Biological Cybernetics

, Volume 112, Issue 4, pp 305–321 | Cite as

The role of long-range coupling in crayfish swimmeret phase-locking

  • Lucy E. SpardyEmail author
  • Timothy J. Lewis
Original Article


During forward swimming, crayfish and other long-tailed crustaceans rhythmically move four pairs of limbs called swimmerets to propel themselves through the water. This behavior is characterized by a particular stroke pattern in which the most posterior limb pair leads the rhythmic cycle and adjacent swimmerets paddle sequentially with a delay of roughly 25% of the period. The neural circuit underlying limb coordination consists of a chain of local modules, each of which controls a pair of limbs. All modules are directly coupled to one another, but the inter-module coupling strengths decrease with the distance of the connection. Prior modeling studies of the swimmeret neural circuit have included only the dominant nearest-neighbor coupling. Here, we investigate the potential modulatory role of long-range connections between modules. Numerical simulations and analytical arguments show that these connections cause decreases in the phase-differences between neighboring modules. Combined with previous results from a computational fluid dynamics model, we posit that this phenomenon might ensure that the resultant limb coordination lies within a range where propulsion is optimal. To further assess the effects of long-range coupling, we modify the model to reflect an experimental preparation where synaptic transmission from a middle module is blocked, and we generate predictions for the phase-locking properties in this system.


Phase-locking Synchronization Phase-wave Central pattern generator Half-center oscillator Metachronal wave Locomotor control Long-tail crustacean Perturbation analysis Limb coordination Locomotion 



The authors thank Brian Mulloney for helpful discussions. This work was partially supported by the National Science Foundation under Grant CRCNS 0905063 to TJL, and Grant DMS-0931642 to LES.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsSkidmore CollegeSaratoga SpringsUSA
  2. 2.Department of MathematicsUniversity of CaliforniaDavisUSA

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