Axonal Competition

Arjen van Ooyen A.van.Ooyen at nih.knaw.nl
Tue Sep 5 05:31:57 EST 2000


New Paper:

Development of Nerve Connections under the Control
of Neurotrophic Factors: Parallels with
Consumer-Resource Systems in Population Biology.

Arjen van Ooyen & David J. Willshaw, 
J. Theor. Biol. (2000) 206: 195-210.

Download in gzipped PostScript format 
or PDF format from:

http://www.anc.ed.ac.uk/~arjen/competition.html

or request reprint:

A.van.Ooyen at nih.knaw.nl 


Abstract
--------

We show that a recently formulated model of axonal competition can be
rewritten as a general consumer-resource system. 
This allows neurobiological phenomena to be interpreted in population
biological terms and, conversely, results from population biology 
(where competition is better understood) to be applied to neurobiology. 
Using findings from population biology, we study two extensions of our
axonal competition model. In the first extension, the spatial dimension 
of the target is explicitly taken into account. We show that distance
between axons on their target mitigates competition and permits the
coexistence of axons. The model can account for the fact that, in many
types of neurons, a positive 
correlation exists between the size of the dendritic tree and the number 
of innervating axons surviving into adulthood. In the second extension,
axons are allowed to respond to more than one neurotrophic factor. We
show that this permits competitive exclusion within one type of 
axons, while at the same time there is coexistence with a different 
type of axons innervating the same target. The model offers an
explanation for the innervation pattern found on cerebellar Purkinje 
cells, where climbing fibres compete with each other until only a
single one remains, which coexists with parallel fibre input to the
same Purkinje cell. 



-- 
Arjen van Ooyen, Netherlands Institute for Brain Research,
Meibergdreef 33, 1105 AZ Amsterdam, The Netherlands.
email: A.van.Ooyen at nih.knaw.nl 
website: http://www.anc.ed.ac.uk/~arjen
phone: +31.20.5665483  fax: +31.20.6961006


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