the neuron only spikes during the onset of the stimulus.  He goes on to
|> show how a neuron can also spike in response to the offset of a constant
|> stimulus as well, and all of this with the simple mechanism of threshold
|> accommodation.  I admit that there is probably different mechanisms for
|> different cells/areas of a nervous system, but threshold accommodation
|> is the most convincing mechanism I've seen yet. 

Quite a lot can be done with a simple dynamic threshold scheme which
allows threshold accommodation. MacGregor's model is actually based on
work that happened 50 years earlier. AV Hill postulated a two state-variable
system (Proc. Royal. Soc. London, B, 119:305-355, 1936). He had a variable
corresponding to membrane potential and another corresponding to a (supposed)
dynamic threshold. With this he was able to reproduce quite a number of
results found in experimental work. This was before intracellular recording, and
before any good description of spikes, so it describes subthreshold phenomena,
but does it very well.

Hill had two time constants in his dynamic threshold equation, beta and lambda.
the equations look like

dV/dt = -(V - V0)/k
dU/dt = -(U -U0)/lambda + (V-V0)/beta

where V is the membrane potential and U is the dynamic threshold. Hill constrained
beta and lambda to be equal. I have done a lot of work with variants of this
equation (the main variation was to incorporate a spiking scheme) and found that,
when beta and lambda can be varied independently, it is possible to get the "onset"
response mentioned above and sustained-firing neuron models with amplitude
dependent frequencies.  When noise (as a model of intrinsic neuronal noise) is
added to the picture, the range of possible behaviors becomes large, including
the cases mentioned above and all flavors in between.

It's funny: a lot of people attribute the model to MacGregor (who did some
very interesting work with it), but people seem to have forgotten Hill, the
originator. He also did a good deal of work on muscle models.

|> Michael Kisley
|> kisley at magellan.colorado.edu
dr bruce parnas
brp at psychomo.arc.nasa.gov
/usr/local/Std.Disclaimer:  The opinions expressed here are mine and
not those of NASA, but you probably could have guessed that.

It's not my fault.  Not all of us here at NASA are Rocket Scientists

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