Theory of the locomotion of nematodes: Dynamics of undulatory progression on a surface

We develop a model of the undulatory locomotion of nematodes, in particular that of Caenorhabditis elegans, based on mechanics. The model takes into account the most important forces acting on a moving worm and allows the computer simulation of a creeping nematode. These forces are produced by the interior pressure in the liquid-filled body cavity, the elasticity of the cuticle, the excitation of certain sets of muscles and the friction between the body and its support.

We propose that muscle excitation patterns can be generated by stretch receptor control. By solving numerically the equations of motion of the model of the nematode, we demonstrate that these muscle excitation patterns are suitable for the propulsion of the animal.

     

Undulatory locomotion of Caenorhabditis elegans on wet surfaces

The physical and biomechanical principles that govern undulatory movement on wet surfaces have important applications in physiology, physics, and engineering. The nematode Caenorhabditis elegans, with its highly stereotypical and functionally distinct sinusoidal locomotory gaits, is an excellent system in which to dissect these properties. Measurements of the main forces governing the C. elegans crawling gait on lubricated surfaces have been scarce, primarily due to difficulties in estimating the physical features at the nematode-gel interface. Using kinematic data and a hydrodynamic model based on lubrication theory, we calculate both the surface drag forces and the nematode's bending force while crawling on the surface of agar gels within a preexisting groove. We find that the normal and tangential surface drag coefficients during crawling are ～222 and 22, respectively, and the drag coefficient ratio is ～10. During crawling, the calculated internal bending force is time-periodic and spatially complex, exhibiting a phase lag with respect to the nematode's body bending curvature. This phase lag is largely due to viscous drag forces, which are higher during crawling as compared to swimming in an aqueous buffer solution. The spatial patterns of bending force generated during either swimming or crawling correlate well with previously described gait-specific features of calcium signals in muscle. Further, our analysis indicates that one may be able to control the motility gait of C. elegans by judiciously adjusting the magnitude of the surface drag coefficients.     

Shape memory alloy-based small crawling robots inspired by C. elegans

Inspired by its simple musculature, actuation and motion mechanisms, we have developed a small crawling robot that closely mimics the model organism of our choice: Caenorhabditis elegans. A thermal shape memory alloy (SMA) was selected as an actuator due to the similarities of its properties to C. elegans muscles. Based on the anatomy of C. elegans, a 12-unit robot was designed to generate a sinusoidal undulating motion. Each body unit consisting of a pair of SMA actuators is serially connected by rigid links with an embedded motion control circuit. A simple binary operation-based motion control mechanism was implemented using a microcontroller. The assembled robot can execute C. elegans-like motion with a 0.17 Hz undulation frequency. Its motion is comparable to that of a real worm.     

Strategies for automated analysis of <Emphasis Type="Italic">C. elegans</Emphasis> locomotion

Automated analysis of C. elegans behaviour is a rapidly developing field, offering the possibility of behaviour-based, high-throughput drug screens and systematic phenotyping. Standard methods for parameterizing worm shapes and movements are emerging, and progress has been made towards overcoming the difficulties introduced by interactions between worms, as well as worm coiling and omega turning. Current methods have facilitated the identification of subtle phenotypes and the characterisation of roles of neurones in forward locomotion and chemotaxis, as well as the quantitative characterisation of behaviour choice and circadian patterns of activity. Given the speed with which C. elegans has been deployed in genetic screens and chemical screens, it is to be hoped that wormtrackers may eventually provide similar rapidity in assaying behavioural phenotypes. However, considerable progress must be made before this can be accomplished. In the case of genome-wide RNAi screens, for example, the presence in the worm genome of some 19,000 genes means that even the minimal user intervention in an automatic phenotyping system will be very costly. Nonetheless, recent advances have shown that drug actions on large numbers of worms can be tracked, raising hopes that high-throughput behavioural screens may soon be available.     

Conservation rules, their breakdown, and optimality in Caenorhabditis sinusoidal locomotion

Undulatory locomotion is common to nematodes as well as to limbless vertebrates, but its control is not understood in spite of the identification of hundred of genes involved in Caenorhabditis elegans locomotion. To reveal the mechanisms of nematode undulatory locomotion, we quantitatively analysed the movement of C. elegans with genetic perturbations to neurons, muscles, and skeleton (cuticle). We also compared locomotion of different Caenorhabditis species. We constructed a theoretical model that combines mechanics and biophysics, and that is constrained by the observations of propulsion and muscular velocities, as well as wavelength and amplitude of undulations. We find that normalized wavelength is a conserved quantity among wild-type C. elegans individuals, across mutants, and across different species. The velocity of forward propulsion scales linearly with the velocity of the muscular wave and the corresponding slope is also a conserved quantity and almost optimal; the exceptions are in some mutants affecting cuticle structure. In theoretical terms, the optimality of the slope is equivalent to the exact balance between muscular and visco-elastic body reaction bending moments. We find that the amplitude and frequency of undulations are inversely correlated and provide a theoretical explanation for this fact. These experimental results are valid both for young adults and for all larval stages of wild-type C. elegans. In particular, during development, the amplitude scales linearly with the wavelength, consistent with our theory. We also investigated the influence of substrate firmness on motion parameters, and found that it does not affect the above invariants. In general, our biomechanical model can explain the observed robustness of the mechanisms controlling nematode undulatory locomotion.     

Meandering worms: mechanics of undulatory burrowing in muds

Recent work has shown that muddy sediments are elastic solids through which animals extend burrows by fracture, whereas non-cohesive granular sands fluidize around some burrowers. These different mechanical responses are reflected in the morphologies and behaviours of their respective inhabitants. However, Armandia brevis, a mud-burrowing opheliid polychaete, lacks an expansible anterior consistent with fracturing mud, and instead uses undulatory movements similar to those of sandfish lizards that fluidize desert sands. Here, we show that A. brevis neither fractures nor fluidizes sediments, but instead uses a third mechanism, plastically rearranging sediment grains to create a burrow. The curvature of the undulating body fits meander geometry used to describe rivers, and changes in curvature driven by muscle contraction are similar for swimming and burrowing worms, indicating that the same gait is used in both sediments and water. Large calculated friction forces for undulatory burrowers suggest that sediment mechanics affect undulatory and peristaltic burrowers differently; undulatory burrowing may be more effective for small worms that live in sediments not compacted or cohesive enough to extend burrows by fracture.     

Direct Measurements of Drag Forces in C. elegans Crawling Locomotion

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

On-line Optimization of Biomimetic Undulatory Swimming by an Experiment-based Approach

An experiment-based approach is proposed to improve the performance of biomimetic undulatory locomotion through on-line optimization. The approach is implemented through two steps： （1） the generation of coordinated swimming gaits by artificial Central Pattern Generators （CPGs）; （2） an on-line searching of optimal parameter sets for the CPG model using Genetic Algorithm （GA）. The effectiveness of the approach is demonstrated in the optimization of swimming speed and energy effi- ciency for a biomimetic fin propulsor. To evaluate how well the input energy is converted into the kinetic energy of the pro- pulsor, an energy-efficiency index is presented and utilized as a feedback to regulate the on-line searching with a closed-loop swimming control. Experiments were conducted on propulsor prototypes with different fin segments and the optimal swimming patterns were found separately. Comparisons of results show that the optimal curvature of undulatory propulsor, which might have different shapes depending on the actual prototype design and control scheme. It is also found that the propulsor with six fin segments, is preferable because of hizher speed and lower energy efficiency.     

Direct Measurements of Drag Forces in C.?elegans Crawling Locomotion

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

Caenorhabditis elegans: an emerging genetic model for the study of innate immunity

Invaluable insights into how animals, humans included, defend themselves against infection have been provided by more than a decade of genetic studies that have used fruitflies. In the past few years, attention has also turned to another simple animal model, the nematode worm Caenorhabditis elegans. What exactly have we learned from the work in Drosophila? And will research with C. elegans teach us anything new about our response to pathogen attack?     

The retinoblastoma tumour suppressor in model organisms--new insights from flies and worms

All forms of life on Earth share a common ancestry. As a consequence, Homo sapiens shares a large number of genes essential for the development and maintenance of multicellular life with "simple" animals, such as the fruit fly Drosophila melanogaster and the nematode worm Caenorhabdites elegans. Indeed, Drosophila and C. elegans have successfully been used to unravel fundamental mechanisms underlying animal development. The sequencing of their genomes has revealed that a surprisingly large proportion of genes relevant for human disease have counterparts in the worm and in the fly. This includes many oncogenes and tumour suppressor genes and provides us with a unique opportunity to exploit the advantages of simple model organisms to further our understanding of the molecular basis of cancer. Recent work on the fly and worm homologs of the Retinoblastoma tumour suppressor (pRb) has uncovered some unexpected pRb functions: Evolutionary conserved pRb complexes participate in cell fate determination, repress germline-specific gene expression and interact with RNA interference pathways. Similar complexes appear to operate in human cells.     

Corollary discharge enables proprioception from lateral line sensory feedback

Animals modulate sensory processing in concert with motor actions. Parallel copies of motor signals, called corollary discharge (CD), prepare the nervous system to process the mixture of externally and self-generated (reafferent) feedback that arises during locomotion. Commonly, CD in the peripheral nervous system cancels reafference to protect sensors and the central nervous system from being fatigued and overwhelmed by self-generated feedback. However, cancellation also limits the feedback that contributes to an animal’s awareness of its body position and motion within the environment, the sense of proprioception. We propose that, rather than cancellation, CD to the fish lateral line organ restructures reafference to maximize proprioceptive information content. Fishes’ undulatory body motions induce reafferent feedback that can encode the body’s instantaneous configuration with respect to fluid flows. We combined experimental and computational analyses of swimming biomechanics and hair cell physiology to develop a neuromechanical model of how fish can track peak body curvature, a key signature of axial undulatory locomotion. Without CD, this computation would be challenged by sensory adaptation, typified by decaying sensitivity and phase distortions with respect to an input stimulus. We find that CD interacts synergistically with sensor polarization to sharpen sensitivity along sensors’ preferred axes. The sharpening of sensitivity regulates spiking to a narrow interval coinciding with peak reafferent stimulation, which prevents adaptation and homogenizes the otherwise variable sensor output. Our integrative model reveals a vital role of CD for ensuring precise proprioceptive feedback during undulatory locomotion, which we term external proprioception.

Animals modulate sensory processing in concert with motor actions. A study of the corollary discharge in zebrafish reveals that it modulates the sensitivity of the lateral line during swimming to prevent sensor adaptation and maintain the high-quality feedback necessary for kinematic control.     

The Mup-4 Locus in Caenorhabditis Elegans Is Essential for Hypodermal Integrity, Organismal Morphogenesis and Embryonic Body Wall Muscle Position

mup-4 is a member of a set of genes essential for correct embryonic body wall muscle cell positions in Caenorhabditis elegans. The mup-4 phenotype is variably expressed and three discrete arrest phenotypes arise during the phase of embryonic development when the worm elongates from a ball of cells to its worm shape (organismal morphogenesis). Mutants representing two of the phenotypic classes arrest without successful completion of elongation. Mutants of the third phenotypic class arrest after completion of elongation. Mutants that arrest after elongation display profound dorsal and ventral body wall muscle cell position abnormalities and a characteristic kinked body shape (the Mup phenotype) due to the muscle cell position abnormalities. Significantly, genetic mosaic analysis of mup-4 mutants demonstrates that mup-4 gene function is essential in the AB lineage, which generates most of the hypodermis (epidermis), a tissue with which muscle interacts. Consistent with the genetic mosaic data, phenotypic characterizations reveal that mutants have defects in hypodermal integrity and morphology. Our analyses support the conclusion that mup-4 is essential for hypodermal function and that this function is necessary for organismal morphogenesis and for the maintenance of body wall muscle position.     

Go reconfigure: how fish change shape as they swim and evolve

The bodies of fish change shape over propulsive, behavioral, developmental, and evolutionary time scales, a general phenomenon that we call "reconfiguration". Undulatory, postural, and form-reconfiguration can be distinguished, studied independently, and examined in terms of mechanical interactions and evolutionary importance. Using a combination of live, swimming fishes and digital robotic fish that are autonomous and self-propelled, we examined the functional relation between undulatory and postural reconfiguration in forward swimming, backward swimming, and yaw turning. To probe how postural and form reconfiguration interact, the yaw turning of leopard sharks was examined using morphometric and kinematic analyses. To test how undulatory reconfiguration might evolve, the digital robotic fish were subjected to selection for enhanced performance in a simulated ecology in which each individual had to detect and move towards a food source. In addition to the general issue of reconfiguration, these investigations are united by the fact that the dynamics of undulatory and postural reconfigurations are predicted to be determined, in part, by the structural stiffness of the fish's body. Our method defines undulatory reconfiguration as the combined, point-by-point periodic motion of the body, leaving postural reconfiguration as the combined deviations from undulatory reconfiguration. While undulatory reconfiguration appears to be the sole or primary propulsive driver, postural reconfiguration may contribute to propulsion in hagfish and it is correlated with differences in forward, and backward, swimming in lamprey. Form reconfigures over developmental time in leopard sharks in a manner that is consistent with an allometric scaling theory in which structural stiffness of the body is held constant. However, correlation of a form proxy for structural stiffness of the body suggests that body stiffness may scale in order to limit maximum postural reconfiguration during routine yaw turns. When structural stiffness and undulatory frequency are modeled as determining the tail's undulatory wave speed, both factors evolve under selection for enhanced foraging behavior in the digital fish-like robots. The methods used in making these distinctions between kinds of reconfiguration have broad applicability in fish biology, especially for quantifying complex motor behaviors in the wild and for simulating selection on behavior that leads to directional evolution of functional phenotypes.     

Caenorhabditis elegans as a chemical screening tool for the study o f neuromuscular disorders. Manual and semi-automated methods

We previously reported the use of the cheap and fast-growing nematode Caenorhabditis elegans to search for molecules, which reduce muscle degeneration in a model for Duchenne Muscular Dystrophy (DMD). We showed that Prednisone, a steroid that is generally prescribed as a palliative treatment to DMD patients, also reduced muscle degeneration in the C. elegans DMD model. We further showed that this strategy could lead to the discovery of new and unsuspected small molecules, which have been further validated in a mammalian model of DMD, i.e. the mdx mouse model. These proof-of-principles demonstrate that C. elegans can serve as a screening tool to search for drugs against neuromuscular disorders. Here, we report and discuss two methodologies used to screen chemical libraries for drugs against muscle disorders in C. elegans. We first describe a manual method used to find drugs against DMD. We further present a semi-automated method, which is currently in use for the search of drugs against the Schwartz-Jampel Syndrome (SJS). Both assays are simple to implement and can be readily transposed and/or adapted to screens against other muscle/neuromuscular diseases, which can be modeled in the worm. Finally we discuss, with respect to our experience and knowledge, the different parameters that have to be taken into account before choosing one or the other method.     

Bacterium-induced internal egg hatching frequency is predictive of life span in Caenorhabditis elegans populations

Internal egg hatching in Caenorhabditis elegans, "worm bagging," is induced by exposure to bacteria. This study demonstrates that the determination of worm bagging frequency allows for advanced insight into the degree of bacterial pathogenicity and is highly predictive of the survival of worm populations. Therefore, worm bagging frequency can be regarded as a reliable population-wide stress reporter.