is the model sound?

Eugen Leitl ui22204 at sunmail.lrz-muenchen.de
Thu Mar 9 14:37:21 EST 1995


Hi neuronetters,

this is a forwarded posting (originally to sci.cryonics),
which discusses how NN/brain works on a very simplicistic 
level. I'd like to receive feedback whether the reasoning 
is basically sound and where major deviation from reality
do occur. (Received results will be used for improving 
neural modeling basics.)

Oppinions/comments are welcome. Please post. (Thanks).

-- Eugene
----------------------------------------------------------

There are a lot of technical difficulties associated with
the (in vitro) scan of vitrified brain tissue. The task
is essentially:

0) to read the neuron type (susceptibility function)
1) to trace the tubular structures of neuron's axons
   and cell body (graph connectivity, edge weight)
2) distinguish them from the background (glia cells)
3) read the synapse value and sign (weighted edge 2)

To 0) Whether this is discernible from shape alone or
the membrane proteins type.. No one knows.. (BTW, there
are some 50 types of neurons.)

To 1),2): One can view the tubular lipid membrane bilayer
as an active wire, with the top bandwidth of roughly 1000 s^-1
spikes traveling along myelinated axons (wrapped in Swann cell
sheets).
After each spike the active membrane (ion pumps driven by ATP)
the membrane becomes insusceptable to subsequent signals (refractory
time) which enhances signal distinction. Since the signals are 
electrochemical (tipping a potential gradient to a temporary collapse)
the signal propagation velocity is much slower than the speed of light,
being only about 100 ms^-1 for saltatory signal propagation in mammals.
(Much slower for lower beasties, e.g. like squids).
Contrary to common belief, signal coding is analogue: though the spike
levels are binary, they get integrated over time slices of some 10 ms
at the synapse junction. Frequency encoding's dynamic range of values
is limited, but signal encoding robustness is excellent. Alternative
codings my be used by higher order cerebral modules: since there is
no spatial neuron structuring (logical only) their detection is 
quite nontrivial.

Because of their functional simplicity (binary frequency coded channel
with limited bandwidth and a delay which is directly proportional to
axon length) their biochemical and structural makeup is simple (provided,
there are not unknown (chemical) modulation variables).
Ion pumps and ion channel protein density is high, they are uniform
and easily accessable (as they are embedded in the membrane lipid
bilayer) and can be easily immunostained to enhance imaging contrast.
In short, axons alone can be approximated/modeled by weighted edges
(graph theory lingo), the weight being the delay. Propagation
velocity is a global constant. /* I was told it is not. What 
are the propagation velocity limits? Can they be estimated 
from morophology?) */

Applying 3d image processing and recognition techniques (edge detection
and tracing) upon voxel blocks (critical maximum size determined by
the processing systems' memory size) makes for a high hope for 
easy/successful axon scan/tracing/modeling. 

The state of the neuron is the probability of firing in the next
instant or the overall (time slice) firing frequency. By applying several 
transmitters (excitatory/inhibitory), which get depleted into
the subsynaptic cleft by the synapse upon signal spike transit 
and diffuse (through passive physical transport) to the postsynaptic 
membrane of the neuron body and modify the probability of the 
individual neuron to fire the next instant the whole
of NN signal processing is done. The synapse sign is the
basic property of a synapse-dumped neurotransmitter: positive
(excitatory) or negative (inhibitory), the amount of above to
be dumped is the synapse value. Alternatively, the postsynaptical
membrane patch might be the location where signal modulation is 
done. (Might, mark). The susceptibility function of the neuron body to 
transmitter packet input can be linear or sigmoidal (or (m)any other). 
Overall function can be modulated by neuromodulators, 
which' sphere of influence scale is much wider than a synapse.
(Read: encompassing many neurons, whole isles of them).
What we might well expect that the dynamic range of a synapse
is quite limited. While certainly not binary it should not 
exceed 6 bits, tops 8 bit. The main difficulty in scanning is
to attribute such a value to a tiny physical structure (say, 500-100
nm sized) with a tolerable accuracy. Really tough.

-- Eugene









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