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

Abstract

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.

Towards an Understanding of Control of Complex Rhythmical ‘Wavelike’ Coordination in Humans

“…While it is useful to compare control of these wavelike motions to that of other species it is also necessary to recognize that control of cephalo-caudal wave propagation by CPGs to produce undulating waves along the spine of animals such as Lamprey [31], and salamander [38] amphibians, quadraped mammals, and primates. Indeed this review has revealed organizational models with commonalities among species including Lamprey [31], salamander [38] and crayfish [39][40], and in mammals such as rats [33,42], mice [43] and cats [30,34]. suggested a 'temporal grid'.…”

“…For example, Zhang et al[30] used computational fluid dynamics in conjunction with a neural model of CPG circuits to show that a locked phase difference between adjacent crayfish swimmerets of approximately 0.25 of the period is more hydrodynamically efficient than being in phase (0) or 0.75 of the cycle period regardless of speed, size of the crayfish, or swimmeret cycling frequency. Spardy and Lewis[40] have subsequently extended the model of Zhang et al for control of crayfish swimmerets to include effects of neighboring neural circuits that are beyond the nearest neighbor. While the nearest neighbor circuits have the dominant effect of setting the phase difference to 25%, the model showed that the longer neighbors can also have a small effect.…”

“…While the nearest neighbor circuits have the dominant effect of setting the phase difference to 25%, the model showed that the longer neighbors can also have a small effect. The authors posited that this may reduce the phase difference between neighboring swimmerets towards a phase difference that is even more hydrodynamically efficient.The modelling of Zhang et al[39]and Spardy and Lewis[40] is interesting in relation to human swimming for two reasons -it illustrates control by CPGs of separate appendages that is neither inphase or 180 degrees-out-of-phase; and it shows that a stable pattern has evolved to optimize…”

Towards an Understanding of Control of Complex Rhythmical “Wavelike” Coordination in Humans

“…For example, Zhang et al [23] used computational fluid dynamics in conjunction with a neural model of CPG circuits to show that a locked phase difference between adjacent crayfish swimmerets of approximately 0.25 of the period is more hydrodynamically efficient than being in-phase (0) or 0.75 of the cycle period regardless of speed, size of the crayfish, or swimmeret cycling frequency. Spardy and Lewis [36] have subsequently extended the model of Zhang et al for control of crayfish swimmerets to include the effects of neighbouring neural circuits that are beyond the nearest neighbour. While the nearest neighbour circuits have the dominant effect of setting the phase difference to 25%, the model showed that the longer neighbours can also have a small effect.…”

Adaptive Encoding of Coordinating Information in the Crayfish Central Nervous System

“…However, modeling studies have shown that the DSC input from the immediate neighboring ganglion is crucial to maintain the phase lag. With only long-range DSC input, phase lags decreased (Spardy and Lewis, 2018).…”