Information Flow through a Model of the C. elegans Klinotaxis Circuit

Understanding how information about external stimuli is transformed into behavior is one of the central goals of neuroscience. Here we characterize the information flow through a complete sensorimotor circuit: from stimulus, to sensory neurons, to interneurons, to motor neurons, to muscles, to motion. Specifically, we apply a recently developed framework for quantifying information flow to a previously published ensemble of models of salt klinotaxis in the nematode worm Caenorhabditis elegans. Despite large variations in the neural parameters of individual circuits, we found that the overall information flow architecture circuit is remarkably consistent across the ensemble. This suggests structural connectivity is not necessarily predictive of effective connectivity. It also suggests information flow analysis captures general principles of operation for the klinotaxis circuit. In addition, information flow analysis reveals several key principles underlying how the models operate: (1) Interneuron class AIY is responsible for integrating information about positive and negative changes in concentration, and exhibits a strong left/right information asymmetry. (2) Gap junctions play a crucial role in the transfer of information responsible for the information symmetry observed in interneuron class AIZ. (3) Neck motor neuron class SMB implements an information gating mechanism that underlies the circuit’s state-dependent response. (4) The neck carries more information about small changes in concentration than about large ones, and more information about positive changes in concentration than about negative ones. Thus, not all directions of movement are equally informative for the worm. Each of these findings corresponds to hypotheses that could potentially be tested in the worm. Knowing the results of these experiments would greatly refine our understanding of the neural circuit underlying klinotaxis.     

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.     

A Model of Drosophila Larva Chemotaxis

Detailed observations of larval Drosophila chemotaxis have characterised the relationship between the odour gradient and the runs, head casts and turns made by the animal. We use a computational model to test whether hypothesised sensorimotor control mechanisms are sufficient to account for larval behaviour. The model combines three mechanisms based on simple transformations of the recent history of odour intensity at the head location. The first is an increased probability of terminating runs in response to gradually decreasing concentration, the second an increased probability of terminating head casts in response to rapidly increasing concentration, and the third a biasing of run directions up concentration gradients through modulation of small head casts. We show that this model can be tuned to produce behavioural statistics comparable to those reported for the larva, and that this tuning results in similar chemotaxis performance to the larva. We demonstrate that each mechanism can enable odour approach but the combination of mechanisms is most effective, and investigate how these low-level control mechanisms relate to behavioural measures such as the preference indices used to investigate larval learning behaviour in group assays.     

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.     

The Parallel Worm Tracker: a platform for measuring average speed and drug-induced paralysis in nematodes

Background

Caenorhabditis elegans locomotion is a simple behavior that has been widely used to dissect genetic components of behavior, synaptic transmission, and muscle function. Many of the paradigms that have been created to study C. elegans locomotion rely on qualitative experimenter observation. Here we report the implementation of an automated tracking system developed to quantify the locomotion of multiple individual worms in parallel.

Methodology/Principal Findings

Our tracking system generates a consistent measurement of locomotion that allows direct comparison of results across experiments and experimenters and provides a standard method to share data between laboratories. The tracker utilizes a video camera attached to a zoom lens and a software package implemented in MATLAB®. We demonstrate several proof-of-principle applications for the tracker including measuring speed in the absence and presence of food and in the presence of serotonin. We further use the tracker to automatically quantify the time course of paralysis of worms exposed to aldicarb and levamisole and show that tracker performance compares favorably to data generated using a hand-scored metric.

Conclusions/Signficance

Although this is not the first automated tracking system developed to measure C. elegans locomotion, our tracking software package is freely available and provides a simple interface that includes tools for rapid data collection and analysis. By contrast with other tools, it is not dependent on a specific set of hardware. We propose that the tracker may be used for a broad range of additional worm locomotion applications including genetic and chemical screening.     

Multiplicative multi-fractal modeling of electromyography signals for discerning neuropathic conditions

In this paper, we present a new method for multi-scale analysis of electromyography signals based on an interesting fractal process known as multiplicative cascade multi-fractal. Using simulated needle electromyography signals, we show this method provides a means for discrimination of normal and neuropathic electromyography signals. We also present experimental results that show the new parameters, computed using multiplicative cascade multi-fractal modeling, are more robust than the conventional signal parameter, number of turns, in the presence of additive noise. Results of multiplicative cascade multi-fractal modeling are consistent with other multi-scale approaches; advantages and differences are high lighted.     

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.

     

Grip and limb force limits to turning performance in competition horses

Manoeuverability is a key requirement for successful terrestrial locomotion, especially on variable terrain, and is a deciding factor in predator-prey interaction. Compared with straight-line running, bend running requires additional leg force to generate centripetal acceleration. In humans, this results in a reduction in maximum speed during bend running and a published model assuming maximum limb force as a constraint accurately predicts how much a sprinter must slow down on a bend given his maximum straight-line speed. In contrast, greyhounds do not slow down or change stride parameters during bend running, which suggests that their limbs can apply the additional force for this manoeuvre. We collected horizontal speed and angular velocity of heading of horses while they turned in different scenarios during competitive polo and horse racing. The data were used to evaluate the limits of turning performance. During high-speed turns of large radius horizontal speed was lower on the bend, as would be predicted from a model assuming a limb force limit to running speed. During small radius turns the angular velocity of heading decreased with increasing speed in a manner consistent with the coefficient of friction of the hoof-surface interaction setting the limit to centripetal force to avoid slipping.     

Turning field size and its effects upon computer-simulated klinotactic orientation

The turning field is defined in the context of klinotaxis as the angular region(s) into which an organism may direct itself at any point in time and space while orienting within a stimulus gradient. The turning field size determines the size distribution of turns an organism can make during klinotaxis. Changes in turning field size affect the efficiency of klinotactic source location as measured by computer simulations of ideal behaviors. The optimal field size lies between 90 and 150 degrees. Turning field size also affects the appearance of search paths made by organisms locating an attractant source. The significance of turning field size is discussed and the described klinotactic model is proposed as a predictive model for orientation research.     

Bending amplitude - a new quantitative assay of C. elegans locomotion: identification of phenotypes for mutants in genes encoding muscle focal adhesion components

The nematode Caenorhabditis elegans uses striated muscle in its body wall for locomotion. The myofilament lattice is organized such that all the thin filament attachment structures (dense bodies, analogous to Z-disks) and thick filament organizing centers (M-lines) are attached to the muscle cell membrane. Thus, the force of muscle contraction is transmitted through these structures and allows locomotion of the worm. Dense bodies and M-lines are compositionally similar to focal adhesions and costameres, and are based on integrin and associated proteins. Null mutants for many of the newly discovered dense body and M-line proteins do not have obvious locomotion defects when observed casually, or when assayed by counting the number of times a worm moves back and forth in liquid. We hypothesized that many of these proteins, located as they are in muscle focal adhesions, function in force transmission, but we had not used an appropriate or sufficiently sensitive assay to reveal this function. Recently, we have developed a new quantitative assay of C. elegans locomotion that measures the maximum bending amplitude of an adult worm as it moves backwards. The assay had been used to reveal locomotion defects for null mutants of genes encoding ATN-1 (α-actinin) and PKN-1 (protein kinase N). Here, we describe the details of this method, and apply it to 21 loss of function mutants in 17 additional genes, most of which encode components of muscle attachment structures. As compared to wild type, mutants in 11 genes were found to have less ability to bend, and mutants in one gene were found to have greater ability to bend. Loss of function mutants for eight proteins had been reported to have normal locomotion (ZYX-1 (zyxin), ALP-1 (Enigma), DIM-1, SCPL-1), or locomotion that was not previously investigated (FRG-1 (FRG1), KIN-32 (focal adhesion kinase), LIM-8), or had only slightly decreased locomotion (PFN-3 (profilin)).     

Rhizobium meliloti swims by unidirectional, intermittent rotation of right-handed flagellar helices.

The 5 to 10 peritrichously inserted complex flagella of Rhizobium meliloti MVII-1 were found to form right-handed flagellar bundles. Bacteria swam at speeds up to 60 microns/s, their random three-dimensional walk consisting of straight runs and quick directional changes (turns) without the vigorous angular motion (tumbling) seen in swimming Escherichia coli cells. Observations of R. meliloti cells tethered by a single flagellar filament revealed that flagellar rotation was exclusively clockwise, interrupted by very brief stops (shorter than 0.1 s), typically every 1 to 2 s. Swimming bacteria responded to chemotactic stimuli by extending their runs, and tethered bacteria responded by prolonged intervals of clockwise rotation. Moreover, the motility tracks of a generally nonchemotactic ("smooth") mutant consisted of long runs without sharp turns, and tethered mutant cells showed continuous clockwise rotation without detectable stops. These observations suggested that the runs of swimming cells correspond to clockwise flagellar rotation, and the turns correspond to the brief rotation stops. We propose that single rotating flagella (depending on their insertion point on the rod-shaped bacterial surface) can reorient a swimming cell whenever the majority of flagellar motors stop.     

Trunk orientation causes asymmetries in leg function in small bird terrestrial locomotion

In contrast to the upright trunk in humans, trunk orientation in most birds is almost horizontal (pronograde). It is conceivable that the orientation of the heavy trunk strongly influences the dynamics of bipedal terrestrial locomotion. Here, we analyse for the first time the effects of a pronograde trunk orientation on leg function and stability during bipedal locomotion. For this, we first inferred the leg function and trunk control strategy applied by a generalized small bird during terrestrial locomotion by analysing synchronously recorded kinematic (three-dimensional X-ray videography) and kinetic (three-dimensional force measurement) quail locomotion data. Then, by simulating quail gaits using a simplistic bioinspired numerical model which made use of parameters obtained in in vivo experiments with real quail, we show that the observed asymmetric leg function (left-skewed ground reaction force and longer leg at touchdown than at lift-off) is necessary for pronograde steady-state locomotion. In addition, steady-state locomotion becomes stable for specific morphological parameters. For quail-like parameters, the most common stable solution is grounded running, a gait preferred by quail and most of the other small birds. We hypothesize that stability of bipedal locomotion is a functional demand that, depending on trunk orientation and centre of mass location, constrains basic hind limb morphology and function, such as leg length, leg stiffness and leg damping.     

Underwater locomotion strategy by a benthic pennate diatom Navicula sp.

The mechanism of diatom locomotion has been widely researched but still remains a hypothesis. There are several questionable points on the prevailing model proposed by Edgar, and some of the observed phenomena cannot be completely explained by this model. In this paper, we undertook detailed investigations of cell structures, locomotion, secreted mucilage, and bending deformation for a benthic pennate diatom Navicula species. According to these broad evidences, an updated locomotion model is proposed. For Navicula sp., locomotion is realized via two or more pseudopods or stalks protruded out of the frustules. The adhesion can be produced due to the pull-off of one pseudopod or stalk from the substratum through extracellular polymeric substances. And the positive pressure is generated to balance the adhesion because of the push-down of another pseudopod or stalk onto the substratum. Because of the positive pressure, friction is generated, acting as a driving force of locomotion, and the other pseudopod or stalk can detach from the substratum, resulting in the locomotion. Furthermore, this model is validated by the force evaluation and can better explain observed phenomena. This updated model would provide a novel aspect on underwater locomotion strategy, hence can be useful in terms of artificial underwater locomotion devices.     

Modelling of microscale patch encounter by chemotactic protozoa

A model of protozoan chemotaxis, based on the rate of change of chemoreceptor occupancy, was used to analyse the efficiency of chemotaxis in a variety of situations. Simulated swimming behaviour replicated patterns observed experimentally. These were classified into three forms of chemosensory behaviour; run-tumble, steered turning, and helical klinotaxis. All three could be simulated from a basic model of chemotaxis by modifying memory times and rotational velocities. In order to steer during helical klinotaxis, the cell must have a short term memory for responding to a signal within a fraction of the time period of the helix. Steered turning was identified as a form where cells react to negative changes in concentration by steering around the turn to swim back up the gradient. All 3 forms were quite effective for encountering targets within the response radius. A response to negative changes in concentration, experienced when the cell is moving away from a target, was found to be important in the absence of periodic changes in swimming direction. The frequency of patch encounter at a fixed density was calculated to be roughly proportional to swimming speed. On the basis of the model, cells are only able to sense point sources within a radius of a few mm. However, even a response radius of 1 mm is enough to increase encounter probability of otherwise minute targets by 2 orders of magnitude. The mean time for patch encounter was calculated to be an exponential function of the mean distance between patches. This results in a very sharp threshold at approximately 6 cm, above which they are not encountered by protozoa within time periods of several days.     

Adaptation of the nematode Caenorhabditis elegans to medium high temperature

Action of high temperature (36°C) on the nematode Caenorhabditis elegans organism was manifested in errors of the motor program of swimming induced by a mechanical stimulus (37 ± 2 min), the complete, but reversible cessation of locomotion (57 ± 3 min), while damage—in thermal death (215 ± 5 min). Addition into medium of atropine (10^?8–10^?9 M) and chemical stimuli (10^?8–10^?6 cAMP or lysine) causes considerable changes of thermal stability of the worm locomotion. Analysis of these data has shown that the cause of the reversible thermal disturbance of the C. elegans locomotion is disintegration of neurons in the nervous centers regulating behavior. The obtained data indicate the presence in the simple organism of C. elegans of adaptations increasing stability of processes of integration of neurons to a high temperature, which were found earlier in arthropods and vertebrates.     

True Chemotaxis in Oxygen Gradients of the Sulfur-Oxidizing Bacterium Thiovulum majus

Observations of free-swimming Thiovulum majus cells show that these bacteria exhibit a phobic response as well as true chemotaxis in oxygen gradients. Both phenomena of their chemotactic behavior are integrated into a single model of helical klinotaxis, which is demonstrated by computer simulations.     

Dynamics of Two Picophytoplankton Groups in Mediterranean Sea: Analysis of the Deep Chlorophyll Maximum by a Stochastic Advection-Reaction-Diffusion Model

A stochastic advection-reaction-diffusion model with terms of multiplicative white Gaussian noise, valid for weakly mixed waters, is studied to obtain the vertical stationary spatial distributions of two groups of picophytoplankton, i.e., picoeukaryotes and Prochlorococcus, which account about for 60% of total chlorophyll on average in Mediterranean Sea. By numerically solving the equations of the model, we analyze the one-dimensional spatio-temporal dynamics of the total picophytoplankton biomass and nutrient concentration along the water column at different depths. In particular, we integrate the equations over a time interval long enough, obtaining the steady spatial distributions for the cell concentrations of the two picophytoplankton groups. The results are converted into chlorophyll a and divinil chlorophyll a concentrations and compared with experimental data collected in two different sites of the Sicily Channel (southern Mediterranean Sea). The comparison shows that real distributions are well reproduced by theoretical profiles. Specifically, position, shape and magnitude of the theoretical deep chlorophyll maximum exhibit a good agreement with the experimental values.     

Separation of propulsive and adhesive traction stresses in locomoting keratocytes

Strong, actomyosin-dependent, pinching tractions in steadily locomoting (gliding) fish keratocytes revealed by traction imaging present a paradox, since only forces perpendicular to the direction of locomotion are apparent, leaving the actual propulsive forces unresolved. When keratocytes become transiently "stuck" by their trailing edge and adopt a fibroblast-like morphology, the tractions opposing locomotion are concentrated into the tail, leaving the active pinching and propulsive tractions clearly visible under the cell body. Stuck keratocytes can develop approximately 1 mdyn (10,000 pN) total propulsive thrust, originating in the wings of the cell. The leading lamella develops no detectable propulsive traction, even when the cell pulls on its transient tail anchorage. The separation of propulsive and adhesive tractions in the stuck phenotype leads to a mechanically consistent hypothesis that resolves the traction paradox for gliding keratocytes: the propulsive tractions driving locomotion are normally canceled by adhesive tractions resisting locomotion, leaving only the pinching tractions as a resultant. The resolution of the traction pattern into its components specifies conditions to be met for models of cytoskeletal force production, such as the dynamic network contraction model (Svitkina, T.M., A.B. Verkhovsky, K.M. McQuade, and G.G. Borisy. 1997. J. Cell Biol. 139:397-415). The traction pattern associated with cells undergoing sharp turns differs markedly from the normal pinching traction pattern, and can be accounted for by postulating an asymmetry in contractile activity of the opposed lateral wings of the cell.     

A Biomimetic Approach to Robot Locomotion in Unstructured and Slippery Environments

While much attention has been given to bio-robotics in recent years, not much of this has been given to the challenging subject of locomotion in slippery conditions. This study begins to rectify this by proposing a biomimetic approach to generating the friction required to give sufficient propulsive force on a slippery substrate. We took inspiration from a successful biological solution-that of applying hair-like structures to the propulsive appendages, similar to the setae found in nereid polychaetes living in muddy habitats. We began by examining the morphology and the mean locomotion parameters of one of the most common nereids: Nereis diversicolor. Following this study, we designed and fabricated a robotic system with appendages imitating the biological shape found in the worm. A flexible control system was developed to allow most of the locomotion parameters observed in the real worm to be applied to the robot. Experiments on three different natural substrates ranging from fine sand to gravel showed