A neuromechanical model of multiple network rhythmic pattern generators for forward locomotion inC. elegans

Abstract

Multiple mechanisms contribute to the generation, propagation, and coordination of 8 rhythmic patterns necessary for locomotion in Caenorhabditis elegans. Current experiments have 9 focused on two possibilities: pacemaker neurons and stretch-receptor feedback. Here, we focus on 10 whether locomotion behavior can be produced by a chain of network oscillators in the ventral 11 nerve cord. We use a simulation model to demonstrate that a repeating neural circuit identified in 12 the worm's connectome can be chained together to drive forward locomotion on agar in a 13 neuromechanical model of the nematode, in the absence of pacemaker neurons or 14 stretch-receptor feedback. Systematic exploration of the space of possible solutions reveals that 15 there are multiple configurations that result in locomotion that match the kinematics of the worm 16 on agar. Analysis of the best solutions reveals that gap junctions between different classes of 17 motoneurons are likely to play key roles in coordinating oscillations along the ventral nerve cord. 18 19 40 1 of 24 Manuscript submitted to eLife that modulate C. elegans locomotion (Tavernarakis et al., 1997), as well as evidence of a direct 41 relationship between body curvature and neural activity (Wen et al., 2012). However, coordinated 42 rhythmic patterns can also be produced internally, while remaining open to modulation through 43 external contributions. Central pattern generators (CPGs) are known to be involved in a wide variety 44 of behaviors in a number of different organisms, including insect flight, swimming in molluscs, gut 45 movements in crustaceans, and swimming and respiration in vertebrates (Marder and Bucher, 2001; 46 Goulding, 2009; Katz, 2016; Arshavsky et al., 2016; Dasen, 2018; Minassian et al., 2017). In a CPG, 47 the rhythmic pattern can be generated through the intrinsic oscillatory properties of pacemaker 48 neurons or it can emerge from the interaction of networks of non-oscillatory neurons (Goulding, 49 2009). Recent experiments have provided support for the role of intrinsic oscillations in C. elegans 50 locomotion (Gao et al., 2018; Fouad et al., 2018; Xu et al., 2018). Although the work attributes the 51 source of these rhythm generators to pacemaker neurons, the evidence provided does not discard 52 the possibility of network oscillators (Wen et al., 2018). 53 It is increasingly acknowledged that simulation models play an important role in elucidating 54 how brain-body-environment systems produce behavior (Ijspeert, 2008; Abbott, 2008; Izquierdo, 55 2018). In C. elegans, there has been an surge of theoretical work focused on understanding the 56 neuromechanical basis of locomotion. Several computational models have demonstrated that 57 proprioception alone can be used to generate rhythmic patterns and propagate them along the 58 body (Niebur and Erdös, 1991; Karbowski et al., 2008; Boyle, 2009; Mailler et al., 2010; Wen et al., 59 2012; Izquierdo and Beer, 2018; Fieseler et al., 2018; Gleeson et al., 2018). There have also been a 60 number of m...

Phase response analyses support a relaxation oscillator model of locomotor rhythm generation in Caenorhabditis elegans

“…Our phase portrait analysis of worm's free locomotory dynamics has described a previously undescribed methods for measuring the bending relaxation time scale and the muscle moment transition time scale (see Appendix for details), which may be compared with previous studies of worm biomechanics (Berri et al, 2009;Fang-Yen et al, 2010) and neurophysiology (Milligan et al, 1997 ) is consistent with a previously measured value for muscle time scale (Milligan et al, 1997) that has been widely adopted for other detailed models of nematode locomotion (Boyle et al, 2012;Bryden and Cohen, 2008;Butler et al, 2015;Chen et al, 2011;Denham et al, 2018;Izquierdo and Beer, 2018;Johnson et al, 2021;Karbowski et al, 2008;Olivares et al, 2021;Wen et al, 2012).…”

“…Other computational models have aimed to describe how the motor circuit generates rhythmicity. Several neural models for the forward-moving circuit (Karbowski et al, 2008;Olivares et al, 2021) incorporating of all major neural components and connectivity have been developed. These models included a CPG in the head based on effective cross-inhibition between ventral and dorsal groups of interneurons.…”

“…Computational models for C. elegans motor behavior have long been an important complement to experimental approaches, since an integrative understanding of locomotion requires consideration of neural, muscular, and mechanical degrees of freedom, and are often tractable only by modeling (Boyle et al, 2012;Bryden and Cohen, 2008;Denham et al, 2018;Izquierdo and Beer, 2018;Johnson et al, 2021;Karbowski et al, 2008;Kunert et al, 2017;Olivares et al, 2021). We sought to develop a phenomenological model to describe an overall mechanism of rhythm generation but not the detailed dynamics of specific circuit elements.…”

A Neuromechanical Model of Multiple Network Rhythmic Pattern Generators for Forward Locomotion in C. elegans

“…This manuscript has been released as a pre-print at https://www.biorxiv.org/content/10.1101/710566v4 (Olivares et al, 2020 ).…”

A minimal reaction-diffusion neural model generates $\textit{C. elegans}$ undulation

“…There are many other CPG models; for example, Olivares et al [4] proposes a distributed network of self-oscillating systems of neurons, instead of a structured chain like our proposed CPG. Here we describe a minimal working model, rather than striving for fuller realism, in order to explore the fundamental components of a small CPG.…”