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

With 302 neurons and a near-complete reconstruction of the neural and muscle anatomy at the cellular level, Caenorhabditis elegans 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 C. elegans, 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 C. elegans at cellular resolution’.

[1]  A. Hill.  The heat of shortening and the dynamic constants of muscle , 1938 .

[2]  R. Hall,et al.  Relationship of Muscle Apolipoprotein E Expression with Markers of Cellular Stress, Metabolism, and Blood Biomarkers in Cognitively Healthy and Impaired Older Adults , 2023, Journal of Alzheimer's disease : JAD.

[3]  H. R. Wallace.  Wave Formation By Infective Larvae of the Plant Parasitic Nematode Meloidogyne Javanica , 1969 .

[4]  S. Brenner,et al.  The structure of the ventral nerve cord of Caenorhabditis elegans. , 1976, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[5]  S. Brenner,et al.  The neural circuit for touch sensitivity in Caenorhabditis elegans , 1985, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[6]  S. Brenner,et al.  The structure of the nervous system of the nematode Caenorhabditis elegans. , 1986, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[7]  P. Erdös,et al.  Theory of the locomotion of nematodes: Dynamics of undulatory progression on a surface. , 1991, Biophysical journal.

[8]  H. Horvitz,et al.  The GABAergic nervous system of Caenorhabditis elegans , 1993, Nature.

[9]  Randall D. Beer,et al.  On the Dynamics of Small Continuous-Time Recurrent Neural Networks , 1995, Adapt. Behav..

[10]  S. R. Wicks,et al.  A Dynamic Network Simulation of the Nematode Tap Withdrawal Circuit: Predictions Concerning Synaptic Function Using Behavioral Criteria , 1996, The Journal of Neuroscience.

[11]  Nektarios Tavernarakis,et al.  unc-8, a DEG/ENaC Family Member, Encodes a Subunit of a Candidate Mechanically Gated Channel That Modulates C. elegans Locomotion , 1997, Neuron.

[12]  Curtin,et al.  Contractile properties of obliquely striated muscle from the mantle of squid (Alloteuthis subulata) and cuttlefish (Sepia officinalis) , 1997, The Journal of experimental biology.

[13]  D. Riddle.  C. Elegans II , 1998 .

[14]  Christopher J. Cronin,et al.  An automated system for measuring parameters of nematode sinusoidal movement , 2005, BMC Genetics.

[15]  F. Watrin,et al.  The Prader-Willi syndrome murine imprinting center is not involved in the spatio-temporal transcriptional regulation of the Necdin gene , 2005, BMC Genetics.

[16]  R. Shingai,et al.  Neural network model to generate head swing in locomotion of Caenorhabditis elegans. , 2004 .

[17]  P. Sternberg,et al.  A C. elegans stretch receptor neuron revealed by a mechanosensitive TRP channel homologue , 2006, Nature.

[18]  Christopher J. Cronin,et al.  Conservation rules, their breakdown, and optimality in Caenorhabditis sinusoidal locomotion. , 2006, Journal of theoretical biology.

[19]  W. Schafer.  Proprioception: A Channel for Body Sense in the Worm , 2006, Current Biology.

[20]  Paul W. Sternberg,et al.  Systems level circuit model of C. elegans undulatory locomotion: mathematical modeling and molecular genetics , 2007, Journal of Computational Neuroscience.

[21]  P. Sauvage.  Étude de la locomotion de C. elegans et perturbations mécaniques du mouvement , 2007 .

[22]  Jonathan T. Pierce-Shimomura,et al.  Genetic analysis of crawling and swimming locomotory patterns in C. elegans , 2008, Proceedings of the National Academy of Sciences.

[23]  A. V. Maricq,et al.  Action potentials contribute to neuronal signaling in C. elegans , 2008, Nature Neuroscience.

[24]  J. Boyle.  C. elegans locomotion : an integrated approach , 2009 .

[25]  S. Lockery,et al.  The quest for action potentials in C. elegans neurons hits a plateau , 2009, Nature Neuroscience.

[26]  N. Cohen,et al.  Forward locomotion of the nematode C. elegans is achieved through modulation of a single gait , 2009, HFSP journal.

[27]  N. Cohen,et al.  Swimming at low Reynolds number: a beginners guide to undulatory locomotion , 2010 .

[28]  Aravinthan D. T. Samuel,et al.  Biomechanical analysis of gait adaptation in the nematode Caenorhabditis elegans , 2010, Proceedings of the National Academy of Sciences.

[29]  S. Lockery,et al.  Evolution and Analysis of Minimal Neural Circuits for Klinotaxis in Caenorhabditis elegans , 2010, The Journal of Neuroscience.

[30]  Michael J. O'Donovan,et al.  Motoneurons Dedicated to Either Forward or Backward Locomotion in the Nematode Caenorhabditis elegans , 2010, The Journal of Neuroscience.

[31]  Aravinthan D. T. Samuel,et al.  Optogenetic manipulation of neural activity in freely moving Caenorhabditis elegans , 2011, Nature Methods.

[32]  M. Brauner,et al.  Caenorhabditis elegans selects distinct crawling and swimming gaits via dopamine and serotonin , 2011, Proceedings of the National Academy of Sciences.

[33]  Michael J. O'Donovan,et al.  A Perimotor Framework Reveals Functional Segmentation in the Motoneuronal Network Controlling Locomotion in Caenorhabditis elegans , 2011, The Journal of Neuroscience.

[34]  P. Sauvage,et al.  An elasto-hydrodynamical model of friction for the locomotion of Caenorhabditis elegans. , 2011, Journal of biomechanics.

[35]  Lav R. Varshney,et al.  Structural Properties of the Caenorhabditis elegans Neuronal Network , 2009, PLoS Comput. Biol..

[36]  S. Lockery,et al.  Optogenetic analysis of synaptic transmission in the central nervous system of the nematode Caenorhabditis elegans. , 2011, Nature communications.

[37]  William S. Ryu,et al.  An Imbalancing Act: Gap Junctions Reduce the Backward Motor Circuit Activity to Bias C. elegans for Forward Locomotion , 2011, Neuron.

[38]  S. Lockery,et al.  An Image-Free Opto-Mechanical System for Creating Virtual Environments and Imaging Neuronal Activity in Freely Moving Caenorhabditis elegans , 2011, PloS one.

[39]  Aravinthan D. T. Samuel,et al.  Proprioceptive Coupling within Motor Neurons Drives C. elegans Forward Locomotion , 2012, Neuron.

[40]  Damon A. Clark,et al.  Dopamine Signaling Is Essential for Precise Rates of Locomotion by C. elegans , 2012, PloS one.

[41]  Jordan H. Boyle,et al.  Gait Modulation in C. elegans: An Integrated Neuromechanical Model , 2012, Front. Comput. Neurosci..

[42]  R. Jewkes,et al.  Perceptions and Experiences of Research Participants on Gender-Based Violence Community Based Survey: Implications for Ethical Guidelines , 2012, PloS one.

[43]  W. Schafer,et al.  Locomotion analysis identifies roles of mechanosensory neurons in governing locomotion dynamics of C. elegans , 2012, Journal of Experimental Biology.

[44]  P. Arratia,et al.  Undulatory locomotion of Caenorhabditis elegans on wet surfaces. , 2011, Biophysical journal.

[45]  Laura J. Grundy,et al.  A database of C. elegans behavioral phenotypes , 2013, Nature Methods.

[46]  Randall D. Beer,et al.  Connecting a Connectome to Behavior: An Ensemble of Neuroanatomical Models of C. elegans Klinotaxis , 2013, PLoS Comput. Biol..

[47]  N. Cohen,et al.  Nematode locomotion: dissecting the neuronal–environmental loop , 2014, Current Opinion in Neurobiology.

[48]  Jian-Xin Xu,et al.  A 3D undulatory locomotion model inspired by C. elegans through DNN approach , 2014, Neurocomputing.

[49]  W. Ryu,et al.  Direct measurements of drag forces in C. elegans crawling locomotion. , 2014, Biophysical journal.

[50]  J. Gjorgjieva,et al.  Neurobiology of Caenorhabditis elegans Locomotion: Where Do We Stand? , 2014, Bioscience.

[51]  R. Kerr,et al.  A consistent muscle activation strategy underlies crawling and swimming in Caenorhabditis elegans , 2015, Journal of The Royal Society Interface.

[52]  Aravinthan D. T. Samuel,et al.  C. elegans locomotion: small circuits, complex functions , 2015, Current Opinion in Neurobiology.

[53]  Guoyin Wang,et al.  Biological modeling the undulatory locomotion of C. elegans using dynamic neural network approach , 2016, Neurocomputing.

[54]  Masahiro Kuramochi,et al.  A Computational Model Based on Multi-Regional Calcium Imaging Represents the Spatio-Temporal Dynamics in a Caenorhabditis elegans Sensory Neuron , 2017, PloS one.

[55]  O. Schmitt.  The heat of shortening and the dynamic constants of muscle , 2017 .

[56]  Steven L. Brunton,et al.  Spatiotemporal Feedback and Network Structure Drive and Encode Caenorhabditis elegans Locomotion , 2017, PLoS Comput. Biol..

[57]  Michelle D. Po,et al.  A descending pathway facilitates undulatory wave propagation in Caenorhabditis elegans through gap junctions , 2017, bioRxiv.

[58]  Michelle D. Po,et al.  Descending pathway facilitates undulatory wave propagation in Caenorhabditis elegans through gap junctions , 2018, Proceedings of the National Academy of Sciences.

[59]  Eli J. Cornblath,et al.  Distributed rhythm generators underlie Caenorhabditis elegans forward locomotion , 2017, bioRxiv.

[60]  R. Beer,et al.  Potential role of a ventral nerve cord central pattern generator in forward and backward locomotion in Caenorhabditis elegans , 2017, Network Neuroscience.