[Comp-neuro] "realistic models"

G. Bard Ermentrout bard at math.pitt.edu
Sun Aug 17 15:30:23 CEST 2008


Carson Chow, a former colleague,  has an interesting summary of this 
doscussion on
sciencehouse.blogspot.com

- Years ago Carson and I would go to neuro lectures (which I generally 
find far more accessible than math colloquia - and I am a professional 
mathematician! - which speaks on the issue that I think it is far easier 
form a mathematician  to gain an appreciation for biology than vice versa, 
but I digress) and there were a number on the complex channels found in 
dendrites which from an evolutionary point of view, must be quite costly. 
However, in almost all the cases, the final point of the speaker was that 
this was to compensate fro being out at the end of the dendrite, so that 
we used to say that nature is trying to make all neurons point neurons. 
Computationally, we can put as many inputs as we want into a point - but 
anatomy and physiology prevent this in real cells, hence the complex 
structure.

- This leads to a second point - the neural turing test. (There have been 
contests related to this). I recently heard Eugene Izhikevich give a talk 
and he showed a picture of a recording froma cortical pyramidal cell 
receiving a complex stimulus pattern (whatever that means, Jim) and his 
2 variable 4 parameter model - the sub and super threshold behavior was 
almost indistinguishable and this model was fit for the FI curve only. I 
realize that the pyramidal cell stimulus was quite simplistic, but one 
could presumably do the same stim mixed with other stimuli in the 
dendrites. maybe there are complex dendritic calculations going on - but 
the bottom line is what is the output of the cell - that is all that 
matters. So any model that does this in a reasonable way will, to me, be a 
realistic model since the cell on the other side of the wall cannot 
distinguish it. I would guess that Jim Bower would claim there is no such 
model that does this except the most delatiled model with all the channels 
and structure. However, I am less pessimistic about this for the following 
reason:

-Yannis Kevrikides has deveolped some very useful numerical tools that 
exploit a common freature in many complex physical and biological systems 
(here, I am a strong reductionist and believe with every fiber of my body 
that biology is describable by physical pronciples - I lost all shreds of 
mysticism in Nov 1969 - although I continued to exploit others making 
money casting horoscopes - a mathematical exercise, in fact)
basically, most systems, even complex ones, behave in such a manner as to 
drastically reduce dimensionality. They are strongly contracting or 
dissipative and as a consequence, are captured by far fewer degrees of 
freedom. Kevrikides methods allow one to compute in these lower degrees 
without knowing the underlying reduced equations. Nevertheless, they are 
there. Mathematicians and physicists have used these ideas for years and 
call it averaging, mean field reduction, etc and of course 
experimentalists do use these ideas as well and call it PCA in which they 
show that only a few modes capture the majority of the variance. Thus, the 
Turing test neuron is not pie in the sky and I believe that there are 
reduced models that will do what the "realistic" model does with as much 
precision as you would like.

Regards

Bard Ermentrout


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