Modeling cell gradient sensing and migration in competing chemoattractant fields

Directed cell migration mediates physiological and pathological processes. In particular, immune cell trafficking in tissues is crucial for inducing immune responses and is coordinated by multiple environmental cues such as chemoattractant gradients. Although the chemotaxis mechanism has been extensively studied, how cells integrate multiple chemotactic signals for effective trafficking and positioning in tissues is not clearly defined. Results from previous neutrophil chemotaxis experiments and modeling studies suggested that ligand-induced homologous receptor desensitization may provide an important mechanism for cell migration in competing chemoattractant gradients. However, the previous mathematical model is oversimplified to cell gradient sensing in one-dimensional (1-D) environment. To better understand the receptor desensitization mechanism for chemotactic navigation, we further developed the model to test the role of homologous receptor desensitization in regulating both cell gradient sensing and migration in different configurations of chemoattractant fields in two-dimension (2-D). Our results show that cells expressing normal desensitizable receptors preferentially orient and migrate toward the distant gradient in the presence of a second local competing gradient, which are consistent with the experimentally observed preferential migration of cells toward the distant attractant source and confirm the requirement of receptor desensitization for such migratory behaviors. Furthermore, our results are in qualitative agreement with the experimentally observed cell migration patterns in different configurations of competing chemoattractant fields.     

Integrating conflicting chemotactic signals. The role of memory in leukocyte navigation.

Leukocytes navigate through complex chemoattractant arrays, and in so doing, they must migrate from one chemoattractant source to another. By evaluating directional persistence and chemotaxis during neutrophil migration under agarose, we show that cells migrating away from a local chemoattractant, against a gradient, display true chemotaxis to distant agonists, often behaving as if the local gradient were without effect. We describe two interrelated properties of migrating cells that allow this to occur. First, migrating leukocytes can integrate competing chemoattractant signals, responding as if to the vector sum of the orienting signals present. Second, migrating cells display memory of their recent environment: cells' perception of the relative strength of orienting signals is influenced by their history, so that cells prioritize newly arising or newly encountered attractants. We propose that this cellular memory, by promoting sequential chemotaxis to one attractant after another, is in fact responsible for the integration of competitive orienting signals over time, and allows combinations of chemoattractants to guide leukocytes in a step-by-step fashion to their destinations within tissues.     

Dynamic Interpretation of Hedgehog Signaling in the Drosophila Wing Disc

Morphogens are classically defined as molecules that control patterning by acting at a distance to regulate gene expression in a concentration-dependent manner. In the Drosophila wing imaginal disc, secreted Hedgehog (Hh) forms an extracellular gradient that organizes patterning along the anterior–posterior axis and specifies at least three different domains of gene expression. Although the prevailing view is that Hh functions in the Drosophila wing disc as a classical morphogen, a direct correspondence between the borders of these patterns and Hh concentration thresholds has not been demonstrated. Here, we provide evidence that the interpretation of Hh signaling depends on the history of exposure to Hh and propose that a single concentration threshold is sufficient to support multiple outputs. Using mathematical modeling, we predict that at steady state, only two domains can be defined in response to Hh, suggesting that the boundaries of two or more gene expression patterns cannot be specified by a static Hh gradient. Computer simulations suggest that a spatial “overshoot” of the Hh gradient occurs, i.e., a transient state in which the Hh profile is expanded compared to the Hh steady-state gradient. Through a temporal examination of Hh target gene expression, we observe that the patterns initially expand anteriorly and then refine, providing in vivo evidence for the overshoot. The Hh gene network architecture suggests this overshoot results from the Hh-dependent up-regulation of the receptor, Patched (Ptc). In fact, when the network structure was altered such that the ptc gene is no longer up-regulated in response to Hh-signaling activation, we found that the patterns of gene expression, which have distinct borders in wild-type discs, now overlap. Our results support a model in which Hh gradient dynamics, resulting from Ptc up-regulation, play an instructional role in the establishment of patterns of gene expression.     

A Dynamic Model of Chemoattractant-Induced Cell Migration

Cell migration refers to a directional cell movement in response to chemoattractant stimulation. In this work, we developed a cell-migration model by mimicking in vivo migration using optically manipulated chemoattractant-loaded microsources. The model facilitates a quantitative characterization of the relationship among the protrusion force, cell motility, and chemoattractant gradient for the first time (to our knowledge). We verified the correctness of the model using migrating leukemia cancer Jurkat cells. The results show that one can achieve the ideal migrating capacity by choosing the appropriate chemoattractant gradient and concentration at the leading edge of the cell.     

How Entorhinal Grid Cells May Learn Multiple Spatial Scales from a Dorsoventral Gradient of Cell Response Rates in a Self-organizing Map

Place cells in the hippocampus of higher mammals are critical for spatial navigation. Recent modeling clarifies how this may be achieved by how grid cells in the medial entorhinal cortex (MEC) input to place cells. Grid cells exhibit hexagonal grid firing patterns across space in multiple spatial scales along the MEC dorsoventral axis. Signals from grid cells of multiple scales combine adaptively to activate place cells that represent much larger spaces than grid cells. But how do grid cells learn to fire at multiple positions that form a hexagonal grid, and with spatial scales that increase along the dorsoventral axis? In vitro recordings of medial entorhinal layer II stellate cells have revealed subthreshold membrane potential oscillations (MPOs) whose temporal periods, and time constants of excitatory postsynaptic potentials (EPSPs), both increase along this axis. Slower (faster) subthreshold MPOs and slower (faster) EPSPs correlate with larger (smaller) grid spacings and field widths. A self-organizing map neural model explains how the anatomical gradient of grid spatial scales can be learned by cells that respond more slowly along the gradient to their inputs from stripe cells of multiple scales, which perform linear velocity path integration. The model cells also exhibit MPO frequencies that covary with their response rates. The gradient in intrinsic rhythmicity is thus not compelling evidence for oscillatory interference as a mechanism of grid cell firing. A response rate gradient combined with input stripe cells that have normalized receptive fields can reproduce all known spatial and temporal properties of grid cells along the MEC dorsoventral axis. This spatial gradient mechanism is homologous to a gradient mechanism for temporal learning in the lateral entorhinal cortex and its hippocampal projections. Spatial and temporal representations may hereby arise from homologous mechanisms, thereby embodying a mechanistic “neural relativity” that may clarify how episodic memories are learned.     

Neutrophils Regulate Tissue Neutrophilia in Inflammation via the Oxidant-modified Lipid Lysophosphatidylserine

Resolution of neutrophilia characteristic of acute inflammation requires cessation of neutrophil recruitment and removal of tissue neutrophils. Based on in vitro studies, a role in these events was hypothesized for oxidant-generated lysophosphatidylserine (lyso-PS) on recruited neutrophils signaling via the G2A receptor on macrophages. Peritoneal exudate neutrophils harvested from wild type (WT) mice had 5-fold more lyso-PS (lyso-PS^high) than those of gp91^phox−/− (lyso-PS^low) mice. Ex vivo engulfment of lyso-PS^high neutrophils (95% viable) by WT peritoneal macrophages was quantitatively similar to UV-irradiated apoptotic blood neutrophils, although the signaling pathway for the former was uniquely dependent on macrophage G2A. In contrast, lyso-PS^low neutrophils were poorly engulfed unless presented with exogenous lyso-PS. Enhanced clearance of lyso-PS^high neutrophils was also seen in vivo following their adoptive transfer into inflamed peritonea of WT but not G2A^−/− mice, further supporting a requirement for signaling via G2A. To investigate downstream effects of lyso-PS/G2A signaling, antibody blockade of G2A in WT mice reduced macrophage CD206 expression and efferocytosis during peritonitis. Conversely, adoptive transfer of lyso-PS^high neutrophils early in inflammation in gp91^phox−/− mice led to accelerated development of efferocytic^high and CD206^high macrophages. This macrophage reprogramming was associated with suppressed production of pro-inflammatory mediators and reduced neutrophilia. These effects were not seen if G2A was blocked or lyso-PS^low neutrophils were transferred. Taken together, the results demonstrate that oxidant-generated lyso-PS made by viable tissue neutrophils is an endogenous anti-inflammatory mediator working in vivo to orchestrate the “early” and rapid clearance of recruited neutrophils as well as the reprogramming of “resolving” macrophages.     

Pannexin 1 Channels Link Chemoattractant Receptor Signaling to Local Excitation and Global Inhibition Responses at the Front and Back of Polarized Neutrophils

Neutrophil chemotaxis requires excitatory signals at the front and inhibitory signals at the back of cells, which regulate cell migration in a chemotactic gradient field. We have previously shown that ATP release via pannexin 1 (PANX1) channels and autocrine stimulation of P2Y₂ receptors contribute to the excitatory signals at the front. Here we show that PANX1 also contributes to the inhibitory signals at the back, namely by providing the ligand for A_2A adenosine receptors. In resting neutrophils, we found that A_2A receptors are uniformly distributed across the cell surface. In polarized cells, A_2A receptors redistributed to the back where their stimulation triggered intracellular cAMP accumulation and protein kinase A (PKA) activation, which blocked chemoattractant receptor signaling. Inhibition of PANX1 blocked A_2A receptor stimulation and cAMP accumulation in response to formyl peptide receptor stimulation. Treatments that blocked endogenous A_2A receptor signaling impaired the polarization and migration of neutrophils in a chemotactic gradient field and resulted in enhanced ERK and p38 MAPK signaling in response to formyl peptide receptor stimulation. These findings suggest that chemoattractant receptors require PANX1 to trigger excitatory and inhibitory signals that synergize to fine-tune chemotactic responses at the front and back of neutrophils. PANX1 channels thus link local excitatory signals to the global inhibitory signals that orchestrate chemotaxis of neutrophils in gradient fields.     

Mechanisms of Gradient Sensing and Chemotaxis: Conserved Pathways,Diverse Regulation

Directed cell migration is critical for normal development, immune responses, and wound healing and plays a prominent role in tumor metastasis. In eukaryotes, cell orientation is biased by an external chemoattractant gradient through a spatial contrast in chemoattractant receptor-mediated signal transduction processes that differentially affect cytoskeletal dynamics at the cell front and rear. Mechanisms of spatial gradient sensing and chemotaxis have been studied extensively in the social amoeba Dictyostelium discoideum and mammalian leukocytes (neutrophils), which are similar in their remarkable sensitivity to shallow gradients and robustness of response over a broad range of chemoattractant concentration. Recently, we have quantitatively characterized a different gradient sensing system, that of platelet-derived growth factor-stimulated fibroblasts, an important component of dermal wound healing. The marked differences between this system and the others have led us to speculate on the diversity of gradient sensing mechanisms and their biological implications.     

Frequency and orientation of pseudopod formation of Dictyostelium discoideum amebae chemotaxing in a spatial gradient: further evidence for a temporal mechanism

Amebae of Dictyostelium discoideum normally chemotax to aggregation centers by assessing the direction of outwardly moving, nondissipating waves of the chemoattractant cAMP. However, D. discoideum amebae can also assess the direction of a relatively stable spatial gradient. We demonstrate that amebae migrating towards the "source" of a stable, spatial gradient move faster, extend fewer pseudopodia, and turn less frequently than amebae migrating away from the "source" in the same spatial gradient. In addition, amebae extend lateral pseudopods in a polarized fashion from the anterior half of the cell, and do so as frequently towards the source as away from the source. However, those formed towards the source more often produce a turn than those formed away from the source. These results suggest that there may be two decision-making systems, one localized in the pseudopods, and one along the entire cell body; they support the suggestion that Dictyostelium amebae may employ a temporal mechanism to assess the direction of a spatial gradient of chemoattractant.     

Collective cell migration requires vesicular trafficking for chemoattractant delivery at the trailing edge

Chemoattractant signaling induces the polarization and directed movement of cells secondary to the activation of multiple effector pathways. In addition, chemotactic signals can be amplified and relayed to proximal cells via the synthesis and secretion of additional chemoattractant. The mechanisms underlying such remarkable features remain ill defined. We show that the asymmetrical distribution of adenylyl cyclase (ACA) at the back of Dictyostelium discoideum cells, an essential determinant of their ability to migrate in a head-to-tail fashion, requires vesicular trafficking. This trafficking results in a local accumulation of ACA-containing intracellular vesicles and involves intact actin, microtubule networks, and de novo protein synthesis. We also show that migrating cells leave behind ACA-containing vesicles, likely secreted as multivesicular bodies and presumably involved in the formation of head-to-tail arrays of migrating cells. We propose that similar compartmentalization and shedding mechanisms exist in mammalian cells during embryogenesis, wound healing, neuron growth, and metastasis.     

A stochastic model for chemosensory cell movement: application to neutrophil and macrophage persistence and orientation

Two central features of 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 report on a stochastic mathematical model for cell locomotion based on kinetic fluctuations in chemoattractant receptor binding. This model proves to be capable of stimulating cell paths similar to those observed experimentally for two cell types examined to date: neutrophils and alveolar macrophages, under conditions of uniform chemoattractant concentrations as well as chemoattractant concentration gradients. Further, this model can quantitatively predict both cell persistence time and dependence of orientation bias on gradient size. The model also successfully predicts that an increase in persistence time is associated with a decrease in orientation for typical system parameter values, as is observed for alveolar macrophages in comparison to neutrophils. 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. This suggests that chemosensory cell movement behavior may be based on a “usefully” imperfect integrated signal response system, which allows both random and directed searches under appropriate conditions.     

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.     

Imaging G Protein-coupled Receptor-mediated Chemotaxis and its Signaling Events in Neutrophil-like HL60 Cells

Eukaryotic cells sense and move towards a chemoattractant gradient, a cellular process referred as chemotaxis. Chemotaxis plays critical roles in many physiological processes, such as embryogenesis, neuron patterning, metastasis of cancer cells, recruitment of neutrophils to sites of inflammation, and the development of the model organism Dictyostelium discoideum. Eukaryotic cells sense chemo-attractants using G protein-coupled receptors. Visual chemotaxis assays are essential for a better understanding of how eukaryotic cells control chemoattractant-mediated directional cell migration. Here, we describe detailed methods for: 1) real-time, high-resolution monitoring of multiple chemotaxis assays, and 2) simultaneously visualizing the chemoattractant gradient and the spatiotemporal dynamics of signaling events in neutrophil-like HL60 cells.     

Do release-site biases reflect response to the Earth's magnetic field during position determination by homing pigeons?

How homing pigeons (Columba livia) return to their loft from distant, unfamiliar sites has long been a mystery. At many release sites, untreated birds consistently vanish from view in a direction different from the home direction, a phenomenon called the release-site bias. These deviations in flight direction have been implicated in the position determination (or map) step of navigation because they may reflect local distortions in information about location that the birds obtain from the geophysical environment at the release site. Here, we performed a post hoc analysis of the relationship between vanishing bearings and local variations in magnetic intensity using previously published datasets for pigeons homing to lofts in Germany. Vanishing bearings of both experienced and naïve birds were strongly associated with magnetic intensity variations at release sites, with 90 per cent of bearings lying within ±29° of the magnetic intensity slope or contour direction. Our results (i) demonstrate that pigeons respond in an orderly manner to the local structure of the magnetic field at release sites, (ii) provide a mechanism for the occurrence of release-site biases and (iii) suggest that pigeons may derive spatial information from the magnetic field at the release site that could be used to estimate their current position relative to their loft.     

A two-step search and run response to gradients shapes leukocyte navigation in vivo

Migrating cells must interpret chemical gradients to guide themselves within tissues. A long-held principle is that gradients guide cells via reorientation of leading-edge protrusions. However, recent evidence indicates that protrusions can be dispensable for locomotion in some contexts, raising questions about how cells interpret endogenous gradients in vivo and whether other mechanisms are involved. Using laser wound assays in zebrafish to elicit acute endogenous gradients and quantitative analyses, we demonstrate a two-stage process for leukocyte chemotaxis in vivo: first a “search” phase, with stimulation of actin networks at the leading edge, cell deceleration, and turning. This is followed by a “run” phase, with fast actin flows, cell acceleration, and persistence. When actin dynamics are perturbed, cells fail to resolve the gradient, suggesting that pure spatial sensing of the gradient is insufficient for navigation. Our data suggest that cell contractility and actin flows provide memory for temporal sensing, while expansion of the leading edge serves to enhance gradient sampling.     

Learning multiple routes in homing pigeons

The aerial lifestyle of central-place foraging birds allows wide-ranging movements, raising fundamental questions about their remarkable navigation and memory systems. For example, we know that pigeons (Columba livia), long-standing models for avian navigation, rely on individually distinct routes when homing from familiar sites. But it remains unknown how they cope with the task of learning several routes in parallel. Here, we examined how learning multiple routes influences homing in pigeons. We subjected groups of pigeons to different training protocols, defined by the sequence in which they were repeatedly released from three different sites, either sequentially, in rotation or randomly. We observed that pigeons from all groups successfully developed and applied memories of the different release sites (RSs), irrespective of the training protocol, and that learning several routes in parallel did not impair their capacity to quickly improve their homing efficiency over multiple releases. Our data also indicated that they coped with increasing RS uncertainty by adjusting both their initial behaviour upon release and subsequent homing efficiency. The results of our study broaden our understanding of avian route following and open new possibilities for studying learning and memory in free-flying animals.     

Point-estimating observer models for latent cause detection

The spatial distribution of visual items allows us to infer the presence of latent causes in the world. For instance, a spatial cluster of ants allows us to infer the presence of a common food source. However, optimal inference requires the integration of a computationally intractable number of world states in real world situations. For example, optimal inference about whether a common cause exists based on N spatially distributed visual items requires marginalizing over both the location of the latent cause and 2^N possible affiliation patterns (where each item may be affiliated or non-affiliated with the latent cause). How might the brain approximate this inference? We show that subject behaviour deviates qualitatively from Bayes-optimal, in particular showing an unexpected positive effect of N (the number of visual items) on the false-alarm rate. We propose several “point-estimating” observer models that fit subject behaviour better than the Bayesian model. They each avoid a costly computational marginalization over at least one of the variables of the generative model by “committing” to a point estimate of at least one of the two generative model variables. These findings suggest that the brain may implement partially committal variants of Bayesian models when detecting latent causes based on complex real world data.     

Phenotypic stability in scalar calcium of freshwater fish across a wide range of aqueous calcium availability in nature

Spatial environmental gradients can promote adaptive differences among conspecific populations as a result of local adaptation or phenotypic plasticity. Such divergence can be opposed by various constraints, including gene flow, limited genetic variation, temporal fluctuations, or developmental constraints. We focus on the constraint that can be imposed when some populations are found in locations characterized by low levels of an essential nutrient. We use scales of wild fish to investigate phenotypic effects of spatial variation in a potentially limiting nutrient—calcium. If scale calcium (we use “scalar” calcium for consistency with the physiology literature) simply reflects environmental calcium availability, we expect higher levels of scalar calcium in fish from calcium‐rich water, compared to fish from calcium‐poor water. To consider this “passive response” scenario, we analyzed scalar calcium concentrations from three native fish species (Lepomis gibbosus, Percina caprodes, and Perca flavescens) collected at multiple sites across a dissolved calcium gradient in the Upper St. Lawrence River. Contradicting the “passive response" scenario, we did not detect strong or consistent relationships between scalar calcium and water calcium. Instead, for a given proportional increase in water calcium across the wide environmental gradient, the corresponding proportional change in scalar calcium was much smaller. We thus favor the alternative “active homeostasis” scenario, wherein fish from calcium‐poor water are better able to uptake, mobilize, and deposit calcium than are fish from calcium‐rich water. We further highlight the importance of studying functional traits, such as scales, in their natural setting as opposed to only laboratory studies.