Forward locomotion of the nematode C. elegans is achieved through modulation of a single gait

Remodeling of extracellular matrix collagen IV by MIG-6/papilin regulates neuronal architecture

Neuronal architecture established embryonically must persist lifelong to ensure normal brain function. However, little is understood about the mechanisms behind the long-term maintenance of neuronal organization. To uncover maintenance mechanisms, we performed a suppressor screen in sax-7/L1CAM mutants, which exhibit progressive disorganization with age. We identified the conserved extracellular matrix protein MIG-6/papilin as a key regulator of neuronal maintenance. Combining incisive molecular genetics, structural predictions, in vivo quantitative imaging, and cutting-edge Brillouin microscopy, we show that MIG-6/papilin remodels extracellular matrix collagen IV, working in concert with the secreted enzymes MIG-17/ADAMTS and PXN-2/peroxidasin. This remodeling impacts tissue biomechanics and ensures neuronal stability, even under increased mechanical stress. Our findings highlight an extracellular mechanism by which MIG-6/papilin supports the integrity of neuronal architecture throughout life. This work provides critical insights into the molecular basis of sustaining neuronal architecture and offers a foundation for understanding age-related and neurodegenerative disorders.

Remodeling of extracellular matrix collagen IV by MIG-6/papilin regulates neuronal architecture

Neuronal architecture established embryonically must persist lifelong to ensure normal brain function. However, little is understood about the mechanisms behind the long-term maintenance of neuronal organization. To uncover maintenance mechanisms, we performed a suppressor screen in sax-7 / L1CAM mutants, which exhibit progressive disorganization with age. We identified the conserved extracellular matrix protein MIG-6/papilin as a key regulator of neuronal maintenance. Combining incisive molecular genetics, structural predictions, in vivo quantitative imaging, and cutting-edge Brillouin microscopy, we show that MIG-6/papilin remodels extracellular matrix collagen IV, working in concert with the secreted enzymes MIG-17/ADAMTS and PXN-2/peroxidasin. This remodeling impacts tissue biomechanics and ensures neuronal stability, even under increased mechanical stress. Our findings highlight an extracellular mechanism by which MIG-6/papilin supports the integrity of neuronal architecture throughout life. This work provides critical insights into the molecular basis of sustaining neuronal architecture and offers a foundation for understanding age-related and neurodegenerative disorders.

Memristive Circuit Implementation of Caenorhabditis Elegans Mechanism for Neuromorphic Computing

To overcome the energy efficiency bottleneck of the von Neumann architecture and scaling limit of silicon transistors, an emerging but promising solution is neuromorphic computing, a new computing paradigm inspired by how biological neural networks handle the massive amount of information in a parallel and efficient way. Recently, there is a surge of interest in the nematode worm Caenorhabditis elegans (C. elegans), an ideal model organism to probe the mechanisms of biological neural networks. In this article, we propose a neuron model for C. elegans with leaky integrate-and-fire (LIF) dynamics and adjustable integration time. We utilize these neurons to build the C. elegans neural network according to their neural physiology, which comprises: 1) sensory modules; 2) interneuron modules; and 3) motoneuron modules. Leveraging these block designs, we develop a serpentine robot system, which mimics the locomotion behavior of C. elegans upon external stimulus. Moreover, experimental results of C. elegans neurons presented in this article reveals the robustness (1% error w.r.t. 10% random noise) and flexibility of our design in term of parameter setting. The work paves the way for future intelligent systems by mimicking the C. elegans neural system.

Geometric phase predicts locomotion performance in undulating living systems across scales

Self-propelling organisms locomote via generation of patterns of self-deformation. Despite the diversity of body plans, internal actuation schemes and environments in limbless vertebrates and invertebrates, such organisms often use similar traveling waves of axial body bending for movement. Delineating how self-deformation parameters lead to locomotor performance (e.g. speed, energy, turning capabilities) remains challenging. We show that a geometric framework, replacing laborious calculation with a diagrammatic scheme, is well-suited to discovery and comparison of effective patterns of wave dynamics in diverse living systems. We focus on a regime of undulatory locomotion, that of highly damped environments, which is applicable not only to small organisms in viscous fluids, but also larger animals in frictional fluids (sand) and on frictional ground. We find that the traveling wave dynamics used by mm-scale nematode worms and cm-scale desert dwelling snakes and lizards can be described by time series of weights associated with two principal modes. The approximately circular closed path trajectories of mode weights in a self-deformation space enclose near-maximal surface integral (geometric phase) for organisms spanning two decades in body length. We hypothesize that such trajectories are targets of control (which we refer to as "serpenoid templates"). Further, the geometric approach reveals how seemingly complex behaviors such as turning in worms and sidewinding snakes can be described as modulations of templates. Thus, the use of differential geometry in the locomotion of living systems generates a common description of locomotion across taxa and provides hypotheses for neuromechanical control schemes at lower levels of organization.

Development of equation of motion deciphering locomotion including omega turns of Caenorhabditis elegans

Locomotion is a fundamental behavior of Caenorhabditis elegans (C. elegans). Previous works on kinetic simulations of animals helped researchers understand the physical mechanisms of locomotion and the muscle-controlling principles of neuronal circuits as an actuator part. It has yet to be understood how C. elegans utilizes the frictional forces caused by the tension of its muscles to perform sequenced locomotive behaviors. Here, we present a two-dimensional rigid body chain model for the locomotion of C. elegans by developing Newtonian equations of motion for each body segment of C. elegans. Having accounted for friction-coefficients of the surrounding environment, elastic constants of C. elegans, and its kymogram from experiments, our kinetic model (ElegansBot) reproduced various locomotion of C. elegans such as, but not limited to, forward-backward-(omega turn)-forward locomotion constituting escaping behavior and delta-turn navigation. Additionally, ElegansBot precisely quantified the forces acting on each body segment of C. elegans to allow investigation of the force distribution. This model will facilitate our understanding of the detailed mechanism of various locomotive behaviors at any given friction-coefficients of the surrounding environment. Furthermore, as the model ensures the performance of realistic behavior, it can be used to research actuator-controller interaction between muscles and neuronal circuits.

Assessing locomotory rate in response to food for the identification of neuronal and muscular defects in C. elegans

C. elegans is a bacteria-eating soil-dwelling nematode. Typical cultivation of laboratory-reared populations occurs on bacteria-covered solid media, where they move along with sinusoidal undulations. Nematodes decelerate when they encounter food. Dopaminergic and serotonergic neurotransmission regulate this behavior. Here, we describe the procedure for determining food-dependent locomotion rate of fed and fasting nematodes. We detail steps for assay plate preparation, C. elegans synchronization, and assessment of locomotion. The behaviors we describe provide information regarding the animal's physiological neuronal and muscular function. For complete details on the use and execution of this protocol, please refer to Petratou et al. (2023)1 and Sawin et al. (2000).2.

Dimensionality of locomotor behaviors in developing C. elegans

Adult animals display robust locomotion, yet the timeline and mechanisms of how juvenile animals acquire coordinated movements and how these movements evolve during development are not well understood. Recent advances in quantitative behavioral analyses have paved the way for investigating complex natural behaviors like locomotion. In this study, we tracked the swimming and crawling behaviors of the nematode Caenorhabditis elegans from postembryonic development through to adulthood. Our principal component analyses revealed that adult C. elegans swimming is low dimensional, suggesting that a small number of distinct postures, or eigenworms, account for most of the variance in the body shapes that constitute swimming behavior. Additionally, we found that crawling behavior in adult C. elegans is similarly low dimensional, corroborating previous studies. Further, our analysis revealed that swimming and crawling are distinguishable within the eigenworm space. Remarkably, young L1 larvae are capable of producing the postural shapes for swimming and crawling seen in adults, despite frequent instances of uncoordinated body movements. In contrast, late L1 larvae exhibit robust coordination of locomotion, while many neurons crucial for adult locomotion are still under development. In conclusion, this study establishes a comprehensive quantitative behavioral framework for understanding the neural basis of locomotor development, including distinct gaits such as swimming and crawling in C. elegans.

Steering undulatory micro-swimmers in a fluid flow through reinforcement learning

This work aims at finding optimal navigation policies for thin, deformable microswimmers that progress in a viscous fluid by propagating a sinusoidal undulation along their slender body. These active filaments are embedded in a prescribed, non-homogeneous flow, in which their swimming undulations have to compete with the drifts, strains, and deformations inflicted by the outer velocity field. Such an intricate situation, where swimming and navigation are tightly bonded, is addressed using various methods of reinforcement learning. Each swimmer has only access to restricted information on its configuration and has to select accordingly an action among a limited set. The optimisation problem then consists in finding the policy leading to the most efficient displacement in a given direction. It is found that usual methods do not converge and this pitfall is interpreted as a combined consequence of the non-Markovianity of the decision process, together with the highly chaotic nature of the dynamics, which is responsible for high variability in learning efficiencies. Still, we provide an alternative method to construct efficient policies, which is based on running several independent realisations of Q-learning. This allows the construction of a set of admissible policies whose properties can be studied in detail and compared to assess their efficiency and robustness.

A Quantitative Analysis of Locomotor Patterns in Developing C. elegans

Adult animals display robust locomotion, yet the timeline and mechanisms of how juvenile animals acquire coordinated movements and how these movements evolve during development are not well understood. Recent advances in quantitative behavioral analyses have paved the way for investigating complex natural behaviors like locomotion. In this study, we tracked the swimming and crawling behaviors of the nematode Caenorhabditis elegans from postembryonic development through to adulthood. Our principal component analyses revealed that adult C. elegans swimming is low dimensional, suggesting that a small number of distinct postures, or eigenworms, account for most of the variance in the body shapes that constitute swimming behavior. Additionally, we found that crawling behavior in adult C. elegans is similarly low dimensional, corroborating previous studies. However, our analysis revealed that swimming and crawling are distinct gaits in adult animals, clearly distinguishable within the eigenworm space. Remarkably, young L1 larvae are capable of producing the postural shapes for swimming and crawling seen in adults, despite frequent instances of uncoordinated body movements. In contrast, late L1 larvae exhibit robust coordination of locomotion, while many neurons crucial for adult locomotion are still under development. In conclusion, this study establishes a comprehensive quantitative behavioral framework for understanding the neural basis of locomotor development, including distinct gaits such as swimming and crawling in C. elegans.

A proprioceptive feedback circuit drives Caenorhabditis elegans locomotor adaptation through dopamine signaling

An animal adapts its motor behavior to navigate the external environment. This adaptation depends on proprioception, which provides feedback on an animal's body postures. How proprioception mechanisms interact with motor circuits and contribute to locomotor adaptation remains unclear. Here, we describe and characterize proprioception-mediated homeostatic control of undulatory movement in the roundworm Caenorhabditis elegans. We found that the worm responds to optogenetically or mechanically induced decreases in midbody bending amplitude by increasing its anterior amplitude. Conversely, it responds to increased midbody amplitude by decreasing the anterior amplitude. Using genetics, microfluidic and optogenetic perturbation response analyses, and optical neurophysiology, we elucidated the neural circuit underlying this compensatory postural response. The dopaminergic PDE neurons proprioceptively sense midbody bending and signal to AVK interneurons via the D2-like dopamine receptor DOP-3. The FMRFamide-like neuropeptide FLP-1, released by AVK, regulates SMB head motor neurons to modulate anterior bending. We propose that this homeostatic behavioral control optimizes locomotor efficiency. Our findings demonstrate a mechanism in which proprioception works with dopamine and neuropeptide signaling to mediate motor control, a motif that may be conserved in other animals.

Self-propulsion via slipping: Frictional swimming in multilegged locomotors

Locomotion is typically studied either in continuous media where bodies and legs experience forces generated by the flowing medium or on solid substrates dominated by friction. In the former, centralized whole-body coordination is believed to facilitate appropriate slipping through the medium for propulsion. In the latter, slip is often assumed minimal and thus avoided via decentralized control schemes. We find in laboratory experiments that terrestrial locomotion of a meter-scale multisegmented/legged robophysical model resembles undulatory fluid swimming. Experiments varying waves of leg stepping and body bending reveal how these parameters result in effective terrestrial locomotion despite seemingly ineffective isotropic frictional contacts. Dissipation dominates over inertial effects in this macroscopic-scaled regime, resulting in essentially geometric locomotion on land akin to microscopic-scale swimming in fluids. Theoretical analysis demonstrates that the high-dimensional multisegmented/legged dynamics can be simplified to a centralized low-dimensional model, which reveals an effective resistive force theory with an acquired viscous drag anisotropy. We extend our low-dimensional, geometric analysis to illustrate how body undulation can aid performance in non-flat obstacle-rich terrains and also use the scheme to quantitatively model how body undulation affects performance of biological centipede locomotion (the desert centipede Scolopendra polymorpha) moving at relatively high speeds (∼0.5 body lengths/sec). Our results could facilitate control of multilegged robots in complex terradynamic scenarios.

Mechanics and optimization of undulatory locomotion in different environments, tuning geometry, stiffness, damping and frictional anisotropy

One of the oldest yet most common modalities of locomotion known among limbless animals is undulatory, also recognized for its stability compared to legged locomotion. Multiple forms of active mechanisms, e.g. active gait control, and passive mechanisms, e.g. body morphology and material properties, have adapted to different environments. The current research explores the passive role of body stiffness and internal losses in meeting terrain requirements. Furthermore, it addresses the influence of the environment on the resultant gait and how the interplay between various environments and body properties can lead to different speeds. We modelled undulatory locomotion in a dry friction environment where frictional anisotropy determines propulsion. We found that the body stiffness, the moment of inertia, the dry frictional coefficient ratio between normal and tangential frictional constants, and the internal damping of the body play an essential role in optimizing speed and animal adaptability to external conditions. Furthermore, we demonstrate that various known gaits like swimming, crawling and polychaete-like locomotion are achieved as a result of the interaction between body and environment parameters. Moreover, we validated the model by retrieving a corn snake's speed using data from the literature. This study demonstrates that the dependence between morphology, body material properties and environment can be exploited to design long-segmented robots to perform in specialized situations.

Phase response analyses support a relaxation oscillator model of locomotor rhythm generation in Caenorhabditis elegans

Neural circuits coordinate with muscles and sensory feedback to generate motor behaviors appropriate to an animal's environment. In C. elegans, the mechanisms by which the motor circuit generates undulations and modulates them based on the environment are largely unclear. We quantitatively analyzed C. elegans locomotion during free movement and during transient optogenetic muscle inhibition. Undulatory movements were highly asymmetrical with respect to the duration of bending and unbending during each cycle. Phase response curves induced by brief optogenetic inhibition of head muscles showed gradual increases and rapid decreases as a function of phase at which the perturbation was applied. A relaxation oscillator model based on proprioceptive thresholds that switch the active muscle moment was developed and is shown to quantitatively agree with data from free movement, phase responses, and previous results for gait adaptation to mechanical loadings. Our results suggest a neuromuscular mechanism underlying C. elegans motor pattern generation within a compact circuit.

Metachronal waves in concentrations of swimming Turbatrix aceti nematodes and an oscillator chain model for their coordinated motions

At high concentration, free swimming nematodes known as vinegar eels (Turbatrix aceti), collectively exhibit metachronal waves near a boundary. We find that the frequency of the collective traveling wave is lower than that of the freely swimming organisms. We explore models based on a chain of oscillators with nearest-neighbor interactions that inhibit oscillator phase velocity. The phase of each oscillator represents the phase of the motion of the eel's head back and forth about its mean position. A strongly interacting directed chain model mimicking steric repulsion between organisms robustly gives traveling wave states and can approximately match the observed wavelength and oscillation frequency of the observed traveling wave. We predict body shapes assuming that waves propagate down the eel body at a constant speed. The phase oscillator model that impedes eel head overlaps also reduces close interactions throughout the eel bodies.

Resilience of neural networks for locomotion

Locomotion is an essential behaviour for the survival of all animals. The neural circuitry underlying locomotion is therefore highly robust to a wide variety of perturbations, including injury and abrupt changes in the environment. In the short term, fault tolerance in neural networks allows locomotion to persist immediately after mild to moderate injury. In the longer term, in many invertebrates and vertebrates, neural reorganization including anatomical regeneration can restore locomotion after severe perturbations that initially caused paralysis. Despite decades of research, very little is known about the mechanisms underlying locomotor resilience at the level of the underlying neural circuits and coordination of central pattern generators (CPGs). Undulatory locomotion is an ideal behaviour for exploring principles of circuit organization, neural control and resilience of locomotion, offering a number of unique advantages including experimental accessibility and modelling tractability. In comparing three well-characterized undulatory swimmers, lampreys, larval zebrafish and Caenorhabditis elegans, we find similarities in the manifestation of locomotor resilience. To advance our understanding, we propose a comparative approach, integrating experimental and modelling studies, that will allow the field to begin identifying shared and distinct solutions for overcoming perturbations to persist in orchestrating this essential behaviour.

Biophysical analysis of drug efficacy on C. elegans models for neurodegenerative and neuromuscular diseases

Caenorhabditis elegans has emerged as a powerful model organism for drug screening due to its cellular simplicity, genetic amenability and homology to humans combined with its small size and low cost. Currently, high-throughput drug screening assays are mostly based on image-based phenotyping with the focus on morphological-descriptive traits not exploiting key locomotory parameters of this multicellular model with muscles such as its thrashing force, a critical biophysical parameter when screening drugs for muscle-related diseases. In this study, we demonstrated the use of a micropillar-based force assay chip in combination with a fluorescence assay to evaluate the efficacy of various drugs currently used in treatment of neurodegenerative and neuromuscular diseases. Using this two-dimensional approach, we showed that the force assay was generally more sensitive in measuring efficacy of drug treatment in Duchenne Muscular Dystrophy and Parkinson's Disease mutant worms as well as partly in Amyotrophic Lateral Sclerosis model. These results underline the potential of our force assay chip in screening of potential drug candidates for the treatment of neurodegenerative and neuromuscular diseases when combined with a fluorescence assay in a two-dimensional analysis approach.

Soft-bodied adaptive multimodal locomotion strategies in fluid-filled confined spaces

Soft-bodied locomotion in fluid-filled confined spaces is critical for future wireless medical robots operating inside vessels, tubes, channels, and cavities of the human body, which are filled with stagnant or flowing biological fluids. However, the active soft-bodied locomotion is challenging to achieve when the robot size is comparable with the cross-sectional dimension of these confined spaces. Here, we propose various control and performance enhancement strategies to let the sheet-shaped soft millirobots achieve multimodal locomotion, including rolling, undulatory crawling, undulatory swimming, and helical surface crawling depending on different fluid-filled confined environments. With these locomotion modes, the sheet-shaped soft robot can navigate through straight or bent gaps with varying sizes, tortuous channels, and tubes with a flowing fluid inside. Such soft robot design along with its control and performance enhancement strategies are promising to be applied in future wireless soft medical robots inside various fluid-filled tight regions of the human body.

Inhibition Underlies Fast Undulatory Locomotion in Caenorhabditis elegans

Inhibition plays important roles in modulating the neural activities of sensory and motor systems at different levels from synapses to brain regions. To achieve coordinated movement, motor systems produce alternating contractions of antagonist muscles, whether along the body axis or within and among limbs, which often involves direct or indirect cross-inhibitory pathways. In the nematode Caenorhabditis elegans, a small network involving excitatory cholinergic and inhibitory GABAergic motoneurons generates the dorsoventral alternation of body-wall muscles that supports undulatory locomotion. Inhibition has been suggested to be necessary for backward undulation because mutants that are defective in GABA transmission exhibit a shrinking phenotype in response to a harsh touch to the head, whereas wild-type animals produce a backward escape response. Here, we demonstrate that the shrinking phenotype is exhibited by wild-type as well as mutant animals in response to harsh touch to the head or tail, but only GABA transmission mutants show slow locomotion after stimulation. Impairment of GABA transmission, either genetically or optogenetically, induces lower undulation frequency and lower translocation speed during crawling and swimming in both directions. The activity patterns of GABAergic motoneurons are different during low-frequency and high-frequency undulation. During low-frequency undulation, GABAergic VD and DD motoneurons show correlated activity patterns, while during high-frequency undulation, their activity alternates. The experimental results suggest at least three non-mutually exclusive roles for inhibition that could underlie fast undulatory locomotion in C. elegans, which we tested with computational models: cross-inhibition or disinhibition of body-wall muscles, or neuronal reset.

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.

Living System Adapts Harmonics of Peristaltic Wave for Cost-Efficient Optimization of Pumping Performance

Wavelike patterns driving transport are ubiquitous in life. Peristaltic pumps are a paradigm of efficient mass transport by contraction driven flows-often limited by energetic constraints. We show that a cost-efficient increase in pumping performance can be achieved by modulating the phase difference between harmonics to increase occlusion. In experiments we find a phase difference shift in the living peristalsis model P. polycephalum as dynamic response to forced mass transport. Our findings provide a novel metric for wavelike patterns and demonstrate the crucial role of nonlinearities in life.

Modelling the mechanics of exploration in larval Drosophila

The Drosophila larva executes a stereotypical exploratory routine that appears to consist of stochastic alternation between straight peristaltic crawling and reorientation events through lateral bending. We present a model of larval mechanics for axial and transverse motion over a planar substrate, and use it to develop a simple, reflexive neuromuscular model from physical principles. The mechanical model represents the midline of the larva as a set of point masses which interact with each other via damped translational and torsional springs, and with the environment via sliding friction forces. The neuromuscular model consists of: 1. segmentally localised reflexes that amplify axial compression in order to counteract frictive energy losses, and 2. long-range mutual inhibition between reflexes in distant segments, enabling overall motion of the model larva relative to its substrate. In the absence of damping and driving, the mechanical model produces axial travelling waves, lateral oscillations, and unpredictable, chaotic deformations. The neuromuscular model counteracts friction to recover these motion patterns, giving rise to forward and backward peristalsis in addition to turning. Our model produces spontaneous exploration, even though the nervous system has no intrinsic pattern generating or decision making ability, and neither senses nor drives bending motions. Ultimately, our model suggests a novel view of larval exploration as a deterministic superdiffusion process which is mechanistically grounded in the chaotic mechanics of the body. We discuss how this may provide new interpretations for existing observations at the level of tissue-scale activity patterns and neural circuitry, and provide some experimental predictions that would test the extent to which the mechanisms we present translate to the real larva.

We investigate the relationship between brain, body and environment in the exploratory behaviour of fruitfly larva. A larva crawls forward by propagating a wave of compression through its segmented body, and changes its crawling direction by bending to one side or the other. We show first that a purely mechanical model of the larva’s body can produce travelling compression waves, sideways bending, and unpredictable, chaotic motions. For this body to locomote through its environment, it is necessary to add a neuromuscular system to counteract the loss of energy due to friction, and to limit the simultaneous compression of segments. These simple additions allow our model larva to generate life-like forward and backward crawling as well as spontaneous turns, which occur without any direct sensing or control of reorientation. The unpredictability inherent in the larva’s physics causes the model to explore its environment, despite the lack of any neural mechanism for rhythm generation or for deciding when to switch from crawling to turning. Our model thus demonstrates how understanding body mechanics can generate and simplify neurobiological hypotheses as to how behaviour arises.

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'.

Caenorhabditis elegans excitatory ventral cord motor neurons derive rhythm for body undulation

The intrinsic oscillatory activity of central pattern generators underlies motor rhythm. We review and discuss recent findings that address the origin of Caenorhabditis elegans motor rhythm. These studies propose that the A- and mid-body B-class excitatory motor neurons at the ventral cord function as non-bursting intrinsic oscillators to underlie body undulation during reversal and forward movements, respectively. Proprioception entrains their intrinsic activities, allows phase-coupling between members of the same class motor neurons, and thereby facilitates directional propagation of undulations. Distinct pools of premotor interneurons project along the ventral nerve cord to innervate all members of the A- and B-class motor neurons, modulating their oscillations, as well as promoting their bi-directional coupling. The two motor sub-circuits, which consist of oscillators and descending inputs with distinct properties, form the structural base of dynamic rhythmicity and flexible partition of the forward and backward motor states. These results contribute to a continuous effort to establish a mechanistic and dynamic model of the C. elegans sensorimotor system. C. elegans exhibits rich sensorimotor functions despite a small neuron number. These findings implicate a circuit-level functional compression. By integrating the role of rhythm generation and proprioception into motor neurons, and the role of descending regulation of oscillators into premotor interneurons, this numerically simple nervous system can achieve a circuit infrastructure analogous to that of anatomically complex systems. C. elegans has manifested itself as a compact model to search for general principles of sensorimotor behaviours.This article is part of a discussion meeting issue 'Connectome to behaviour: modelling C. elegans at cellular resolution'.

Signatures of proprioceptive control in Caenorhabditis elegans locomotion

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.This article is part of a discussion meeting issue 'Connectome to behaviour: modelling C. elegans at cellular resolution'.

Potential role of a ventral nerve cord central pattern generator in forward and backward locomotion in Caenorhabditis elegans

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.

Transition and formation of the torque pattern of undulatory locomotion in resistive force dominated media

In undulatory locomotion, torques along the body are required to overcome external forces from the environment and bend the body. These torques are usually generated by muscles in animals and closely related to muscle activations. In previous studies, researchers observed a single traveling wave pattern of the torque or muscle activation, but the formation of the torque pattern is still not well understood. To elucidate the formation of the torque pattern required by external resistive forces and the transition as kinematic parameters vary, we use simplistic resistive force theory models of self-propelled, steady undulatory locomotors and examine the spatio-temporal variation of the internal torque. We find that the internal torque has a traveling wave pattern with a decreasing speed normalized by the curvature speed as the wave number (the number of wavelengths on the locomotor's body) increases from 0.5 to 1.8. As the wave number increases to 2 and greater values, the torque transitions into a two-wave-like pattern and complex patterns. Using phasor diagram analysis, we reveal that the formation and transitions of the pattern are consequences of the integration and cancellation of force phasors.

The control structure of the nematode Caenorhabditis elegans: Neuro-sensory integration and proprioceptive feedback

We develop a biophysically realistic model of the nematode C. elegans that includes: (i) its muscle structure and activation, (ii) key connectomic activation circuitry, and (iii) a weighted and time-dynamic proprioception. In combination, we show that these model components can reproduce the complex waveforms exhibited in C. elegans locomotive behaviors, chiefly omega turns. This is achieved via weighted, time-dependent suppression of the proprioceptive signal. Though speculative, such dynamics are biologically plausible due to the presence of neuromodulators which have recently been experimentally implicated in the escape response, which includes an omega turn. This is the first integrated neuromechanical model to reveal a mechanism capable of generating the complex waveforms observed in the behavior of C. elegans, thus contributing to a mathematical framework for understanding how control decisions can be executed at the connectome level in order to produce the full repertoire of observed behaviors.

Roll maneuvers are essential for active reorientation of Caenorhabditis elegans in 3D media

Locomotion of the nematode Caenorhabditis elegans is a key observable used in investigations ranging from behavior to neuroscience to aging. However, while the natural environment of this model organism is 3D, quantitative investigations of its locomotion have been mostly limited to 2D motion. Here, we present a quantitative analysis of how the nematode reorients itself in 3D media. We identify a unique behavioral state of C. elegans-a roll maneuver-which is an essential component of 3D locomotion in burrowing and swimming. The rolls, associated with nonzero torsion of the nematode body, result in rotation of the plane of dorsoventral body undulations about the symmetry axis of the trajectory. When combined with planar turns in a new undulation plane, the rolls allow the nematode to reorient its body in any direction, thus enabling complete exploration of 3D space. The rolls observed in swimming are much faster than the ones in burrowing; we show that this difference stems from a purely hydrodynamic enhancement mechanism and not from a gait change or an increase in the body torsion. This result demonstrates that hydrodynamic viscous forces can enhance 3D reorientation in undulatory locomotion, in contrast to known hydrodynamic hindrance of both forward motion and planar turns.

Identification of cis-regulatory elements associated with salinity and drought stress tolerance in rice from co-expressed gene interaction networks

Rice, a staple food crop, is often subjected to drought and salinity stresses thereby limiting its yield potential. Since there is a cross talk between these abiotic stresses, identification of common and/or overlapping regulatory elements is pivotal for generating rice cultivars that showed tolerance towards them. Analysis of the gene interaction network (GIN) facilitates identifying the role of individual genes and their interactions with others that constitute important molecular determinants in sensing and signaling cascade governing drought and/or salinity stresses. Identification of the various cis-regulatory elements of the genes constituting GIN is equally important. Here, in this study graphical Gaussian model (GGM) was used for generating GIN for an array of genes that were differentially regulated during salinity and/or drought stresses to contrasting rice cultivars (salt-tolerant [CSR11], salt-sensitive [VSR156], drought-tolerant [Vandana], drought-sensitive [IR64]). Whole genome transcriptom profiling by using microarray were employed in this study. Markov Chain completed co-expression analyses of differentially expressed genes using Dynamic Bayesian Network, Probabilistic Boolean Network and Steady State Analysis. A compact GIN was identified for commonly co-expressed genes during salinity and drought stresses with three major hubs constituted by Myb2 transcription factor (TF), phosphoglycerate kinase and heat shock protein (Hsp). The analysis suggested a pivotal role of these genes in salinity and/or drought stress responses. Further, analysis of cis-regulatory elements (CREs) of commonly differentially expressed genes during salinity and drought stresses revealed the presence of 20 different motifs.

Distributed rhythm generators underlie Caenorhabditis elegans forward locomotion

Coordinated rhythmic movements are ubiquitous in animal behavior. In many organisms, chains of neural oscillators underlie the generation of these rhythms. In C. elegans, locomotor wave generation has been poorly understood; in particular, it is unclear where in the circuit rhythms are generated, and whether there exists more than one such generator. We used optogenetic and ablation experiments to probe the nature of rhythm generation in the locomotor circuit. We found that multiple sections of forward locomotor circuitry are capable of independently generating rhythms. By perturbing different components of the motor circuit, we localize the source of secondary rhythms to cholinergic motor neurons in the midbody. Using rhythmic optogenetic perturbation, we demonstrate bidirectional entrainment of oscillations between different body regions. These results show that, as in many other vertebrates and invertebrates, the C. elegans motor circuit contains multiple oscillators that coordinate activity to generate behavior.

Terrain following and applications: Caenorhabditis elegans swims along the floor using a bump and undulate strategy

Nematodes such as Caenorhabditis elegans are heavier than water. When submerged in water, they settle to the bottom surface. Observations reveal that the animals do not lie flat on the bottom surface, but remain substantially suspended above the surface through continuous collisions with the surface, while maintaining their swimming gaits. Consequently, the swimming animals follow the bottom surface topography. When the bottom surface is inclined, the animals swim up or down along the incline. As the magnitude of the gravitational force can be easily estimated, this behaviour provides a convenient means to estimate the animal's propulsive thrust. The animals' tendency to follow the surface topography provides a means to control the swimmers' trajectories and direction of motion, which we demonstrate with a saw tooth-like ratchet that biases the animals to swim in a selected direction. The animals can also serve as surface topography probes since their residence time as a function of position provides information on surface features. Finally, we take advantage of surface following to construct a simple motility-based sorter that can sort animals based on genotype and state of health.

On the kinematics-wave motion of living particles in suspension

This work presents theoretical and experimental analyses on the kinematics-wave motion of suspended active particles in a biological fluid. The fluid is an active suspension of nematodes immersed in a gel-like biological structure, moving at a low Reynolds number. The nematode chosen for the study is Caenorhabditis elegans. Its motion is subjected to the time reversibility of creeping flows. We investigate how this worm reacts to this reversibility condition in order to break the flow symmetry and move in the surrounding fluid. We show that the relationship between the length of an individual nematode and the wavelength of its motion is linear and can be fitted by a theoretical prediction proposed in this work. We provide a deep discussion regarding the propulsion mechanics based on a scaling analysis that identifies three major forces acting on an individual nematode. These forces are a viscous force, a yield stress force due to gelification of agar molecules in the gel-like medium, and a bending force associated with the muscular tension imposed by the nematodes in the medium. By the scalings, we identify the most relevant physical parameters of the nematode's motion. In order to examine and quantify the motion, dynamical system tools such as FFT are used in the present analysis. The motion characterization is performed by examining (or studying) two different populations: (i) in the absence of food with starving nematodes and (ii) with well-fed nematodes. In addition, several kinematic quantities of the head, center of mass, and tail for a sample of nematodes are also investigated: their slip velocities, wavelengths, trajectories, frequency spectra, and mean curvatures. The main findings of this work are the confirmation of a linear relationship between the nematode's physical length and its motion wavelength, the identification of secondary movements in high frequencies that helps breaking the time-reversibility in which the worms are bonded, and the observation and interpretation of a systematic difference between the individual motion of well-fed and starving nematodes.

Durotaxis in Nematode Caenorhabditis elegans

Durotaxis is a process where cells are able to sense the stiffness of substrates and preferentially migrate toward stiffer regions. Here, we show that the 1-mm-long nematode, Caenorhabditis elegans are also able to detect the rigidity of underlying substrates and always migrate to regions of higher stiffness. Our results indicate that C. elegans are able to judiciously make a decision to stay on stiffer regions. We found that the, undulation frequency, and wavelength of worms, crawling on surfaces show nonmonotonic behavior with increasing stiffness. A number of control experiments were also conducted to verify whether C. elegans are really able to detect the rigidity of substrates or whether the migration to stiffer regions is due to other factors already reported in the literature. As it is known that bacteria and other single-celled organisms exhibit durotaxis toward stiffer surfaces, we conjecture that durotaxis in C. elegans may be one of the strategies developed to improve their chances of locating food.

Food responsiveness regulates episodic behavioral states in Caenorhabditis elegans

Animals optimize survival and reproduction in part through control of behavioral states, which depend on an organism's internal and external environments. In the nematode Caenorhabditis elegans a variety of behavioral states have been described, including roaming, dwelling, quiescence, and episodic swimming. These states have been considered in isolation under varied experimental conditions, making it difficult to establish a unified picture of how they are regulated. Using long-term imaging, we examined C. elegans episodic behavioral states under varied mechanical and nutritional environments. We found that animals alternate between high-activity (active) and low-activity (sedentary) episodes in any mechanical environment, while the incidence of episodes and their behavioral composition depend on food levels. During active episodes, worms primarily roam, as characterized by continuous whole body movement. During sedentary episodes, animals exhibit dwelling (slower movements confined to the anterior half of the body) and quiescence (a complete lack of movement). Roaming, dwelling, and quiescent states are manifest not only through locomotory characteristics but also in pharyngeal pumping (feeding) and in egg-laying behaviors. Next, we analyzed the genetic basis of behavioral states. We found that modulation of behavioral states depends on neuropeptides and insulin-like signaling in the nervous system. Sensory neurons and the Foraging homolog EGL-4 regulate behavior through control of active/sedentary episodes. Optogenetic stimulation of dopaminergic and serotonergic neurons induced dwelling, implicating dopamine as a dwell-promoting neurotransmitter. Our findings provide a more unified description of behavioral states and suggest that perception of nutrition is a conserved mechanism for regulating animal behavior.NEW & NOTEWORTHY One strategy by which animals adapt to their internal states and external environments is by adopting behavioral states. The roundworm Caenorhabditis elegans is an attractive model for investigating how behavioral states are genetically and neuronally controlled. Here we describe the hierarchical organization of behavioral states characterized by locomotory activity, feeding, and egg-laying. We show that decisions to engage in these behaviors are controlled by the nervous system through insulin-like signaling and the perception of food.

Single swim sessions in C. elegans induce key features of mammalian exercise

BACKGROUND

Exercise exerts remarkably powerful effects on metabolism and health, with anti-disease and anti-aging outcomes. Pharmacological manipulation of exercise benefit circuits might improve the health of the sedentary and the aging populations. Still, how exercised muscle signals to induce system-wide health improvement remains poorly understood. With a long-term interest in interventions that promote animal-wide health improvement, we sought to define exercise options for Caenorhabditis elegans.

RESULTS

Here, we report on the impact of single swim sessions on C. elegans physiology. We used microcalorimetry to show that C. elegans swimming has a greater energy cost than crawling. Animals that swam continuously for 90 min specifically consumed muscle fat supplies and exhibited post-swim locomotory fatigue, with both muscle fat depletion and fatigue indicators recovering within 1 hour of exercise cessation. Quantitative polymerase chain reaction (qPCR) transcript analyses also suggested an increase in fat metabolism during the swim, followed by the downregulation of specific carbohydrate metabolism transcripts in the hours post-exercise. During a 90 min swim, muscle mitochondria matrix environments became more oxidized, as visualized by a localized mitochondrial reduction-oxidation-sensitive green fluorescent protein reporter. qPCR data supported specific transcriptional changes in oxidative stress defense genes during and immediately after a swim. Consistent with potential antioxidant defense induction, we found that a single swim session sufficed to confer protection against juglone-induced oxidative stress inflicted 4 hours post-exercise.

CONCLUSIONS

In addition to showing that even a single swim exercise bout confers physiological changes that increase robustness, our data reveal that acute swimming-induced changes share common features with some acute exercise responses reported in humans. Overall, our data validate an easily implemented swim experience as C. elegans exercise, setting the foundation for exploiting the experimental advantages of this model to genetically or pharmacologically identify the exercise-associated molecules and signaling pathways that confer system-wide health benefits.

Predicting path from undulations for C. elegans using linear and nonlinear resistive force theory

A basic issue in the physics of behaviour is the mechanical relationship between an animal and its surroundings. The model nematode C. elegans provides an excellent platform to explore this relationship due to its anatomical simplicity. Nonetheless, the physics of nematode crawling, in which the worm undulates its body to move on a wet surface, is not completely understood and the mathematical models often used to describe this phenomenon are empirical. We confirm that linear resistive force theory, one such empirical model, is effective at predicting a worm's path from its sequence of body postures for forward crawling, reversing, and turning and for a broad range of different behavioural phenotypes observed in mutant worms. Worms recently isolated from the wild have a higher effective drag anisotropy than the laboratory-adapted strain N2 and most mutant strains. This means the wild isolates crawl with less surface slip, perhaps reflecting more efficient gaits. The drag anisotropies required to fit the observed locomotion data (70  ±  28 for the wild isolates) are significantly larger than the values measured by directly dragging worms along agar surfaces (3-10 in Rabets et al (2014 Biophys. J. 107 1980-7)). A proposed nonlinear extension of the resistive force theory model also provides accurate predictions, but does not resolve the discrepancy between the parameters required to achieve good path prediction and the experimentally measured parameters. We confirm that linear resistive force theory provides a good effective model of worm crawling that can be used in applications such as whole-animal simulations and advanced tracking algorithms, but that the nature of the physical interaction between worms and their most commonly studied laboratory substrate remains unresolved.

The effects of groove height and substrate stiffness on C. elegans locomotion

The physical environment surrounding an animal has a significant impact on its behavior. The nematode Caenorhabditis elegans (C. elegans) has proved to be an excellent choice for understanding the adaptability of organisms crawling on soft surfaces. In this work, we investigate the modulation of C. elegans' behavioral kinematics in response to changes in the stiffness of the substrate and study the effect of grooves incised by the worms on their locomotion speed and efficiency. We measure the height of the grooves created by the animals on surfaces with different rigidity using confocal microscopy. Our results indicate that the kinematic properties of C. elegans, including amplitude (A), wavelength (λ) and frequency (f) of head turns depend strongly on surface properties and the height of the grooves created by them. During crawling, we observe that the animal assumes two distinct shapes depending on the stiffness of substrates. As the stiffness increases, the worm's body shape changes gradually from a 'W' shape, which is characterized by low amplitude curvature to the more common 'S' shape, which is characterized by high amplitude curvature, at intermediate values and back to 'W' on stiffer substrates. Although the efficiency is found to vary monotonically with surface stiffness, the forward velocity shows a non-monotonic behavior with the maximum on a surface, where the animal makes the 'S' shape.

Spatiotemporal Feedback and Network Structure Drive and Encode Caenorhabditis elegans Locomotion

Using a computational model of the Caenorhabditis elegans connectome dynamics, we show that proprioceptive feedback is necessary for sustained dynamic responses to external input. This is consistent with the lack of biophysical evidence for a central pattern generator, and recent experimental evidence that proprioception drives locomotion. The low-dimensional functional response of the Caenorhabditis elegans network of neurons to proprioception-like feedback is optimized by input of specific spatial wavelengths which correspond to the spatial scale of real body shape dynamics. Furthermore, we find that the motor subcircuit of the network is responsible for regulating this response, in agreement with experimental expectations. To explore how the connectomic dynamics produces the observed two-mode, oscillatory limit cycle behavior from a static fixed point, we probe the fixed point's low-dimensional structure using Dynamic Mode Decomposition. This reveals that the nonlinear network dynamics encode six clusters of dynamic modes, with timescales spanning three orders of magnitude. Two of these six dynamic mode clusters correspond to previously-discovered behavioral modes related to locomotion. These dynamic modes and their timescales are encoded by the network's degree distribution and specific connectivity. This suggests that behavioral dynamics are partially encoded within the connectome itself, the connectivity of which facilitates proprioceptive control.

Evolution of central pattern generators and rhythmic behaviours

Comparisons of rhythmic movements and the central pattern generators (CPGs) that control them uncover principles about the evolution of behaviour and neural circuits. Over the course of evolutionary history, gradual evolution of behaviours and their neural circuitry within any lineage of animals has been a predominant occurrence. Small changes in gene regulation can lead to divergence of circuit organization and corresponding changes in behaviour. However, some behavioural divergence has resulted from large-scale rewiring of the neural network. Divergence of CPG circuits has also occurred without a corresponding change in behaviour. When analogous rhythmic behaviours have evolved independently, it has generally been with different neural mechanisms. Repeated evolution of particular rhythmic behaviours has occurred within some lineages due to parallel evolution or latent CPGs. Particular motor pattern generating mechanisms have also evolved independently in separate lineages. The evolution of CPGs and rhythmic behaviours shows that although most behaviours and neural circuits are highly conserved, the nature of the behaviour does not dictate the neural mechanism and that the presence of homologous neural components does not determine the behaviour. This suggests that although behaviour is generated by neural circuits, natural selection can act separately on these two levels of biological organization.

Searching for motifs in the behaviour of larval Drosophila melanogaster and Caenorhabditis elegans reveals continuity between behavioural states

We present a novel method for the unsupervised discovery of behavioural motifs in larval Drosophila melanogaster and Caenorhabditis elegans. A motif is defined as a particular sequence of postures that recurs frequently. The animal's changing posture is represented by an eigenshape time series, and we look for motifs in this time series. To find motifs, the eigenshape time series is segmented, and the segments clustered using spline regression. Unlike previous approaches, our method can classify sequences of unequal duration as the same motif. The behavioural motifs are used as the basis of a probabilistic behavioural annotator, the eigenshape annotator (ESA). Probabilistic annotation avoids rigid threshold values and allows classification uncertainty to be quantified. We apply eigenshape annotation to both larval Drosophila and C. elegans and produce a good match to hand annotation of behavioural states. However, we find many behavioural events cannot be unambiguously classified. By comparing the results with ESA of an artificial agent's behaviour, we argue that the ambiguity is due to greater continuity between behavioural states than is generally assumed for these organisms.

Fluid dynamics alter Caenorhabditis elegans body length via TGF-β/DBL-1 neuromuscular signaling

Skeletal muscle wasting is a major obstacle for long-term space exploration. Similar to astronauts, the nematode Caenorhabditis elegans displays negative muscular and physical effects when in microgravity in space. It remains unclear what signaling molecules and behavior(s) cause these negative alterations. Here we studied key signaling molecules involved in alterations of C. elegans physique in response to fluid dynamics in ground-based experiments. Placing worms in space on a 1G accelerator increased a myosin heavy chain, myo-3, and a transforming growth factor-β (TGF-β), dbl-1, gene expression. These changes also occurred when the fluid dynamic parameters viscosity/drag resistance or depth of liquid culture were increased on the ground. In addition, body length increased in wild type and body wall cuticle collagen mutants, rol-6 and dpy-5, grown in liquid culture. In contrast, body length did not increase in TGF-β, dbl-1, or downstream signaling pathway, sma-4/Smad, mutants. Similarly, a D1-like dopamine receptor, DOP-4, and a mechanosensory channel, UNC-8, were required for increased dbl-1 expression and altered physique in liquid culture. As C. elegans contraction rates are much higher when swimming in liquid than when crawling on an agar surface, we also examined the relationship between body length enhancement and rate of contraction. Mutants with significantly reduced contraction rates were typically smaller. However, in dop-4, dbl-1, and sma-4 mutants, contraction rates still increased in liquid. These results suggest that neuromuscular signaling via TGF-β/DBL-1 acts to alter body physique in response to environmental conditions including fluid dynamics.

A consistent muscle activation strategy underlies crawling and swimming in Caenorhabditis elegans

Although undulatory swimming is observed in many organisms, the neuromuscular basis for undulatory movement patterns is not well understood. To better understand the basis for the generation of these movement patterns, we studied muscle activity in the nematode Caenorhabditis elegans. Caenorhabditis elegans exhibits a range of locomotion patterns: in low viscosity fluids the undulation has a wavelength longer than the body and propagates rapidly, while in high viscosity fluids or on agar media the undulatory waves are shorter and slower. Theoretical treatment of observed behaviour has suggested a large change in force–posture relationships at different viscosities, but analysis of bend propagation suggests that short-range proprioceptive feedback is used to control and generate body bends. How muscles could be activated in a way consistent with both these results is unclear. We therefore combined automated worm tracking with calcium imaging to determine muscle activation strategy in a variety of external substrates. Remarkably, we observed that across locomotion patterns spanning a threefold change in wavelength, peak muscle activation occurs approximately 45° (1/8th of a cycle) ahead of peak midline curvature. Although the location of peak force is predicted to vary widely, the activation pattern is consistent with required force in a model incorporating putative length- and velocity-dependence of muscle strength. Furthermore, a linear combination of local curvature and velocity can match the pattern of activation. This suggests that proprioception can enable the worm to swim effectively while working within the limitations of muscle biomechanics and neural control.

Direct measurements of drag forces in C. elegans crawling locomotion

With a simple and versatile microcantilever-based force measurement technique, we have probed the drag forces involved in Caenorhabditis elegans locomotion. As a worm crawls on an agar surface, we found that substrate viscoelasticity introduces nonlinearities in the force-velocity relationships, yielding nonconstant drag coefficients that are not captured by original resistive force theory. A major contributing factor to these nonlinearities is the formation of a shallow groove on the agar surface. We measured both the adhesion forces that cause the worm's body to settle into the agar and the resulting dynamics of groove formation. Furthermore, we quantified the locomotive forces produced by C. elegans undulatory motions on a wet viscoelastic agar surface. We show that an extension of resistive force theory is able to use the dynamics of a nematode's body shape along with the measured drag coefficients to predict the forces generated by a crawling nematode.

The nematode C. elegans as a complex viscoelastic fluid

The viscoelastic material properties of the model organism C. elegans were probed with a micropipette deflection technique and modelled with the standard linear solid model. Dynamic relaxation measurements were performed on the millimetric nematode to investigate its viscous characteristics in detail. We show that the internal properties of C. elegans can not be fully described by a simple Newtonian fluid. Instead, a power-law fluid model was implemented and shown to be in excellent agreement with experimental results. The nematode exhibits shear thinning properties and its complex fluid characteristics were quantified. The bending-rate dependence of the internal damping coefficient of C. elegans could affect its gait modulation in different external environments.

C. elegans locomotion: small circuits, complex functions

With 302 neurons in the adult Caenorhabditis elegans nervous system, it should be possible to build models of complex behaviors spanning sensory input to motor output. The logic of the motor circuit is an essential component of such models. Advances in physiological, anatomical, and neurogenetic analysis are revealing a surprisingly complex signaling network in the worm's small motor circuit. We are progressing towards a systems level dissection of the network of premotor interneurons, motor neurons, and muscle cells that move the animal forward and backward in its environment.

Locomotor benefits of being a slender and slick sand swimmer

Squamates classified as 'subarenaceous' possess the ability to move long distances within dry sand; body elongation among sand and soil burrowers has been hypothesized to enhance subsurface performance. Using X-ray imaging, we performed the first kinematic investigation of the subsurface locomotion of the long, slender shovel-nosed snake (Chionactis occipitalis) and compared its biomechanics with those of the shorter, limbed sandfish lizard (Scincus scincus). The sandfish was previously shown to maximize swimming speed and minimize the mechanical cost of transport during burial. Our measurements revealed that the snake also swims through sand by propagating traveling waves down the body, head to tail. Unlike the sandfish, the snake nearly followed its own tracks, thus swimming in an approximate tube of self-fluidized granular media. We measured deviations from tube movement by introducing a parameter, the local slip angle, βs, which measures the angle between the direction of movement of each segment and body orientation. The average βs was smaller for the snake than for the sandfish; granular resistive force theory (RFT) revealed that the curvature utilized by each animal optimized its performance. The snake benefits from its slender body shape (and increased vertebral number), which allows propagation of a higher number of optimal curvature body undulations. The snake's low skin friction also increases performance. The agreement between experiment and RFT combined with the relatively simple properties of the granular 'frictional fluid' make subarenaceous swimming an attractive system to study functional morphology and bauplan evolution.

OpenWorm: an open-science approach to modeling Caenorhabditis elegans

OpenWorm is an international collaboration with the aim of understanding how the behavior of Caenorhabditis elegans (C. elegans) emerges from its underlying physiological processes. The project has developed a modular simulation engine to create computational models of the worm. The modularity of the engine makes it possible to easily modify the model, incorporate new experimental data and test hypotheses. The modeling framework incorporates both biophysical neuronal simulations and a novel fluid-dynamics-based soft-tissue simulation for physical environment-body interactions. The project's open-science approach is aimed at overcoming the difficulties of integrative modeling within a traditional academic environment. In this article the rationale is presented for creating the OpenWorm collaboration, the tools and resources developed thus far are outlined and the unique challenges associated with the project are discussed.