Looking for mathematical models of biological neurons

Joern Erbguth jnerbgut at immd2.informatik.uni-erlangen.de
Wed Jun 16 09:10:36 EST 1993

In article <1vda2iEbp7 at uni-erlangen.de> I wrote:
>We are working on a neural net simulator with a wide range of net-models.
>My part is to implement some models which should simulate the functioning
>of real (biological) neurons.
>Do you know of any mathematic models that could be implemented?
>Do you know of any books or articles which deal with real neurons and
>offer a mathematic model to simulate their behavior.

Thank you for your replies to my questions. 

I got about 10 replies. I negligently deleted 5 of them. Luckily I copied
the book-references before. But for some references I cannot tell you,
who told me about that book.

Mitchell Maltenfort (mgm at nwu.edu):

Ronald J. MacGregor, "Neural and Brain Modeling"
     Acad. Press 1987, (Addison Wesley 1988?)

has a model that is quasi-realistic (integrate-and-fire plus
afterhyperpolarization conductance and optional accomodation and dendritic
model).  I've implemented the point-neuron model into a C program for my own
simulation work.  

	There are more realistic models out, but they are also more
complicated - the strength of the MacGregor model is that known behaviors
can be modeled based on known physiological parameters (passive conductance,
membrane time constant, etc.).  

Paul Fawcett (paulf at manor.demon.co.uk):

Look no further! Get yourself a copy of

Trends in Neurosciences, Vol. 15, No. 11 1992.

This is a special edition on 'Modeling the Nervous System'.
Here is part of the introduction:

'.....The papers in this issue were selected to demonstrate the
considerable diversity of model based approaches currently in use in
neurobiology. The majority of these articles describe computer-based 
modeling efforts intent on replicating stimulus-induced neuronal
response or neurally controlled behavior.......'

It is worth reading just for the references, most of the classical
and contemporary computational neuroscience literature is listed.

Jacques Brisson (x042.hec.ca) pointed to the same issue
"As for articles, a good start would be to take a look at ... . You
might particularly be interested in NEURON and GENESIS, two neural networks
simulation packages that are based on biologically plausible considerations. 

The subject you want to cover is HUGE. You might want to check those
books :
- An Introduction to the Mathematics of Neurons
  FC Hoppensteadt, Cambridge U Press, 1986
- Corticonics; Neural Circuits of the Cerebral Cortex
  M Abeles, Cambridge U Press,  1991
- Modeling Brain Function
  DJ Amit, Cambridge U Press, 1989
and of course...
- Methods in Neuronal Modeling; from Synapses to Networks
  C Koch, I Segev (eds), MIT Press, 1989

Gene Wallenstein (wallenstein at walt.ccs.fau.edu):

There are several books:

1) The physiology of excitable cells by Aidley; Cambridge University
2) Ionic channels of excitable membranes by Bertil; Sinauer Press.

These are biophysical in nature - they are NOT texts on building
perceptrons or backpropagation nets. If you are interested in building
a general purpose simulator, you should be aware that several extremely
sophisticated packages are already available. For instance GENESIS
from Caltech can model single neurons (multpile compartments) or circuits,
etc. There is also a package called NEURON written by M. Hines which is 
very functional. It is not capable of circuit analysis but is much smaller
than GENESIS (which has about 60,000 lines of C code).

I saw a post in comp.ai.neural-nets
From: georgiou at silicon.csci.csusb.edu (George M. Georgiou)
Subject: Re: Neural Nets and Neurophysiology

Another book that that deals to a great extent with the relation of
biological and artificial NNs is:

"An introduction to the Modeling of Neural Networks," Pierre Peretto,
Cambridge University Press, 1992.

The level is introductory graduate. It includes chapters/sections on the
anatomy of the nervous system, neurophysiology, and a critique of
artificial vs biological NNs.  The bulk of the book is on artificial
Now the book-references where I negligently deleted the mail. If you want
to stay in touch with me, please mail again - Sorry.

"Signal processing by model neural networks"
SIAM Review 34(3), pp.426-444 Spet'92

Single Neuron Computation, MacKenna Thomas, Acad. Press Boston 1992

Electric Current Flow in Excitable Cells, Julian J. Jack, D. Noble, R.W. Tsien
Oxford: Clarendon 1975, 1985; Oxford Science Publications 1983

"The distribution of the intervals between neural impulses in the maintained
discharges of retinal ganglion cells" by M.W. Levine
Biological Cybernetics (Springer) 65, 459-467 (1991)

I haven't looked at all those articles and books yet. So far I think the
Special Issue of "Trends in Neurosciences" is the best way to start.


Joern Erbguth   email: jnerbgut at cip.informatik.uni-erlangen.de 
Change of       snail: Helmstrasse 6, W8510 <90762> Fuerth, Germany 
Address!        phone: +49 911 7419528 

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