Bifurcation theory explains waveform variability in a congenital eye movement disorder

In dynamical systems, configurations that permit flexible control are also prone to undesirable behavior. We study a bilateral model of the oculomotor pre-motor network that conforms with the neuroanatomical constraint that brainstem neurons project to cerebellar Purkinje cells on both sides, but Purkinje cells project back to brainstem neurons on the same side only. Bifurcation analysis reveals that this network asymmetry enables flexible control by the cerebellum of brainstem network dynamics, but small changes in connection pattern or strength lead to behavior that is unstable, oscillatory, or both. The model produces the full range of waveform types associated with the hereditary eye movement disorder know as congenital nystagmus, and is consistent with findings linking the disorder with abnormal connectivity or limited plasticity in the cerebellum.