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

Abstract

Multiple mechanisms contribute to the generation, propagation, and coordination of the rhythmic patterns necessary for locomotion in Caenorhabditis elegans. Current experiments have focused on two possibilities: pacemaker neurons and stretch-receptor feedback. Here, we focus on whether it is possible that a chain of multiple network rhythmic pattern generators in the ventral nerve cord also contribute to locomotion. We use a simulation model to search for parameters of the anatomically constrained ventral nerve cord circuit that, when embodied and situated, can drive forward locomotion on agar, in the absence of pacemaker neurons or stretch-receptor feedback. Systematic exploration of the space of possible solutions reveals that there are multiple configurations that result in locomotion that is consistent with certain aspects of the kinematics of worm locomotion on agar. Analysis of the best solutions reveals that gap junctions between different classes of motorneurons in the ventral nerve cord can play key roles in coordinating the multiple rhythmic pattern generators.

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

“…Through an extrapolation based on that linear relationship, the relaxation time scale in 17% dextran NGM fluid (approximately 120 mPa·s in viscosity) is estimated to be ≈ 282 ms , which is quite close to our measured result, τ u ≈ 260 ms . Furthermore, our measurement of the muscle moment transition time scale ( τ m ≈ 100) is consistent with previously measured value for muscle time scale (Milligan et al, 1997) that has also 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).…”

“…We used these findings to develop a computational model of rhythm generation in the C. elegans motor circuit in which a relaxation-oscillation process, with switching based on proprioceptive feedback, underlies the worm’s rhythmic dorsal-ventral alternation. 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.…”

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

“…Through an extrapolation based on that linear relationship, the relaxation time scale in 17% dextran NGM fluid (approximately 120 mPa·s in viscosity) is estimated to be , which is quite close to our measured result, . Furthermore, our measurement of the muscle moment transition time scale ( ) 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.…”

“…We used these findings to develop a computational model of rhythm generation in the C. elegans motor circuit in which a relaxation-oscillation process, with switching based on proprioceptive feedback, underlies the worm’s rhythmic dorsal-ventral alternation. 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.…”