Competition amongst neurons for neurotrophins
In the development of nerve connections, neurons are believed to compete for target-derived neurotrophic factors which support their survival and maintenance of their synapses. We introduce a mathematical framework for neurotrophin release and its uptake by the innervating neurons. We explore the idea that central to the action of neurotrophins is their capacity to upregulate their own receptors.
Using nerve growth factor (NGF) as the paradigm case, we show theoretically how the form of the upregulation determines the nature and outcome of the competitive process. Under some conditions, the target structure becomes singly innervated, under others, multiple innervation results, the amount of multiple innervation depending on the supply of neurotrophins. The finding that electrical activity increases the numbers of receptors means that competition for neurotrophin amongst synapses leads to the survival of the more active ones. Reduction in receptor upregulation or in the supply of neurotrophin (which may occur in ageing and disease-related neurodegeneration), can lead to a complete loss of innervation.
Our model encompasses previous models of neuronal competition during development and couples the field of neurobiology to that of population biology, where the notion of competition is better developed.
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