Influence of dendritic morphology on axonal competition
Introduction
The development of connections between neurons and their target cells often involves an initial stage of hyperinnervation followed by elimination of axons [7]. Competition among innervating axons for target-derived neurotrophins, which are taken up by the axons via specific receptors at their terminals [1] and which affect the growth and branching of the axons, is thought to be involved in the elimination of axons [9].
In many types of neurons, a positive correlation exists between the complexity of the dendritic tree and the number of innervating axons surviving into adulthood [6], [8]. In the ciliary ganglion of adult rabbits, for example, neurons that lack dendrites are innervated by a single axon, whereas neurons with many dendrites are innervated by the largest number of axons. This is not a matter of available space, since in newborn animals all neurons are innervated by approximately the same number of axons. The presence of dendrites somehow mitigates the competitive interactions involved in the elimination of axons.
In this paper, we offer an explanation for this phenomenon, using a compartmental version of our model of axonal competition [11]. Before introducing the compartmental version, we summarize [11] in the next section.
Section snippets
Competition for neurotrophins
In [11], a single target cell (e.g. a neuron) is considered at which there are n innervating axons each from a different neuron (Fig. 1). Neurotrophin is released by the target into the extracellular space (which is considered to be a single compartment) at rate σ and is removed by diffusion and degradation with rate constant δ. In addition, at each axon i, neurotrophin is bound to receptor, with association and dissociation constants ka,i and kd,i, respectively. Bound neurotrophin
Compartmental model
We investigate how axonal competition is affected if the extracellular space around the target is not uniform with respect to the concentration of neurotrophin. To this end, we consider two compartments in the extracellular space, each with a single innervating axon. We deliberately use this simple two-compartment model to demonstrate clearly how competition is affected. Axon i grows in compartment i (i=1,2), in which Li is the concentration of neurotrophin. Each compartment has volume vc. The
Results
In contrast to the single-compartment model, in the two-compartment model both axons can coexist. Coexistence occurs for relatively small , i.e. if the axons are far apart (large λ) (Figs. 2a–c). In the limit for , there is no interaction between the compartments and consequently no competition between the axons.
For relatively large , i.e. if the axons are close to each other (small λ), no more than one axon can survive (Figs. 2d–f ). In the limit for infinitely large , the
Discussion
The development of connections between neurons and their targets involves competition among axons for target-derived neurotrophins. To study how the dendritic tree of the target cell affects the competition, we have formulated a compartmental version of our model of axonal competition [11]. We show that if the innervating axons are spatially near each other on the target, they compete more strongly than if they are further separated, in which case coexistence of axons becomes permissible.
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