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

An integrative data-driven model simulating C. elegans brain, body and environment interactions

The behavior of an organism is influenced by the complex interplay between its brain, body and environment. Existing data-driven models focus on either the brain or the body-environment. Here we present BAAIWorm, an integrative data-driven model of Caenorhabditis elegans, which consists of two submodels: the brain model and the body-environment model. The brain model was built by multicompartment models with realistic morphology, connectome and neural population dynamics based on experimental data. Simultaneously, the body-environment model used a lifelike body and a three-dimensional physical environment. Through the closed-loop interaction between the two submodels, BAAIWorm reproduced the realistic zigzag movement toward attractors observed in C. elegans. Leveraging this model, we investigated the impact of neural system structure on both neural activities and behaviors. Consequently, BAAIWorm can enhance our understanding of how the brain controls the body to interact with its surrounding environment.

Milking a spherical cow: Toy models in neuroscience

There are many different kinds of models, and they play many different roles in the scientific endeavour. Neuroscience, and biology more generally, has understandably tended to emphasise empirical models that are grounded in data and make specific, experimentally testable predictions. Meanwhile, strongly idealised or 'toy' models have played a central role in the theoretical development of other sciences such as physics. In this paper, we examine the nature of toy models and their prospects in neuroscience.

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.

Neuronal sensorimotor integration guiding salt concentration navigation in Caenorhabditis elegans

Animals navigate their environment by manipulating their movements and adjusting their trajectory which requires a sophisticated integration of sensory data with their current motor status. Here, we utilize the nematode Caenorhabditis elegans to explore the neural mechanisms of processing the sensory and motor information for navigation. We developed a microfluidic device which allows animals to freely move their heads while receiving temporal NaCl stimuli. We found that C. elegans regulates neck bending direction in response to temporal NaCl concentration changes in a way which is consistent with a C. elegans' navigational strategy which regulates traveling direction toward preferred NaCl concentrations. Our analysis also revealed that the activity of a neck motor neuron is significantly correlated with neck bending and activated by the decrease in NaCl concentration in a phase-dependent manner. By combining the analysis of behavioral and neural response to NaCl stimuli and optogenetic perturbation experiments, we revealed that NaCl decrease during ventral bending activates the neck motor neuron which counteracts ipsilateral bending. Simulations further suggest that this phase-dependent response of neck motor neurons can facilitate curving toward preferred salt concentrations.

Neural signal propagation atlas of Caenorhabditis elegans

Establishing how neural function emerges from network properties is a fundamental problem in neuroscience1. Here, to better understand the relationship between the structure and the function of a nervous system, we systematically measure signal propagation in 23,433 pairs of neurons across the head of the nematode Caenorhabditis elegans by direct optogenetic activation and simultaneous whole-brain calcium imaging. We measure the sign (excitatory or inhibitory), strength, temporal properties and causal direction of signal propagation between these neurons to create a functional atlas. We find that signal propagation differs from model predictions that are based on anatomy. Using mutants, we show that extrasynaptic signalling not visible from anatomy contributes to this difference. We identify many instances of dense-core-vesicle-dependent signalling, including on timescales of less than a second, that evoke acute calcium transients-often where no direct wired connection exists but where relevant neuropeptides and receptors are expressed. We propose that, in such cases, extrasynaptically released neuropeptides serve a similar function to that of classical neurotransmitters. Finally, our measured signal propagation atlas better predicts the neural dynamics of spontaneous activity than do models based on anatomy. We conclude that both synaptic and extrasynaptic signalling drive neural dynamics on short timescales, and that measurements of evoked signal propagation are crucial for interpreting neural function.

Abduction and Deduction in Dynamical Cognitive Science

This paper reviews the recent history of a subset of research in dynamical cognitive science, in particular that subset that allies itself with the sciences of complexity and casts cognitive systems as interaction dominant, noncomputational, and nonmodular. I look at this history in the light of C.S. Peirce's understanding of scientific reasoning as progressing from abduction to deduction to induction. In particular, I examine the development of a controversy concerning the use of the interaction dominance of human cognitive systems as an explanation of the ubiquitous 1/f noise, multifractality, and complexity matching in human behavior.

The neuromechanics of animal locomotion: From biology to robotics and back

Robotics and neuroscience are sister disciplines that both aim to understand how agile, efficient, and robust locomotion can be achieved in autonomous agents. Robotics has already benefitted from neuromechanical principles discovered by investigating animals. These include the use of high-level commands to control low-level central pattern generator-like controllers, which, in turn, are informed by sensory feedback. Reciprocally, neuroscience has benefited from tools and intuitions in robotics to reveal how embodiment, physical interactions with the environment, and sensory feedback help sculpt animal behavior. We illustrate and discuss exemplar studies of this dialog between robotics and neuroscience. We also reveal how the increasing biorealism of simulations and robots is driving these two disciplines together, forging an integrative science of autonomous behavioral control with many exciting future opportunities.

A complete biomechanical model of Hydra contractile behaviors, from neural drive to muscle to movement

How does neural activity drive muscles to produce behavior? The recent development of genetic lines in Hydra that allow complete calcium imaging of both neuronal and muscle activity, as well as systematic machine learning quantification of behaviors, makes this small cnidarian an ideal model system to understand and model the complete transformation from neural firing to body movements. To achieve this, we have built a neuromechanical model of Hydra's fluid-filled hydrostatic skeleton, showing how drive by neuronal activity activates distinct patterns of muscle activity and body column biomechanics. Our model is based on experimental measurements of neuronal and muscle activity and assumes gap junctional coupling among muscle cells and calcium-dependent force generation by muscles. With these assumptions, we can robustly reproduce a basic set of Hydra's behaviors. We can further explain puzzling experimental observations, including the dual timescale kinetics observed in muscle activation and the engagement of ectodermal and endodermal muscles in different behaviors. This work delineates the spatiotemporal control space of Hydra movement and can serve as a template for future efforts to systematically decipher the transformations in the neural basis of behavior.

A GNN-based model for capturing spatio-temporal changes in locomotion behaviors of aging C. elegans

Investigating the locomotion of aging C. elegans is an important way for understanding the basic mechanisms behind age-related changes in organisms. However, the locomotion of aging C. elegans is often quantified using insufficient physical variables, which makes it challenging to capture essential dynamics. To study changes in the locomotion pattern of aging C. elegans, we developed a novel data-driven model based on graph neural networks, in which the C. elegans body is modeled as a long chain with interactions within and between adjacent segments, and their interactions are described by high-dimensional variables. Using this model, we discovered that each segment of the C. elegans body generally tends to maintain its locomotion, i.e., tries to keep the bending angle unchanged, and expects to change the locomotion of the adjacent segments. The ability to maintain its locomotion strengthens with age. Besides, a subtle distinguish in the changes in the locomotion pattern of C. elegans at various aging stages were observed. Our model is anticipated to provide a data-driven method for quantifying the changes in the locomotion pattern of aging C. elegans and for mining the underlying causes of these changes.

NeuroMechFly, a neuromechanical model of adult Drosophila melanogaster

Animal behavior emerges from an interaction between neural network dynamics, musculoskeletal properties and the physical environment. Accessing and understanding the interplay between these elements requires the development of integrative and morphologically realistic neuromechanical simulations. Here we present NeuroMechFly, a data-driven model of the widely studied organism, Drosophila melanogaster. NeuroMechFly combines four independent computational modules: a physics-based simulation environment, a biomechanical exoskeleton, muscle models and neural network controllers. To enable use cases, we first define the minimum degrees of freedom of the leg from real three-dimensional kinematic measurements during walking and grooming. Then, we show how, by replaying these behaviors in the simulator, one can predict otherwise unmeasured torques and contact forces. Finally, we leverage NeuroMechFly's full neuromechanical capacity to discover neural networks and muscle parameters that drive locomotor gaits optimized for speed and stability. Thus, NeuroMechFly can increase our understanding of how behaviors emerge from interactions between complex neuromechanical systems and their physical surroundings.

A Graph Network Model for Neural Connection Prediction and Connection Strength Estimation

Objective. Reconstruction of connectomes at the cellular scale is a prerequisite for understanding the principles of neural circuits. However, due to methodological limits, scientists have reconstructed the connectomes of only a few organisms such as C. elegans, and estimated synaptic strength indirectly according to their size and number. Approach. Here, we propose a graph network model to predict synaptic connections and estimate synaptic strength by using the calcium activity data from C. elegans. Main results. The results show that this model can reliably predict synaptic connections in the neural circuits of C. elegans, and estimate their synaptic strength, which is an intricate and comprehensive reflection of multiple factors such as synaptic type and size, neurotransmitter and receptor type, and even activity dependence. In addition, the excitability or inhibition of synapses can be identified by this model. We also found that chemical synaptic strength is almost linearly positively correlated to electrical synaptic strength, and the influence of one neuron on another is non-linearly correlated with the number between them. This reflects the intrinsic interaction between electrical and chemical synapses. Significance. Our model is expected to provide a more accessible quantitative and data-driven approach for the reconstruction of connectomes in more complex nervous systems, as well as a promising method for accurately estimating synaptic strength.

Neural model generating klinotaxis behavior accompanied by a random walk based on C. elegans connectome

Klinotaxis is a strategy of chemotaxis behavior in Caenorhabditis elegans (C. elegans), and random walking is evident during its locomotion. As yet, the understanding of the neural mechanisms underlying these behaviors has remained limited. In this study, we present a connectome-based simulation model of C. elegans to concurrently realize realistic klinotaxis and random walk behaviors and explore their neural mechanisms. First, input to the model is derived from an ASE sensory neuron model in which the all-or-none depolarization characteristic of ASEL neuron is incorporated for the first time. Then, the neural network is evolved by an evolutionary algorithm; klinotaxis emerged spontaneously. We identify a plausible mechanism of klinotaxis in this model. Next, we propose the liquid synapse according to the stochastic nature of biological synapses and introduce it into the model. Adopting this, the random walk is generated autonomously by the neural network, providing a new hypothesis as to the neural mechanism underlying the random walk. Finally, simulated ablation results are fairly consistent with the biological conclusion, suggesting the similarity between our model and the biological network. Our study is a useful step forward in behavioral simulation and understanding the neural mechanisms of behaviors in C. elegans.

Effects of essential oil components exposure on biological parameters of Caenorhabditis elegans

The extensive use of essential oil components in an increasing number of applications can substantially enhance exposure to these compounds, which leads to potential health and environmental hazards. This work aimed to evaluate the toxicity of four widely used essential oil components (carvacrol, eugenol, thymol, vanillin) using the in vivo model Caenorhabditis elegans. For this purpose, the LC₅₀ value of acute exposure to these components was first established; then the effect of sublethal concentrations on nematodes' locomotion behaviour, reproduction, heat and oxidative stress resistance and chemotaxis was evaluated. The results showed that all the components had a concentration-dependent effect on nematode survival at moderate to high concentrations. Carvacrol and thymol were the two most toxic compounds, while vanillin had the mildest toxicological effect. Reproduction resulted in a more sensitive endpoint than lethality to evaluate toxicity. Only pre-exposure to carvacrol and eugenol at the highest tested sublethal concentrations conferred worms oxidative stress resistance. However, at these and lower concentrations, both components induced reproductive toxicity. Our results evidence that these compounds can be toxic at lower doses than those required for their biological action. These findings highlight the need for a specific toxicological assessment of every EOC application.

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.

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.

Connectome to behaviour: modelling Caenorhabditis elegans at cellular resolution

It has been 30 years since the 'mind of the worm' was published in Philosophical Transactions B (White et al 1986 Phil. Trans. R. Soc. Lond. B314, 1-340). Predicting Caenorhabditis elegans' behaviour from its wiring diagram has been an enduring challenge since then. This special theme issue of Philosophical Transactions B combines research from neuroscientists, physicists, mathematicians and engineers to discuss advances in neural activity imaging, behaviour quantification and multiscale simulations, and how they are bringing the goal of whole-animal modelling at cellular resolution within reach.This article is part of a discussion meeting issue 'Connectome to behaviour: modelling C. elegans at cellular resolution'.