Locomotion of C. elegans: a piecewise-harmonic curvature representation of nematode behavior

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

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

A Quantitative Analysis of Micrurus Coral Snakes Reveals Unexpected Variation in Stereotyped Anti-Predator Displays Within a Mimicry System

Warning signals in chemically defended organisms are critical components of predator–prey interactions, often requiring multiple coordinated display components for effective communication. When threatened by a predator, venomous coral snakes (genus Micrurus) display a vigorous, non-locomotory thrashing behavior that has previously been qualitatively described. Given the high contrast and colorful banding patterns of these snakes, this thrashing display is hypothesized to be a key component of a complex aposematic signal under strong stabilizing selection across species in a mimicry system. By experimentally testing snake response across simulated predator cues, we analyzed variation in the presence and expression of a thrashing display across five species of South American coral snakes. Although the major features of the thrash display were conserved across species, we found that predator cue type, snake body size, and species identity predict significant inter- and intraspecific variation in the propensity to perform a display, the duration of thrashing, and the curvature of snake bodies. We also found an interaction between curve magnitude and body location that clearly shows which parts of the display vary most across individuals and species. Our results suggest that contrary to the assumption that all Micrurus species and individuals perform the same display, a high degree of variation exists despite presumably strong selection to conserve a common signal. This quantitative behavioral characterization presents a new framework for analyzing the non-locomotory motions displayed by snakes in a broader ecological context, especially for signaling systems with complex interaction across multiple modalities.

Continuous body 3-D reconstruction of limbless animals

Limbless animals such as snakes, limbless lizards, worms, eels and lampreys move their slender, long bodies in three dimensions to traverse diverse environments. Accurately quantifying their continuous body's 3-D shape and motion is important for understanding body-environment interactions in complex terrain, but this is difficult to achieve (especially for local orientation and rotation). Here, we describe an interpolation method to quantify continuous body 3-D position and orientation. We simplify the body as an elastic rod and apply a backbone optimization method to interpolate continuous body shape between end constraints imposed by tracked markers. Despite over-simplifying the biomechanics, our method achieves a higher interpolation accuracy (∼50% error) in both 3-D position and orientation compared with the widely used cubic B-spline interpolation method. Beyond snakes traversing large obstacles as demonstrated, our method applies to other long, slender, limbless animals and continuum robots. We provide codes and demo files for easy application of our method.

Lateral Oscillation and Body Compliance Help Snakes and Snake Robots Stably Traverse Large, Smooth Obstacles

Snakes can move through almost any terrain. Similarly, snake robots hold the promise as a versatile platform to traverse complex environments such as earthquake rubble. Unlike snake locomotion on flat surfaces which is inherently stable, when snakes traverse complex terrain by deforming their body out of plane, it becomes challenging to maintain stability. Here, we review our recent progress in understanding how snakes and snake robots traverse large, smooth obstacles such as boulders and felled trees that lack "anchor points" for gripping or bracing. First, we discovered that the generalist variable kingsnake combines lateral oscillation and cantilevering. Regardless of step height and surface friction, the overall gait is preserved. Next, to quantify static stability of the snake, we developed a method to interpolate continuous body in three dimensions (3D) (both position and orientation) between discrete tracked markers. By analyzing the base of support using the interpolated continuous body 3-D kinematics, we discovered that the snake maintained perfect stability during traversal, even on the most challenging low friction, high step. Finally, we applied this gait to a snake robot and systematically tested its performance traversing large steps with variable heights to further understand stability principles. The robot rapidly and stably traversed steps nearly as high as a third of its body length. As step height increased, the robot rolled more frequently to the extent of flipping over, reducing traversal probability. The absence of such failure in the snake with a compliant body inspired us to add body compliance to the robot. With better surface contact, the compliant body robot suffered less roll instability and traversed high steps at higher probability, without sacrificing traversal speed. Our robot traversed large step-like obstacles more rapidly than most previous snake robots, approaching that of the animal. The combination of lateral oscillation and body compliance to form a large, reliable base of support may be useful for snakes and snake robots to traverse diverse 3-D environments with large, smooth obstacles.

Diving into a Simple Anguilliform Swimmer’s Sensitivity

Computational models of aquatic locomotion range from modest individual simple swimmers in 2D to sophisticated 3D multi-swimmer models that attempt to parse collective behavioral dynamics. Each of these models contain a multitude of model input parameters to which its outputs are inherently dependent, that is, various performance metrics. In this work, the swimming performance’s sensitivity to parameters is investigated for an idealized, simple anguilliform swimming model in 2D. The swimmer considered here propagates forward by dynamically varying its body curvature, similar to motion of a Caenorhabditis elegans. The parameter sensitivities were explored with respect to the fluid scale (Reynolds number), stroke (undulation) frequency, as well as a kinematic parameter controlling the velocity and acceleration of each upstroke and downstroke. The input Reynolds number and stroke frequencies sampled were from [450, 2200] and [1, 3] Hz, respectively. In total, 5000 fluid–structure interaction simulations were performed, each with a unique parameter combination selected via a Sobol sequence, in order to conduct global sensitivity analysis. Results indicate that the swimmer’s performance is most sensitive to variations in its stroke frequency. Trends in swimming performance were discovered by projecting the performance data onto particular 2D subspaces. Pareto-like optimal fronts were identified. This work is a natural extension of the parameter explorations of the same model from Battista in 2020.

Swimming Through Parameter Subspaces of a Simple Anguilliform Swimmer

Computational scientists have investigated swimming performance across a multitude of different systems for decades. Most models depend on numerous model input parameters and performance is sensitive to those parameters. In this article, parameter subspaces are qualitatively identified in which there exists enhanced swimming performance for an idealized, simple swimming model that resembles a Caenorhabditis elegans, an organism that exhibits an anguilliform mode of locomotion. The computational model uses the immersed boundary method to solve the fluid-interaction system. The 1D swimmer propagates itself forward by dynamically changing its preferred body curvature. Observations indicate that the swimmer’s performance appears more sensitive to fluid scale and stroke frequency, rather than variations in the velocity and acceleration of either its upstroke or downstroke as a whole. Pareto-like optimal fronts were also identified within the data for the cost of transport and swimming speed. While this methodology allows one to locate robust parameter subspaces for desired performance in a straight-forward manner, it comes at the cost of simulating orders of magnitude more simulations than traditional fluid–structure interaction studies.

A new method for measuring the size of nematodes using image processing

Many studies have been made on nematodes, especially Caenorhabditis Elegans, which are used as a model organism. In many studies, the size of the nematode is important. This article describes a method of measuring the length, volume and surface area of nematodes from photographs. The method uses the imaging software ImageJ, which is in the public domain. Two macros are described. The first converts the images into binary form, and the second uses several built-in functions to measure the length of the worm and its diameter along its length. If it is assumed that the worm has a circular cross-section, then the volume and surface area of the nematode can be calculated. This is a cheap and easy technique.

Pluronic gel-based burrowing assay for rapid assessment of neuromuscular health in C. elegans

Whole-organism phenotypic assays are central to the assessment of neuromuscular function and health in model organisms such as the nematode C. elegans. In this study, we report a new assay format for engaging C. elegans in burrowing that enables rapid assessment of nematode neuromuscular health. In contrast to agar environments that pose specific drawbacks for characterization of C. elegans burrowing ability, here we use the optically transparent and biocompatible Pluronic F-127 gel that transitions from liquid to gel at room temperature, enabling convenient and safe handling of animals. The burrowing assay methodology involves loading animals at the bottom of well plates, casting a liquid-phase of Pluronic on top that solidifies via a modest temperature upshift, enticing animals to reach the surface via chemotaxis to food, and quantifying the relative success animals have in reaching the chemoattractant. We study the influence of Pluronic concentration, gel height and chemoattractant choice to optimize assay performance. To demonstrate the simplicity of the assay workflow and versatility, we show its novel application in multiple areas including (i) evaluating muscle mutants with defects in dense bodies and/or M-lines (pfn-3, atn-1, uig-1, dyc-1, zyx-1, unc-95 and tln-1), (ii) tuning assay conditions to reveal changes in the mutant gei-8, (iii) sorting of fast burrowers in a genetically-uniform wild-type population for later quantitation of their distinct muscle gene expression, and (iv) testing proteotoxic animal models of Huntington and Parkinson's disease. Results from our studies show that stimulating animals to navigate in a dense environment that offers mechanical resistance to three-dimensional locomotion challenges the neuromuscular system in a manner distinct from standard crawling and thrashing assays. Our simple and high throughput burrowing assay can provide insight into molecular mechanisms for maintenance of neuromuscular health and facilitate screening for therapeutic targets.

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

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

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

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

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

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

A Run-Length Encoding Approach for Path Analysis of C. elegans Search Behavior

The nematode Caenorhabditis elegans explores the environment using a combination of different movement patterns, which include straight movement, reversal, and turns. We propose to quantify C. elegans movement behavior using a computer vision approach based on run-length encoding of step-length data. In this approach, the path of C. elegans is encoded as a string of characters, where each character represents a path segment of a specific type of movement. With these encoded string data, we perform k-means cluster analysis to distinguish movement behaviors resulting from different genotypes and food availability. We found that shallow and sharp turns are the most critical factors in distinguishing the differences among the movement behaviors. To validate our approach, we examined the movement behavior of tph-1 mutants that lack an enzyme responsible for serotonin biosynthesis. A k-means cluster analysis with the path string-encoded data showed that tph-1 movement behavior on food is similar to that of wild-type animals off food. We suggest that this run-length encoding approach is applicable to trajectory data in animal or human mobility data.

Robust tracking and quantification of C. elegans body shape and locomotion through coiling, entanglement, and omega bends

The behavior of the well-characterized nematode, Caenorhabditis elegans (C. elegans), is often used to study the neurologic control of sensory and motor systems in models of health and neurodegenerative disease. To advance the quantification of behaviors to match the progress made in the breakthroughs of genetics, RNA, proteins, and neuronal circuitry, analysis must be able to extract subtle changes in worm locomotion across a population. The analysis of worm crawling motion is complex due to self-overlap, coiling, and entanglement. Using current techniques, the scope of the analysis is typically restricted to worms to their non-occluded, uncoiled state which is incomplete and fundamentally biased. Using a model describing the worm shape and crawling motion, we designed a deformable shape estimation algorithm that is robust to coiling and entanglement. This model-based shape estimation algorithm has been incorporated into a framework where multiple worms can be automatically detected and tracked simultaneously throughout the entire video sequence, thereby increasing throughput as well as data validity. The newly developed algorithms were validated against 10 manually labeled datasets obtained from video sequences comprised of various image resolutions and video frame rates. The data presented demonstrate that tracking methods incorporated in WormLab enable stable and accurate detection of these worms through coiling and entanglement. Such challenging tracking scenarios are common occurrences during normal worm locomotion. The ability for the described approach to provide stable and accurate detection of C. elegans is critical to achieve unbiased locomotory analysis of worm motion.

Effect of temperature pre-exposure on the locomotion and chemotaxis of C. elegans

The effect of temperature pre-exposure on locomotion and chemotaxis of the soil-dwelling nematode Caenorhabditis elegans has been extensively studied. The behavior of C. elegans was quantified using a simple harmonic curvature-based model. Animals showed increased levels of activity, compared to control worms, immediately after pre-exposure to 30 °C. This high level of activity in C. elegans translated into frequent turns by making 'complex' shapes, higher velocity of locomotion, and higher chemotaxis index (CI) in presence of a gradient of chemoattractant. The effect of pre-exposure was observed to be persistent for about 20 minutes after which the behavior (including velocity and CI) appeared to be comparable to that of control animals (maintained at 20 °C). Surprisingly, after 30 minutes of recovery, the behavior of C. elegans continued to deteriorate further below that of control worms with a drastic reduction in the curvature of the worms' body. A majority of these worms also showed negative chemotaxis index indicating a loss in their chemotaxis ability.