Development of nerve connections under the control of neurotrophic factors: parallels with consumer-resource systems in population biology

Van Ooyen, A., and Willshaw, D. J. (2000). J. Theor. Biol. 206: 195-210. [Full text: PDF]

Abstract

The development of connections between neurons and their target cells involves competition between axons for target-derived neurotrophic factors. Although the notion of competition is commonly used in neurobiology, the process is not well understood, and only a few formal models exist. In population biology, in contrast, the concept of competition is well developed and has been studied by means of many formal models of consumer-resource systems.

Here 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 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.