Dynamics of Mammalian Neurons

HARRY R. ERWIN herwin at mason1.gmu.edu
Fri Jul 29 10:48:54 EST 1994

Leslie Kay (lmk2 at garnet.berkeley.edu) wrote:

: The dynamics of a single neuron are clearly different from those of
: a population.  Freeman's explication of the assymetric sigmoid relationship
: of the wave to pulse conversion applies to a population.  (The wave to
: pulse conversion is the conversion of the dendritic potential to an
: the spiking of the neurons.) In a single neuron the operation is
: piecewise linear, with the threshold, the linear increase in firing
: rate with applied voltage, and the saturation level, beyond which the
: neuron cannot fire.  The sigmoid which represents the population is
: static and not time varying, and has saturation and threshold values.
: I don't think it is proper to think of a dendritic spine as functioning
: as a whole neuron avoids the fact that many invertebrate neurons also
: spike.  The KI dynamics rely on the sigmoid relationship and so are
: purely a population phenomenon.

I would expect the sigmoid relationship at the population level to be
robust for almost any reasonable model of the neuron. The assymetry is
interesting (increasing gain with increased background level of
activation), but I think there is at least some understanding of why that
occurs, and it doesn't constrain neurons to be piecewise linear. Freeman's
KI and KII dynamics are also robust (from the viewpoint of topological
dynamics); the first basically requiring positive feedback and the sigmoid
relationship, and the second more general (but balanced) feedback. 
However the piecewise linear neuron is not robust. True, if you increase
the amplitude of the pulse scenario--without changing the mean
distribution--you get something that is approximately piecewise linear,
but if you change the distribution of activated synapses and hold the
amplitude constant, you get a signficantly changed response, and ->that<-
is directly related to NCA dynamics.  You have major compartments in the
pyramidal neuron--apical dendritic tree, basal dendrites, soma, and axon;
their operation is different and their interaction is dynamic. At the next
level up, you have marked differences in how pyramidal and granule cells
function. Those are some of the issues that the biologists here in the DC
area keep telling me I need to understand better if I want to have a
biologically realistic KIII model that preserves the features that make
it such an elegant explanation of how the brain works (which is my goal). 

Harry Erwin
Internet: herwin at gmu.edu 
Just a dumb engineer working on Katchalsky nets....

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