Symmetry in locomotor central pattern generators and animal gaits

Martin Golubitsky (), Ian Stewart, Pietro-Luciano Buono and J. J. Collins
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Martin Golubitsky: University of Houston
Ian Stewart: Mathematics Institute, University of Warwick
Pietro-Luciano Buono: Mathematics Institute, University of Warwick
J. J. Collins: Center for BioDynamics, Boston University

Nature, 1999, vol. 401, issue 6754, 693-695

Abstract: Abstract Animal locomotion is controlled, in part, by a central pattern generator (CPG), which is an intraspinal network of neurons capable of generating a rhythmic output1,2,3,4. The spatio-temporal symmetries of the quadrupedal gaits walk, trot and pace5,6,7,8 lead to plausible assumptions about the symmetries of locomotor CPGs9,10,11. These assumptions imply that the CPG of a quadruped should consist of eight nominally identical subcircuits, arranged in an essentially unique matter. Here we apply analogous arguments to myriapod CPGs. 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 primary gait called ‘jump’, and the occurrence of half-integer wave numbers in myriapod gaits. For bipeds, our analysis also predicts two gaits with the out-of-phase symmetry of the walk and two gaits with the in-phase symmetry of the hop. We present data that support each of these predictions. This work suggests that symmetry can be used to infer a plausible class of CPG network architectures from observed patterns of animal gaits.

Date: 1999
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DOI: 10.1038/44416

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