Bifurcations of Limit Cycles in a Reduced Model of the Xenopus Tadpole Central Pattern Generator

Andrea Ferrario,Robert Merrison-Hort,Roman Borisyuk,Stephen R Soffe,Wen-Chang Li

doi:10.1186/s13408-018-0065-9

Abstract

We present the study of a minimal microcircuit controlling locomotion in two-day-old Xenopus tadpoles. During swimming, neurons in the spinal central pattern generator (CPG) generate anti-phase oscillations between left and right half-centres. Experimental recordings show that the same CPG neurons can also generate transient bouts of long-lasting in-phase oscillations between left-right centres. These synchronous episodes are rarely recorded and have no identified behavioural purpose. However, metamorphosing tadpoles require both anti-phase and in-phase oscillations for swimming locomotion. Previous models have shown the ability to generate biologically realistic patterns of synchrony and swimming oscillations in tadpoles, but a mathematical description of how these oscillations appear is still missing. We define a simplified model that incorporates the key operating principles of tadpole locomotion. The model generates the various outputs seen in experimental recordings, including swimming and synchrony. To study the model, we perform detailed one- and two-parameter bifurcation analysis. This reveals the critical boundaries that separate different dynamical regimes and demonstrates the existence of parameter regions of bi-stable swimming and synchrony. We show that swimming is stable in a significantly larger range of parameters, and can be initiated more robustly, than synchrony. Our results can explain the appearance of long-lasting synchrony bouts seen in experiments at the start of a swimming episode.

Highlights

Rhythmic neuronal activity is the basis for many locomotor activities, such as swimming, flying and walking [1,2,3,4,5,6]
Experiments have shown that the start of movement occurs shortly after the first descending interneurons (dINs) spikes [41], and that dIN activity drives spiking of other neurons during swimming [27]
We show that the reduced model can reproduce transitions from swimming to synchrony and switch back to swimming to what is observed in experimental recordings [12]

Summary

Introduction

Rhythmic neuronal activity is the basis for many locomotor activities, such as swimming, flying and walking [1,2,3,4,5,6]. Experimental and modelling evidences suggest that such rhythmicity is generated by specialised neuronal networks called central pattern generators (CPGs) [7, 8]. Different motor behaviours require different rhythmic patterns, such as left-right anti-phase oscillations for walking and running [9], or in-phase left-right firing for some forms of crawling [10] and flying [4]. Experiments show that some CPG neurons can be active during different motor patterns displaying either in- or antiphase oscillations [12], it is unclear whether the same group of CPG neurons could be responsible for the generation of these different rhythmic patterns. An alternative hypothesis is that the CPG includes a repertoire of diverse CPG sub-networks, each responsible for a single motor pattern with its own specific firing [13,14,15]

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Conclusion