question: job of a neuron - wavelets revisited...

Matt Jones jonesmat at
Thu Sep 13 10:20:39 EST 2001

Hi all,

It occurred to me that one might think of the job of a neuron as the

"To participate as an element of an excitable medium, such that the
entire medium acquires information-processing capabilities."

This definition is verging on the same sort of thing being hinted at
by Ron Blue, when he refers to wavelets, ocscillons (a much more
appropriate term) and wavefunctions. I said in a previous post that I
didn't really love the verbiage Ron uses to express these ideas, but
that it wouldn't surprise me if there were parts of the brain that
perfromed wavelet transforms.

However, a wavelet transform is a very specific operation, similar to
a Fourier transform, but better able to deal with real-world signals.
So I'm still not aware of any evidence for this from direct
experiments, although I know some people who try to make models of
visual and audio processing that use wavelet-like filter banks.

But to put aside thinking about wavelets, per se, and just to consider
-waves-, either travelling or standing (not the same thing as
wavelets), then there's an awful lot of suggestive evidence that such
things have an important role in brain function.

First, an individual neuron is an example of an excitable medium
itself. The action potential is a regenerative travelling wave. If you
excite a point in the middle of an axon, the spike will propagate in
both directions away from the stimulus, like a wave. Further, two
spikes travelling in opposite directions will extinguish each other
(but -not- "interfere with" or "diffract" each other in the physics
textbook sense ). Aside from spikes, there are also calcium
concentration waves, second messenger diffusional waves,  lots of
waves. So a neuron is like a collection of superimposed excitable
media, each with different spatial and temporal dynamics. These media
also interact with each other.  Spikes cause calcium influx, which
triggers calcium waves, which activate calcium-dependent potassium
currents, which modulate spikes.

Second, a collection of neurons wired up together is an additional
level of excitable media. There's been a lot of recent work on
travelling waves in hippocampal and cortical tissue slices, even to
the point of identifying which neurotransmitter systems play which
roles in dictating wave velocity, frequency, refractoriness, etc.
Calcium waves spread between astrocytes as well, and waves of
extracellular neurotransmitter concentration (i.e., volume
transmission) also occur.

Inhibitory interneurons have a key role in these network waves, most
obviously because they provide the "refractoriness", but for other
reasons as well. I couldn't have summarized these roles better than
Richard did in his most recent post, so refer to that for some
examples. In fact, different types of interneurons seem to be
preferentially wired up with others of the same type, thereby
providing many different potential excitable media that are again
superimposed on each other within the same tissue, and able to
interact in complex ways.

There is a tendency recently to see brain function, especially higher
brain function, in the context of oscillations. Some of them have been
proposed to act as a synchronization for neurons carrying different
aspects about the same perceptual object (i.e., perceptual binding),
and I think this is a nice hypothesis, though still under heated

However, I am wary of seeing -everything- in terms of ongoing
oscillations. I just don't think oscillations are, by themselves,
capable of transmitting or encoding very much information. They can
help neurons to encode certain types of informatin by acting as a
reference signal, sort of like a timestamp. But oscillations
themselves are relatively information-poor (because they are highly
orderly and thus entropy-poor).

On the other hand, travelling waves with limited range, or standing
waves of limited duration, are more like pulses than oscillations.
They can therefore be arranged into patterns with much higher entropy,
and thus much higher information capacity (for exactly the same
reasons that digital cell phones work better than analog cell phones).

So, maybe in -addition- to moving information from point A to point B,
the job of a neuron includes moving that information by being an
element of a complex series of nested excitable media, with -local-
temporal and spatial range.

I -would not- describe this as "wavelet", however. Maybe "oscillons",
but only in very specific cases. The phrase "excitable media" is
probably most accurate. Further, I should note that these ideas have
been around for a while, probably since the turn of the century when
people thought the brain was a "syncitium" rather than a collection of
discrete elements. Syncitia are good at supporting travelling waves.
The heart is a good example.

OK, enough of that. Better go do something useful...



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