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.

Time-off-pick Assay to Measure Caenorhabditis elegans Motility

Caenorhabditis elegans is a simple metazoan that is often used as a model organism to study various human ailments with impaired motility phenotypes, including protein conformational diseases. Numerous motility assays that measure neuro-muscular function have been employed using C. elegans . Here, we describe "time-off-pick" (TOP), a novel assay for assessing motility in C. elegans . TOP is conducted by sliding an eyebrow hair under the mid-section of the worm and counting the number of seconds it takes for the worm to crawl completely off. The time it takes for the worm to crawl off the eyebrow hair is proportional to the severity of its motility defect. Other readouts of motility include crawling or swimming phenotypes, and although widely established, have some limitations. For example, worms that are roller mutants are less suitable for crawling or swimming assays. We demonstrated that our novel TOP assay is sensitive to age-dependent changes in motility, thus, providing another more inclusive method to assess motor function in C. elegans . Graphical abstract: Conceptual overview of the "time-off-pick" (TOP) assay. Various C. elegans models exhibit age-dependent defects in motility. The time it takes for a worm to crawl off of an eyebrow pick that is slid under its mid-section is measured in TOP seconds. A greater TOP is indicative of a greater motility defect. Eventually, worms with phenotypes that lead to paralysis will not be able to leave the pick.

Collective pattern formations of animals in active matter physics

Active matter refers to systems composed of elements that are self-propelled by the dissipation of energy, in which dynamical patterns emerge, as is the case of flocks of birds and schools of fish. Some researchers in active matter physics seek to identify unified descriptions of such collective motions through interdisciplinary approaches by biologists and physicists. Through such collaborations, experimental studies pertaining to active matter physics have been developing recently, which allow us to verify the proposed mathematical models. Here, we review collective pattern formations and behaviors of animals from the perspective of active matter physics.

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.

A C. elegans model for neurodegeneration in Cockayne syndrome

Cockayne syndrome (CS) is a congenital syndrome characterized by growth and mental retardation, and premature ageing. The complexity of CS and mammalian models warrants simpler metazoan models that display CS-like phenotypes that could be studied in the context of a live organism. Here, we provide a characterization of neuronal and mitochondrial aberrations caused by a mutation in the csb-1 gene in Caenorhabditis elegans. We report a progressive neurodegeneration in adult animals that is enhanced upon UV-induced DNA damage. The csb-1 mutants show dysfunctional hyperfused mitochondria that degrade upon DNA damage, resulting in diminished respiratory activity. Our data support the role of endogenous DNA damage as a driving factor of CS-related neuropathology and underline the role of mitochondrial dysfunction in the disease.

GTL-1, a Calcium Activated TRPM Channel, Enhances Nociception

C. elegans PVD neurons are conserved for morphology, function and molecular determinants with mammalian polymodal nociceptors. Functions of polymodal nociceptors require activities of multiple ion channels and receptors including members of the TRP family. GTL-1, a member of the TRPM subclass of TRP channels, was previously shown to amplify PVD-mediated responses to optogenetic stimuli. Here we characterize effects of GTL-1 on PVD-mediated behavioral responses to noxious stimuli. We show that GTL-1 is required within PVD for the immediate and enduring response to thermal (cold) stimuli. But, find no significant reduction in percent animals responding to single or to repeated noxious mechanical stimuli. Nevertheless, PVD specific knockdown of gtl-1expression reduces the magnitude of responses to noxious mechanical stimuli. To understand GTL-1's mechanism of action we expressed it in HEK293 cells. Our results show GTL-1-dependent currents induced by activation of a Gαq-coupled Designer Receptor Exclusively Activated by Designer Drugs (DREADD). In addition, using excised patches we show that GTL-1 can be activated by internal calcium. Our results are consistent with indirect, calcium dependent, activation of GTL-1 by noxious stimuli. This mechanism explains the GTL-1-dependent amplification of responses to multiple stimuli optogenetic and sensory in PVD.

How Caenorhabditis elegans Senses Mechanical Stress, Temperature, and Other Physical Stimuli

Caenorhabditis elegans lives in a complex habitat in which they routinely experience large fluctuations in temperature, and encounter physical obstacles that vary in size and composition. Their habitat is shared by other nematodes, by beneficial and harmful bacteria, and nematode-trapping fungi. Not surprisingly, these nematodes can detect and discriminate among diverse environmental cues, and exhibit sensory-evoked behaviors that are readily quantifiable in the laboratory at high resolution. Their ability to perform these behaviors depends on <100 sensory neurons, and this compact sensory nervous system together with powerful molecular genetic tools has allowed individual neuron types to be linked to specific sensory responses. Here, we describe the sensory neurons and molecules that enable C. elegans to sense and respond to physical stimuli. We focus primarily on the pathways that allow sensation of mechanical and thermal stimuli, and briefly consider this animal’s ability to sense magnetic and electrical fields, light, and relative humidity. As the study of sensory transduction is critically dependent upon the techniques for stimulus delivery, we also include a section on appropriate laboratory methods for such studies. This chapter summarizes current knowledge about the sensitivity and response dynamics of individual classes of C. elegans mechano- and thermosensory neurons from in vivo calcium imaging and whole-cell patch-clamp electrophysiology studies. We also describe the roles of conserved molecules and signaling pathways in mediating the remarkably sensitive responses of these nematodes to mechanical and thermal cues. These studies have shown that the protein partners that form mechanotransduction channels are drawn from multiple superfamilies of ion channel proteins, and that signal transduction pathways responsible for temperature sensing in C. elegans share many features with those responsible for phototransduction in vertebrates.

Automated behavioural analysis reveals the basic behavioural repertoire of the urochordate Ciona intestinalis

Quantitative analysis of animal behaviour in model organisms is becoming an increasingly essential approach for tackling the great challenge of understanding how activity in the brain gives rise to behaviour. Here we used automated image-based tracking to extract behavioural features from an organism of great importance in understanding the evolution of chordates, the free-swimming larval form of the tunicate Ciona intestinalis, which has a compact and fully mapped nervous system composed of only 231 neurons. We analysed hundreds of videos of larvae and we extracted basic geometric and physical descriptors of larval behaviour. Importantly, we used machine learning methods to create an objective ontology of behaviours for C. intestinalis larvae. We identified eleven behavioural modes using agglomerative clustering. Using our pipeline for quantitative behavioural analysis, we demonstrate that C. intestinalis larvae exhibit sensory arousal and thigmotaxis. Notably, the anxiotropic drug modafinil modulates thigmotactic behaviour. Furthermore, we tested the robustness of the larval behavioural repertoire by comparing different rearing conditions, ages and group sizes. This study shows that C. intestinalis larval behaviour can be broken down to a set of stereotyped behaviours that are used to different extents in a context-dependent manner.

C. elegans collectively forms dynamical networks

Understanding physical rules underlying collective motions requires perturbation of controllable parameters in self-propelled particles. However, controlling parameters in animals is generally not easy, which makes collective behaviours of animals elusive. Here, we report an experimental system in which a conventional model animal, Caenorhabditis elegans, collectively forms dynamical networks of bundle-shaped aggregates. We investigate the dependence of our experimental system on various extrinsic parameters (material of substrate, ambient humidity and density of worms). Taking advantage of well-established C. elegans genetics, we also control intrinsic parameters (genetically determined motility) by mutations and by forced neural activation via optogenetics. Furthermore, we develop a minimal agent-based model that reproduces the dynamical network formation and its dependence on the parameters, suggesting that the key factors are alignment of worms after collision and smooth turning. Our findings imply that the concepts of active matter physics may help us to understand biological functions of animal groups.

Understanding collective motions in a group of interacting animal is a challenge owing to the lack of control over, for example, real fish schools. Here, the authors study the aggregation of C. elegans at controllable conditions and reproduce the experimental observations using a minimal model.

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'.

Vibration sensitivity found in Caenorhabditis elegans

Mechanical sensing is important for all organisms, but is the least understood of the senses. As mechanical stimuli come in diverse forms, organisms often have sensors or sensory systems that specialise in a form of mechanical stimuli, such as touch or vibration. Here, we tested the hypothesis that the nematode worm Caenorhabditis elegans exhibits a behavioural response to vibration that is distinct from its responses to touch. We show that wild-type strain worms respond to sustained low-frequency vibration in a manner distinct from the known responses to non-localised mechanical stimuli. Furthermore, the behavioural responses of mutant strains suggest different roles for ciliated versus non-ciliated neurons in mediating the response. Although further study is required to identify the vibration-sensing pathway, our data support that C. elegans can sense substrate-borne vibrations using cells distinct from those used in gentle touch.

Collective motion of rod-shaped self-propelled particles through collision

Self-propelled rods, which propel by themselves in the direction from the tail to the head and align nematically through collision, have been well-investigated theoretically. Various phenomena including true long-range ordered phase with the Giant number fluctuations, and the collective motion composed of many vorices were predicted using the minimal mathematical models of self-propelled rods. Using filamentous bacteria and running microtubules, we found that the predicted phenomena by the minimal models occur in the real world. This strongly indicates that there exists the unified description of self-propelled rods independent of the details of the systems. The theoretically predicted phenomena and the experimental results concerning the phenomena are reviewed.

Determining the biomechanics of touch sensation in C. elegans

The sense of touch is a fundamental mechanism that nearly all organisms use to interact with their surroundings. However, the process of mechanotransduction whereby a mechanical stimulus gives rise to a neuronal response is not well understood. In this paper we present an investigation of the biomechanics of touch using the model organism C. elegans. By developing a custom micromanipulation and force sensing system around a high resolution optical microscope, we measured the spatial deformation of the organism’s cuticle and force response to controlled uniaxial indentations. We combined these experimental results with anatomical data to create a multilayer computational biomechanical model of the organism and accurately derive its material properties such as the elastic modulus and poisson’s ratio. We demonstrate the utility of this model by combining it with previously published electrophysiological data to provide quantitative insights into different biomechanical states for mechanotransduction, including the first estimate of the sensitivity of an individual mechanoreceptor to an applied stimulus (parameterised as strain energy density). We also interpret empirical behavioural data to estimate the minimum number of mechanoreceptors which must be activated to elicit a behavioural response.

A network approach to discerning the identities of C. elegans in a free moving population

The study of C. elegans has led to ground-breaking discoveries in gene-function, neuronal circuits, and physiological responses. Subtle behavioral phenotypes, however, are often difficult to measure reproducibly. We have developed an experimental and computational infrastructure to simultaneously record and analyze the physical characteristics, movement, and social behaviors of dozens of interacting free-moving nematodes. Our algorithm implements a directed acyclic network that reconstructs the complex behavioral trajectories generated by individual C. elegans in a free moving population by chaining hundreds to thousands of short tracks into long contiguous trails. This technique allows for the high-throughput quantification of behavioral characteristics that require long-term observation of individual animals. The graphical interface we developed will enable researchers to uncover, in a reproducible manner, subtle time-dependent behavioral phenotypes that will allow dissection of the molecular mechanisms that give rise to organism-level behavior.

Colored polydimethylsiloxane micropillar arrays for high throughput measurements of forces applied by genetic model organisms

Measuring forces applied by multi-cellular organisms is valuable in investigating biomechanics of their locomotion. Several technologies have been developed to measure such forces, for example, strain gauges, micro-machined sensors, and calibrated cantilevers. We introduce an innovative combination of techniques as a high throughput screening tool to assess forces applied by multiple genetic model organisms. First, we fabricated colored Polydimethylsiloxane (PDMS) micropillars where the color enhances contrast making it easier to detect and track pillar displacement driven by the organism. Second, we developed a semi-automated graphical user interface to analyze the images for pillar displacement, thus reducing the analysis time for each animal to minutes. The addition of color reduced the Young's modulus of PDMS. Therefore, the dye-PDMS composite was characterized using Yeoh's hyperelastic model and the pillars were calibrated using a silicon based force sensor. We used our device to measure forces exerted by wild type and mutant Caenorhabditis elegans moving on an agarose surface. Wild type C. elegans exert an average force of ∼1 μN on an individual pillar and a total average force of ∼7.68 μN. We show that the middle of C. elegans exerts more force than its extremities. We find that C. elegans mutants with defective body wall muscles apply significantly lower force on individual pillars, while mutants defective in sensing externally applied mechanical forces still apply the same average force per pillar compared to wild type animals. Average forces applied per pillar are independent of the length, diameter, or cuticle stiffness of the animal. We also used the device to measure, for the first time, forces applied by Drosophila melanogaster larvae. Peristaltic waves occurred at 0.4 Hz applying an average force of ∼1.58 μN on a single pillar. Our colored microfluidic device along with its displacement tracking software allows us to measure forces applied by multiple model organisms that crawl or slither to travel through their environment.

The Caenorhabditis elegans interneuron ALA is (also) a high-threshold mechanosensor

BACKGROUND

To survive dynamic environments, it is essential for all animals to appropriately modulate their behavior in response to various stimulus intensities. For instance, the nematode Caenorhabditis elegans suppresses the rate of egg-laying in response to intense mechanical stimuli, in a manner dependent on the mechanosensory neurons FLP and PVD. We have found that the unilaterally placed single interneuron ALA acted as a high-threshold mechanosensor, and that it was required for this protective behavioral response.

RESULTS

ALA was required for the inhibition of egg-laying in response to a strong (picking-like) mechanical stimulus, characteristic of routine handling of the animals. Moreover, ALA did not respond physiologically to less intense touch stimuli, but exhibited distinct physiological responses to anterior and posterior picking-like touch, suggesting that it could distinguish between spatially separated stimuli. These responses required neither neurotransmitter nor neuropeptide release from potential upstream neurons. In contrast, the long, bilaterally symmetric processes of ALA itself were required for producing its physiological responses; when they were severed, responses to stimuli administered between the cut and the cell body were unaffected, while responses to stimuli administered posterior to the cut were abolished.

CONCLUSION

C. elegans neurons are typically classified into three major groups: sensory neurons with specialized sensory dendrites, interneurons, and motoneurons with neuromuscular junctions. Our findings suggest that ALA can autonomously sense intense touch and is thus a dual-function neuron, i.e., an interneuron as well as a novel high-threshold mechanosensor.