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.     

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.

     

Cellular interactions in early C. elegans embryos

In normal development both the anterior and posterior blastomeres in a 2-cell C. elegans embryo produce some descendants that become muscles. We show that cellular interactions appear to be necessary in order for the anterior blastomere to produce these muscles. The anterior blastomere does not produce any muscle descendants after either the posterior blastomere or one of the daughters of the posterior blastomere is removed from the egg. Moreover, we demonstrate that a daughter of the anterior blastomere that normally does not produce muscles appears capable of generating muscles when interchanged with its sister, a cell that normally does produce muscles. Embryos develop normally after these blastomeres are interchanged, suggesting that cellular interactions play a major role in determining the fates of some cells in early embryogenesis.     

Rhythms of locomotion expressed by Limulus polyphemus, the American horseshoe crab: II. Relationship to circadian rhythms of visual sensitivity

In the laboratory, horseshoe crabs express a circadian rhythm of visual sensitivity as well as daily and circatidal rhythms of locomotion. The major goal of this investigation was to determine whether the circadian clock underlying changes in visual sensitivity also modulates locomotion. To address this question, we developed a method for simultaneously recording changes in visual sensitivity and locomotion. Although every animal (24) expressed consistent circadian rhythms of visual sensitivity, rhythms of locomotion were more variable: 44% expressed a tidal rhythm, 28% were most active at night, and the rest lacked statistically significant rhythms. When exposed to artificial tides, 8 of 16 animals expressed circatidal rhythms of locomotion that continued after tidal cycles were stopped. However, rhythms of visual sensitivity remained stable and showed no tendency to be influenced by the imposed tides or locomotor activity. These results indicate that horseshoe crabs possess at least two biological clocks: one circadian clock primarily used for modulating visual sensitivity, and one or more clocks that control patterns of locomotion. This arrangement allows horseshoe crabs to see quite well while mating during both daytime and nighttime high tides.     

A novel gain-of-function mutant of the cyclic GMP-dependent protein kinase egl-4 affects multiple physiological processes in Caenorhabditis elegans

cGMP-dependent protein kinases are key intracellular transducers of cell signaling. We identified a novel dominant mutation in the C. elegans egl-4 cGMP-dependent protein kinase (PKG) and show that this mutation causes increased normal gene activity although it is associated with a reduced EGL-4 protein level. Prior phenotypic analyses of this gain-of-function mutant demonstrated a reduced longevity and a reduced feeding behavior when the animals were left unperturbed. We characterize several additional phenotypes caused by increased gene activity of egl-4. These phenotypes include a small body size, reduced locomotion in the presence of food, a pale intestine, increased intestinal fat storage, and a decreased propensity to form dauer larvae. The multiple phenotypes of egl-4 dominant mutants are consistent with an instructive signaling role of PKG to control many aspects of animal physiology. This is among the first reported gain-of-function mutations in this enzyme of central physiological importance. In a genetic screen we have identified extragenic suppressors of this gain-of-function mutant. Thus, this mutant promises to be a useful tool for identifying downstream targets of PKG.     

Modelling Feedback Excitation,Pacemaker Properties and Sensory Switching of Electrically Coupled Brainstem Neurons Controlling Rhythmic Activity

What cellular and network properties allow reliable neuronal rhythm generation or firing that can be started and stopped by brief synaptic inputs? We investigate rhythmic activity in an electrically-coupled population of brainstem neurons driving swimming locomotion in young frog tadpoles, and how activity is switched on and off by brief sensory stimulation. We build a computational model of 30 electrically-coupled conditional pacemaker neurons on one side of the tadpole hindbrain and spinal cord. Based on experimental estimates for neuron properties, population sizes, synapse strengths and connections, we show that: long-lasting, mutual, glutamatergic excitation between the neurons allows the network to sustain rhythmic pacemaker firing at swimming frequencies following brief synaptic excitation; activity persists but rhythm breaks down without electrical coupling; NMDA voltage-dependency doubles the range of synaptic feedback strengths generating sustained rhythm. The network can be switched on and off at short latency by brief synaptic excitation and inhibition. We demonstrate that a population of generic Hodgkin-Huxley type neurons coupled by glutamatergic excitatory feedback can generate sustained asynchronous firing switched on and off synaptically. We conclude that networks of neurons with NMDAR mediated feedback excitation can generate self-sustained activity following brief synaptic excitation. The frequency of activity is limited by the kinetics of the neuron membrane channels and can be stopped by brief inhibitory input. Network activity can be rhythmic at lower frequencies if the neurons are electrically coupled. Our key finding is that excitatory synaptic feedback within a population of neurons can produce switchable, stable, sustained firing without synaptic inhibition.     

Caenorhabditis elegans neprilysin NEP-1: an effector of locomotion and pharyngeal pumping

The control of signal peptide activity by cell surface proteases is one of the main factors that regulate the development and behaviour of organisms. In mammals, neprilysins (NEPs) are known to play a key role in these processes and their inactivation can initiate cellular disorganisation, which in turn may lead to prostate cancer or Hirschsprung disease. Although the proteome of the nematode Caenorhabditis elegans has been intensively studied, very little is known about the function of neprilysins. ZK20.6 (NEP-1), the C.elegans protein with highest identity to mammalian neprilysins, is a 753 amino acid residue protein that displays all neprilysin-typical characteristics, including a short intracellular domain, a transmembrane domain and a long extracellular active domain. Here we show that the expression pattern of nep-1 is limited to pharyngeal cells and a single head neuron. Compared to wild-type, the locomotion of nep-1 knockout animals is significantly impaired, a phenotype that can be rescued by the extrachromosomal re-introduction of nep-1. This suggests that this enzyme plays an important role in the regulation of nematode locomotion. Finally, electrophysiological recording of the pharyngeal activity showed a high sensitivity of the nep-1 pharynx to serotonin (5-HT) and to the neuropeptide AF1 (C.elegans FLP-8), indicating that NEP-1 is a central component that controls the neuronal innervation of pharyngeal pumping in C.elegans.     

Multi-layered multi-pattern CPG for adaptive locomotion of humanoid robots

In this paper, we present an extended mathematical model of the central pattern generator (CPG) in the spinal cord. The proposed CPG model is used as the underlying low-level controller of a humanoid robot to generate various walking patterns. Such biological mechanisms have been demonstrated to be robust in locomotion of animal. Our model is supported by two neurophysiological studies. The first study identified a neural circuitry consisting of a two-layered CPG, in which pattern formation and rhythm generation are produced at different levels. The second study focused on a specific neural model that can generate different patterns, including oscillation. This neural model was employed in the pattern generation layer of our CPG, which enables it to produce different motion patterns—rhythmic as well as non-rhythmic motions. Due to the pattern-formation layer, the CPG is able to produce behaviors related to the dominating rhythm (extension/flexion) and rhythm deletion without rhythm resetting. The proposed multi-layered multi-pattern CPG model (MLMP-CPG) has been deployed in a 3D humanoid robot (NAO) while it performs locomotion tasks. The effectiveness of our model is demonstrated in simulations and through experimental results.     

An imbalancing act: gap junctions reduce the backward motor circuit activity to bias C. elegans for forward locomotion

A neural network can sustain and switch between different activity patterns to execute multiple behaviors. By monitoring the decision making for directional locomotion through motor circuit calcium imaging in?behaving Caenorhabditis elegans (C.?elegans), we reveal that C.?elegans determines the directionality of movements by establishing an imbalanced output between the forward and backward motor circuits and that it alters directions by switching between these imbalanced states. We further demonstrate that premotor interneurons modulate endogenous motoneuron activity to establish the output imbalance. Specifically, the UNC-7 and UNC-9 innexin-dependent premotor interneuron-motoneuron coupling prevents a balanced output state that leads to movements without directionality. Moreover, they act as shunts to decrease the backward-circuit activity, establishing a persistent bias for the high forward-circuit output state that results in the inherent preference of C.?elegans for forward locomotion. This study demonstrates that imbalanced motoneuron activity underlies directional movement and establishes gap junctions as critical modulators of the properties and outputs of neural circuits.     

Probing spinal circuits controlling walking in mammals

Locomotion in mammals is a complex motor act that involves the activation of a large number of muscles in a well-coordinated pattern. Understanding the network organization of the intrinsic spinal networks that control the locomotion, the central pattern generators, has been a challenge to neuroscientists. However, experiments using the isolated rodent spinal cord and combining electrophysiology and molecular genetics to dissect the locomotor network have started to shed new light on the network structure. In the present review, we will discuss findings that have revealed the role of designated populations of neurons for the key network functions including coordinating muscle activity and generating rhythmic activity. These findings are summarized in proposed organizational principles for the mammalian segmental CPG.     

A model of the neuro-musculo-skeletal system for human locomotion

The generation of human locomotion was examined by linking computational neuroscience with biomechanics from the perspective of nonlinear dynamical theory. We constructed a model of human locomotion, which includes a musculo-skeletal system with 8 segments and 20 muscles, a neural rhythm generator composed of 7 pairs of neural oscillators, and mechanisms for processing and transporting sensory and motor signals. Using a computer simulation, we found that locomotion emerged as a stable limit cycle that was generated by the global entrainment between the musculo-skeletal system, the neural system, and the environment. Moreover, the walking movements of the model could be compared quantitatively with those of experimental studies in humans.Part of this paper was presented to IVth International Symposium on Computer Simulation in Biomechanics, Paris, France, July 1, 1993     

Coupling between respiratory and stepping rhythms during locomotion in decerebrate cats

To determine whether and how the strength of coupling between respiratory and stepping rhythms varies depending on locomotor patterns, correlation analysis was done of diaphragmatic and gastrocnemius muscle activities. In spontaneously breathing cats decerebrated at the precollicular-post-mammillary level, tonic electrical stimulation was delivered to the mesencephalic locomotor region to induce locomotion on a treadmill. Electromyograms were recorded from the left hemidiaphragm and the bilateral gastrocnemius muscles. Various locomotor patterns were elicited by changes in the belt speed of the treadmill and in the intensity of stimulation of the mesencephalic locomotor region. Cross-correlograms between diaphragmatic and gastrocnemius activities showed that coupling was absent or weak when the cats walked slowly. The strength of locomotor-respiratory coupling tended to increase as the mean stepping interval shortened. When the animals were galloping, the respiratory rhythm was entrained 1:1 with the stepping rhythm. This study showed that the strength of coupling between respiratory and stepping rhythms varied depending on the locomotor patterns elicited, especially on whether the animals were running.     

Towards a virtual C. elegans: a framework for simulation and visualization of the neuromuscular system in a 3D physical environment

The nematode C. elegans is the only animal with a known neuronal wiring diagram, or "connectome". During the last three decades, extensive studies of the C. elegans have provided wide-ranging data about it, but few systematic ways of integrating these data into a dynamic model have been put forward. Here we present a detailed demonstration of a virtual C. elegans aimed at integrating these data in the form of a 3D dynamic model operating in a simulated physical environment. Our current demonstration includes a realistic flexible worm body model, muscular system and a partially implemented ventral neural cord. Our virtual C. elegans demonstrates successful forward and backward locomotion when sending sinusoidal patterns of neuronal activity to groups of motor neurons. To account for the relatively slow propagation velocity and the attenuation of neuronal signals, we introduced "pseudo neurons" into our model to simulate simplified neuronal dynamics. The pseudo neurons also provide a good way of visualizing the nervous system's structure and activity dynamics.     

Lung and buccal ventilation in the frog: uncoupling coupled oscillators

The frog, with two distinct ventilatory acts, provides a useful model to investigate the prospective interaction of two oscillators in generating the respiratory rhythm. Building on evidence supporting the existence of separate oscillators generating buccal and lung ventilation, we have attempted to uncouple the two rhythms in the isolated brain stem preparation. Opioid preferentially inhibits the lung rhythm, suggesting an uncoupling of the lung from the buccal oscillator. Reduction of the superfusate chloride concentration alters both the buccal and the lung rhythms. Joint application of opioid and reduced-chloride superfusate leads to an increase in the variability of the buccal burst-to-lung burst intervals. This increase in variability suggests that chloride-mediated mechanisms are involved in coupling the buccal oscillator to the lung oscillator. Given the results from these interventions, we propose a simple schematic model of the frog respiratory rhythm generator, outlining the coupling of the lung and buccal oscillators.     

Tyramine Functions independently of octopamine in the Caenorhabditis elegans nervous system

Octopamine biosynthesis requires tyrosine decarboxylase to convert tyrosine into tyramine and tyramine beta-hydroxylase to convert tyramine into octopamine. We identified and characterized a Caenorhabditis elegans tyrosine decarboxylase gene, tdc-1, and a tyramine beta-hydroxylase gene, tbh-1. The TBH-1 protein is expressed in a subset of TDC-1-expressing cells, indicating that C. elegans has tyraminergic cells that are distinct from its octopaminergic cells. tdc-1 mutants have behavioral defects not shared by tbh-1 mutants. We show that tyramine plays a specific role in the inhibition of egg laying, the modulation of reversal behavior, and the suppression of head oscillations in response to anterior touch. We propose a model for the neural circuit that coordinates locomotion and head oscillations in response to anterior touch. Our findings establish tyramine as a neurotransmitter in C. elegans, and we suggest that tyramine is a genuine neurotransmitter in other invertebrates and possibly in vertebrates as well.     

Evolution of locomotion in arachnida: The hydraulic pressure pump of the giant whipscorpion,Mastigoproctus Giganteus (Uropygi)

Many arachnids lack extensor muscles at the femoropatellar (knee) joint of their legs and extend this joint with hydraulic pressure during locomotion. Pressure is generated through compression of the prosoma, but there is disagreement about which muscles are involved in this process. Many arachhnologists consider contraction of the musculi laterales, a group of modified extrinsic leg muscles, as the cause of high prosomal pressure and regard hydraulic extension as a derived feature. However, integration of results from phylogenetic and comparative anatomical studies supports the view that hydraulic extension is primitive in Arachnida and that fluid pressure is generated by contraction of endosternal suspensor muscles. The functional predictions of the musculi laterales and endosternite hypotheses were tested by measuring muscle activity and prosomal pressure during unrestrained locomotion in a primitively “extensorless” arachnid, the giant whipscorpion. The results corroborate the endosternite model and refute the musculi laterales model. Changes in the prosomal pressure baseline were correlated with changes in endosternal muscle activity, while the musculi laterales fired in a step-coupled pattern of discrete bursts that appeared to be incapable of generating the pressure observed during locomotion. Step-coupled fluctuations in prosomal pressure were observed but were apparently caused by rapid flexing of the femoropatellar joints of the fourth leg pair rather than contraction of the musculi laterales.     

Membrane and cellular properties in oscillating networks: implications for respiration

Because of a number of major advances in the past one to two decades, there is little doubt that the inherent cellular and membrane properties of neurons in an oscillating network play an important role in shaping the output of that network. There are a number of such examples in vertebrate and invertebrate systems. In this review, we present some of the newer methods that have been used in the identification of membrane properties and detail some cellular studies performed in both vertebrate (locomotion and sleep/waking rhythms) and invertebrate network systems (escape swimming in Tritonia diomedia and pyloric rhythm in Panulirus interruptus). Studies examining the cellular or membrane properties of respiratory neurons have been scarce until recently. The importance of these properties in dictating respiratory rhythm generation and output in the mature and immature animal is not yet known; however, we put this issue in perspective by building a parallel between mammalian respiration and other vertebrate networks that have been better investigated and characterized.     

Effects of the novel anthelmintic emodepside on the locomotion, egg-laying behaviour and development of Caenorhabditis elegans

Emodepside, a cyclooctadepsipeptide, is a broad-spectrum anthelmintic previously shown to paralyse body wall muscle and pharyngeal muscle in the model nematode Caenorhabditis elegans. We demonstrate that wild-type C. elegans L4 are less sensitive than adults to emodepside in two independent assays of locomotor behaviour: body bend generation on agar (adult IC(50) 3.7 nM, L4 IC(50) 13.4 nM) and thrashing behaviour in liquid (thrashing behaviour as a % of controls after 1h in 10 microM emodepside: adults 16%, L4 worms 48%). We also show that continuous exposure of wild-type C. elegans to emodepside throughout the life-cycle from egg onwards, slows worm development, an effect that is emodepside concentration-dependent. The rate of worm-hatching from eggs on agar plates containing emodepside was not significantly different from controls, suggesting that it is development post-hatching rather than hatching itself that is affected by the drug. Emodepside also inhibits wild-type C. elegans egg-laying, with acute exposure to the drug at 500 nM resulting in an almost total inhibition within the first hour. However, the rate of egg production was not inhibited and therefore emodepside-treated worms became bloated with eggs, eventually rupturing. This suggests that the effect of emodepside on reproduction is not due to an inhibition of egg production but rather a paralytic effect on the egg-laying muscles. These results, when coupled with previous research, suggest that emodepside interferes with signalling at the neuromuscular junction on the body-wall muscles (Willson et al., 2003), pharynx (Willson et al., 2004) and egg-laying muscles and thus inhibits three important physiological functions: locomotion, feeding and reproduction.