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+# Neuromechanical model of forward and backward locomotion in _C. elegans_
+
+A listing of the various publications and code releases related to this model of C. elegans forward and backward locomotion by Dr. Eduardo J. Izquiredo, Dr. Erick Olivares and Prof. Randall Beer.
+
+## 2007
+
+### An integrated neuro-mechanical model of C. elegans forward locomotion.
+
+**Boyle, J. H., Bryden, J., & Cohen, N.**
+
+Technical description of a neuro-mechanical model integrating known neural connectivity, muscle dynamics, and body mechanics to generate forward undulatory locomotion; groundwork for later expanded models of gait modulation.
+
+Abstract
+One of the most tractable organisms for the study of nervous systems is the nematode Caenorhabditis elegans, whose locomotion in particular has been the subject of a number of models. In this paper we present a first integrated neuro-mechanical model of forward locomotion. We find that a previous neural model is robust to the addition of a body with mechanical properties, and that the integrated model produces oscillations with a more realistic frequency and waveform than the neural model alone. We conclude that the body and environment are likely to be important components of the worm’s locomotion subsystem.
+Abstract
+To establish the relationship between locomotory behavior and dynamics of neural circuits in the nematode C. elegans we combined molecular and theoretical approaches. In particular, we quantitatively analyzed the motion of C. elegans with defective synaptic GABA and acetylcholine transmission, defective muscle calcium signaling, and defective muscles and cuticle structures, and compared the data with our systems level circuit model. The major experimental findings are: (1) anterior-to-posterior gradients of body bending flex for almost all strains both for forward and backward motion, and for neuronal mutants, also analogous weak gradients of undulatory frequency, (2) existence of some form of neuromuscular (stretch receptor) feedback, (3) invariance of neuromuscular wavelength, (4) biphasic dependence of frequency on synaptic signaling, and (5) decrease of frequency with increase of the muscle time constant. Based on (1) we hypothesize that the Central Pattern Generator (CPG) is located in the head both for forward and backward motion. Points (1) and (2) are the starting assumptions for our theoretical model, whose dynamical patterns are qualitatively insensitive to the details of the CPG design if stretch receptor feedback is sufficiently strong and slow. The model reveals that stretch receptor coupling in the body wall is critical for generation of the neuromuscular wave. Our model agrees with our behavioral data (3), (4), and (5), and with other pertinent published data, e.g., that frequency is an increasing function of muscle gap-junction coupling.
+Abstract
+Equipped with its 302-cell nervous system, the nematode Caenorhabditis elegans adapts its locomotion in different environments, exhibiting so-called swimming in liquids and crawling on dense gels. Recent experiments have demonstrated that the worm displays the full range of intermediate behaviors when placed in intermediate environments. The continuous nature of this transition strongly suggests that these behaviors all stem from modulation of a single underlying mechanism. We present a model of C. elegans forward locomotion that includes a neuromuscular control system that relies on a sensory feedback mechanism to generate undulations and is integrated with a physical model of the body and environment. We find that the model reproduces the entire swim-crawl transition, as well as locomotion in complex and heterogeneous environments. This is achieved with no modulatory mechanism, except via the proprioceptive response to the physical environment. Manipulations of the model are used to dissect the proposed pattern generation mechanism and its modulation. The model suggests a possible role for GABAergic D-class neurons in forward locomotion and makes a number of experimental predictions, in particular with respect to non-linearities in the model and to symmetry breaking between the neuromuscular systems on the ventral and dorsal sides of the body.
+Abstract
+Increased efforts in the assembly and analysis of connectome data are providing new insights into the principles underlying the connectivity of neural circuits. However, despite these considerable advances in connectomics, neuroanatomical data must be integrated with neurophysiological and behavioral data in order to obtain a complete picture of neural function. Due to its nearly complete wiring diagram and large behavioral repertoire, the nematode worm Caenorhaditis elegans is an ideal organism in which to explore in detail this link between neural connectivity and behavior. In this paper, we develop a neuroanatomically-grounded model of salt klinotaxis, a form of chemotaxis in which changes in orientation are directed towards the source through gradual continual adjustments. We identify a minimal klinotaxis circuit by systematically searching the C. elegans connectome for pathways linking chemosensory neurons to neck motor neurons, and prune the resulting network based on both experimental considerations and several simplifying assumptions. We then use an evolutionary algorithm to find possible values for the unknown electrophsyiological parameters in the network such that the behavioral performance of the entire model is optimized to match that of the animal. Multiple runs of the evolutionary algorithm produce an ensemble of such models. We analyze in some detail the mechanisms by which one of the best evolved circuits operates and characterize the similarities and differences between this mechanism and other solutions in the ensemble. Finally, we propose a series of experiments to determine which of these alternatives the worm may be using.
+Abstract
+Animals use a nervous system for locomotion in some stage of their life cycle. The nematode Caenorhabditis elegans, a major animal model for almost all fields of experimental biology, has long been used for detailed studies of genetic and physiological locomotion mechanisms. Of its 959 somatic cells, 302 are neurons that are identifiable by lineage, location, morphology, and neurochemistry in every adult hermaphrodite. Of those, 75 motoneurons innervate body wall muscles that provide the thrust during locomotion. In this Overview, we concentrate on the generation of either forward- or backward-directed motion during crawling and swimming. We describe locomotion behavior, the parts constituting the locomotion system, and the relevant neuronal connectivity. Because it is not yet fully understood how these components combine to generate locomotion, we discuss competing hypotheses and models.
+Abstract
+Locomotion is driven by shape changes coordinated by the nervous system through time; thus, enumerating an animal's complete repertoire of shape transitions would provide a basis for a comprehensive understanding of locomotor behaviour. Here we introduce a discrete representation of behaviour in the nematode C. elegans. At each point in time, the worm’s posture is approximated by its closest matching template from a set of 90 postures and locomotion is represented as sequences of postures. The frequency distribution of postural sequences is heavy-tailed with a core of frequent behaviours and a much larger set of rarely used behaviours. Responses to optogenetic and environmental stimuli can be quantified as changes in postural syntax: worms show different preferences for different sequences of postures drawn from the same set of templates. A discrete representation of behaviour will enable the use of methods developed for other kinds of discrete data in bioinformatics and language processing to be harnessed for the study of behaviour.
+Abstract
+With 302 neurons and a fully reconstructed connectome, Caernohabditis elegans is an ideal candidate organism to study how behavior is grounded in the interaction between an organism's brain, its body, and its environment. Since nearly its entire behavioral repertoire is expressed through movement, understanding the neuromechanical basis of locomotion is especially critical as a foundation upon which analyses of all other behaviors must build. In this extended abstract, we report on the evolution and analysis of an integrated neuromechanical model of forward locomotion.
+Abstract
+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.
+Abstract
+C. elegans locomotes in an undulatory fashion, generating thrust by propagating dorsoventral bends along its body. Although central pattern generators (CPGs) are typically involved in animal locomotion, their presence in C. elegans has been questioned, mainly because there has been no evident circuit that supports intrinsic network oscillations. With a fully reconstructed connectome, the question of whether it is possible to have a CPG in the ventral nerve cord (VNC) of C. elegans can be answered through computational models. We modeled a repeating neural unit based on segmentation analysis of the connectome. We then used an evolutionary algorithm to determine the unknown physiological parameters of each neuron so as to match the features of the neural traces of the worm during forward and backward locomotion. We performed 1,000 evolutionary runs and consistently found configurations of the neural circuit that produced oscillations matching the main characteristic observed in experimental recordings. In addition to providing an existence proof for the possibility of a CPG in the VNC, we suggest a series of testable hypotheses about its operation. More generally, we show the feasibility and fruitfulness of a methodology to study behavior based on a connectome, in the absence of complete neurophysiological details.
+Abstract
+Animal neuromechanics describes the coordinated self-propelled movement of a body, subject to the combined effects of internal neural control and mechanical forces. Here we use a computational model to identify effects of neural and mechanical modulation on undulatory forward locomotion of Caenorhabditis elegans, with a focus on proprioceptively driven neural control. We reveal a fundamental relationship between body elasticity and environmental drag in determining the dynamics of the body and demonstrate the manifestation of this relationship in the context of proprioceptively driven control. By considering characteristics unique to proprioceptive neurons, we predict the signatures of internal gait modulation that contrast with the known signatures of externally or biomechanically modulated gait. We further show that proprioceptive feedback can suppress neuromechanical phase lags during undulatory locomotion, contrasting with well studied advancing phase lags that have long been a signature of centrally generated, feed-forward control.
+Abstract
+Animal neuromechanics describes the coordin
+Cell- or network-driven oscillators underlie motor rhythmicity. The identity of C. elegans oscillators remains unknown. Through cell ablation, electrophysiology, and calcium imaging, we show: (1) forward and backward locomotion is driven by different oscillators; (2) the cholinergic and excitatory A-class motor neurons exhibit intrinsic and oscillatory activity that is sufficient to drive backward locomotion in the absence of premotor interneurons; (3) the UNC-2 P/Q/N high-voltage-activated calcium current underlies A motor neuron’s oscillation; (4) descending premotor interneurons AVA, via an evolutionarily conserved, mixed gap junction and chemical synapse configuration, exert state-dependent inhibition and potentiation of A motor neuron’s intrinsic activity to regulate backward locomotion. Thus, motor neurons themselves derive rhythms, which are dually regulated by the descending interneurons to control the reversal motor state. These and previous findings exemplify compression: essential circuit properties are conserved but executed by fewer numbers and layers of neurons in a small locomotor network.
+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.
+Abstract
+Previous studies tracking the relationship between manipulations of C. elegans neurons and the resulting behavioral changes have called for the development of a connectome-constrained neural network model that describes the cascade from neurons to behavior. However, the model using anatomical connectome weights as they are did not achieve that. Here, we introduce a concept of learning the synaptic weights in our connectome-constrained neural network model based on the leaky-integrator equation while preserving the structural proportions of anatomical synapses. In this process, the weights of gap junctions and chemical synapses in C. elegans neurons are optimized. As a result, our neural network model generates plausible C. elegans behavior mediated by activity changes in forward and backward command neurons, even without the introduction of pacemaker neurons with intrinsic oscillatory activity. Additionally, we identified necessary or sufficient neurons for maintaining oscillatory patterns on muscular activity that could serve as clues for the central pattern generator in our neural network model. Finally, we provide 10 optimized synaptic weights sets of C. elegans that reproduce the results of manipulation experiments on the SMD neurons. This study will facilitate the future study for unraveling the multiscale relationship of “from synapse to behavior” in nervous system.
+