Quantitative elucidation of a distinct spatial gradient-sensing mechanism in fibroblasts

Migration of eukaryotic cells toward a chemoattractant often relies on their ability to distinguish receptor-mediated signaling at different subcellular locations, a phenomenon known as spatial sensing. A prominent example that is seen during wound healing is fibroblast migration in platelet-derived growth factor (PDGF) gradients. As in the well-characterized chemotactic cells Dictyostelium discoideum and neutrophils, signaling to the cytoskeleton via the phosphoinositide 3-kinase pathway in fibroblasts is spatially polarized by a PDGF gradient; however, the sensitivity of this process and how it is regulated are unknown. Through a quantitative analysis of mathematical models and live cell total internal reflection fluorescence microscopy experiments, we demonstrate that PDGF detection is governed by mechanisms that are fundamentally different from those in D. discoideum and neutrophils. Robust PDGF sensing requires steeper gradients and a much narrower range of absolute chemoattractant concentration, which is consistent with a simpler system lacking the feedback loops that yield signal amplification and adaptation in amoeboid cells.     

Feedback signaling controls leading-edge formation during chemotaxis

Chemotactic cells translate shallow chemoattractant gradients into a highly polarized intracellular response that includes the localized production of PI(3,4,5)P(3) on the side of the cell facing the highest chemoattractant concentration. Research over the past decade began to uncover the molecular mechanisms involved in this localized signal amplification controlling the leading edge of chemotaxing cells. These mechanisms have been shown to involve multiple positive feedback loops, in which the PI(3,4,5)P(3) signal amplifies itself independently of the original stimulus, as well as inhibitory signals that restrict PI(3,4,5)P(3) to the leading edge, thereby creating a steep intracellular PI(3,4,5)P(3) gradient. Molecules involved in positive feedback signaling at the leading edge include the small G-proteins Rac and Ras, phosphatidylinositol-3 kinase and F-actin, as part of interlinked feedback loops that lead to a robust production of PI(3,4,5)P(3).     

Spatiotemporal regulation of Ras activity provides directional sensing

Cells' ability to detect and orient themselves in chemoattractant gradients has been the subject of numerous studies, but the underlying molecular mechanisms remain largely unknown [1]. Ras activation is the earliest polarized response to chemoattractant gradients downstream from heterotrimeric G proteins in Dictyostelium, and inhibition of Ras signaling results in directional migration defects [2]. Activated Ras is enriched at the leading edge, promoting the localized activation of key chemotactic effectors, such as PI3K and TORC2 [2-5]. To investigate the role of Ras in directional sensing, we studied the effect of its misregulation by using cells with disrupted RasGAP activity. We identified an ortholog of mammalian NF1, DdNF1, as a major regulator of Ras activity in Dictyostelium. We show that disruption of nfaA leads to spatially and temporally unregulated Ras activity, causing cytokinesis and chemotaxis defects. By using unpolarized, latrunculin-treated cells, we show that tight regulation of Ras is important for gradient sensing. Together, our findings suggest that Ras is part of the cell's compass and that the RasGAP-mediated regulation of Ras activity affects directional sensing.     

Modelling cell polarization driven by synthetic spatially graded Rac activation

The small GTPase Rac is known to be an important regulator of cell polarization, cytoskeletal reorganization, and motility of mammalian cells. In recent microfluidic experiments, HeLa cells endowed with appropriate constructs were subjected to gradients of the small molecule rapamycin leading to synthetic membrane recruitment of a Rac activator and direct graded activation of membrane-associated Rac. Rac activation could thus be triggered independent of upstream signaling mechanisms otherwise responsible for transducing activating gradient signals. The response of the cells to such stimulation depended on exceeding a threshold of activated Rac. Here we develop a minimal reaction-diffusion model for the GTPase network alone and for GTPase-phosphoinositide crosstalk that is consistent with experimental observations for the polarization of the cells. The modeling suggests that mutual inhibition is a more likely mode of cell polarization than positive feedback of Rac onto its own activation. We use a new analytical tool, Local Perturbation Analysis, to approximate the partial differential equations by ordinary differential equations for local and global variables. This method helps to analyze the parameter space and behaviour of the proposed models. The models and experiments suggest that (1) spatially uniform stimulation serves to sensitize a cell to applied gradients. (2) Feedback between phosphoinositides and Rho GTPases sensitizes a cell. (3) Cell lengthening/flattening accompanying polarization can increase the sensitivity of a cell and stabilize an otherwise unstable polarization.     

Adaptive molecular networks controlling chemotactic migration: dynamic inputs and selection of the network architecture

Eukaryotic signalling networks underlying the cell''s ability to sense the gradient of chemotactic cues frequently have the dual property of perfect adaptation to spatially homogeneous inputs, and persistent activation by inputs that are spatially graded. This property is also shared by bacterial chemotaxis networks, raising the question of whether these two types of chemotactic processes also have similar organization of the underlying biomolecular processes. Interestingly, perfect adaptation can only be achieved robustly by a handful of mechanisms, and while eukaryotic chemotactic networks appear to rely on one of these—the incoherent feed-forward loop, bacterial chemotaxis depends on another—the negative feedback loop. In this review, we discuss how this conclusion can be reached even if the details of the molecular networks are incompletely understood. Furthermore, we argue that the use of distinct network architectures is not accidental and may be a consequence of the nature of the signalling inputs and the limitations of the sensory properties of different cell types.     

Two complementary, local excitation, global inhibition mechanisms acting in parallel can explain the chemoattractant-induced regulation of PI(3,4,5)P3 response in dictyostelium cells

Chemotaxing cells, such as Dictyostelium and mammalian neutrophils, sense shallow chemoattractant gradients and respond with highly polarized changes in cell morphology and motility. Uniform chemoattractant stimulation induces the transient translocations of several downstream signaling components, including phosphoinositide 3-kinase (PI3K), tensin homology protein (PTEN), and phosphatidylinositol 3,4,5-trisphosphate (PI(3,4,5)P3). In contrast, static spatial chemoattractant gradients elicit the persistent, amplified localization of these molecules. We have proposed a model in which the response to chemoattractant is regulated by a balance of a local excitation and a global inhibition, both of which are controlled by receptor occupancy. This model can account for both the transient and spatial responses to chemoattractants, but alone does not amplify the external gradient. In this article, we develop a model in which parallel local excitation, global inhibition mechanisms control the membrane binding of PI3K and PTEN. Together, the action of these enzymes induces an amplified PI(3,4,5)P3 response that agrees quantitatively with experimentally obtained plekstrin homology-green fluorescent protein distributions in latrunculin-treated cells. We compare the model's performance with that of several mutants in which one or both of the enzymes are disrupted. The model accounts for the observed response to multiple, simultaneous chemoattractant cues and can recreate the cellular response to combinations of temporal and spatial stimuli. Finally, we use the model to predict the response of a cell where only a fraction is stimulated by a saturating dose of chemoattractant.     

Spontaneous polarization in eukaryotic gradient sensing: a mathematical model based on mutual inhibition of frontness and backness pathways

A key problem of eukaryotic cell motility is the signaling mechanism of chemoattractant gradient sensing. Recent experiments have revealed the molecular correlate of gradient sensing: Frontness molecules, such as PI3P and Rac, localize at the front end of the cell, and backness molecules, such as Rho and myosin II, accumulate at the back of the cell. Importantly, this frontness-backness polarization occurs spontaneously even if the cells are exposed to uniform chemoattractant profiles. The spontaneous polarization suggests that the gradient sensing machinery undergoes a Turing bifurcation. This has led to several classical activator-inhibitor and activator-substrate models which identify the frontness molecules with the activator. Conspicuously absent from these models is any accounting of the backness molecules. This stands in sharp contrast to experiments which show that the backness pathways inhibit the frontness pathways. Here, we formulate a model based on the mutually inhibitory interaction between the frontness and backness pathways. The model builds upon the mutual inhibition model proposed by Bourne and coworkers [Xu et al., 2003. Divergent signals and cytoskeletal assemblies regulate self-organizing polarity in neutrophils. Cell 114, 201-214.]. We show that mutual inhibition alone, without the help of any positive feedback (autocatalysis), can trigger spontaneous polarization of the frontness and backness pathways. The spatial distribution of the frontness and backness molecules in response to inhibition and activation of the frontness and backness pathways are consistent with those observed in experiments. Furthermore, depending on the parameter values, the model yields spatial distributions corresponding to chemoattraction (frontness pathways in-phase with the external gradient) and chemorepulsion (frontness pathways out-of-phase with the external gradient). Analysis of the model suggests a mechanism for the chemorepulsion-to-chemoattraction transition observed in neurons.     

A stochastic model for leukocyte random motility and chemotaxis based on receptor binding fluctuations

Two central features of polymorphonuclear leukocyte chemosensory movement behavior demand fundamental theoretical understanding. In uniform concentrations of chemoattractant, these cells exhibit a persistent random walk, with a characteristic "persistence time" between significant changes in direction. In chemoattractant concentration gradients, they demonstrate a biased random walk, with an "orientation bias" characterizing the fraction of cells moving up the gradient. A coherent picture of cell movement responses to chemoattractant requires that both the persistence time and the orientation bias be explained within a unifying framework. In this paper, we offer the possibility that "noise" in the cellular signal perception/response mechanism can simultaneously account for these two key phenomena. In particular, we develop a stochastic mathematical model for cell locomotion based on kinetic fluctuations in chemoattractant/receptor binding. This model can simulate cell paths similar to those observed experimentally, under conditions of uniform chemoattractant concentrations as well as chemoattractant concentration gradients. Furthermore, this model can quantitatively predict both cell persistence time and dependence of orientation bias on gradient size. Thus, the concept of signal "noise" can quantitatively unify the major characteristics of leukocyte random motility and chemotaxis. The same level of noise large enough to account for the observed frequency of turning in uniform environments is simultaneously small enough to allow for the observed degree of directional bias in gradients.     

Adaptive-Control Model for Neutrophil Orientation in the Direction of Chemical Gradients

Neutrophils have a remarkable ability to detect the direction of chemoattractant gradients and move directionally in response to bacterial infections and tissue injuries. For their role in health and disease, neutrophils have been extensively studied, and many of the molecules involved in the signaling mechanisms of gradient detection and chemotaxis have been identified. However, the cellular-scale mechanisms of gradient sensing and directional neutrophil migration have been more elusive, and existent models provide only limited insight into these processes. Here, we propose a what we believe is a novel adaptive-control model for the initiation of cell polarization in response to gradients. In this model, the neutrophils first sample the environment by extending protrusions in random directions and subsequently adapt their sensitivity depending on localized, temporal changes in stimulation levels. Our results suggest that microtubules may play a critical role in integrating all the sensing events from the cellular periphery through their redistribution inside the neutrophils, and may also be involved in modulating local signaling. An unexpected finding was that model neutrophils exhibit significant randomness in timing and directionality of activation, comparable to our experimental observations in microfluidic devices. Moreover, their responses are robust against alterations of the rate and amplitude of the signaling reactions, and for a broad range in chemoattractant concentrations and spatial gradients.     

Mediation of chemoattractant-induced changes in [Ca2+]i and cell shape, polarity, and locomotion by InsP3, DAG, and protein kinase C in newt eosinophils

During chemotaxis large eosinophils from newts exhibit a gradient of [Ca2+]i from rear to front. The direction of the gradient changes on relocation of the chemoattractant source, suggesting that the Ca2+ signal may trigger the cytoskeletal reorganization required for cell reorientation during chemotaxis. The initial stimulatory effect of chemoattractant on [Ca2+]i and the opposite orientations of the intracellular Ca2+ gradient and the external stimulus gradient suggest that more than one chemoattractant-sensitive messenger pathway may be responsible for the generation of spatially graded Ca2+ signals. To identify these messengers, Ca2+ changes were measured in single live cells stimulated with spatially uniform chemoattractant. On stimulation spatially averaged [Ca2+]i increased rapidly from < or = 100 nM to > or = 400 nM and was accompanied by formation of lamellipods. Subsequently cells flattened, polarized and crawled, and [Ca2+]i fluctuated around a mean value of approximately 200 nM. The initial Ca2+ spike was insensitive acutely to removal of extracellular Ca2+ but was abolished by treatments expected to deplete internal Ca2+ stores and by blocking receptors for inositol-trisphosphate, indicating that it is produced by discharge of internal stores, at least some of which are sensitive to InsP3. Activators of protein kinase C (PKC) (diacyl glycerol and phorbol ester) induced flattening and lamellipod activity and suppressed the Ca2+ spike, while cells injected with PKC inhibitors (an inhibitory peptide and low concentrations of heparin-like compounds) produced an enhanced Ca2+ spike on stimulation. Although cell flattening and lamellipod activity were induced by chemoattractant when the normal Ca2+ response was blocked, cells failed to polarize and crawl, indicating that Ca2+ homeostasis is required for these processes. We conclude that InsP3 acting on Ca2+ stores and DAG acting via PKC regulate chemoattractant-induced changes in [Ca2+]i, which in turn control polarization and locomotion. We propose that differences in the spatial distributions of InsP3 and DAG resulting from their respective hydrophilic and lipophilic properties may change Ca2+ distribution in response to stimulus reorientation, enabling the cell to follow the stimulus.     

Asymmetrical Macromolecular Complex Formation of Lysophosphatidic Acid Receptor 2 (LPA2) Mediates Gradient Sensing in Fibroblasts

Chemotactic migration of fibroblasts toward growth factors relies on their capacity to sense minute extracellular gradients and respond to spatially confined receptor-mediated signals. Currently, mechanisms underlying the gradient sensing of fibroblasts remain poorly understood. Using single-particle tracking methodology, we determined that a lysophosphatidic acid (LPA) gradient induces a spatiotemporally restricted decrease in the mobility of LPA receptor 2 (LPA₂) on chemotactic fibroblasts. The onset of decreased LPA₂ mobility correlates to the spatial recruitment and coupling to LPA₂-interacting proteins that anchor the complex to the cytoskeleton. These localized PDZ motif-mediated macromolecular complexes of LPA₂ trigger a Ca²⁺ puff gradient that governs gradient sensing and directional migration in response to LPA. Disruption of the PDZ motif-mediated assembly of the macromolecular complex of LPA₂ disorganizes the gradient of Ca²⁺ puffs, disrupts gradient sensing, and reduces the directional migration of fibroblasts toward LPA. Our findings illustrate that the asymmetric macromolecular complex formation of chemoattractant receptors mediates gradient sensing and provides a new mechanistic basis for models to describe gradient sensing of fibroblasts.     

Neutrophil chemotaxis in linear and complex gradients of interleukin-8 formed in a microfabricated device

Although a wealth of knowledge about chemotaxis has accumulated in the past 40 years, these studies have been hampered by the inability of researchers to generate simple linear gradients instantaneously and to maintain them at steady state. Here we describe a device microfabricated by soft lithography and consisting of a network of microfluidic channels that can generate spatially and temporally controlled gradients of chemotactic factors. When human neutrophils are positioned within a microchannel, their migration in simple and complex interleukin-8 (IL-8) gradients can be tested. The cells exhibit strong directional migration toward increasing concentrations of IL-8 in linear gradients. Neutrophil migration halts abruptly when cells encounter a sudden drop in the chemoattractant concentration to zero ("cliff" gradient). When neutrophils are challenged with a gradual increase and decrease in chemoattractant ("hill" gradient), however, the cells traverse the crest of maximum concentration and migrate further before reversing direction. The technique described in this paper provides a robust method to investigate migratory cells under a variety of conditions not accessible to study by earlier techniques.     

Sensory adaptation of Dictyostelium discoideum cells to chemotactic signals

Postvegetative Dictyostelium discoideum cells react chemotactically to gradients of cAMP, folic acid, and pterin. In the presence of a constant concentration of 10(-5) M cAMP cells move at random. They still are able to respond to superimposed gradients of cAMP, although the response is less efficient than without the high background level of cAMP. Cells which are accommodated to 10(-5) M cAMP do not react to a gradient of cAMP if the mean cAMP concentration is decreasing with time. This indicates the involvement of adaptation in the detection of chemotactic gradients: cells adapt to the mean concentration of chemoattractant and respond to positive deviations from the mean concentration. Cells adapted to high cAMP concentrations react normally to gradients of folic acid or pterin. Adaptation to one of these compounds does not affect the response to the other attractants. This suggests that cAMP, folic acid, and pterin are detected by different receptors, and that adaptation is localized at a step in the transduction process before the signals from these receptors coincide into one pathway. I discuss the implications of adaptation for chemotaxis and cell aggregation.     

Tuning sperm chemotaxis by calcium burst timing

Marine invertebrate oocytes establish chemoattractant gradients that guide spermatozoa towards their source. In sea urchin spermatozoa, this relocation requires coordinated motility changes initiated by Ca²⁺-driven alterations in sperm flagellar curvature. We discovered that Lytechinus pictus spermatozoa undergo chemotaxis in response to speract, an egg-derived decapeptide previously noted to stimulate non-chemotactic motility alterations in Strongylocentrotus purpuratus spermatozoa. Sperm of both species responded to speract gradients with a sequence of turning episodes that correlate with transient flagellar Ca²⁺ increases, yet only L. pictus spermatozoa accumulated at the gradient source. Detailed analysis of sperm behavior revealed that L. pictus spermatozoa selectively undergo Ca²⁺ fluctuations while swimming along negative speract gradients while S. purpuratus sperm generate Ca²⁺ fluctuations in a spatially non-selective manner. This difference is attributed to the selective suppression of Ca²⁺ fluctuations of L. pictus spermatozoa as they swim towards the source of the chemoattractant gradient. This is the first study to compare and characterize the motility components that differ in chemotactic and non-chemotactic spermatozoa. Tuning of Ca²⁺ fluctuations and associated turning episodes to the chemoattractant gradient polarity is a central feature of sea urchin sperm chemotaxis and may be a feature of sperm chemotaxis in general.     

Melanoma Cells Break Down LPA to Establish Local Gradients That Drive Chemotactic Dispersal

The high mortality of melanoma is caused by rapid spread of cancer cells, which occurs unusually early in tumour evolution. Unlike most solid tumours, thickness rather than cytological markers or differentiation is the best guide to metastatic potential. Multiple stimuli that drive melanoma cell migration have been described, but it is not clear which are responsible for invasion, nor if chemotactic gradients exist in real tumours. In a chamber-based assay for melanoma dispersal, we find that cells migrate efficiently away from one another, even in initially homogeneous medium. This dispersal is driven by positive chemotaxis rather than chemorepulsion or contact inhibition. The principal chemoattractant, unexpectedly active across all tumour stages, is the lipid agonist lysophosphatidic acid (LPA) acting through the LPA receptor LPAR1. LPA induces chemotaxis of remarkable accuracy, and is both necessary and sufficient for chemotaxis and invasion in 2-D and 3-D assays. Growth factors, often described as tumour attractants, cause negligible chemotaxis themselves, but potentiate chemotaxis to LPA. Cells rapidly break down LPA present at substantial levels in culture medium and normal skin to generate outward-facing gradients. We measure LPA gradients across the margins of melanomas in vivo, confirming the physiological importance of our results. We conclude that LPA chemotaxis provides a strong drive for melanoma cells to invade outwards. Cells create their own gradients by acting as a sink, breaking down locally present LPA, and thus forming a gradient that is low in the tumour and high in the surrounding areas. The key step is not acquisition of sensitivity to the chemoattractant, but rather the tumour growing to break down enough LPA to form a gradient. Thus the stimulus that drives cell dispersal is not the presence of LPA itself, but the self-generated, outward-directed gradient.     

Regulation of the MEX-5 gradient by a spatially segregated kinase/phosphatase cycle

Protein concentration gradients encode spatial information across cells and tissues and often depend on spatially localized protein synthesis. Here, we report that a different mechanism underlies the MEX-5 gradient. MEX-5 is an RNA-binding protein that becomes distributed in a cytoplasmic gradient along the anterior-to-posterior axis of the one-cell C. elegans embryo. We demonstrate that the MEX-5 gradient is a direct consequence of an underlying gradient in MEX-5 diffusivity. The MEX-5 diffusion gradient arises when the PAR-1 kinase stimulates the release of MEX-5 from slow-diffusive, RNA-containing complexes in the posterior cytoplasm. PAR-1 directly phosphorylates MEX-5 and is antagonized by the spatially uniform phosphatase PP2A. Mathematical modeling and in vivo observations demonstrate that spatially segregated phosphorylation and dephosphorylation reactions are sufficient to generate stable protein concentration gradients in the cytoplasm. The principles demonstrated here apply to any spatially segregated modification cycle that affects protein diffusion and do not require protein synthesis or degradation.     

Elevational gradient in the cyclicity of a forest-defoliating insect

Observed changes in the cyclicity of herbivore populations along latitudinal gradients and the hypothesis that shifts in the importance of generalist versus specialist predators explain such gradients has long been a matter of intense interest. In contrast, elevational gradients in population cyclicity are largely unexplored. We quantified the cyclicity of gypsy moth populations along an elevational gradient by applying wavelet analysis to spatially referenced 31-year records (1975–2005) of defoliation. Based on geographically weighted regression and nonlinear regression, we found either a hump-shaped or plateauing relationship between elevation and the cyclicity of gypsy moth populations and a positive relationship between cyclicity and the density of the gypsy moth’s preferred host-tree species. The potential effects of elevational gradients in the density of generalist predators and preferred host-tree species on the cyclicity of gypsy moth populations were evaluated with mechanistic simulation models. The models suggested that an elevational gradient in the densities of preferred host tree species could partially explain elevational patterns of gypsy moth cyclicity. Results from a model assuming a type-III functional response of generalist predators to changes in gypsy moth density were inconsistent with the observed elevational gradient in gypsy moth cyclicity. However, a model with a more realistic type-II functional response gave results roughly consistent with the empirical findings. In contrast to classical studies on the effects of generalist predators on prey population cycles, our model with a type-II functional response predicts a unimodal relationship between generalist-predator density and the cyclicity of gypsy moth populations.     

Complex Regulation of cyp26a1 Creates a Robust Retinoic Acid Gradient in the Zebrafish Embryo

Positional identities along the anterior–posterior axis of the vertebrate nervous system are assigned during gastrulation by multiple posteriorizing signals, including retinoic acid (RA), fibroblast growth factors (Fgfs), and Wnts. Experimental evidence has suggested that RA, which is produced in paraxial mesoderm posterior to the hindbrain by aldehyde dehydrogenase 1a2 (aldh1a2/raldh2), forms a posterior-to-anterior gradient across the hindbrain field, and provides the positional information that specifies the locations and fates of rhombomeres. Recently, alternative models have been proposed in which RA plays only a permissive role, signaling wherever it is not degraded. Here we use a combination of experimental and modeling tools to address the role of RA in providing long-range positional cues in the zebrafish hindbrain. Using cell transplantation and implantation of RA-coated beads into RA-deficient zebrafish embryos, we demonstrate that RA can directly convey graded positional information over long distances. We also show that expression of Cyp26a1, the major RA-degrading enzyme during gastrulation, is under complex feedback and feedforward control by RA and Fgf signaling. The predicted consequence of such control is that RA gradients will be both robust to fluctuations in RA synthesis and adaptive to changes in embryo length during gastrulation. Such control also provides an explanation for the fact that loss of an endogenous RA gradient can be compensated for by RA that is provided in a spatially uniform manner.     

Quantitative imaging of single live cells reveals spatiotemporal dynamics of multistep signaling events of chemoattractant gradient sensing in Dictyostelium

Activation of G-protein-coupled chemoattractant receptors triggers dissociation of Galpha and Gbetagamma subunits. These subunits induce intracellular responses that can be highly polarized when a cell experiences a gradient of chemoattractant. Exactly how a cell achieves this amplified signal polarization is still not well understood. Here, we quantitatively measure temporal and spatial changes of receptor occupancy, G-protein activation by FRET imaging, and PIP3 levels by monitoring the dynamics of PH(Crac)-GFP translocation in single living cells in response to different chemoattractant fields. Our results provided the first direct evidence that G-proteins are activated to different extents on the cell surface in response to asymmetrical stimulations. A stronger, uniformly applied stimulation triggers not only a stronger G-protein activation but also a faster adaptation of downstream responses. When naive cells (which have not experienced chemoattractant) were abruptly exposed to stable cAMP gradients, G-proteins were persistently activated throughout the entire cell surface, whereas the response of PH(Crac)-GFP translocation surprisingly consisted of two phases, an initial transient and asymmetrical translocation around the cell membrane, followed by a second phase producing a highly polarized distribution of PH(Crac)-GFP. We propose a revised model of gradient sensing, suggesting an important role for locally controlled components that inhibit PI3Kinase activity.