M. Golubitsky

Symmetry and Neuroscience

Current Events, Amer. Math. Soc. January 14 (2006)

Symmetry may appear to be an unlikely part of the structure of the nervous system. However, there are (at least) three rather different areas where symmetry has a role to play: animal gaits, the vestibular system, and the visual cortex.

Collins and Stewart point out that the standard gaits of quadrupeds (walk, trot, pace, etc.) are highly stylized symmetric motions. Understanding the spatio-temporal symmetries of gaits leads to interesting conjectures on the form that a locomotor central pattern generator can have. McCollum and Boyle show that the network of connections between the six semicircular canals in the inner ears and the eight muscle groups surrounding the neck have the symmetries of a cube. Finally, Cowan and Bressloff exploit symmetries in the connectivity of the primary visual cortex to create models for this system.

It remains to be seen how important symmetry is in enabling these systems to carry out their tasks. At the very least, however, these are curious and interesting observations.