M. Golubitsky, I. Stewart, P.L. Buono and J.J. Collins
The Role of Symmetry in Locomotor Central Pattern Generators and Animal Gaits
Nature. Submitted.
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.