Neural Basis of Stimulus-Angle-Dependent Motor Control of Wind-Elicited Walking Behavior in the Cricket Gryllus bimaculatus

Crickets exhibit oriented walking behavior in response to air-current stimuli. Because crickets move in the opposite direction from the stimulus source, this behavior is considered to represent ‘escape behavior’ from an approaching predator. However, details of the stimulus-angle-dependent control of locomotion during the immediate phase, and the neural basis underlying the directional motor control of this behavior remain unclear. In this study, we used a spherical-treadmill system to measure locomotory parameters including trajectory, turn angle and velocity during the immediate phase of responses to air-puff stimuli applied from various angles. Both walking direction and turn angle were correlated with stimulus angle, but their relationships followed different rules. A shorter stimulus also induced directionally-controlled walking, but reduced the yaw rotation in stimulus-angle-dependent turning. These results suggest that neural control of the turn angle requires different sensory information than that required for oriented walking. Hemi-severance of the ventral nerve cords containing descending axons from the cephalic to the prothoracic ganglion abolished stimulus-angle-dependent control, indicating that this control required descending signals from the brain. Furthermore, we selectively ablated identified ascending giant interneurons (GIs) in vivo to examine their functional roles in wind-elicited walking. Ablation of GI8-1 diminished control of the turn angle and decreased walking distance in the initial response. Meanwhile, GI9-1b ablation had no discernible effect on stimulus-angle-dependent control or walking distance, but delayed the reaction time. These results suggest that the ascending signals conveyed by GI8-1 are required for turn-angle control and maintenance of walking behavior, and that GI9-1b is responsible for rapid initiation of walking. It is possible that individual types of GIs separately supply the sensory signals required to control wind-elicited walking.     

Biased random walk models for chemotaxis and related diffusion approximations

Summary Stochastic models of biased random walk are discussed, which describe the behavior of chemosensitive cells like bacteria or leukocytes in the gradient of a chemotactic factor. In particular the turning frequency and turn angle distributions are derived from certain biological hypotheses on the background of related experimental observations. Under suitable assumptions it is shown that solutions of the underlying differential-integral equation approximately satisfy the well-known Patlak-Keller-Segel diffusion equation, whose coefficients can be expressed in terms of the microscopic parameters. By an appropriate energy functional a precise error estimation of the diffusion approximation is given within the framework of singular perturbation theory.     

Unidirectional motility of Escherichia coli in restrictive capillaries.

In a 6-microns capillary filled with buffer and in the absence of any chemotactic stimuli, Escherichia coli K-12 cells swim persistently in only one direction. This behavior of E. coli can be simply explained by means of the length and relative rigidity of their flagella. Single-cell motility parameters--swimming speed, turn angle, and run length time--were measured. Compared with the motility parameters measured in bulk phase, turn angle was influenced because of the effect of the geometrical restriction.     

Bacterial chemotaxis transverse to axial flow in a microfluidic channel

Swimming bacteria sense and respond to chemical signals in their environment. Chemotaxis is the directed migration of a bacterial population toward increasing concentrations of a chemical that they perceive to be beneficial to their survival. Bacteria that are indigenous to groundwater environments exhibit chemotaxis toward chemical contaminants such as hydrocarbons, which they are also able to degrade. This phenomenon may facilitate bioremediation processes by bringing bacteria into closer proximity to these contaminants. A microfluidic device was assembled to study chemotaxis transverse to advective flow. Using a T-shaped channel design (T-sensor), two fluid streams were brought into contact by impinging flow. They then flowed adjacent to each other along a transparent channel. An advantage to this design is that it allows real-time visualization of bacterial distributions within the channel. Under laminar flow conditions a chemotactic driving force was created perpendicular to the direction of flow by diffusion of the chemical attractant from one input stream to the other. A comparison of the chemotactic band behavior in the absence and presence of flow showed that fluid velocity did not significantly impede chemotactic migration in the transverse direction.     

Mathematical analysis of cell-target encounter rates in three dimensions. Effect of chemotaxis.

Efficient and rapid immune response upon challenge by an infectious agent is vital to host defense. The encounter of leukocytes (white blood cells of the immune system) with their targets is the first step in this response. Analysis of the kinetics of this process is essential not only to understanding dynamic behavior of the immune response, but also to elucidating the consequences of many leukocyte functional abnormalities. The motion of leukocytes in the presence of targets typically involves a directed, or chemotactic component. These immune cells orient the direction of their motion in the presence of gradients in chemical attractants generated by pathogens. Fisher and Lauffenburger (1987. Biophys. J. 51:705-716) developed a model for macrophage/bacterium encounter in two dimensions which includes chemotaxis, and applied it to the particular system of alveolar macrophages (phagocytic leukocytes on the lung surface). Their model showed that macrophage/target encounter is likely the rate-limiting step in clearance of bacteria from the lung surface (Fisher, E. S., D. A. Lauffenburger, and R. P. Daniele. 1988. Am. Rev. Resp. Dis. 137:1129-1134). We have extended this model to analyze the effects of cell motility properties and geometric parameters on cell-target encounter in three dimensions. The differential equation governing encounter time in three dimensions is essentially the same as that in two dimensions, except for changed probability values. Our results show that more highly directed motion is necessary in three dimensions to achieve substantially decreased encounter times than in two dimensions, because of the increased search dimensionality. These general results were applied to the particular system of neutrophils operating in three dimensions in response to a bacterial challenge in connective tissue. Our results provide a plausible rationalization for both the chemotactic and chemokinetic behavior observed in neutrophils. That is, these cells exhibit in vitro a greater chemotactic bias and a more dramatic variation of speed with attractant concentration than alveolar macrophages, and our results indicate that these behaviors can have a greater influence in three-dimensional connective tissue infection situations than in two-dimensional lung surface infection cases. In addition, we show that encounter apparently is not generally the rate-limiting step in this neutrophil response. These findings have important implications for correlating in vitro measured defects in cell motility and chemotaxis properties with in vivo functions of host defense against infection.     

Thrombin chemotactic stimulation of HL-60 cells: studies on thrombin responsiveness as a function of differentiation

Thrombin, a major procoagulant enzyme and growth factor, is also selectively chemotactic for monocytes and macrophages but not for neutrophils. This effect stands in contrast to other well-known chemotactic agents such as fMet-Leu-Phe, C5a fragments, and LTB4, which stimulate directed cell movement in both cell types, and have important physiological implications. The human leukemic cell line HL-60, which is capable of differentiating either along granulocytic or monocytic lineages, was therefore used to explore the development of this selective monocyte/macrophage chemotactic response to thrombin. Esterolytically inactive DIP-alpha-thrombin, as well as the thrombin-derived chemotactic peptide CB67-129, elicits a dose-dependent chemotactic response in HL-60 cells differentiated to monocytelike cells by treatment with 1,25(OH)2D3 (HL-60/mono), whereas no such response is evident in either undifferentiated HL-60 cells or in cells differentiated into granulocytes by treatment with DMSO (HL-60/gran). Similarly, early events which characterize stimulation of inflammatory cells by chemotactic agents are also evident, but only in monocyte-differentiated cells. In HL-60/mono, thrombin selectively stimulates rapid cytosolic Ca2+ elevation as well as rapid cytoskeletal association of cytosolic actin. Following thrombin stimulation, maximal actin association in these cells occurs within 30 sec (declining to basal levels at the end of 5 min), and maximal Ca2+ elevations are also evident within 15-20 sec, suggesting a temporal relationship between these two events. Thus, the events accompanying stimulation of HL-60/mono by thrombin are characteristic of those seen following stimulation of inflammatory cells by chemotaxins, with a major difference being the selectivity of thrombin as a chemotaxin for cells of macrophage/monocytic lineage. The selective chemotactic responsiveness of HL-60/mono to thrombin appears to relate to the development of specific receptors on these cells as part of monocytic differentiation: HL-60/mono (but HL-60/gran nor undifferentiated HL-60) are capable of significant specific 125-I-labeled alpha-thrombin-binding (ka approximately 20 nM), and possess an estimated 400,000 thrombin-binding sites per cell. Our findings further suggest that the thrombin response of HL-60 and particularly the expression of thrombin receptors on these cells may serve as a useful model system for exploring the biology of monocyte/macrophage differentiation.     

Biased reorientation in the chemotaxis of peritrichous bacteria Salmonella enterica serovar Typhimurium

Many kinds of peritrichous bacteria that repeat runs and tumbles by using multiple flagella exhibit chemotaxis by sensing a difference in the concentration of the attractant or repellent between two adjacent time points. If a cell senses that the concentration of an attractant has increased, their flagellar motors decrease the switching frequency from counterclockwise to clockwise direction of rotation, which causes a longer run in swimming up the concentration gradient than swimming down. We investigated the turn angle in tumbles of peritrichous bacteria swimming across the concentration gradient of a chemoattractant because the change in the switching frequency in the rotational direction may affect the way tumbles. We tracked several hundreds of runs and tumbles of single cells of Salmonella enterica serovar Typhimurium in the concentration gradient of L-serine and found that the turn angle depends on the concentration gradient that the cell senses just before the tumble. The turn angle is biased toward a smaller value when the cells swim up the concentration gradient, whereas the distribution of the angle is almost uniform (random direction) when the cells swim down the gradient. The effect of the observed bias in the turn angle on the degree of chemotaxis was investigated by random walk simulation. In the concentration field where attractants diffuse concentrically from the point source, we found that this angular distribution clearly affects the reduction of the mean-square displacement of the cell that has started at the attractant source, that is, the bias in the turn angle distribution contributes to chemotaxis in peritrichous bacteria.     

Bias in the gradient-sensing response of chemotactic cells

We apply linear stability theory and perform perturbation studies to better characterize, and to generate new experimental predictions from, a model of chemotactic gradient sensing in eukaryotic cells. The model uses reaction-diffusion equations to describe 3(') phosphoinositide signaling and its regulation at the plasma membrane. It demonstrates a range of possible gradient-sensing mechanisms and captures such characteristic behaviors as strong polarization in response to static gradients, adaptation to differing mean levels of stimulus, and plasticity in response to changing gradients. An analysis of the stability of polarized steady-state solutions indicates that the model is most sensitive to off-axis perturbations. This biased sensitivity is also reflected in responses to localized external stimuli, and leads to a clear experimental prediction, namely, that a cell which is polarized in a background gradient will be most sensitive to transient point-source stimuli lying within a range of angles that are oblique with respect to the polarization axis. Stimuli at angles below this range will elicit responses whose directions overshoot the stimulus angle, while responses to stimuli applied at larger angles will undershoot the stimulus angle. We argue that such a bias is likely to be a general feature of gradient sensing in highly motile cells, particularly if they are optimized to respond to small gradients. Finally, an angular bias in gradient sensing might lead to preferred turn angles and zigzag movements of cells moving up chemotactic gradients, as has been noted under certain experimental conditions.     

Intracellular Encoding of Spatiotemporal Guidance Cues in a Self-Organizing Signaling System for Chemotaxis in Dictyostelium Cells

Even in the absence of guidance cues, chemotactic cells are often spontaneously motile, which should accompany a spontaneous symmetry breaking inside the cells. A shallow chemoattractant gradient can induce these cells to move directionally without much change in cell morphology. As the gradient becomes steeper, the accuracy of chemotaxis increases. It is not clear how the steepness is expressed or encoded internally in the signaling network, which in turn coordinately activates the motile apparatus for chemotaxis. In Dictyostelium cells, self-organizing polarization activities in the signaling network have been reported. In this paper, we conducted a theoretical study of the response of this self-organizing system to guidance cues. Our analyses indicate that self-organizing systems respond sharply to a shallow external gradient by increasing the precision of polarity direction and modulating the frequency of self-polarization. We also show how the precision increase and frequency modulation are achieved. Our results indicate that self-organizing activity, independent of external cues, is the basis for the sensitive and robust response to shallow gradients. Finally, we show that the system can sense the direction of space-time waves of a stimulus, for which Dictyostelium cells exhibit chemotaxis in the developmental process.     

Intracellular Encoding of Spatiotemporal Guidance Cues in a Self-Organizing Signaling System for Chemotaxis in Dictyostelium Cells

Even in the absence of guidance cues, chemotactic cells are often spontaneously motile, which should accompany a spontaneous symmetry breaking inside the cells. A shallow chemoattractant gradient can induce these cells to move directionally without much change in cell morphology. As the gradient becomes steeper, the accuracy of chemotaxis increases. It is not clear how the steepness is expressed or encoded internally in the signaling network, which in turn coordinately activates the motile apparatus for chemotaxis. In Dictyostelium cells, self-organizing polarization activities in the signaling network have been reported. In this paper, we conducted a theoretical study of the response of this self-organizing system to guidance cues. Our analyses indicate that self-organizing systems respond sharply to a shallow external gradient by increasing the precision of polarity direction and modulating the frequency of self-polarization. We also show how the precision increase and frequency modulation are achieved. Our results indicate that self-organizing activity, independent of external cues, is the basis for the sensitive and robust response to shallow gradients. Finally, we show that the system can sense the direction of space-time waves of a stimulus, for which Dictyostelium cells exhibit chemotaxis in the developmental process.     

Interaction of Motility,Directional Sensing,and Polarity Modules Recreates the Behaviors of Chemotaxing Cells

Chemotaxis involves the coordinated action of separable but interrelated processes: motility, gradient sensing, and polarization. We have hypothesized that these are mediated by separate modules that account for these processes individually and that, when combined, recreate most of the behaviors of chemotactic cells. Here, we describe a mathematical model where the modules are implemented in terms of reaction-diffusion equations. Migration and the accompanying changes in cellular morphology are demonstrated in simulations using a mechanical model of the cell cortex implemented in the level set framework. The central module is an excitable network that accounts for random migration. The response to combinations of uniform stimuli and gradients is mediated by a local excitation, global inhibition module that biases the direction in which excitability is directed. A polarization module linked to the excitable network through the cytoskeleton allows unstimulated cells to move persistently and, for cells in gradients, to gradually acquire distinct sensitivity between front and back. Finally, by varying the strengths of various feedback loops in the model we obtain cellular behaviors that mirror those of genetically altered cell lines.     

Extracellular matrix-mediated chemotaxis can impede cell migration

Cells use a combination of changes in adhesion, proteolysis and motility (directed and random) during the process of migration. Proteolysis of the extracellular matrix (ECM) results in thecreation of haptotactic gradients which cells use to move in a directed fashion. The proteolytic creation of these gradients also results in the production of digested fragments of ECM. In this study we show that in the human fibrosarcoma cell line HT1080, matrix metalloproteinase-2(MMP-2)-digested fragments of fibronectin exert a chemotactic pull stronger than that of undigested fibronectin. During invasion, this gradient of ECM fragments is established in the wake of an invading cell, running counter to the direction of invasion. The resultant chemotactic pull is anti-invasive, contrary to the traditional view of the role of chemotaxis in invasion. Uncontrolled ECM degradation by high concentrations of MMP can thus result in steep gradients of ECM fragments, which run against the direction of invasion. Consequently, the invasive potential of a cell depends on MMP production in a biphasic mannerimplying that MMP inhibitors will upregulate invasion in high-MMPexpressing cells. Hence the therapeutic use of protease inhibitors against tumours expressing high levels of MMP could produce an augmentation of invasion.     

Extracellular Matrix Regulates UNC-6 (Netrin) Axon Guidance by Controlling the Direction of Intracellular UNC-40 (DCC) Outgrowth Activity

How extracellular molecules influence the direction of axon guidance is poorly understood. The HSN axon of Caenorhabditis elegans is guided towards a ventral source of secreted UNC-6 (netrin). The axon’s outgrowth response to UNC-6 is mediated by the UNC-40 (DCC) receptor. We have proposed that in response to the UNC-6 molecule the direction of UNC-40-mediated axon outgrowth is stochastically determined. The direction of guidance is controlled by asymmetric cues, including the gradient of UNC-6, that regulate the probability that UNC-40-mediated axon outgrowth is directed on average, over time, in a specific direction. Here we provide genetic evidence that a specialized extracellular matrix, which lies ventral to the HSN cell body, regulates the probability that UNC-40-mediated axon outgrowth will be directed ventrally towards the matrix. We show that mutations that disrupt the function of proteins associated with this matrix, UNC-52 (perlecan), UNC-112 (kindlin), VAB-19 (Kank), and UNC-97 (PINCH), decrease the probability of UNC-40-mediated axon outgrowth in the ventral direction, while increasing the probability of outgrowth in the anterior and posterior directions. Other results suggest that INA-1 (α integrin) and MIG-15 (NIK kinase) signaling mediate the response in HSN. Although the AVM axon also migrates through this matrix, the mutations have little effect on the direction of AVM axon outgrowth, indicating that responses to the matrix are cell-specific. Together, these results suggest that an extracellular matrix can regulate the direction of UNC-6 guidance by increasing the probability that UNC-40-mediated axon outgrowth activity will be oriented in a specific direction.     

Migration of connective tissue-derived cells is mediated by ultra-low concentration gradient fields of EGF

The directed migration of cells towards chemical stimuli incorporates simultaneous changes in both the concentration of a chemotactic agent and its concentration gradient, each of which may influence cell migratory response. In this study, we utilized a microfluidic system to examine the interactions between epidermal growth factor (EGF) concentration and EGF gradient in stimulating the chemotaxis of connective tissue-derived fibroblast cells. Cells seeded within microfluidic devices were exposed to concentration gradients established by EGF concentrations that matched or exceeded those required for maximum chemotactic responses seen in transfilter migration assays. The migration of individual cells within the device was measured optically after steady-state gradients had been experimentally established. Results illustrate that motility was maximal at EGF concentration gradients between .01- and 0.1-ng/(mL.mm) for all concentrations used. In contrast, the number of motile cells continually increased with increasing gradient steepness for all concentrations examined. Microfluidics-based experiments exposed cells to minute changes in EGF concentration and gradient that were in line with the acute EGFR phosphorylation measured. Correlation of experimental data with established mathematical models illustrated that the fibroblasts studied exhibit an unreported chemosensitivity to minute changes in EGF concentration, similar to that reported for highly motile cells, such as macrophages. Our results demonstrate that shallow chemotactic gradients, while previously unexplored, are necessary to induce the rate of directed cellular migration and the number of motile cells in the connective tissue-derived cells examined.     

Food Searching Strategy of Amoeboid Cells by Starvation Induced Run Length Extension

Food searching strategies of animals are key to their success in heterogeneous environments. The optimal search strategy may include specialized random walks such as Levy walks with heavy power-law tail distributions, or persistent walks with preferred movement in a similar direction. We have investigated the movement of the soil amoebae Dictyostelium searching for food. Dictyostelium cells move by extending pseudopodia, either in the direction of the previous pseudopod (persistent step) or in a different direction (turn). The analysis of ∼4000 pseudopodia reveals that step and turn pseudopodia are drawn from a probability distribution that is determined by cGMP/PLA2 signaling pathways. Starvation activates these pathways thereby suppressing turns and inducing steps. As a consequence, starved cells make very long nearly straight runs and disperse over ∼30-fold larger areas, without extending more or larger pseudopodia than vegetative cells. This ‘win-stay/lose-shift’ strategy for food searching is called Starvation Induced Run-length Extension. The SIRE walk explains very well the observed differences in search behavior between fed and starving organisms such as bumble-bees, flower bug, hoverfly and zooplankton.     

Chemoresponsiveness to cAMP and Folic Acid during Growth, Development, and Dedifferentiation in Dictyostelium discoideum

Chemoresponsiveness to cAMP and to folic acid are monitored in growing, developing, and dedifferentiating amebae of the cellular slime mold Dictyostelium discoideum . Two semiquantitative assays are employed, one measuring the directed movement of cells up a gradient of chemoattractant ('chemotaxis' assay) and the other measuring the outward spreading of cells in response to a chemical stimulant distributed equally throughout the substratum ('spreading' assay). Vegetative amebae possess relatively insignificant levels of chemotactic responsiveness to cAMP. Six h after the initiation of development, at approximately the same time as the onset of aggregation, cells rapidly acquire chemotactic responsiveness to cAMP. During 'erasure', a dedifferentiation induced by resuspending aggregating cells in fresh nutrient medium, chemotactic responsiveness to cAMP is lost just after the erasure event. By the same chemotactic assay, it is demonstrated that vegetative amebae possess a significant level of chemotactic responsiveness to folic acid. Two h after the initiation of development, cells completely lose chemotactic responsiveness to folic acid. During erasure, cells reacquire chemotactic responsiveness to folic acid at approximately the same time that they lose responsiveness to cAMP.
Dramatically different results are obtained by the spreading assay. When cells lose chemotactic responsiveness to folic acid early in development and when erasing cells lose chemotactic responsiveness to cAMP, they retain the spreading response to the two stimulants, respectively. The different results obtained for chemoreception employing the two assays are discussed in terms of molecular mechanisms, and a testable hypothesis is proposed for the possible roles of chemoresponsiveness and erasure in late morphogenesis.     

Cell balance equation for chemotactic bacteria with a biphasic tumbling frequency

Alts three-dimensional cell balance equation characterizing the chemotactic bacteria was analyzed under the presence of one-dimensional spatial chemoattractant gradients. Our work differs from that of others who have developed rather general models for chemotaxis in the use of a non-smooth anisotropic tumbling frequency function that responds biphasically to the combined temporal and spatial chemoattractant gradients. General three-dimensional expressions for the bacterial transport parameters were derived for chemotactic bacteria, followed by a perturbation analysis under the planar geometry. The bacterial random motility and chemotaxis were summarized by a motility tensor and a chemotactic velocity vector, respectively. The consequence of invoking the diffusion-approximation assumption and using intrinsic one-dimensional models with modified cellular swimming speeds was investigated by numerical simulations. Characterizing the bacterial random orientation after tumbles by a turn angle probability distribution function, we found that only the first-order angular moment of this turn angle probability distribution is important in influencing the bacterial long-term transport. Mathematics Subject Classification (2000):60G05, 60J60, 82A70     

A visual analysis of chemotactic and chemokinetic locomotion of human neutrophil leucocytes. Use of a new chemotaxis assay with Candida albicans as gradient source.

The locomotion of human blood neutrophil leucocytes was observed and analysed by time-lapse cinematography (1) under conditions where chemokinetic locomotion was stimulated, i.e. in a uniform concentration of casein; (2) in response to chemotactic gradients generated at a point-like source, namely blastospores of the pathogenic yeast Candida albicans in normal human plasma, and (3) in response to soluble chemotactic factors diffusing from Sephadex beads. Neutrophils moving in purely chemokinetic conditions tended to persist in straight paths and showed a preference for narrow angles of turn suggesting a “persistent random walk” type of locomotion rather than a pure random walk. Cells responding to Candida spores showed near straight-line locomotion to the gradient source over short distances (ca 50 μm) and brief time periods. They phagocytosed the spores on arrival and were usually immediately able to respond to a new gradient. Colchicine treatment caused the cells to turn through wider angles, but they were still able to home onto and phagocytose the spores. Colchicine-treated cells showed bizarre and fluctuating shapes but were nonetheless usually polarized towards the gradient source. Gradients from large sources, such as Sephadex beads containing soluble chemotactic factors, were more easily disturbed than those from Candida spores and directional locomotion of cells towards the beads was only seen in certain sectors. The angles of turn made by moving cells under these conditions were an important determinant of chemotaxis since paths of those cells reaching beads showed longer straight segments and narrower angles of turn than those which failed to show a directional response.     

A stochastic description of Dictyostelium chemotaxis

Chemotaxis, the directed motion of a cell toward a chemical source, plays a key role in many essential biological processes. Here, we derive a statistical model that quantitatively describes the chemotactic motion of eukaryotic cells in a chemical gradient. Our model is based on observations of the chemotactic motion of the social ameba Dictyostelium discoideum, a model organism for eukaryotic chemotaxis. A large number of cell trajectories in stationary, linear chemoattractant gradients is measured, using microfluidic tools in combination with automated cell tracking. We describe the directional motion as the interplay between deterministic and stochastic contributions based on a Langevin equation. The functional form of this equation is directly extracted from experimental data by angle-resolved conditional averages. It contains quadratic deterministic damping and multiplicative noise. In the presence of an external gradient, the deterministic part shows a clear angular dependence that takes the form of a force pointing in gradient direction. With increasing gradient steepness, this force passes through a maximum that coincides with maxima in both speed and directionality of the cells. The stochastic part, on the other hand, does not depend on the orientation of the directional cue and remains independent of the gradient magnitude. Numerical simulations of our probabilistic model yield quantitative agreement with the experimental distribution functions. Thus our model captures well the dynamics of chemotactic cells and can serve to quantify differences and similarities of different chemotactic eukaryotes. Finally, on the basis of our model, we can characterize the heterogeneity within a population of chemotactic cells.