Neural competition and statistical mechanics

Computational models of activity-dependent competitive neural plasticity typically impose competition in networks in which plasticity is accommodated by permitting changes in the efficacies of synapses in an anatomically fixed network. This is despite the fact that much evidence suggests that neurons compete for neurotrophins, during both target innervation and activity-dependent synaptic re-arrangement, which influence the sprouting and retraction of axonal processes. We therefore present a new approach to the computational modelling of competitive neural plasticity which permits neurons to compete explicitly for neurotrophins. This competition is associated with the sprouting and retraction of axonal processes. Because there is much uncertainty regarding the basic mechanisms, we adopt the powerful machinery of statistical mechanics to avoid the need to address these issues. We show that such an approach can readily account for a wide range of plasticity phenomena in a range of systems, including the results of various pharmacological manipulations.