Navigation of chemotactic cells by parallel signaling to pseudopod persistence and orientation

PTEN and the PTEN-like phosphatase CnrN have both distinct and overlapping roles in a Dictyostelium chemorepulsion pathway

The directed movement of eukaryotic cells is crucial for processes such as embryogenesis and immune cell trafficking. The enzyme Phosphatase and tensin homolog (PTEN) dephosphorylates phosphatidylinositol 3,4,5-trisphosphate [PI(3,4,5)P 3 ] to phosphatidylinositol 4,5-bisphosphate [PI(4,5)P 2 ]. Dictyostelium discoideum cells require both PTEN and the PTEN-like phosphatase CnrN to locally inhibit Ras activation to induce biased movement of cells away from the secreted chemorepellent protein AprA. Both PTEN and CnrN decrease basal levels of PI(3,4,5)P 3 and increase basal numbers of macropinosomes, and AprA prevents this increase. AprA requires both PTEN and CnrN to increase PI(4,5)P 2 levels, decrease PI(3,4,5)P 3 levels, inhibit proliferation, decrease myosin II phosphorylation, and increase filopod sizes. AprA causes PTEN, similar to CnrN, to localize to the side of the cell towards AprA in an AprA gradient. However, PTEN and CnrN also have distinct roles in some signaling pathways. PTEN, but not CnrN, decreases basal levels of PI(4,5)P 2 , AprA requires PTEN, but not CnrN, to induce cell roundness, and CnrN and PTEN have different effects on the number of filopods and pseudopods, and the sizes of filopods. Together, our results suggest that CnrN and PTEN play unique roles in D. discoideum signaling pathways, and possibly dephosphorylate PI(3,4,5)P 3 in different membrane domains, to mediate chemorepulsion away from AprA.

Three-component contour dynamics model to simulate and analyze amoeboid cell motility in two dimensions

Amoeboid cell motility is relevant in a wide variety of biomedical processes such as wound healing, cancer metastasis, and embryonic morphogenesis. It is characterized by pronounced changes of the cell shape associated with expansions and retractions of the cell membrane, which result in a crawling kind of locomotion. Despite existing computational models of amoeboid motion, the inference of expansion and retraction components of individual cells, the corresponding classification of cells, and the a priori specification of the parameter regime to achieve a specific motility behavior remain challenging open problems. We propose a novel model of the spatio-temporal evolution of two-dimensional cell contours comprising three biophysiologically motivated components: a stochastic term accounting for membrane protrusions and two deterministic terms accounting for membrane retractions by regularizing the shape and area of the contour. Mathematically, these correspond to the intensity of a self-exciting Poisson point process, the area-preserving curve-shortening flow, and an area adjustment flow. The model is used to generate contour data for a variety of qualitatively different, e.g., polarized and non-polarized, cell tracks that visually resemble experimental data very closely. In application to experimental cell tracks, we inferred the protrusion component and examined its correlation to common biomarkers: the F-actin density close to the membrane and its local motion. Due to the low model complexity, parameter estimation is fast, straightforward, and offers a simple way to classify contour dynamics based on two locomotion types: the amoeboid and a so-called fan-shaped type. For both types, we use cell tracks segmented from fluorescence imaging data of the model organism Dictyostelium discoideum. An implementation of the model is provided within the open-source software package AmoePy, a Python-based toolbox for analyzing and simulating amoeboid cell motility.

AKT and SGK kinases regulate cell migration by altering Scar/WAVE complex activation and Arp2/3 complex recruitment

Cell polarity and cell migration both depend on pseudopodia and lamellipodia formation. These are regulated by coordinated signaling acting through G-protein coupled receptors and kinases such as PKB/AKT and SGK, as well as the actin cytoskeletal machinery. Here we show that both Dictyostelium PKB and SGK kinases (encoded by pkbA and pkgB) are dispensable for chemotaxis towards folate. However, both are involved in the regulation of pseudopod formation and thus cell motility. Cells lacking pkbA and pkgB showed a substantial drop in cell speed. Actin polymerization is perturbed in pkbA- and reduced in pkgB- and pkbA-/pkgB- mutants. The Scar/WAVE complex, key catalyst of pseudopod formation, is recruited normally to the fronts of all mutant cells (pkbA-, pkgB- and pkbA-/pkgB-), but is unexpectedly unable to recruit the Arp2/3 complex in cells lacking SGK. Consequently, loss of SGK causes a near-complete loss of normal actin pseudopodia, though this can be rescued by overexpression of PKB. Hence both PKB and SGK are required for correct assembly of F-actin and recruitment of the Arp2/3 complex by the Scar/WAVE complex during pseudopodia formation.

Short-term bioelectric stimulation of collective cell migration in tissues reprograms long-term supracellular dynamics

The ability to program collective cell migration can allow us to control critical multicellular processes in development, regenerative medicine, and invasive disease. However, while various technologies exist to make individual cells migrate, translating these tools to control myriad, collectively interacting cells within a single tissue poses many challenges. For instance, do cells within the same tissue interpret a global migration 'command' differently based on where they are in the tissue? Similarly, since no stimulus is permanent, what are the long-term effects of transient commands on collective cell dynamics? We investigate these questions by bioelectrically programming large epithelial tissues to globally migrate 'rightward' via electrotaxis. Tissues clearly developed distinct rear, middle, side, and front responses to a single global migration stimulus. Furthermore, at no point poststimulation did tissues return to their prestimulation behavior, instead equilibrating to a 3rd, new migratory state. These unique dynamics suggested that programmed migration resets tissue mechanical state, which was confirmed by transient chemical disruption of cell-cell junctions, analysis of strain wave propagation patterns, and quantification of cellular crowd dynamics. Overall, this work demonstrates how externally driving the collective migration of a tissue can reprogram baseline cell-cell interactions and collective dynamics, even well beyond the end of the global migratory cue, and emphasizes the importance of considering the supracellular context of tissues and other collectives when attempting to program crowd behaviors.

Multifactorial assessment of neutrophil chemotaxis efficiency from a drop of blood

Following injury and infection, neutrophils are guided to the affected site by chemoattractants released from injured tissues and invading microbes. During this process (chemotaxis), neutrophils must integrate multiple chemical signals, while also responding to physical constraints and prioritizing their directional decisions to generate an efficient immune response. In some clinical conditions, human neutrophils appear to lose the ability to chemotax efficiently, which may contribute both directly and indirectly to disease pathology. Here, a range of microfluidic designs is utilized to test the sensitivity of chemotaxing neutrophils to various perturbations, including binary decision-making in the context of channels with different chemoattractant gradients, hydraulic resistance, and angle of approach. Neutrophil migration in long narrow channels and planar environments is measured. Conditions in which neutrophils are significantly more likely to choose paths with the steepest chemoattractant gradient and the most direct approach angle, and find that migration efficiency across planar chambers is inversely correlated with chamber diameter. By sequential measurement of neutrophil binary decision-making to different chemoattractant gradients, or chemotactic index in sequential planar environments, data supporting a model of biased random walk for neutrophil chemotaxis are presented.

A chemorepellent inhibits local Ras activation to inhibit pseudopod formation to bias cell movement away from the chemorepellent

The ability of cells to sense chemical gradients is essential during development, morphogenesis, and immune responses. Although much is known about chemoattraction, chemorepulsion remains poorly understood. Proliferating Dictyostelium cells secrete a chemorepellent protein called AprA. AprA prevents pseudopod formation at the region of the cell closest to the source of AprA, causing the random movement of cells to be biased away from the AprA. Activation of Ras proteins in a localized sector of a cell cortex helps to induce pseudopod formation, and Ras proteins are needed for AprA chemorepulsion. Here we show that AprA locally inhibits Ras cortical activation through the G protein–coupled receptor GrlH, the G protein subunits Gβ and Gα8, Ras protein RasG, protein kinase B, the p21-activated kinase PakD, and the extracellular signal–regulated kinase Erk1. Diffusion calculations and experiments indicate that in a colony of cells, high extracellular concentrations of AprA in the center can globally inhibit Ras activation, while a gradient of AprA that naturally forms at the edge of the colony allows cells to activate Ras at sectors of the cell other than the sector of the cell closest to the center of the colony, effectively inducing both repulsion from the colony and cell differentiation. Together, these results suggest that a pathway that inhibits local Ras activation can mediate chemorepulsion.

Analysis of protrusion dynamics in amoeboid cell motility by means of regularized contour flows

Amoeboid cell motility is essential for a wide range of biological processes including wound healing, embryonic morphogenesis, and cancer metastasis. It relies on complex dynamical patterns of cell shape changes that pose long-standing challenges to mathematical modeling and raise a need for automated and reproducible approaches to extract quantitative morphological features from image sequences. Here, we introduce a theoretical framework and a computational method for obtaining smooth representations of the spatiotemporal contour dynamics from stacks of segmented microscopy images. Based on a Gaussian process regression we propose a one-parameter family of regularized contour flows that allows us to continuously track reference points (virtual markers) between successive cell contours. We use this approach to define a coordinate system on the moving cell boundary and to represent different local geometric quantities in this frame of reference. In particular, we introduce the local marker dispersion as a measure to identify localized membrane expansions and provide a fully automated way to extract the properties of such expansions, including their area and growth time. The methods are available as an open-source software package called AmoePy, a Python-based toolbox for analyzing amoeboid cell motility (based on time-lapse microscopy data), including a graphical user interface and detailed documentation. Due to the mathematical rigor of our framework, we envision it to be of use for the development of novel cell motility models. We mainly use experimental data of the social amoeba Dictyostelium discoideum to illustrate and validate our approach.

Amoeboid motion is a crawling-like cell migration that plays an important key role in multiple biological processes such as wound healing and cancer metastasis. This type of cell motility results from expanding and simultaneously contracting parts of the cell membrane. From fluorescence images, we obtain a sequence of points, representing the cell membrane, for each time step. By using regression analysis on these sequences, we derive smooth representations, so-called contours, of the membrane. Since the number of measurements is discrete and often limited, the question is raised of how to link consecutive contours with each other. In this work, we present a novel mathematical framework in which these links are described by regularized flows allowing a certain degree of concentration or stretching of neighboring reference points on the same contour. This stretching rate, the so-called local dispersion, is used to identify expansions and contractions of the cell membrane providing a fully automated way of extracting properties of these cell shape changes. We applied our methods to time-lapse microscopy data of the social amoeba Dictyostelium discoideum.

Adhesion strength and contractility enable metastatic cells to become adurotactic

Significant changes in cell stiffness, contractility, and adhesion, i.e., mechanotype, are observed during a variety of biological processes. Whether cell mechanics merely change as a side effect of or driver for biological processes is still unclear. Here, we sort genotypically similar metastatic cancer cells into strongly adherent (SA) versus weakly adherent (WA) phenotypes to study how contractility and adhesion differences alter the ability of cells to sense and respond to gradients in material stiffness. We observe that SA cells migrate up a stiffness gradient, or durotax, while WA cells largely ignore the gradient, i.e., adurotax. Biophysical modeling and experimental validation suggest that differences in cell migration and durotaxis between weakly and strongly adherent cells are driven by differences in intra-cellular actomyosin activity. These results provide a direct relationship between cell phenotype and durotaxis and suggest how, unlike other senescent cells, metastatic cancer cells navigate against stiffness gradients.

Cellular memory in eukaryotic chemotaxis depends on the background chemoattractant concentration

Cells of the social amoeba Dictyostelium discoideum migrate to a source of periodic traveling waves of chemoattractant as part of a self-organized aggregation process. An important part of this process is cellular memory, which enables cells to respond to the front of the wave and ignore the downward gradient in the back of the wave. During this aggregation, the background concentration of the chemoattractant gradually rises. In our microfluidic experiments, we exogenously applied periodic waves of chemoattractant with various background levels. We find that increasing background does not make detection of the wave more difficult, as would be naively expected. Instead, we see that the chemotactic efficiency significantly increases for intermediate values of the background concentration but decreases to almost zero for large values in a switch-like manner. These results are consistent with a computational model that contains a bistable memory module, along with a nonadaptive component. Within this model, an intermediate background level helps preserve directed migration by keeping the memory activated, but when the background level is higher, the directional stimulus from the wave is no longer sufficient to activate the bistable memory, suppressing directed migration. These results suggest that raising levels of chemoattractant background may facilitate the self-organized aggregation in Dictyostelium colonies.

Unified control of amoeboid pseudopod extension in multiple organisms by branched F-actin in the front and parallel F-actin/myosin in the cortex

The trajectory of moving eukaryotic cells depends on the kinetics and direction of extending pseudopods. The direction of pseudopods has been well studied to unravel mechanisms for chemotaxis, wound healing and inflammation. However, the kinetics of pseudopod extension-when and why do pseudopods start and stop- is equally important, but is largely unknown. Here the START and STOP of about 4000 pseudopods was determined in four different species, at four conditions and in nine mutants (fast amoeboids Dictyostelium and neutrophils, slow mesenchymal stem cells, and fungus B.d. chytrid with pseudopod and a flagellum). The START of a first pseudopod is a random event with a probability that is species-specific (23%/s for neutrophils). In all species and conditions, the START of a second pseudopod is strongly inhibited by the extending first pseudopod, which depends on parallel filamentous actin/myosin in the cell cortex. Pseudopods extend at a constant rate by polymerization of branched F-actin at the pseudopod tip, which requires the Scar complex. The STOP of pseudopod extension is induced by multiple inhibitory processes that evolve during pseudopod extension and mainly depend on the increasing size of the pseudopod. Surprisingly, no differences in pseudopod kinetics are detectable between polarized, unpolarized or chemotactic cells, and also not between different species except for small differences in numerical values. This suggests that the analysis has uncovered the fundament of cell movement with distinct roles for stimulatory branched F-actin in the protrusion and inhibitory parallel F-actin in the contractile cortex.

Computational models of migration modes improve our understanding of metastasis

Tumor cells migrate through changing microenvironments of diseased and healthy tissue, making their migration particularly challenging to describe. To better understand this process, computational models have been developed for both the ameboid and mesenchymal modes of cell migration. Here, we review various approaches that have been used to account for the physical environment's effect on cell migration in computational models, with a focus on their application to understanding cancer metastasis and the related phenomenon of durotaxis. We then discuss how mesenchymal migration models typically simulate complex cell–extracellular matrix (ECM) interactions, while ameboid migration models use a cell-focused approach that largely ignores ECM when not acting as a physical barrier. This approach greatly simplifies or ignores the mechanosensing ability of ameboid migrating cells and should be reevaluated in future models. We conclude by describing future model elements that have not been included to date but would enhance model accuracy.

A Computational Model for Cardiomyocytes Mechano-Electric Stimulation to Enhance Cardiac Tissue Regeneration

Electrical and mechanical stimulations play a key role in cell biological processes, being essential in processes such as cardiac cell maturation, proliferation, migration, alignment, attachment, and organization of the contractile machinery. However, the mechanisms that trigger these processes are still elusive. The coupling of mechanical and electrical stimuli makes it difficult to abstract conclusions. In this sense, computational models can establish parametric assays with a low economic and time cost to determine the optimal conditions of in-vitro experiments. Here, a computational model has been developed, using the finite element method, to study cardiac cell maturation, proliferation, migration, alignment, and organization in 3D matrices, under mechano-electric stimulation. Different types of electric fields (continuous, pulsating, and alternating) in an intensity range of 50–350 Vm−1, and extracellular matrix with stiffnesses in the range of 10–40 kPa, are studied. In these experiments, the group’s morphology and cell orientation are compared to define the best conditions for cell culture. The obtained results are qualitatively consistent with the bibliography. The electric field orientates the cells and stimulates the formation of elongated groups. Group lengthening is observed when applying higher electric fields in lower stiffness extracellular matrix. Groups with higher aspect ratios can be obtained by electrical stimulation, with better results for alternating electric fields.

Cell-substrate adhesion drives Scar/WAVE activation and phosphorylation by a Ste20-family kinase, which controls pseudopod lifetime

The Scar/WAVE complex is the principal catalyst of pseudopod and lamellipod formation. Here we show that Scar/WAVE's proline-rich domain is polyphosphorylated after the complex is activated. Blocking Scar/WAVE activation stops phosphorylation in both Dictyostelium and mammalian cells, implying that phosphorylation modulates pseudopods after they have been formed, rather than controlling whether they are initiated. Unexpectedly, phosphorylation is not promoted by chemotactic signaling but is greatly stimulated by cell:substrate adhesion and diminished when cells deadhere. Phosphorylation-deficient or phosphomimetic Scar/WAVE mutants are both normally functional and rescue the phenotype of knockout cells, demonstrating that phosphorylation is dispensable for activation and actin regulation. However, pseudopods and patches of phosphorylation-deficient Scar/WAVE last substantially longer in mutants, altering the dynamics and size of pseudopods and lamellipods and thus changing migration speed. Scar/WAVE phosphorylation does not require ERK2 in Dictyostelium or mammalian cells. However, the MAPKKK homologue SepA contributes substantially-sepA mutants have less steady-state phosphorylation, which does not increase in response to adhesion. The mutants also behave similarly to cells expressing phosphorylation-deficient Scar, with longer-lived pseudopods and patches of Scar recruitment. We conclude that pseudopod engagement with substratum is more important than extracellular signals at regulating Scar/WAVE's activity and that phosphorylation acts as a pseudopod timer by promoting Scar/WAVE turnover.

Symmetry Breaking during Cell Movement in the Context of Excitability, Kinetic Fine-Tuning and Memory of Pseudopod Formation

The path of moving eukaryotic cells depends on the kinetics and direction of extending pseudopods. Amoeboid cells constantly change their shape with pseudopods extending in different directions. Detailed analysis has revealed that time, place and direction of pseudopod extension are not random, but highly ordered with strong prevalence for only one extending pseudopod, with defined life-times, and with reoccurring events in time and space indicative of memory. Important components are Ras activation and the formation of branched F-actin in the extending pseudopod and inhibition of pseudopod formation in the contractile cortex of parallel F-actin/myosin. In biology, order very often comes with symmetry. In this essay, I discuss cell movement and the dynamics of pseudopod extension from the perspective of symmetry and symmetry changes of Ras activation and the formation of branched F-actin in the extending pseudopod. Combining symmetry of Ras activation with kinetics and memory of pseudopod extension results in a refined model of amoeboid movement that appears to be largely conserved in the fast moving Dictyostelium and neutrophils, the slow moving mesenchymal stem cells and the fungus B.d. chytrid.

ROLE OF OXYGEN CONCENTRATION IN THE OSTEOBLASTS BEHAVIOR: A FINITE ELEMENT MODEL

Oxygen concentration plays a key role in cell survival and viability. Besides, it has important effects on essential cellular biological processes such as cell migration, differentiation, proliferation and apoptosis. Therefore, the prediction of the cellular response to the alterations of the oxygen concentration can help significantly in the advances of cell culture research. Here, we present a 3D computational mechanotactic model to simulate all the previously mentioned cell processes under different oxygen concentrations. With this model, three cases have been studied. Starting with mesenchymal stem cells within an extracellular matrix with mechanical properties suitable for its differentiation into osteoblasts, and under different oxygen conditions to evaluate their behavior under normoxia, hypoxia and anoxia. The obtained results, which are consistent with the experimental observations, indicate that cells tend to migrate toward zones with higher oxygen concentration where they accelerate their differentiation and proliferation. This technique can be employed to control cell migration toward fracture zones to accelerate the healing process. Besides, as expected, to avoid cell apoptosis under conditions of anoxia and to avoid the inhibition of the differentiation and proliferation processes under conditions of hypoxia, the state of normoxia should be maintained throughout the entire cell-culture process.

An endogenous chemorepellent directs cell movement by inhibiting pseudopods at one side of cells

Eukaryotic chemoattraction signal transduction pathways, such as those used by Dictyostelium discoideum to move toward cAMP, use a G protein-coupled receptor to activate multiple conserved pathways such as PI3 kinase/Akt/PKB to induce actin polymerization and pseudopod formation at the front of a cell, and PTEN to localize myosin II to the rear of a cell. Relatively little is known about chemorepulsion. We previously found that AprA is a chemorepellent protein secreted by Dictyostelium cells. Here we used 29 cell lines with disruptions of cAMP and/or AprA signal transduction pathway components, and delineated the AprA chemorepulsion pathway. We find that AprA uses a subset of chemoattraction signal transduction pathways including Ras, protein kinase A, target of rapamycin (TOR), phospholipase A, and ERK1, but does not require the PI3 kinase/Akt/PKB and guanylyl cyclase pathways to induce chemorepulsion. Possibly as a result of not using the PI3 kinase/Akt/PKB pathway and guanylyl cyclases, AprA does not induce actin polymerization or increase the pseudopod formation rate, but rather appears to inhibit pseudopod formation at the side of cells closest to the source of AprA.

A stochastic algorithm for accurately predicting path persistence of cells migrating in 3D matrix environments

Cell mobility plays a critical role in immune response, wound healing, and the rate of cancer metastasis and tumor progression. Mobility within a three-dimensional (3D) matrix environment can be characterized by the average velocity of cell migration and the persistence length of the path it follows. Computational models that aim to predict cell migration within such 3D environments need to be able predict both of these properties as a function of the various cellular and extra-cellular factors that influence the migration process. A large number of models have been developed to predict the velocity of cell migration driven by cellular protrusions in 3D environments. However, prediction of the persistence of a cell's path is a more tedious matter, as it requires simulating cells for a long time while they migrate through the model extra-cellular matrix (ECM). This can be a computationally expensive process, and only recently have there been attempts to quantify cell persistence as a function of key cellular or matrix properties. Here, we propose a new stochastic algorithm that can simulate and analyze 3D cell migration occurring over days with a computation time of minutes, opening new possibilities of testing and predicting long-term cell migration behavior as a function of a large variety of cell and matrix properties. In this model, the matrix elements are generated as needed and stochastically based on the biophysical and biochemical properties of the ECM the cell migrates through. This approach significantly reduces the computational resources required to track and calculate cell matrix interactions. Using this algorithm, we predict the effect of various cellular and matrix properties such as cell polarity, cell mechanoactivity, matrix fiber density, matrix stiffness, fiber alignment, and fiber binding site density on path persistence of cellular migration and the mean squared displacement of cells over long periods of time.

Integration of in vitro and in silico Models Using Bayesian Optimization With an Application to Stochastic Modeling of Mesenchymal 3D Cell Migration

Cellular migration plays a crucial role in many aspects of life and development. In this paper, we propose a computational model of 3D migration that is solved by means of the tau-leaping algorithm and whose parameters have been calibrated using Bayesian optimization. Our main focus is two-fold: to optimize the numerical performance of the mechano-chemical model as well as to automate the calibration process of in silico models using Bayesian optimization. The presented mechano-chemical model allows us to simulate the stochastic behavior of our chemically reacting system in combination with mechanical constraints due to the surrounding collagen-based matrix. This numerical model has been used to simulate fibroblast migration. Moreover, we have performed in vitro analysis of migrating fibroblasts embedded in 3D collagen-based fibrous matrices (2 mg/ml). These in vitro experiments have been performed with the main objective of calibrating our model. Nine model parameters have been calibrated testing 300 different parametrizations using a completely automatic approach. Two competing evaluation metrics based on the Bhattacharyya coefficient have been defined in order to fit the model parameters. These metrics evaluate how accurately the in silico model is replicating in vitro measurements regarding the two main variables quantified in the experimental data (number of protrusions and the length of the longest protrusion). The selection of an optimal parametrization is based on the balance between the defined evaluation metrics. Results show how the calibrated model is able to predict the main features observed in the in vitro experiments.

Modeling random crawling, membrane deformation and intracellular polarity of motile amoeboid cells

Amoeboid movement is one of the most widespread forms of cell motility that plays a key role in numerous biological contexts. While many aspects of this process are well investigated, the large cell-to-cell variability in the motile characteristics of an otherwise uniform population remains an open question that was largely ignored by previous models. In this article, we present a mathematical model of amoeboid motility that combines noisy bistable kinetics with a dynamic phase field for the cell shape. To capture cell-to-cell variability, we introduce a single parameter for tuning the balance between polarity formation and intracellular noise. We compare numerical simulations of our model to experiments with the social amoeba Dictyostelium discoideum. Despite the simple structure of our model, we found close agreement with the experimental results for the center-of-mass motion as well as for the evolution of the cell shape and the overall intracellular patterns. We thus conjecture that the building blocks of our model capture essential features of amoeboid motility and may serve as a starting point for more detailed descriptions of cell motion in chemical gradients and confined environments.

Exploratory cell dynamics: a sense of touch for cells?

Cells need to process multifaceted external cues to steer their dynamic behavior. To efficiently perform this task, cells implement several exploratory mechanisms to actively sample their environment. In particular, cells can use exploratory actin-based cell protrusions and contractions to engage and squeeze the environment and to actively probe its chemical and mechanical properties. Multiple excitable signal networks were identified that can generate local activity pulses to control these exploratory processes. Such excitable signal networks offer particularly efficient mechanisms to process chemical or mechanical signals to steer dynamic cell behavior, such as directional migration, tissue morphogenesis and cell fate decisions.

WASP family proteins and formins compete in pseudopod- and bleb-based migration

Actin pseudopods induced by SCAR/WAVE drive normal migration and chemotaxis in eukaryotic cells. Cells can also migrate using blebs, in which the edge is driven forward by hydrostatic pressure instead of actin. In Dictyostelium discoideum, loss of SCAR is compensated by WASP moving to the leading edge to generate morphologically normal pseudopods. Here we use an inducible double knockout to show that cells lacking both SCAR and WASP are unable to grow, make pseudopods or, unexpectedly, migrate using blebs. Remarkably, amounts and dynamics of actin polymerization are normal. Pseudopods are replaced in double SCAR/WASP mutants by aberrant filopods, induced by the formin dDia2. Further disruption of the gene for dDia2 restores cells' ability to initiate blebs and thus migrate, though pseudopods are still lost. Triple knockout cells still contain near-normal F-actin levels. This work shows that SCAR, WASP, and dDia2 compete for actin. Loss of SCAR and WASP causes excessive dDia2 activity, maintaining F-actin levels but blocking pseudopod and bleb formation and migration.

Parallel signaling pathways regulate excitable dynamics differently for pseudopod formation in eukaryotic chemotaxis

In eukaryotic chemotaxis, parallel signaling pathways regulate the spatiotemporal pseudopod dynamics at the leading edge of a motile cell through characteristic dynamics of an excitable system; however, differences in the excitability and the physiological roles of individual pathways remain to be elucidated. Here we found that two different pathways, soluble guanylyl cyclase (sGC) and phosphatidylinositol 3-kinase (PI3K), exhibited similar all-or-none responses but different refractory periods by simultaneous observations of their excitable properties. Due to the shorter refractory period, sGC signaling responded more frequently to chemoattractants, leading to pseudopod formation with higher frequency. sGC excitability was regulated negatively by its product, cGMP, and cGMP-binding protein C (GbpC) through the suppression of F-actin polymerization, providing the underlying delayed negative feedback mechanism for the cyclical pseudopod formation. These results suggest that parallel pathways respond on different time-scales to environmental cues for chemotactic motility based on their intrinsic excitability. Key words: cGMP signaling, chemotaxis, excitability, pseudopod formation

The cytoskeleton regulates symmetry transitions in moving amoeboid cells

Symmetry and symmetry breaking are essential in biology. Symmetry comes in different forms: rotational symmetry, mirror symmetry and alternating right/left symmetry. Especially the transitions between the different symmetry forms specify crucial points in cell biology, including gastrulation in development, formation of the cleavage furrow in cell division, or the front in cell polarity. However, the mechanisms of these symmetry transitions are not well understood. Here we have investigated the fundaments of symmetry and symmetry transitions of the cytoskeleton during cell movement. Our data show that the dynamic shape changes of amoeboid cells are far from random, but are the consequence of refined symmetries and symmetry changes that are orchestrated by small G-proteins and the cytoskeleton, with local stimulation by F-actin and Scar , and local inhibition by IQGAP2 and myosin.

Modelling of Dictyostelium discoideum movement in a linear gradient of chemoattractant

Chemotaxis is a ubiquitous biological phenomenon in which cells detect a spatial gradient of chemoattractant, and then move towards the source. Here we present a position-dependent advection-diffusion model that quantitatively describes the statistical features of the chemotactic motion of the social amoeba Dictyostelium discoideum in a linear gradient of cAMP (cyclic adenosine monophosphate). We fit the model to experimental trajectories that are recorded in a microfluidic setup with stationary cAMP gradients and extract the diffusion and drift coefficients in the gradient direction. Our analysis shows that for the majority of gradients, both coefficients decrease over time and become negative as the cells crawl up the gradient. The extracted model parameters also show that besides the expected drift in the direction of the chemoattractant gradient, we observe a nonlinear dependency of the corresponding variance on time, which can be explained by the model. Furthermore, the results of the model show that the non-linear term in the mean squared displacement of the cell trajectories can dominate the linear term on large time scales.

Discrete Modeling of Amoeboid Locomotion and Chemotaxis in Dictyostelium discoideum by Tracking Pseudopodium Growth Direction

Dictyostelium discoideum amoeba is a well-established model organism for studying the crawling locomotion of eukaryotic cells. These amoebae extend pseudopodium - a temporary actin-based protrusion of their body membrane to probe the medium and crawl through it. Experiments show highly-ordered patterns in the growth direction of these pseudopodia, which results in persistence cell motility. Here, we propose a discrete model for studying and investigating the cell locomotion based on the experimental evidences. According to our model, Dictyostelium selects its pseudopodium growth direction based on a second-order Markov chain process, in the absence of external cues. Consequently, compared to a random walk process, our model indicates stronger growth in the mean-square displacement of cells, which is consistent with empirical findings. In the presence of external chemical stimulants, cells tend to align with the gradient of chemoattractant molecules. To quantify this tendency, we define a coupling coefficient between the pseudopodium extension direction and the gradient of an external stimulant, which depends on the local stimulant concentration and its gradient. Additionally, we generalize the model to weak-coupling regime by utilizing perturbation methods.

Mechanisms of Cell Polarization

Cell polarization is a key step in the migration, development, and organization of eukaryotic cells, both at the single cell and multicellular level. Research on the mechanisms that give rise to polarization of a given cell, and organization of polarity within a tissue has led to new understanding across cellular and developmental biology. In this review, we describe some of the history of theoretical and experimental aspects of the field, as well as some interesting questions and challenges for the future.

Coupled excitable Ras and F-actin activation mediates spontaneous pseudopod formation and directed cell movement

Chemotaxis is the mechanism by which cells move in the direction of chemical gradients. The central circuit connecting basal movement and gradient sensing is unknown. Ras activation and F-actin form one coupled excitable system, which is the beating heart of cell movement in both the absence and presence of external cues.

Many eukaryotic cells regulate their mobility by external cues. Genetic studies have identified >100 components that participate in chemotaxis, which hinders the identification of the conceptual framework of how cells sense and respond to shallow chemical gradients. The activation of Ras occurs during basal locomotion and is an essential connector between receptor and cytoskeleton during chemotaxis. Using a sensitive assay for activated Ras, we show here that activation of Ras and F-actin forms two excitable systems that are coupled through mutual positive feedback and memory. This coupled excitable system leads to short-lived patches of activated Ras and associated F-actin that precede the extension of protrusions. In buffer, excitability starts frequently with Ras activation in the back/side of the cell or with F-actin in the front of the cell. In a shallow gradient of chemoattractant, local Ras activation triggers full excitation of Ras and subsequently F-actin at the side of the cell facing the chemoattractant, leading to directed pseudopod extension and chemotaxis. A computational model shows that the coupled excitable Ras/F-actin system forms the driving heart for the ordered-stochastic extension of pseudopods in buffer and for efficient directional extension of pseudopods in chemotactic gradients.

Tuning cell migration: contractility as an integrator of intracellular signals from multiple cues

There has been immense progress in our understanding of the factors driving cell migration in both two-dimensional and three-dimensional microenvironments over the years. However, it is becoming increasingly evident that even though most cells share many of the same signaling molecules, they rarely respond in the same way to migration cues. To add to the complexity, cells are generally exposed to multiple cues simultaneously, in the form of growth factors and/or physical cues from the matrix. Understanding the mechanisms that modulate the intracellular signals triggered by multiple cues remains a challenge. Here, we will focus on the molecular mechanism involved in modulating cell migration, with a specific focus on how cell contractility can mediate the crosstalk between signaling initiated at cell-matrix adhesions and growth factor receptors.

A Worldwide Competition to Compare the Speed and Chemotactic Accuracy of Neutrophil-Like Cells

Chemotaxis is the ability to migrate towards the source of chemical gradients. It underlies the ability of neutrophils and other immune cells to hone in on their targets and defend against invading pathogens. Given the importance of neutrophil migration to health and disease, it is crucial to understand the basic mechanisms controlling chemotaxis so that strategies can be developed to modulate cell migration in clinical settings. Because of the complexity of human genetics, Dictyostelium and HL60 cells have long served as models system for studying chemotaxis. Since many of our current insights into chemotaxis have been gained from these two model systems, we decided to compare them side by side in a set of winner-take-all races, the Dicty World Races. These worldwide competitions challenge researchers to genetically engineer and pharmacologically enhance the model systems to compete in microfluidic racecourses. These races bring together technological innovations in genetic engineering and precision measurement of cell motility. Fourteen teams participated in the inaugural Dicty World Race 2014 and contributed cell lines, which they tuned for enhanced speed and chemotactic accuracy. The race enabled large-scale analyses of chemotaxis in complex environments and revealed an intriguing balance of speed and accuracy of the model cell lines. The successes of the first race validated the concept of using fun-spirited competition to gain insights into the complex mechanisms controlling chemotaxis, while the challenges of the first race will guide further technological development and planning of future events.

Challenges in tissue engineering - towards cell control inside artificial scaffolds

Control of living cells is vital for the survival of organisms. Each cell inside an organism is exposed to diverse external mechano-chemical cues, all coordinated in a spatio-temporal pattern triggering individual cell functions. This complex interplay between external chemical cues and mechanical 3D environments is translated into intracellular signaling loops. Here, we describe how external mechano-chemical cues control cell functions, especially cell migration, and influence intracellular information transport. In particular, this work focuses on the quantitative analysis of (1) intracellular vesicle transport to understand intracellular state changes in response to external cues, (2) cellular sensing of external chemotactic cues, and (3) the cells' ability to migrate in 3D structured environments, artificially fabricated to mimic the 3D environment of tissue in the human body.

Gβ Regulates Coupling between Actin Oscillators for Cell Polarity and Directional Migration

For directional movement, eukaryotic cells depend on the proper organization of their actin cytoskeleton. This engine of motility is made up of highly dynamic nonequilibrium actin structures such as flashes, oscillations, and traveling waves. In Dictyostelium, oscillatory actin foci interact with signals such as Ras and phosphatidylinositol 3,4,5-trisphosphate (PIP₃) to form protrusions. However, how signaling cues tame actin dynamics to produce a pseudopod and guide cellular motility is a critical open question in eukaryotic chemotaxis. Here, we demonstrate that the strength of coupling between individual actin oscillators controls cell polarization and directional movement. We implement an inducible sequestration system to inactivate the heterotrimeric G protein subunit Gβ and find that this acute perturbation triggers persistent, high-amplitude cortical oscillations of F-actin. Actin oscillators that are normally weakly coupled to one another in wild-type cells become strongly synchronized following acute inactivation of Gβ. This global coupling impairs sensing of internal cues during spontaneous polarization and sensing of external cues during directional motility. A simple mathematical model of coupled actin oscillators reveals the importance of appropriate coupling strength for chemotaxis: moderate coupling can increase sensitivity to noisy inputs. Taken together, our data suggest that Gβ regulates the strength of coupling between actin oscillators for efficient polarity and directional migration. As these observations are only possible following acute inhibition of Gβ and are masked by slow compensation in genetic knockouts, our work also shows that acute loss-of-function approaches can complement and extend the reach of classical genetics in Dictyostelium and likely other systems as well.

Coupling of individual oscillators regulates biological functions ranging from crickets chirping in unison to the coordination of pacemaker cells of the heart. This study finds that a similar concept—coupling between actin oscillators—is at work within single slime mold cells to establish polarity and guide their direction of migration.

The actin cytoskeleton of motile cells is comprised of highly dynamic structures. Recently, small oscillating actin foci have been discovered around the periphery of Dictyostelium cells. These oscillators are thought to enable pseudopod formation, but how their dynamics are regulated for this is unknown. Here, we demonstrate that the strength of coupling between individual actin oscillators controls cell polarization and directional movement. Actin oscillators are weakly coupled to one another in wild-type cells, but they become strongly synchronized after acute inactivation of the signaling protein Gβ. This global coupling impairs sensing of internal cues during spontaneous polarization and sensing of external cues during directional motility. Supported by a mathematical model, our data suggest that wild-type cells are tuned to an optimal coupling strength for patterning by upstream cues. These observations are only possible following acute inhibition of Gβ, which highlights the value of revisiting classical mutants with acute loss-of-function perturbations.

Directional memory arises from long-lived cytoskeletal asymmetries in polarized chemotactic cells

Chemotaxis, the directional migration of cells in a chemical gradient, is robust to fluctuations associated with low chemical concentrations and dynamically changing gradients as well as high saturating chemical concentrations. Although a number of reports have identified cellular behavior consistent with a directional memory that could account for behavior in these complex environments, the quantitative and molecular details of such a memory process remain unknown. Using microfluidics to confine cellular motion to a 1D channel and control chemoattractant exposure, we observed directional memory in chemotactic neutrophil-like cells. We modeled this directional memory as a long-lived intracellular asymmetry that decays slower than observed membrane phospholipid signaling. Measurements of intracellular dynamics revealed that moesin at the cell rear is a long-lived element that when inhibited, results in a reduction of memory. Inhibition of ROCK (Rho-associated protein kinase), downstream of RhoA (Ras homolog gene family, member A), stabilized moesin and directional memory while depolymerization of microtubules (MTs) disoriented moesin deposition and also reduced directional memory. Our study reveals that long-lived polarized cytoskeletal structures, specifically moesin, actomyosin, and MTs, provide a directional memory in neutrophil-like cells even as they respond on short time scales to external chemical cues.

Zigzag Generalized Lévy Walk: the In Vivo Search Strategy of Immunocytes

Immune responses are based on the coordinated searching behaviors of immunocytes that are aimed at tracking down specific targets. The search efficiency of immunocytes significantly affects the speed of initiation and development of immune responses. Previous studies have shown that not only the intermittent walk but also the zigzag turning preference of immunocytes contributes to the search efficiency. However, among existing models describing immunocytes' search strategy, none has captured both features. Here we propose a zigzag generalized Lévy walk model to describe the search strategy of immunocytes more accurately and comprehensively by considering both the intermittent and the zigzag-turning walk features. Based on the analysis of the searching behaviors of typical immune cell types, dendritic cells and leukocytes, in their native physiological environment, we demonstrate that the model can describe the in vivo search strategy of immunocytes well. Furthermore, by analyzing the search efficiency, we find that this type of search strategy enables immunocytes to capture rare targets in approximately half the time than the previously proposed generalized Lévy walk. This study sheds new light on the fundamental mechanisms that drive the efficient initiation and development of immune responses and in turn may lead to the development of novel therapeutic approaches for diseases ranging from infection to cancer.

Three-dimensional numerical model of cell morphology during migration in multi-signaling substrates

Cell Migration associated with cell shape changes are of central importance in many biological processes ranging from morphogenesis to metastatic cancer cells. Cell movement is a result of cyclic changes of cell morphology due to effective forces on cell body, leading to periodic fluctuations of the cell length and cell membrane area. It is well-known that the cell can be guided by different effective stimuli such as mechanotaxis, thermotaxis, chemotaxis and/or electrotaxis. Regulation of intracellular mechanics and cell's physical interaction with its substrate rely on control of cell shape during cell migration. In this notion, it is essential to understand how each natural or external stimulus may affect the cell behavior. Therefore, a three-dimensional (3D) computational model is here developed to analyze a free mode of cell shape changes during migration in a multi-signaling micro-environment. This model is based on previous models that are presented by the same authors to study cell migration with a constant spherical cell shape in a multi-signaling substrates and mechanotaxis effect on cell morphology. Using the finite element discrete methodology, the cell is represented by a group of finite elements. The cell motion is modeled by equilibrium of effective forces on cell body such as traction, protrusion, electrostatic and drag forces, where the cell traction force is a function of the cell internal deformations. To study cell behavior in the presence of different stimuli, the model has been employed in different numerical cases. Our findings, which are qualitatively consistent with well-known related experimental observations, indicate that adding a new stimulus to the cell substrate pushes the cell to migrate more directionally in more elongated form towards the more effective stimuli. For instance, the presence of thermotaxis, chemotaxis and electrotaxis can further move the cell centroid towards the corresponding stimulus, respectively, diminishing the mechanotaxis effect. Besides, the stronger stimulus imposes a greater cell elongation and more cell membrane area. The present model not only provides new insights into cell morphology in a multi-signaling micro-environment but also enables us to investigate in more precise way the cell migration in the presence of different stimuli.

Extracellular and intracellular factors regulating the migration direction of a chemotactic cell in traveling-wave chemotaxis

This report presents a simple model that describes the motion of a single Dictyostelium discoideum cell exposed to a traveling wave of cyclic adenosine monophosphate (cAMP). The model incorporates two types of responses to stimulation by cAMP: the changes in the polarity and motility of the cell. The periodic change in motility is assumed to be induced by periodic cAMP stimulation on the basis of previous experimental studies. Consequently, the net migration of the cell occurs in a particular direction with respect to wave propagation, which explains the migration of D. discoideum cells in aggregation. The wave period and the difference between the two response times are important parameters that determine the direction of migration. The theoretical prediction compared with experiments presented in another study. The transition from the single-cell state of the population of D. discoideum cells to the aggregation state is understood to be a specific example of spontaneous breakage of symmetry in biology.

Scanning x-ray nanodiffraction on Dictyostelium discoideum

We have performed scanning x-ray nanobeam diffraction experiments on single cells of the amoeba Dictyostelium discoideum. Cells have been investigated in 1), freeze-dried, 2), frozen-hydrated (vitrified), and 3), initially alive states. The spatially resolved small-angle x-ray scattering signal shows characteristic streaklike patterns in reciprocal space, which we attribute to fiber bundles of the actomyosin network. From the intensity distributions, an anisotropy parameter can be derived that indicates pronounced local variations within the cell. In addition to nanobeam small-angle x-ray scattering, we have evaluated the x-ray differential phase contrast in view of the projected electron density. Different experimental aspects of the x-ray experiment, sample preparation, and data analysis are discussed. Finally, the x-ray results are correlated with optical microscopy (differential phase contrast and confocal microscopy of mutant strains with fluorescently labeled actin and myosin II), which have been carried out in live and fixed states, including optical microscopy under cryogenic conditions.

Chemotactic signaling in mesenchymal cells compared to amoeboid cells

Cell chemotaxis plays a pivotal role in normal development, inflammatory response, injury repair and tissue regeneration in all organisms. It is also a critical contributor to cancer metastasis, altered angiogenesis and neurite growth in disease. The molecular mechanisms regulating chemotaxis are currently being identified and key components may be pertinent therapeutic targets. Although these components appear to be mostly common in various cells, there are important differences in chemotactic signaling networks and signal processing that result in the distinct chemotactic behavior of mesenchymal cells compared to much better studied amoeboid blood cells. These differences are not necessarily predetermined based on cell type, but are rather chosen and exploited by cells to modify their chemotactic behavior based on physical constraints and/or environmental conditions. This results in a specific type of chemotactic migration in mesenchymal cells that can be selectively targeted in disease. Here, we compare the chemotactic behavior, signaling and motility of mesenchymal and amoeboid cells. We suggest that the current model of chemotaxis is applicable for small amoeboid cells but needs to be reconsidered for large mesenchymal cells. We focus on new candidate regulatory molecules and feedback mechanisms that may account for mesenchymal cell type-specific chemotaxis.

Cellular memory in eukaryotic chemotaxis

Natural chemical gradients to which cells respond chemotactically are often dynamic, with both spatial and temporal components. A primary example is the social amoeba Dictyostelium, which migrates to the source of traveling waves of chemoattractant as part of a self-organized aggregation process. Despite its physiological importance, little is known about how cells migrate directionally in response to traveling waves. The classic back-of-the-wave problem is how cells chemotax toward the wave source, even though the spatial gradient reverses direction in the back of the wave. Here, we address this problem by using microfluidics to expose cells to traveling waves of chemoattractant with varying periods. We find that cells exhibit memory and maintain directed motion toward the wave source in the back of the wave for the natural period of 6 min, but increasingly reverse direction for longer wave periods. Further insights into cellular memory are provided by experiments quantifying cell motion and localization of a directional-sensing marker after rapid gradient switches. The results can be explained by a model that couples adaptive directional sensing to bistable cellular memory. Our study shows how spatiotemporal cues can guide cell migration over large distances.

Computational modelling of multi-cell migration in a multi-signalling substrate

Cell migration is a vital process in many biological phenomena ranging from wound healing to tissue regeneration. Over the past few years, it has been proven that in addition to cell-cell and cell-substrate mechanical interactions (mechanotaxis), cells can be driven by thermal, chemical and/or electrical stimuli. A numerical model was recently presented by the authors to analyse single cell migration in a multi-signalling substrate. That work is here extended to include multi-cell migration due to cell-cell interaction in a multi-signalling substrate under different conditions. This model is based on balancing the forces that act on the cell population in the presence of different guiding cues. Several numerical experiments are presented to illustrate the effect of different stimuli on the trajectory and final location of the cell population within a 3D heterogeneous multi-signalling substrate. Our findings indicate that although multi-cell migration is relatively similar to single cell migration in some aspects, the associated behaviour is very different. For instance, cell-cell interaction may delay single cell migration towards effective cues while increasing the magnitude of the average net cell traction force as well as the local velocity. Besides, the random movement of a cell within a cell population is slightly greater than that of single cell migration. Moreover, higher electrical field strength causes the cell slug to flatten near the cathode. On the other hand, as with single cell migration, the existence of electrotaxis dominates mechanotaxis, moving the cells to the cathode or anode pole located at the free surface. The numerical results here obtained are qualitatively consistent with related experimental works.

PIP₃-dependent macropinocytosis is incompatible with chemotaxis

In eukaryotic chemotaxis, the mechanisms connecting external signals to the motile apparatus remain unclear. The role of the lipid phosphatidylinositol 3,4,5-trisphosphate (PIP₃) has been particularly controversial. PIP₃ has many cellular roles, notably in growth control and macropinocytosis as well as cell motility. Here we show that PIP₃ is not only unnecessary for Dictyostelium discoideum to migrate toward folate, but actively inhibits chemotaxis. We find that macropinosomes, but not pseudopods, in growing cells are dependent on PIP₃. PIP₃ patches in these cells show no directional bias, and overall only PIP₃-free pseudopods orient up-gradient. The pseudopod driver suppressor of cAR mutations (SCAR)/WASP and verprolin homologue (WAVE) is not recruited to the center of PIP₃ patches, just the edges, where it causes macropinosome formation. Wild-type cells, unlike the widely used axenic mutants, show little macropinocytosis and few large PIP₃ patches, but migrate more efficiently toward folate. Tellingly, folate chemotaxis in axenic cells is rescued by knocking out phosphatidylinositide 3-kinases (PI 3-kinases). Thus PIP₃ promotes macropinocytosis and interferes with pseudopod orientation during chemotaxis of growing cells.

Distinct cell shapes determine accurate chemotaxis

The behaviour of an organism often reflects a strategy for coping with its environment. Such behaviour in higher organisms can often be reduced to a few stereotyped modes of movement due to physiological limitations, but finding such modes in amoeboid cells is more difficult as they lack these constraints. Here, we examine cell shape and movement in starved Dictyostelium amoebae during migration toward a chemoattractant in a microfluidic chamber. We show that the incredible variety in amoeboid shape across a population can be reduced to a few modes of variation. Interestingly, cells use distinct modes depending on the applied chemical gradient, with specific cell shapes associated with shallow, difficult-to-sense gradients. Modelling and drug treatment reveals that these behaviours are intrinsically linked with accurate sensing at the physical limit. Since similar behaviours are observed in a diverse range of cell types, we propose that cell shape and behaviour are conserved traits.

Oscillatory behavior of neutrophils under opposing chemoattractant gradients supports a winner-take-all mechanism

Neutrophils constitute the largest class of white blood cells and are the first responders in the innate immune response. They are able to sense and migrate up concentration gradients of chemoattractants in search of primary sites of infection and inflammation through a process known as chemotaxis. These chemoattractants include formylated peptides and various chemokines. While much is known about chemotaxis to individual chemoattractants, far less is known about chemotaxis towards many. Previous studies have shown that in opposing gradients of intermediate chemoattractants (interleukin-8 and leukotriene B₄), neutrophils preferentially migrate toward the more distant source. In this work, we investigated neutrophil chemotaxis in opposing gradients of chemoattractants using a microfluidic platform. We found that primary neutrophils exhibit oscillatory motion in opposing gradients of intermediate chemoattractants. To understand this behavior, we constructed a mathematical model of neutrophil chemotaxis. Our results suggest that sensory adaptation alone cannot explain the observed oscillatory motion. Rather, our model suggests that neutrophils employ a winner-take-all mechanism that enables them to transiently lock onto sensed targets and continuously switch between the intermediate attractant sources as they are encountered. These findings uncover a previously unseen behavior of neutrophils in opposing gradients of chemoattractants that will further aid in our understanding of neutrophil chemotaxis and the innate immune response. In addition, we propose a winner-take-all mechanism allows the cells to avoid stagnation near local chemical maxima when migrating through a network of chemoattractant sources.

Ras activation and symmetry breaking during Dictyostelium chemotaxis

Central to chemotaxis is the molecular mechanism by which a shallow spatial gradient of chemoattractant induces symmetry breaking of activated signaling molecules. Previously, we have used Dictyostelium mutants to investigate the minimal requirements for chemotaxis, and identified a basal signaling module providing activation of Ras and F-actin at the leading edge. Here, we show that Ras activation after application of a pipette releasing the chemoattractant cAMP has three phases, each depending on specific guanine-nucleotide-exchange factors (GEFs). Initially a transient activation of Ras occurs at the entire cell boundary, which is proportional to the local cAMP concentrations and therefore slightly stronger at the front than in the rear of the cell. This transient Ras activation is present in gα2 (gpbB)-null cells but not in gβ (gpbA)-null cells, suggesting that Gβγ mediates the initial activation of Ras. The second phase is symmetry breaking: Ras is activated only at the side of the cell closest to the pipette. Symmetry breaking absolutely requires Gα2 and Gβγ, but not the cytoskeleton or four cAMP-induced signaling pathways, those dependent on phosphatidylinositol (3,4,5)-triphosphate [PtdIns(3,4,5)P3], cGMP, TorC2 and PLA2. As cells move in the gradient, the crescent of activated Ras in the front half of the cell becomes confined to a small area at the utmost front of the cell. Confinement of Ras activation leads to cell polarization, and depends on cGMP formation, myosin and F-actin. The experiments show that activation, symmetry breaking and confinement of Ras during Dictyostelium chemotaxis uses different G-protein subunits and a multitude of Ras GEFs and GTPase-activating proteins (GAPs).

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.

Chemotaxis is the movement of cells in response to spatial gradients of chemical cues. While single-celled organisms rely on sensing and responding to chemical gradients to search for nutrients, chemotaxis is also an essential component of the mammalian immune system. However, chemotaxis can also be deleterious, since chemotactic tumor cells can lead to metastasis. Due to its importance, understanding the process by which cells sense and respond to chemical gradients has attracted considerable interest. Moreover, because of the complexity of chemotactic signaling, which includes multiple feedback loops and redundant pathways, this has been a research area in which computational models have had a significant impact in understanding experimental findings. Here, we propose a modular description of the signaling network that regulates chemotaxis. The modules describe different processes that are observed in chemotactic cells. In addition to accounting for these behaviors individually, we show that the overall system recreates many features of the directed motion of migrating cells. The signaling described by our modules is implemented as a series of equations, whereas movement and the accompanying cellular deformations are simulated using a mechanical model of the cell and implemented using level set methods, a method that allows simulations of cells as they change morphology.

Modeling and measuring signal relay in noisy directed migration of cell groups

We develop a coarse-grained stochastic model for the influence of signal relay on the collective behavior of migrating Dictyostelium discoideum cells. In the experiment, cells display a range of collective migration patterns, including uncorrelated motion, formation of partially localized streams, and clumping, depending on the type of cell and the strength of the external, linear concentration gradient of the signaling molecule cyclic adenosine monophosphate (cAMP). From our model, we find that the pattern of migration can be quantitatively described by the competition of two processes, the secretion rate of cAMP by the cells and the degradation rate of cAMP in the gradient chamber. Model simulations are compared to experiments for a wide range of strengths of an external linear-gradient signal. With degradation, the model secreting cells form streams and efficiently transverse the gradient, but without degradation, we find that model secreting cells form clumps without streaming. This indicates that the observed effective collective migration in streams requires not only signal relay but also degradation of the signal. In addition, our model allows us to detect and quantify precursors of correlated motion, even when cells do not exhibit obvious streaming.

Collective cell migration is observed in various biological processes including angiogenesis, gastrulation, fruiting body formation, and wound healing. Dictyostelium discoideum, for example, exhibits highly dynamic patterns such as streams and clumps during its early phases of collective motion and has served as a model organism for the study of collective migration. In this study, facilitated by experiments, we develop a conceptual, minimalistic, computational model to analyze the dynamical processes leading to the emergence of collective patterns and the associated dependence on the external injection of a cAMP signal, the intercellular cAMP secretion rate, and the cAMP degradation rate. We demonstrate that degradation is necessary to reproduce the experimentally observed collective migration patterns, and show how our model can be utilized to uncover basic dependences of migration modes on cell characteristics. Our numerical observations elucidate the different possible types of motion and quantify the onset of collective motion. Thus, the model allows us to distinguish noisy motion guided by the external signal from weakly correlated motion.

3D computational modelling of cell migration: a mechano-chemo-thermo-electrotaxis approach

Single cell migration constitutes a fundamental phenomenon involved in many biological events such as wound healing, cancer development and tissue regeneration. Several experiments have demonstrated that, besides the mechanical driving force (mechanotaxis), cell migration may be also influenced by chemical, thermal and/or electrical cues. In this paper, we present an extension of a previous model of the same authors adding the effects of chemotaxis, thermotaxis and electrotaxis to the initial mechanotaxis model of cell migration, allowing us to predict cell migration behaviour under different conditions and substrate properties. The present model is based on the balance of effective forces during cell motility in the presence of the several guiding cues. This model has been applied to several numerical experiments to demonstrate the effect of the different drivers onto the cell path and final location within a certain three-dimensional substrate with heterogeneous properties. Our findings indicate that the presence of the chemotaxis, thermotaxis and/or electrotaxis reduce, in general, the random component of cell movement, being this reduction more important in the case of electrotaxis that can be considered a dominating signal during cell migration (besides the underlying mechanical effects). These results are qualitatively in agreement with well-known experimental ones.