Neuromechanical Mechanisms of Gait Adaptation in C. elegans: Relative Roles of Neural and Mechanical Coupling

Understanding principles of neurolocomotion requires the synthesis of neural activity, sensory feedback, and biomechanics. The nematode C. elegans is an ideal model organism for studying locomotion in an integrated neuromechanical setting because its neural circuit has a well-characterized modular structure and its undulatory forward swimming gait adapts to the surrounding fluid with a shorter wavelength in higher viscosity environments. This adaptive behavior emerges from the neural modules interacting through a combination of mechanical forces, neuronal coupling, and sensory feedback mechanisms. However, the relative contributions of these coupling modes to gait adaptation are not understood. Here, an integrated neuromechanical model of C. elegans forward locomotion is developed and analyzed. The model consists of repeated neuromechanical modules that are coupled through the mechanics of the body, short-range proprioception, and gap-junctions. The model captures the experimentally observed gait adaptation over a wide range of mechanical parameters, provided that the muscle response to input from the nervous system is faster than the body response to changes in internal and external forces. The modularity of the model allows the use of the theory of weakly coupled oscillators to identify the relative roles of body mechanics, gapjunctional coupling, and proprioceptive coupling in coordinating the undulatory gait. The analysis shows that the wavelength of body undulations is set by the relative strengths of these three coupling forms. In a low-viscosity fluid environment, the competition between gap-junctions and proprioception produces a long wavelength undulation, which is only achieved in the model with sufficiently strong gap-junctional coupling. The experimentally observed decrease in wavelength in response to increasing fluid viscosity is the result of an increase in the relative strength of mechanical coupling, which promotes a short wavelength.

[1]  A. Cohen,et al.  Interactions between internal forces, body stiffness, and fluid environment in a neuromechanical model of lamprey swimming , 2010, Proceedings of the National Academy of Sciences.

[2]  P. Arratia,et al.  The Effects of Fluid Viscosity on the Kinematics and Material Properties of C. elegans Swimming at Low Reynolds Number , 2009, 0912.3402.

[3]  T. Williams,et al.  Effects of local oscillator frequency on intersegmental coordination in the lamprey locomotor CPG: theory and experiment. , 1996, Journal of neurophysiology.

[4]  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.

[5]  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.

[6]  W. Ryu,et al.  Viscoelastic properties of the nematode Caenorhabditis elegans, a self-similar, shear-thinning worm , 2013, Proceedings of the National Academy of Sciences.

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

[8]  Joachim Schmidt,et al.  Intersegmental coordination of walking movements in stick insects. , 2005, Journal of neurophysiology.

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

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

[11]  Nancy Kopell,et al.  How Does the Crayfish Swimmeret System Work? Insights from Nearest-Neighbor Coupled Oscillator Models , 1997, Journal of Computational Neuroscience.

[12]  B. Mulloney,et al.  Intersegmental coordination in invertebrates and vertebrates , 1998, Current Opinion in Neurobiology.

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

[14]  Raymond E. Goldstein,et al.  FLEXIVE AND PROPULSIVE DYNAMICS OF ELASTICA AT LOW REYNOLDS NUMBER , 1997, cond-mat/9707346.

[15]  J. T. Hackett,et al.  Neuronal control of swimming behavior: Comparison of vertebrate and invertebrate model systems , 2011, Progress in Neurobiology.

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

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

[18]  P. Holmes,et al.  Frontiers in Neural Circuits Neural Circuits , 2022 .

[19]  P. Erdös,et al.  Theory of the locomotion of nematodes: control of the somatic motor neurons by interneurons. , 1993, Mathematical biosciences.

[20]  G. Ermentrout,et al.  Symmetry and phaselocking in chains of weakly coupled oscillators , 1986 .

[21]  A. Büschges,et al.  Intersegmental coordination: influence of a single walking leg on the neighboring segments in the stick insect walking system. , 2007, Journal of neurophysiology.

[22]  Brian Mulloney,et al.  Neural mechanism of optimal limb coordination in crustacean swimming , 2014, Proceedings of the National Academy of Sciences.

[23]  Michael A. Schwemmer,et al.  The Theory of Weakly Coupled Oscillators , 2012 .

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

[25]  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.

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

[27]  M. Félix,et al.  History of research on C. elegans and other free-living nematodes as model organisms. , 2017, WormBook : the online review of C. elegans biology.

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

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

[30]  John Bryden,et al.  Neural control of Caenorhabditis elegans forward locomotion: the role of sensory feedback , 2008, Biological Cybernetics.

[31]  Timothy J. Lewis,et al.  Phase response properties of half-center oscillators , 2013, Journal of Computational Neuroscience.

[32]  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.

[33]  E. Marder,et al.  Principles of rhythmic motor pattern generation. , 1996, Physiological reviews.

[34]  John Guckenheimer,et al.  The Dynamics of Legged Locomotion: Models, Analyses, and Challenges , 2006, SIAM Rev..

[35]  Becca Thomases,et al.  Mechanisms of elastic enhancement and hindrance for finite-length undulatory swimmers in viscoelastic fluids. , 2014, Physical review letters.

[36]  P. Holmes,et al.  The comparative investigation of the stick insect and cockroach models in the study of insect locomotion , 2015 .

[37]  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.

[38]  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.

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

[40]  Keir G Pearson,et al.  Generating the walking gait: role of sensory feedback. , 2004, Progress in brain research.

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

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

[43]  C. Fang-Yen,et al.  Phase response analyses support a relaxation oscillator model of locomotor rhythm generation in Caenorhabditis elegans , 2020, bioRxiv.