M. Golubitsky, I. Stewart, P.L. Buono and J.J. Collins
Symmetry in locomotor central pattern generators and animal gaits
Nature. 401 (1999) 693-695.
Animal locomotion is controlled, in part, by a central pattern generator (CPG), which is an intraspinal network of neurons capable of generating rhythmic output. The observed spatio-temporal symmetries of the quadrupedal gaits walk, trot, and pace lead to plausible assumptions about the symmetries of a CPG for locomotion. Here we show that these assumptions imply that such a CPG should consist of eight nominally identical subcircuits, arranged in an essentially unique manner. We apply analogous arguments to CPGs for animals with more than four legs. Analyses based on symmetry applied to these networks lead to testable predictions, including a distinction between primary and secondary gaits, the existence of a new gait called `jump', and the occurrence of half-integer wave numbers in the gaits of myriapods. When the network is specialised to bipeds, it predicts two distinct gaits with the out-of-phase symmetry of the walk and two distinct gaits with the in-phase symmetry of the hop. We present experimental data that support each of these predictions. This novel work suggests that symmetry analyses can be used to infer a plausible class of CPG network architectures from the observed patterns of animal gaits.