Poly- and mononeuronal innervation in a model for the development of neuromuscular connections

In the normal development of connections between motor neurons and muscle fibres, an initial stage of polyneuronal innervation is followed by withdrawal of connections until each muscle fibre is innervated by a single axon. However, polyneuronal innervation has been found to persist after prolonged nerve conduction block, in spite of the resumption of normal neuromuscular activity. Here we analyse in detail a model proposed for the withdrawal of nerve connections in developing muscle, based on competition between nerve terminals. The model combines competition for a pre-synaptic resource with competition for a post-synaptic resource. Using bifurcation and phase space analysis, we show that polyneuronal innervation, as well as mononeuronal innervation, can be stable. The model accounts for the development of mononeuronal innervation and for persistent polyneuronal innervation after prolonged nerve conduction block, which appears as a consequence of the general competitive interactions operating during normal development.