Dynamics of Mammalian Neurons

Leslie Kay lmk2 at garnet.berkeley.edu
Tue Jul 26 18:09:15 EST 1994

In article <30r721$g71 at portal.gmu.edu>,
HARRY R. ERWIN <herwin at mason1.gmu.edu> wrote:
>The mammalian neuron is compartmented by dendritic spines. Each spine 
>functions in much the same way as a whole invertebrate neuron, so that 1) 
>the computational capabilities of the mammalian neuron exceed those of 
>the invertebrate neuron by several orders of magnitude and 2) the 
>internal dynamics of the dendritic tree are significant in the processing 
>of the mammalian neuron. For example, if you increase the rate of 
>excitatory pulses arriving at the neuron as a whole, the gain increases. 
>This suggests that Freeman's KI dynamics may have some validity for 
>single, whole mammalian neurons. Has anyone investigated this?

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.

The reference for the sigmoid curve is:
Freeman, W.J. [1979] "Nonlinear gain mediating cortical stimulus-
response relations," Biological Cybernetics 33, 237-247.

Leslie Kay
lmk2 at garnet.berkeley.edu

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