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

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.

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

[2]  Christopher R. Myers,et al.  Universally Sloppy Parameter Sensitivities in Systems Biology Models , 2007, PLoS Comput. Biol..

[3]  I. Putrenko,et al.  A Family of Acetylcholine-gated Chloride Channel Subunits in Caenorhabditis elegans* , 2005, Journal of Biological Chemistry.

[4]  Paul W. Sternberg,et al.  Synaptic polarity of the interneuron circuit controlling C. elegans locomotion , 2013, Front. Comput. Neurosci..

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

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

[7]  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.

[8]  P. Csermely,et al.  Synaptic polarity and sign-balance prediction using gene expression data in the Caenorhabditis elegans chemical synapse neuronal connectome network , 2020, PLoS computational biology.

[9]  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.

[10]  A. Ijspeert,et al.  The Human Central Pattern Generator for Locomotion: Does It Exist and Contribute to Walking? , 2017, The Neuroscientist : a review journal bringing neurobiology, neurology and psychiatry.

[11]  S. Larson,et al.  Three-dimensional simulation of the Caenorhabditis elegans body and muscle cells in liquid and gel environments for behavioural analysis , 2018, Philosophical Transactions of the Royal Society B: Biological Sciences.

[12]  Jason A. Avery,et al.  A Biologically Accurate 3D Model of the Locomotion of Caenorhabditis Elegans , 2010, 2010 International Conference on Biosciences.

[13]  Pascal Hersen,et al.  Locomotion control of Caenorhabditis elegans through confinement. , 2012, Biophysical journal.

[14]  Hyun-Ho Lim,et al.  A sensory-motor neuron type mediates proprioceptive coordination of steering in C. elegans via two TRPC channels , 2018, PLoS biology.

[15]  E. Marder,et al.  Central pattern generators and the control of rhythmic movements , 2001, Current Biology.

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

[17]  Travis A. Jarrell,et al.  The Connectome of a Decision-Making Neural Network , 2012, Science.

[18]  M. A. MacIver,et al.  Neuroscience Needs Behavior: Correcting a Reductionist Bias , 2017, Neuron.

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

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

[21]  Radu Grosu,et al.  c302: a multiscale framework for modelling the nervous system of Caenorhabditis elegans , 2018, Philosophical Transactions of the Royal Society B: Biological Sciences.

[22]  P. Katz Evolution of central pattern generators and rhythmic behaviours , 2016, Philosophical Transactions of the Royal Society B: Biological Sciences.

[23]  G. Haspel,et al.  Inhibition Underlies Fast Undulatory Locomotion in Caenorhabditis elegans , 2020, eNeuro.

[24]  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.

[25]  M. Peliti,et al.  Directional Locomotion of C. elegans in the Absence of External Stimuli , 2013, PloS one.

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

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

[28]  Quan Wen,et al.  Caenorhabditis elegans excitatory ventral cord motor neurons derive rhythm for body undulation , 2018, Philosophical Transactions of the Royal Society B: Biological Sciences.

[29]  Yi Wang,et al.  Whole-animal connectomes of both Caenorhabditis elegans sexes , 2019, Nature.

[30]  S. Lockery,et al.  Active Currents Regulate Sensitivity and Dynamic Range in C. elegans Neurons , 1998, Neuron.

[31]  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.

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

[33]  Y. I. Arshavsky,et al.  Central Pattern Generators: Mechanisms of Operation and Their Role in Controlling Automatic Movements , 2016, Neuroscience and Behavioral Physiology.

[34]  S. Rossignol,et al.  Dynamic sensorimotor interactions in locomotion. , 2006, Physiological reviews.

[35]  Eduardo J. Izquierdo,et al.  Role of simulation models in understanding the generation of behavior in C. elegans , 2019, Current Opinion in Systems Biology.

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

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

[38]  G. Haspel,et al.  Inhibition underlies fast undulatory locomotion in C. elegans , 2020, bioRxiv.

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

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

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

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

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

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

[45]  Zeynep F. Altun,et al.  WormAtlas Hermaphrodite Handbook - Muscle System - Somatic Muscle , 2005 .

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

[47]  Vito Paolo Pastore,et al.  Identification of excitatory-inhibitory links and network topology in large-scale neuronal assemblies from multi-electrode recordings , 2018, PLoS Comput. Biol..

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

[49]  Shimon Marom,et al.  Development, learning and memory in large random networks of cortical neurons: lessons beyond anatomy , 2002, Quarterly Reviews of Biophysics.

[50]  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.

[51]  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.

[52]  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.

[53]  Eli Shlizerman,et al.  Low-dimensional functionality of complex network dynamics: neurosensory integration in the Caenorhabditis Elegans connectome. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[54]  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.

[55]  James M. Kunert-Graf,et al.  The control structure of the nematode Caenorhabditis elegans: Neuro-sensory integration and proprioceptive feedback. , 2017, Journal of biomechanics.

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

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

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

[59]  M. Goulding Circuits controlling vertebrate locomotion: moving in a new direction , 2009, Nature Reviews Neuroscience.

[60]  Evolution of Locomotor Rhythms , 2018, Trends in Neurosciences.

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

[62]  Auke Jan Ijspeert,et al.  Central pattern generators for locomotion control in animals and robots: A review , 2008, Neural Networks.

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

[64]  Yi Wang,et al.  Computer Assisted Assembly of Connectomes from Electron Micrographs: Application to Caenorhabditis elegans , 2013, PloS one.

[65]  E. Jorgensen,et al.  Graded synaptic transmission at the Caenorhabditis elegans neuromuscular junction , 2009, Proceedings of the National Academy of Sciences.

[66]  Thomas Ranner,et al.  Signatures of proprioceptive control in Caenorhabditis elegans locomotion , 2018, Philosophical Transactions of the Royal Society B: Biological Sciences.

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

[68]  Rolf Pfeifer,et al.  How the body shapes the way we think - a new view on intelligence , 2006 .

[69]  Netta Cohen,et al.  Whole animal modeling: piecing together nematode locomotion , 2019, Current Opinion in Systems Biology.

[70]  Sreekanth H. Chalasani,et al.  Dissecting a circuit for olfactory behaviour in Caenorhabditis elegans , 2007, Nature.

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

[72]  Randall D. Beer,et al.  The brain has a body: adaptive behavior emerges from interactions of nervous system, body and environment , 1997, Trends in Neurosciences.

[73]  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.

[74]  E. Marder,et al.  Similar network activity from disparate circuit parameters , 2004, Nature Neuroscience.

[75]  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.

[76]  Zhaoyu Li,et al.  Encoding of Both Analog- and Digital-like Behavioral Outputs by One C. elegans Interneuron , 2014, Cell.

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

[78]  Alexander Gottschalk,et al.  Functionally asymmetric motor neurons contribute to coordinating locomotion of Caenorhabditis elegans , 2018, eLife.

[79]  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.

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

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

[82]  Hillel J. Chiel,et al.  The Brain in Its Body: Motor Control and Sensing in a Biomechanical Context , 2009, The Journal of Neuroscience.

[83]  Mark J Alkema,et al.  Excitatory motor neurons are local oscillators for backward locomotion , 2017, eLife.

[84]  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.

[85]  Neurogenetics of synaptic transmission in Caenorhabditis elegans. , 1998, Advances in pharmacology.

[86]  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.

[87]  R. Beer,et al.  A neuromechanical model of multiple network oscillators for forward locomotion in C. elegans , 2019, bioRxiv.

[88]  R. Beer,et al.  From head to tail: a neuromechanical model of forward locomotion in Caenorhabditis elegans , 2018, Philosophical Transactions of the Royal Society B: Biological Sciences.

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