Systems level circuit model of C. elegans undulatory locomotion: mathematical modeling and molecular genetics

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.

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.

Forward and backward locomotion patterns in C. elegans generated by a connectome-based model simulation

Caenorhabditis elegans (C. elegans) can produce various motion patterns despite having only 69 motor neurons and 95 muscle cells. Previous studies successfully elucidate the connectome and role of the respective motor neuron classes related to movement. However, these models have not analyzed the distribution of the synaptic and gap connection weights. In this study, we examined whether a motor neuron and muscle network can generate oscillations for both forward and backward movement and analyzed the distribution of the trained synaptic and gap connection weights through a machine learning approach. This paper presents a connectome-based neural network model consisting of motor neurons of classes A, B, D, AS, and muscle, considering both synaptic and gap connections. A supervised learning method called backpropagation through time was adapted to train the connection parameters by feeding teacher data composed of the command neuron input and muscle cell activation. Simulation results confirmed that the motor neuron circuit could generate oscillations with different phase patterns corresponding to forward and backward movement, and could be switched at arbitrary times according to the binary inputs simulating the output of command neurons. Subsequently, we confirmed that the trained synaptic and gap connection weights followed a Boltzmann-type distribution. It should be noted that the proposed model can be trained to reproduce the activity patterns measured for an animal (HRB4 strain). Therefore, the supervised learning approach adopted in this study may allow further analysis of complex activity patterns associated with movements.

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.

Cyclic Guanosine Monophosphate Modulates Locomotor Acceleration Induced by Nitric Oxide but not Serotonin in Clione limacina Central Pattern Generator Swim Interneurons

Both nitric oxide (NO) and serotonin (5HT) mediate swim acceleration in the marine mollusk, Clione  limacina. In this study, we examine the role that the second messenger, cyclic guanosine monophosphate (cGMP), plays in mediating NO and 5HT-induced swim acceleration. We observed that the application of an analog of cGMP or an activator of soluble guanylyl cyclase (sGC) increased fictive locomotor speed recorded from Pd-7 interneurons of the animal's locomotor central pattern generator. Moreover, inhibition of sGC decreased fictive locomotor speed. These results suggest that basal levels of cGMP are important for slow swimming and that increased production of cGMP mediates swim acceleration in Clione. Because NO has its effect through cGMP signaling and because we show herein that cGMP produces cellular changes in Clione swim interneurons that are consistent with cellular changes produced by 5HT application, we hypothesize that both NO and 5HT function via a common signal transduction pathway that involves cGMP. Our results show that cGMP mediates NO-induced but not 5HT-induced swim acceleration in Clione.

A multilayer circuit architecture for the generation of distinct locomotor behaviors in Drosophila

Animals generate diverse motor behaviors, yet how the same motor neurons (MNs) generate two distinct or antagonistic behaviors remains an open question. Here, we characterize Drosophila larval muscle activity patterns and premotor/motor circuits to understand how they generate forward and backward locomotion. We show that all body wall MNs are activated during both behaviors, but a subset of MNs change recruitment timing for each behavior. We used TEM to reconstruct a full segment of all 60 MNs and 236 premotor neurons (PMNs), including differentially-recruited MNs. Analysis of this comprehensive connectome identified PMN-MN 'labeled line' connectivity; PMN-MN combinatorial connectivity; asymmetric neuronal morphology; and PMN-MN circuit motifs that could all contribute to generating distinct behaviors. We generated a recurrent network model that reproduced the observed behaviors, and used functional optogenetics to validate selected model predictions. This PMN-MN connectome will provide a foundation for analyzing the full suite of larval behaviors.

A computational model of internal representations of chemical gradients in environments for chemotaxis of Caenorhabditis elegans

The small roundworm Caenorhabditis elegans employs two strategies, termed pirouette and weathervane, which are closely related to the internal representation of chemical gradients parallel and perpendicular to the travelling direction, respectively, to perform chemotaxis. These gradients must be calculated from the chemical information obtained at a single point, because the sensory neurons are located close to each other at the nose tip. To formulate the relationship between this sensory input and internal representations of the chemical gradient, this study proposes a simple computational model derived from the directional decomposition of the chemical concentration at the nose tip that can generate internal representations of the chemical gradient. The ability of the computational model was verified by using a chemotaxis simulator that can simulate the body motions of pirouette and weathervane, which confirmed that the computational model enables the conversion of the sensory input and head-bending angles into both types of gradients with high correlations of approximately r > 0.90 (p < 0.01) with the true gradients. In addition, the chemotaxis index of the model was 0.64, which is slightly higher than that in the actual animal (0.57). In addition, simulation using a connectome-based neural network model confirmed that the proposed computational model is implementable in the actual network structure.

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'.

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.

An Analytical Comparison of Locally-Connected Reconfigurable Neural Network Architectures Using a C. elegans Locomotive Model

The scale of modern neural networks is growing rapidly, with direct hardware implementations providing significant speed and energy improvements over their software counterparts. However, these hardware implementations frequently assume global connectivity between neurons and thus suffer from communication bottlenecks. Such issues are not found in biological neural networks. It should therefore be possible to develop new architectures to reduce the dependence on global communications by considering the connectivity of biological networks. This paper introduces two reconfigurable locally-connected architectures for implementing biologically inspired neural networks in real time. Both proposed architectures are validated using the segmented locomotive model of the C. elegans, performing a demonstration of forwards, backwards serpentine motion and coiling behaviours. Local connectivity is discovered to offer up to a 17.5× speed improvement over hybrid systems that use combinations of local and global infrastructure. Furthermore, the concept of locality of connections is considered in more detail, highlighting the importance of dimensionality when designing neuromorphic architectures. Convolutional Neural Networks are shown to map poorly to locally connected architectures despite their apparent local structure, and both the locality and dimensionality of new neural processing systems is demonstrated as a critical component for matching the function and efficiency seen in biological networks.

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.

Excitatory motor neurons are local oscillators for backward locomotion

Cell- or network-driven oscillators underlie motor rhythmicity. The identity of C. elegans oscillators remains unknown. Through cell ablation, electrophysiology, and calcium imaging, we show: (1) forward and backward locomotion is driven by different oscillators; (2) the cholinergic and excitatory A-class motor neurons exhibit intrinsic and oscillatory activity that is sufficient to drive backward locomotion in the absence of premotor interneurons; (3) the UNC-2 P/Q/N high-voltage-activated calcium current underlies A motor neuron's oscillation; (4) descending premotor interneurons AVA, via an evolutionarily conserved, mixed gap junction and chemical synapse configuration, exert state-dependent inhibition and potentiation of A motor neuron's intrinsic activity to regulate backward locomotion. Thus, motor neurons themselves derive rhythms, which are dually regulated by the descending interneurons to control the reversal motor state. These and previous findings exemplify compression: essential circuit properties are conserved but executed by fewer numbers and layers of neurons in a small locomotor network.

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.

Optimal synaptic signaling connectome for locomotory behavior in Caenorhabditis elegans: Design minimizing energy cost

The detailed knowledge of C. elegans connectome for 3 decades has not contributed dramatically to our understanding of worm's behavior. One of main reasons for this situation has been the lack of data on the type of synaptic signaling between particular neurons in the worm's connectome. The aim of this study was to determine synaptic polarities for each connection in a small pre-motor circuit controlling locomotion. Even in this compact network of just 7 neurons the space of all possible patterns of connection types (excitation vs. inhibition) is huge. To deal effectively with this combinatorial problem we devised a novel and relatively fast technique based on genetic algorithms and large-scale parallel computations, which we combined with detailed neurophysiological modeling of interneuron dynamics and compared the theory to the available behavioral data. As a result of these massive computations, we found that the optimal connectivity pattern that matches the best locomotory data is the one in which all interneuron connections are inhibitory, even those terminating on motor neurons. This finding is consistent with recent experimental data on cholinergic signaling in C. elegans, and it suggests that the system controlling locomotion is designed to save metabolic energy. Moreover, this result provides a solid basis for a more realistic modeling of neural control in these worms, and our novel powerful computational technique can in principle be applied (possibly with some modifications) to other small-scale functional circuits in C. elegans.

A plausible neural circuit for decision making and its formation based on reinforcement learning

A human's, or lower insects', behavior is dominated by its nervous system. Each stable behavior has its own inner steps and control rules, and is regulated by a neural circuit. Understanding how the brain influences perception, thought, and behavior is a central mandate of neuroscience. The phototactic flight of insects is a widely observed deterministic behavior. Since its movement is not stochastic, the behavior should be dominated by a neural circuit. Based on the basic firing characteristics of biological neurons and the neural circuit's constitution, we designed a plausible neural circuit for this phototactic behavior from logic perspective. The circuit's output layer, which generates a stable spike firing rate to encode flight commands, controls the insect's angular velocity when flying. The firing pattern and connection type of excitatory and inhibitory neurons are considered in this computational model. We simulated the circuit's information processing using a distributed PC array, and used the real-time average firing rate of output neuron clusters to drive a flying behavior simulation. In this paper, we also explored how a correct neural decision circuit is generated from network flow view through a bee's behavior experiment based on the reward and punishment feedback mechanism. The significance of this study: firstly, we designed a neural circuit to achieve the behavioral logic rules by strictly following the electrophysiological characteristics of biological neurons and anatomical facts. Secondly, our circuit's generality permits the design and implementation of behavioral logic rules based on the most general information processing and activity mode of biological neurons. Thirdly, through computer simulation, we achieved new understanding about the cooperative condition upon which multi-neurons achieve some behavioral control. Fourthly, this study aims in understanding the information encoding mechanism and how neural circuits achieve behavior control. Finally, this study also helps establish a transitional bridge between the microscopic activity of the nervous system and macroscopic animal behavior.

Estimating Sensorimotor Mapping From Stimuli to Behaviors to Infer C. elegans Movements by Neural Transmission Ability Through Connectome Databases

One of the ultimate goals of computational neuroscience is to quantitatively connect between complex neural circuits and behaviors. In the past decades, the touch response circuit in Caenorhabditis elegans (C. elegans) has extensively been investigated in studies using genetically modified or laser-ablated worms. Synaptic connections, including chemical and electrical synapses, have been identified for most neurons in the C. elegans. However, we still do not know whether the empirically observed touch responses can be derived from connectome reconstructed from databases. To address this issue, we defined the transmission abilities (or levels) of neurons in a rate model in order to infer the behaviors of wild-type and ablated worms in response to posterior/nose/anterior touch stimuli. Our analysis showed that transmission abilities can be used to identify sensorimotor mapping from stimuli to movements and then to infer the C. elegans behaviors under simulations based on the perspective of decision-making, and provide useful information about how chemical and electronic synapses should be combined in the neural network movement analysis. This paper reveals an efficient tool that provided insights into the functions of complex neural circuits.

The Si elegans project at the interface of experimental and computational Caenorhabditis elegans neurobiology and behavior

OBJECTIVE

In light of recent progress in mapping neural function to behavior, we briefly and selectively review past and present endeavors to reveal and reconstruct nervous system function in Caenorhabditis elegans through simulation.

APPROACH

Rather than presenting an all-encompassing review on the mathematical modeling of C. elegans, this contribution collects snapshots of pathfinding key works and emerging technologies that recent single- and multi-center simulation initiatives are building on. We thereby point out a few general limitations and problems that these undertakings are faced with and discuss how these may be addressed and overcome.

MAIN RESULTS

Lessons learned from past and current computational approaches to deciphering and reconstructing information flow in the C. elegans nervous system corroborate the need of refining neural response models and linking them to intra- and extra-environmental interactions to better reflect and understand the actual biological, biochemical and biophysical events that lead to behavior. Together with single-center research efforts, the Si elegans and OpenWorm projects aim at providing the required, in some cases complementary tools for different hardware architectures to support advancement into this direction.

SIGNIFICANCE

Despite its seeming simplicity, the nervous system of the hermaphroditic nematode C. elegans with just 302 neurons gives rise to a rich behavioral repertoire. Besides controlling vital functions (feeding, defecation, reproduction), it encodes different stimuli-induced as well as autonomous locomotion modalities (crawling, swimming and jumping). For this dichotomy between system simplicity and behavioral complexity, C. elegans has challenged neurobiologists and computational scientists alike. Understanding the underlying mechanisms that lead to a context-modulated functionality of individual neurons would not only advance our knowledge on nervous system function and its failure in pathological states, but have directly exploitable benefits for robotics and the engineering of brain-mimetic computational architectures that are orthogonal to current von-Neumann-type machines.

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.

The whole worm: brain-body-environment models of C. elegans

Brain, body and environment are in continuous dynamical interaction, and it is becoming increasingly clear that an animal's behavior must be understood as a product not only of its nervous system, but also of the ongoing feedback of this neural activity through the biomechanics of its body and the ecology of its environment. Modeling has an essential integrative role to play in such an understanding. But successful whole-animal modeling requires an animal for which detailed behavioral, biomechanical and neural information is available and a modeling methodology which can gracefully cope with the constantly changing balance of known and unknown biological constraints. Here we review recent progress on both optogenetic techniques for imaging and manipulating neural activity and neuromechanical modeling in the nematode worm Caenorhabditis elegans. This work demonstrates both the feasibility and challenges of whole-animal modeling.

A Primer on Quantitative Modeling

Caenorhabditis elegans is particularly suitable for obtaining quantitative data about behavior, neuronal activity, gene expression, ecological interactions, quantitative traits, and much more. To exploit the full potential of these data one seeks to interpret them within quantitative models. Using two examples from the C. elegans literature we briefly explore several types of modeling approaches relevant to worm biology, and show how they might be used to interpret data, formulate testable hypotheses, and suggest new experiments. We emphasize that the choice of modeling approach is strongly dependent on the questions of interest and the type of available knowledge.

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.

Toward a science of computational ethology

The new field of “Computational Ethology” is made possible by advances in technology, mathematics, and engineering that allow scientists to automate the measurement and the analysis of animal behavior. We explore the opportunities and long-term directions of research in this area.

Why do sleeping nematodes adopt a hockey-stick-like posture?

A characteristic posture is considered one of the behavioral hallmarks of sleep, and typically includes functional features such as support for the limbs and shielding of sensory organs. The nematode C. elegans exhibits a sleep-like state during a stage termed lethargus, which precedes ecdysis at the transition between larval stages. A hockey-stick-like posture is commonly observed during lethargus. What might its function be? It was previously noted that during lethargus, C. elegans nematodes abruptly rotate about their longitudinal axis. Plausibly, these “flips” facilitate ecdysis by assisting the disassociation of the old cuticle from the new one. We found that body-posture during lethargus was established using a stereotypical motor program and that body bends during lethargus quiescence were actively maintained. Moreover, flips occurred almost exclusively when the animals exhibited a single body bend, preferentially in the anterior or mid section of the body. We describe a simple biomechanical model that imposes the observed lengths of the longitudinally directed body-wall muscles on an otherwise passive elastic rod. We show that this minimal model is sufficient for generating a rotation about the anterior-posterior body axis. Our analysis suggests that posture during lethargus quiescence may serve a developmental role in facilitating flips and that the control of body wall muscles in anterior and posterior body regions are distinct.

Neurobiology of Caenorhabditis elegans Locomotion: Where Do We Stand?

Animals use a nervous system for locomotion in some stage of their life cycle. The nematode Caenorhabditis elegans, a major animal model for almost all fields of experimental biology, has long been used for detailed studies of genetic and physiological locomotion mechanisms. Of its 959 somatic cells, 302 are neurons that are identifiable by lineage, location, morphology, and neurochemistry in every adult hermaphrodite. Of those, 75 motoneurons innervate body wall muscles that provide the thrust during locomotion. In this Overview, we concentrate on the generation of either forward- or backward-directed motion during crawling and swimming. We describe locomotion behavior, the parts constituting the locomotion system, and the relevant neuronal connectivity. Because it is not yet fully understood how these components combine to generate locomotion, we discuss competing hypotheses and models.

Nematode locomotion: dissecting the neuronal-environmental loop

With a fully reconstructed and extensively characterized neural circuit, the nematode Caenorhabditis elegans is a promising model system for integrating our understanding of neuronal, circuit and whole-animal dynamics. Fundamental to addressing this challenge is the need to consider the tight neuronal-environmental coupling that allows the animal to survive and adapt to changing conditions. Locomotion behaviors are affected by environmental variables both at the biomechanical level and via adaptive sensory responses that drive and modulate premotor and motor circuits. Here we review significant advances in our understanding of proprioceptive control of locomotion, and more abstract models of spatial orientation and navigation. The growing evidence of the complexity of the underlying circuits suggests that the intuition gained is but the first step in elucidating the secrets of neural computation in this relatively simple system.

Synaptic polarity of the interneuron circuit controlling C. elegans locomotion

Caenorhabditis elegans is the only animal for which a detailed neural connectivity diagram has been constructed. However, synaptic polarities in this diagram, and thus, circuit functions are largely unknown. Here, we deciphered the likely polarities of seven pre-motor neurons implicated in the control of worm's locomotion, using a combination of experimental and computational tools. We performed single and multiple laser ablations in the locomotor interneuron circuit and recorded times the worms spent in forward and backward locomotion. We constructed a theoretical model of the locomotor circuit and searched its all possible synaptic polarity combinations and sensory input patterns in order to find the best match to the timing data. The optimal solution is when either all or most of the interneurons are inhibitory and forward interneurons receive the strongest input, which suggests that inhibition governs the dynamics of the locomotor interneuron circuit. From the five pre-motor interneurons, only AVB and AVD are equally likely to be excitatory, i.e., they have probably similar number of inhibitory and excitatory connections to distant targets. The method used here has a general character and thus can be also applied to other neural systems consisting of small functional networks.

Evaluation of Head Movement Periodicity and Irregularity during Locomotion of Caenorhabditis elegans

Caenorhabditis elegans is suitable for studying the nervous system, which controls behavior. C. elegans shows sinusoidal locomotion on an agar plate. The head moves not only sinusoidally but also more complexly, which reflects regulation of the head muscles by the nervous system. The head movement becomes more irregular with senescence. To date, the head movement complexity has not been quantitatively analyzed. We propose two simple methods for evaluation of the head movement regularity on an agar plate using image analysis. The methods calculate metrics that are a measure of how the head end movement is correlated with body movement. In the first method, the length along the trace of the head end on the agar plate between adjacent intersecting points of the head trace and the quasi-midline of the head trace, which was made by sliding an averaging window of 1/2 the body wavelength, was obtained. Histograms of the lengths showed periodic movement of the head and deviation from it. In the second method, the intersections between the trace of the head end and the trace of the 5 (near the pharynx) or 50% (the mid-body) point from the head end in the centerline length of the worm image were marked. The length of the head trace between adjacent intersections was measured, and a histogram of the lengths was produced. The histogram for the 5% point showed deviation of the head end movement from the movement near the pharynx. The histogram for the 50% point showed deviation of the head movement from the sinusoidal movement of the body center. Application of these methods to wild type and several mutant strains enabled evaluation of their head movement periodicity and irregularity, and revealed a difference in the age-dependence of head movement irregularity between the strains. A set of five parameters obtained from the histograms reliably identifies differences in head movement between strains.

Viscoelastic properties of the nematode Caenorhabditis elegans, a self-similar, shear-thinning worm

Undulatory motion is common to many creatures across many scales, from sperm to snakes. These organisms must push off against their external environment, such as a viscous medium, grains of sand, or a high-friction surface; additionally they must work to bend their own body. A full understanding of undulatory motion, and locomotion in general, requires the characterization of the material properties of the animal itself. The material properties of the model organism Caenorhabditis elegans were studied with a micromechanical experiment used to carry out a three-point bending measurement of the worm. Worms at various developmental stages (including dauer) were measured and different positions along the worm were probed. From these experiments we calculated the viscoelastic properties of the worm, including the effective spring constant and damping coefficient of bending. C. elegans moves by propagating sinusoidal waves along its body. Whereas previous viscoelastic approaches to describe the undulatory motion have used a Kelvin-Voigt model, where the elastic and viscous components are connected in parallel, our measurements show that the Maxwell model, where the elastic and viscous components are in series, is more appropriate. The viscous component of the worm was shown to be consistent with a non-Newtonian, shear-thinning fluid. We find that as the worm matures it is well described as a self-similar elastic object with a shear-thinning damping term and a stiffness that becomes smaller as one approaches the tail.

Locomotion control of Caenorhabditis elegans through confinement

The model organism Caenorhabditis elegans shows two distinct locomotion patterns in laboratory situations: it swims in low viscosity liquids and it crawls on the surface of an agar gel. This provides a unique opportunity to discern the respective roles of mechanosensation (perception and proprioception) and mechanics in the regulation of locomotion and in the gait selection. Using an original device, we present what to our knowledge are new experiments where the confinement of a worm between a glass plate and a soft agar gel is controlled while recording the worm's motion. We observed that the worm continuously varied its locomotion characteristics from free swimming to slow crawling with increasing confinement so that it was not possible to discriminate between two distinct intrinsic gaits. This unicity of the gait is also proved by the fact that wild-type worms immediately adapted their motion when the imposed confinement was changed with time. We then studied locomotory deficient mutants that also exhibited one single gait and showed that the light touch response was needed for the undulation propagation and that the ciliated sensory neurons participated in the joint selection of motion period and undulation-wave velocity. Our results reveal that the control of maximum curvature, at a sensory or mechanical level, is a key ingredient of the locomotion regulation.

Gait Modulation in C. elegans: An Integrated Neuromechanical Model

Equipped with its 302-cell nervous system, the nematode Caenorhabditis elegans adapts its locomotion in different environments, exhibiting so-called swimming in liquids and crawling on dense gels. Recent experiments have demonstrated that the worm displays the full range of intermediate behaviors when placed in intermediate environments. The continuous nature of this transition strongly suggests that these behaviors all stem from modulation of a single underlying mechanism. We present a model of C. elegans forward locomotion that includes a neuromuscular control system that relies on a sensory feedback mechanism to generate undulations and is integrated with a physical model of the body and environment. We find that the model reproduces the entire swim-crawl transition, as well as locomotion in complex and heterogeneous environments. This is achieved with no modulatory mechanism, except via the proprioceptive response to the physical environment. Manipulations of the model are used to dissect the proposed pattern generation mechanism and its modulation. The model suggests a possible role for GABAergic D-class neurons in forward locomotion and makes a number of experimental predictions, in particular with respect to non-linearities in the model and to symmetry breaking between the neuromuscular systems on the ventral and dorsal sides of the body.

Gap junctions synchronize action potentials and Ca2+ transients in Caenorhabditis elegans body wall muscle

The sinusoidal locomotion of Caenorhabditis elegans requires synchronous activities of neighboring body wall muscle cells. However, it is unknown whether the synchrony results from muscle electrical coupling or neural inputs. We analyzed the effects of mutating gap junction proteins and blocking neuromuscular transmission on the synchrony of action potentials (APs) and Ca2+ transients among neighboring body wall muscle cells. In wild-type worms, the percentage of synchronous APs between two neighboring cells varied depending on the anatomical relationship and junctional conductance (Gj) between them, and Ca2+ transients were synchronous among neighboring muscle cells. Compared with the wild type, knock-out of the gap junction gene unc-9 resulted in greatly reduced coupling coefficient and asynchronous APs and Ca2+ transients. Inhibition of unc-9 expression specifically in muscle by RNAi also reduced the synchrony of APs and Ca2+ transients, whereas expression of wild-type UNC-9 specifically in muscle rescued the synchrony defect. Loss of the stomatin-like protein UNC-1, which is a regulator of UNC-9-based gap junctions, similarly impaired muscle synchrony as unc-9 mutant did. The blockade of muscle ionotropic acetylcholine receptors by (+)-tubocurarine decreased the frequencies of APs and Ca2+ transients, whereas blockade of muscle GABAA receptors by gabazine had opposite effects. However, both APs and Ca2+ transients remained synchronous after the application of (+)-tubocurarine and/or gabazine. These observations suggest that gap junctions in C. elegans body wall muscle cells are responsible for synchronizing muscle APs and Ca2+ transients.

Effects of pathogenic proline mutations on myosin assembly

Laing distal myopathy (MPD1) is a genetically dominant myopathy characterized by early and selective weakness of the distal muscles. Mutations in the MYH7 gene encoding for the β-myosin heavy chain are the underlying genetic cause of MPD1. However, their pathogenic mechanisms are currently unknown. Here, we measure the biological effects of the R1500P and L1706P MPD1 mutations in different cellular systems. We show that, while the two mutations inhibit myosin self-assembly in non-muscle cells, they do not prevent incorporation of the mutant myosin into sarcomeres. Nevertheless, we find that the L1706P mutation affects proper antiparallel myosin association by accumulating in the bare zone of the sarcomere. Furthermore, bimolecular fluorescence complementation assay shows that the α-helix containing the R1500P mutation folds into homodimeric (mutant/mutant) and heterodimeric [mutant/wild type (WT)] myosin molecules that are competent for sarcomere incorporation. Both mutations also form aggregates consisting of cytoplasmic vacuoles surrounding paracrystalline arrays and amorphous rod-like inclusions that sequester WT myosin. Myosin aggregates were also detected in transgenic nematodes expressing the R1500P mutation. By showing that the two MPD1 mutations can have dominant effects on distinct components of the contractile apparatus, our data provide the first insights into the pathogenesis of the disease.

A perimotor framework reveals functional segmentation in the motoneuronal network controlling locomotion in Caenorhabditis elegans

The neuronal connectivity dataset of the nematode Caenorhabditis elegans attracts wide attention from computational neuroscientists and experimentalists. However, the dataset is incomplete. The ventral and dorsal nerve cords of a single nematode were reconstructed halfway along the body and the posterior data are missing, leaving 21 of 75 motoneurons of the locomotor network with partial or no connectivity data. Using a new framework for network analysis, the perimotor space, we identified rules of connectivity that allowed us to approximate the missing data by extrapolation. Motoneurons were mapped into perimotor space in which each motoneuron is located according to the muscle cells it innervates. In this framework, a pattern of iterative connections emerges which includes most (0.90) of the connections. We identified a repeating unit consisting of 12 motoneurons and 12 muscle cells. The cell bodies of the motoneurons of such a unit are not necessarily anatomical neighbors and there is no obvious anatomical segmentation. A connectivity model, composed of six repeating units, is a description of the network that is both simplified (modular and without noniterative connections) and more complete (includes the posterior part) than the original dataset. The perimotor framework of observed connectivity and the segmented connectivity model give insights and advance the study of the neuronal infrastructure underlying locomotion in C. elegans. Furthermore, we suggest that the tools used herein may be useful to interpret, simplify, and represent connectivity data of other motor systems.

Preparation of samples for single-worm tracking

Neurobiological research in genetically tractable organisms relies heavily on robust assays for behavioral phenotypes. The simple body plan of the nematode Caenorhabditis elegans makes it particularly amenable to the use of automated microscopy and image analysis to describe behavioral patterns quantitatively. This protocol first describes the preparation and use of media for growing and maintaining worms for tracking. The second part of the protocol describes how to prepare a single young adult worm for recording during video analysis. Although the protocol was developed for use in a single-worm tracker, it addresses factors important for the generation of reproducible, standardized images in all systems.

Tracking movement behavior of multiple worms on food

Neurobiological research in genetically tractable organisms relies heavily on robust assays for behavioral phenotypes. The simple body plan of the nematode Caenorhabditis elegans makes it particularly amenable to the use of automated microscopy and image analysis to describe behavioral patterns quantitatively. Forward genetic screens and screens of drug libraries require high-throughput phenotyping, a task traditionally incompatible with manual scoring of quantitatively varying behaviors. High-throughput automated analysis of C. elegans movement behavior is now possible with several different tracking software packages. The Multiworm Tracker (MWT) described here is designed for high-throughput analysis: it can record dozens of worms simultaneously at 30 frames per second for hours or days at a time. This is accomplished by performing all image analysis in real time, saving only the worm centroid, bearing, and outline data to the disk. To simplify image processing, the system focuses only on worms that have moved, and detects and discards worms that are touching rather than trying to isolate them computationally. Because the software is entirely automated, protocols can run unattended once the worms have been placed and the software has been started. The MWT does not save images for later analysis, but behavior can be validated manually with a companion analysis tool that replays recorded body postures. This protocol describes a basic basal movement assay on food using the MWT; similar protocols apply to related assays and to similar multiple animal trackers. The protocol can be extended to a variety of assays ranging from tap response to chemotaxis.

Colored motifs reveal computational building blocks in the C. elegans brain

Background

Complex networks can often be decomposed into less complex sub-networks whose structures can give hints about the functional organization of the network as a whole. However, these structural motifs can only tell one part of the functional story because in this analysis each node and edge is treated on an equal footing. In real networks, two motifs that are topologically identical but whose nodes perform very different functions will play very different roles in the network.

Methodology/Principal Findings

Here, we combine structural information derived from the topology of the neuronal network of the nematode C. elegans with information about the biological function of these nodes, thus coloring nodes by function. We discover that particular colorations of motifs are significantly more abundant in the worm brain than expected by chance, and have particular computational functions that emphasize the feed-forward structure of information processing in the network, while evading feedback loops. Interneurons are strongly over-represented among the common motifs, supporting the notion that these motifs process and transduce the information from the sensor neurons towards the muscles. Some of the most common motifs identified in the search for significant colored motifs play a crucial role in the system of neurons controlling the worm's locomotion.

Conclusions/Significance

The analysis of complex networks in terms of colored motifs combines two independent data sets to generate insight about these networks that cannot be obtained with either data set alone. The method is general and should allow a decomposition of any complex networks into its functional (rather than topological) motifs as long as both wiring and functional information is available.

Optogenetic manipulation of neural activity in freely moving Caenorhabditis elegans

We present an optogenetic illumination system capable of real-time light delivery with high spatial resolution to specified targets in freely moving Caenorhabditis elegans. A tracking microscope records the motion of an unrestrained worm expressing channelrhodopsin-2 or halorhodopsin in specific cell types. Image processing software analyzes the worm's position in each video frame, rapidly estimates the locations of targeted cells and instructs a digital micromirror device to illuminate targeted cells with laser light of the appropriate wavelengths to stimulate or inhibit activity. Because each cell in an unrestrained worm is a rapidly moving target, our system operates at high speed (∼50 frames per second) to provide high spatial resolution (∼30 μm). To test the accuracy, flexibility and utility of our system, we performed optogenetic analyses of the worm motor circuit, egg-laying circuit and mechanosensory circuits that have not been possible with previous methods.

Motoneurons dedicated to either forward or backward locomotion in the nematode Caenorhabditis elegans

Multifunctional motoneurons and muscles, which are active during forward and backward locomotion are ubiquitous in animal models. However, studies in the nematode Caenorhabditis elegans suggest that some locomotor motoneurons are necessary only for forward locomotion (dorsal B-motoneurons, DB), while others (dorsal A-motoneurons, DA) are necessary only for backward locomotion. We tested this hypothesis directly by recording the activity of these motoneurons during semirestrained locomotion. For this purpose, we used epifluorescence imaging of the genetically encoded calcium sensor cameleon, expressed in specific motoneurons, while monitoring locomotor behavior through the microscope condenser using a second camera. We found that ventral and dorsal B-motoneurons (DB and VB) were coactive during forward locomotion while ventral A-motoneurons (VA) were only active during backward locomotion. The signals we recorded correlated with the direction of locomotion but not with the faster undulatory cycles. To our knowledge, these are the first recordings of motoneuron activity in C. elegans and the only direction-dedicated motoneurons described to date.

Regulated lysosomal trafficking as a mechanism for regulating GABAA receptor abundance at synapses in Caenorhabditis elegans

GABA(A) receptor plasticity is important for both normal brain function and disease progression. We are studying GABA(A) receptor plasticity in Caenorhabditis elegans using a genetic approach. Acute exposure of worms to the GABA(A) agonist muscimol hyperpolarizes postsynaptic cells, causing paralysis. Worms adapt after several hours, but show uncoordinated locomotion consistent with decreased GABA signaling. Using patch-clamp and immunofluorescence approaches, we show that GABA(A) receptors are selectively removed from synapses during adaptation. Subunit mRNA levels were unchanged, suggesting a post-transcriptional mechanism. Mutants with defective lysosome function (cup-5) show elevated GABA(A) receptor levels at synapses prior to muscimol exposure. During adaptation, these receptors are removed more slowly, and accumulate in intracellular organelles positive for the late endosome marker GFP-RAB-7. These findings suggest that chronic agonist exposure increases endocytosis and lysosomal trafficking of GABA(A) receptors, leading to reduced levels of synaptic GABA(A) receptors and reduced postsynaptic GABA sensitivity.

Caenorhabditis elegans: a model system for systems neuroscience

The nematode Caenorhabditis elegans is an excellent model organism for a systems-level understanding of neural circuits and behavior. Advances in the quantitative analyses of behavior and neuronal activity, and the development of new technologies to precisely control and monitor the workings of interconnected circuits, now allow investigations into the molecular, cellular, and systems-level strategies that transform sensory inputs into precise behavioral outcomes.

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

The ability of an animal to locomote through its environment depends crucially on the interplay between its active endogenous control and the physics of its interactions with the environment. The nematode worm Caenorhabditis elegans serves as an ideal model system for studying the respective roles of neural control and biomechanics, as well as the interaction between them. With only 302 neurons in a hard-wired neural circuit, the worm's apparent anatomical simplicity belies its behavioural complexity. Indeed, C. elegans exhibits a rich repertoire of complex behaviors, the majority of which are mediated by its adaptive undulatory locomotion. The conventional wisdom is that two kinematically distinct C. elegans locomotion behaviors-swimming in liquids and crawling on dense gel-like media-correspond to distinct locomotory gaits. Here we analyze the worm's motion through a series of different media and reveal a smooth transition from swimming to crawling, marked by a linear relationship between key locomotion metrics. These results point to a single locomotory gait, governed by the same underlying control mechanism. We further show that environmental forces play only a small role in determining the shape of the worm, placing conditions on the minimal pattern of internal forces driving locomotion.