Connectionists: A new paper on activity constraints and neuronal variability

[Andrey Olypher]

The following article is now available at
http://calabreselx.biology.emory.edu/andrey/pub/olypher_calabrese_07_jnphys_epub.pdf   
(4.7M)

Using constraints on neuronal activity to reveal compensatory changes in 
neuronal parameters.
Andrey V. Olypher and Ronald L. Calabrese
J Neurophysiol, 2007 (in press).

ABSTRACT:
In this study, we developed a general description of parameter^ 
combinations for which specified characteristics of neuronal^ or network 
activity are constant. Our approach is based on^ the implicit function 
theorem and is applicable to activity^ characteristics which smoothly 
depend on parameters. Such smoothness^ is often intrinsic to neuronal 
systems when they are in stable^ functional states. The conclusions 
about how parameters compensate^ each other, developed in this study, 
can thus be used even without^ regard to the specific mathematical model 
describing a particular^ neuron or neuronal network. We showed that near 
a generic point^ in the parameter space there are infinitely many other 
points,^ or parameter combinations, for which specified characteristics^ 
of activity are the same as in the original point. These parameter^ 
combinations form a smooth manifold. This manifold can be extended^ as 
long as the gradients of characteristics are defined and^ independent. 
All possible variations of parameters compensating^ each other are 
simply all possible charts of the same manifold.^ The number of 
compensating parameters (but not parameters themselves)^ is fixed and 
equal to the number of the independent characteristics^ maintained. The 
algorithm that we developed shows how to find^ compensatory functional 
dependencies between parameters numerically.^ Our method can be used in 
the analysis of the homeostatic regulation,^ neuronal database search, 
model tuning and other applications.

-- 
Andrei Olifer (Andrey Olypher)
Biology Department
Emory University
1510 Clifton Rd
Atlanta, GA 30322

aolifer at emory.edu
tel: 404-727-4202
fax: 404-727-2880