T. Elliott et Nr. Shadbolt, A MATHEMATICAL-MODEL OF ACTIVITY-DEPENDENT, ANATOMICAL SEGREGATION INDUCED BY COMPETITION FOR NEUROTROPHIC SUPPORT, Biological cybernetics, 75(6), 1996, pp. 463-470
Mathematical or computational models of activity-dependent neural comp
etition typically impose competition in anatomically fixed networks by
the use of synaptic normalisation, for which there is very little exp
erimental support. Recent experimental evidence, however, strongly imp
licates neurotrophic factors in neural plasticity and competition, in
addition to their well-known potent effects on neurite outgrowth and s
ynaptogenesis. We therefore present a simple, mathematical model of an
atomical segregation induced by activity-dependent competition for a l
imited supply of a neurotrophic factor provided by target cells to aff
erents. We extract the behaviour of the model in various regimes, in w
hich the neurotrophic factor is either in critical supply or in abunda
nt supply, by a combination of analytical and numerical methods, and s
tudy the effects of correlations in afferent inputs on competition. We
apply the model to three different systems: ocular dominance column f
ormation; elimination of polyneuronal innervation at the vertebrate ne
uromuscular junction; trigeminal brain stem whisker-related structure
formation. Several classes of related predictions emerge, including th
e prediction that kittens reared with strabismus should require a high
er concentration of neurotrophic factor infusion into their primary vi
sual cortex than normally reared cats in order to induce the anatomica
l desegregation of ocular dominance columns. We also speculate on the
mechanisms of support of inhibitory rather than excitatory neurons, an
d suggest the existence of a separate, Cl--mediated activity-dependent
pathway for their neurotrophic support.