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.
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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
that this permits competitive exclusion within one type of axons, while
the same time there is coexistence with a different type of axons
innervating the same target. The model offers an explanation for the
pattern found on cerebellar Purkinje cells, where climbing fibres
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
phone: +31.20.5665483 fax: +31.20.6961006