From head to tail: a neuromechanical model of forward locomotion inCaenorhabditis elegans

Abstract

With 302 neurons and a near-complete reconstruction of the neural and muscle anatomy at the cellular level, is an ideal candidate organism to study the neuromechanical basis of behaviour. Yet despite the breadth of knowledge about the neurobiology, anatomy and physics of, there are still a number of unanswered questions about one of its most basic and fundamental behaviours: forward locomotion. How the rhythmic pattern is generated and propagated along the body is not yet well understood. We report on the development and analysis of a model of forward locomotion that integrates the neuroanatomy, neurophysiology and body mechanics of the worm. Our model is motivated by experimental analysis of the structure of the ventral cord circuitry and the effect of local body curvature on nearby motoneurons. We developed a neuroanatomically grounded model of the head motoneuron circuit and the ventral nerve cord circuit. We integrated the neural model with an existing biomechanical model of the worm's body, with updated musculature and stretch receptors. Unknown parameters were evolved using an evolutionary algorithm to match the speed of the worm on agar. We performed 100 evolutionary runs and consistently found electrophysiological configurations that reproduced realistic control of forward movement. The ensemble of successful solutions reproduced key experimental observations that they were not designed to fit, including the wavelength and frequency of the propagating wave. Analysis of the ensemble revealed that head motoneurons SMD and RMD are sufficient to drive dorsoventral undulations in the head and neck and that short-range posteriorly directed proprioceptive feedback is sufficient to propagate the wave along the rest of the body.This article is part of a discussion meeting issue 'Connectome to behaviour: modelling at cellular resolution'.

Co-Contraction Analyses of the Body Wall Muscles in Caenorhabditis Elegans by Calcium Imaging Assay and Simulation

“…5). To understand the effect of co-contraction on the locomotion dynamics, we used a body dynamics model developed by Cohen's group 4,13,18,19 to simulate motion using muscle activation. The result showed that co-contraction can reduce the phase difference between muscle activity and the local curvature (see Fig.…”

“…To clarify the effect of co-contraction on the motion of the animal, we simulated the motion using a body dynamics model proposed by Cohen's group 4,13 . We used the C++ code provided by Izquierdo et al 19 . The body dynamics model is composed of 51 dorsal and ventral pairs of points (50 segments) that approximate the body shape.…”

“…Because it is difficult to measure the force exerted by the individual muscle cells directly, we measured muscle activity using a strain that expresses a fluorescent protein on the body wall muscle. In addition, we simulated the motion of C. elegans using a body dynamics model incorporated with the measured mechanical property proposed by Cohen's group 13,18,19 to clarify whether co-contraction contributes toward maintaining body stiffness.…”

Inhibition underlies fast undulatory locomotion inC. elegans

“…Although proprioception and endogenous oscillators have been evidenced in C. elegans, their relative contributions during locomotion remain to be determined (Fouad et al, 2018;Gao et al, 2018;Xu et al, 2018). Previous models (Denham et al, 2018;Izquierdo and Beer, 2018) have investigated these regimes separately in order to parse their qualitative differences.…”

Connectome to behaviour: modelling Caenorhabditis elegans at cellular resolution

“…Palyanov et al have developed Sibernetic [15], a simulation framework that uses smoothed particle hydrodynamics [16] to perform detailed mechanical simulations of a morphologically accurate C. elegans moving through virtual environments. Mechanics is not only important to 'translate' neural activity to behaviour, but it also plays an important role in feeding back on neural activity as demonstrated in papers from Denham et al [17] and Izquierdo & Beer [18], which use neuromechanical models to study how locomotion could be shaped by neural activity. A role for proprioception in body wave propagation does not necessarily resolve the origin of oscillations as described by Wen et al [19], who review evidence for intrinsic oscillations in rhythm generation in the ventral nerve cord.…”