Orientation of chemotactic cells and growth cones: models and mechanisms

Co-existence of Ras activation in a chemotactic signal transduction pathway and in an autonomous wave - forming system

The activation of Ras is common to two activities in cells of Dictyostelium discoideum: the directed movement in a gradient of chemoattractant and the autonomous generation of propagating waves of actin polymerization on the substrate-attached cell surface. We produced large cells by electric-pulse induced fusion to simultaneously study both activities in one cell. For imaging, a fluorescent label for activated Ras was combined with labels for filamentous actin, PIP3, or PTEN. Chemotactic responses were elicited in a diffusion gradient of cyclic AMP. Waves initiated at sites separate from the front of the cell propagated in all directions. Nevertheless, the wave-forming cells were capable of recognizing the attractant gradient and managed to migrate in its direction.

Exploring the inhibitory effect of membrane tension on cell polarization

Cell polarization toward an attractant is influenced by both physical and chemical factors. Most existing mathematical models are based on reaction-diffusion systems and only focus on the chemical process occurring during cell polarization. However, membrane tension has been shown to act as a long-range inhibitor of cell polarization. Here, we present a cell polarization model incorporating the interplay between Rac GTPase, filamentous actin (F-actin), and cell membrane tension. We further test the predictions of this model by performing single cell measurements of the spontaneous polarization of cancer stem cells (CSCs) and non-stem cancer cells (NSCCs), as the former have lower cell membrane tension. Based on both our model and the experimental results, cell polarization is more sensitive to stimuli under low membrane tension, and high membrane tension improves the robustness and stability of cell polarization such that polarization persists under random perturbations. Furthermore, our simulations are the first to recapitulate the experimental results described by Houk et al., revealing that aspiration (elevation of tension) and release (reduction of tension) result in a decrease in and recovery of the activity of Rac-GTP, respectively, and that the relaxation of tension induces new polarity of the cell body when a cell with the pseudopod-neck-body morphology is severed.

Biomaterials and computation: a strategic alliance to investigate emergent responses of neural cells

Synergistic use of biomaterials and computation allows to identify and unravel neural cell responses.

Multi-phasic bi-directional chemotactic responses of the growth cone

The nerve growth cone is bi-directionally attracted and repelled by the same cue molecules depending on the situations, while other non-neural chemotactic cells usually show uni-directional attraction or repulsion toward their specific cue molecules. However, how the growth cone differs from other non-neural cells remains unclear. Toward this question, we developed a theory for describing chemotactic response based on a mathematical model of intracellular signaling of activator and inhibitor. Our theory was first able to clarify the conditions of attraction and repulsion, which are determined by balance between activator and inhibitor, and the conditions of uni- and bi-directional responses, which are determined by dose-response profiles of activator and inhibitor to the guidance cue. With biologically realistic sigmoidal dose-responses, our model predicted tri-phasic turning response depending on intracellular Ca²⁺ level, which was then experimentally confirmed by growth cone turning assays and Ca²⁺ imaging. Furthermore, we took a reverse-engineering analysis to identify balanced regulation between CaMKII (activator) and PP1 (inhibitor) and then the model performance was validated by reproducing turning assays with inhibitions of CaMKII and PP1. Thus, our study implies that the balance between activator and inhibitor underlies the multi-phasic bi-directional turning response of the growth cone.

Computational model for amoeboid motion: Coupling membrane and cytosol dynamics

A distinguishing feature of amoeboid motion is that the migrating cell undergoes large deformations, caused by the emergence and retraction of actin-rich protrusions, called pseudopods. Here, we propose a cell motility model that represents pseudopod dynamics, as well as its interaction with membrane signaling molecules. The model accounts for internal and external forces, such as protrusion, contraction, adhesion, surface tension, or those arising from cell-obstacle contacts. By coupling the membrane and cytosol interactions we are able to reproduce a realistic picture of amoeboid motion. The model results are in quantitative agreement with experiments and show how cells may take advantage of the geometry of their microenvironment to migrate more efficiently.

A mathematical model of GTPase pattern formation during single-cell wound repair

Rho GTPases are regulatory proteins whose patterns on the surface of a cell affect cell polarization, cell motility and repair of single-cell wounds. The stereotypical patterns formed by two such proteins, Rho and Cdc42, around laser-injured frog oocytes permit experimental analysis of GTPase activation, inactivation, segregation and crosstalk. Here, we review the development and analysis of a spatial model of GTPase dynamics that describe the formation of concentric zones of Rho and Cdc42 activity around wounds, and describe how this model has provided insights into the roles of the GTPase effector molecules protein kinase C (PKCβ and PKCη) and guanosine nucleotide dissociation inhibitor (GDI) in the wound response. We further demonstrate how the use of a 'sharp switch' model approximation in combination with bifurcation analysis can aid mapping the model behaviour in parameter space (approximate results confirmed with numerical simulation methods). Using these methods in combination with experimental manipulation of PKC activity (PKC overexpression (OE) and dominant negative conditions), we have shown that: (i) PKCβ most probably acts by enhancing existing positive feedbacks (from Rho to itself via the guanosine nucleotide exchange factor domain of Abr, and from Cdc42 to itself), (ii) PKCη most probably increases basal rates of inactivation (or possibly decreases basal rates of activation) of Rho and Cdc42, and (iii) the graded distribution of PKCη and its effect on initial Rho activity accounts for inversion of zones in a fraction (20%) of PKCη OE cells. Finally, we speculate that GDIs (which sequester GTPases) may have a critical role in defining the spatial domain, where the wound response may occur. This paper provides a more thorough exposition of the methods of analysis used in the investigation, whereas previous work on this topic was addressed to biologists and abbreviated such discussion.

Progress and perspectives in signal transduction, actin dynamics, and movement at the cell and tissue level: lessons from Dictyostelium

Movement of cells and tissues is a basic biological process that is used in development, wound repair, the immune response to bacterial invasion, tumour formation and metastasis, and the search for food and mates. While some cell movement is random, directed movement stimulated by extracellular signals is our focus here. This involves a sequence of steps in which cells first detect extracellular chemical and/or mechanical signals via membrane receptors that activate signal transduction cascades and produce intracellular signals. These intracellular signals control the motile machinery of the cell and thereby determine the spatial localization of the sites of force generation needed to produce directed motion. Understanding how force generation within cells and mechanical interactions with their surroundings, including other cells, are controlled in space and time to produce cell-level movement is a major challenge, and involves many issues that are amenable to mathematical modelling.

Local modulation of chemoattractant concentrations by single cells: dissection using a bulk-surface computational model

Chemoattractant gradients are usually considered in terms of sources and sinks that are independent of the chemotactic cell. However, recent interest has focused on 'self-generated' gradients, in which cell populations create their own local gradients as they move. Here, we consider the interplay between chemoattractants and single cells. To achieve this, we extend a recently developed computational model to incorporate breakdown of extracellular attractants by membrane-bound enzymes. Model equations are parametrized, using the published estimates from Dictyostelium cells chemotaxing towards cyclic AMP. We find that individual cells can substantially modulate their local attractant field under physiologically appropriate conditions of attractant and enzymes. This means the attractant concentration perceived by receptors can be a small fraction of the ambient concentration. This allows efficient chemotaxis in chemoattractant concentrations that would be saturating without local breakdown. Similar interactions in which cells locally mould a stimulus could function in many types of directed cell motility, including haptotaxis, durotaxis and even electrotaxis.

Effects of 3D geometries on cellular gradient sensing and polarization

During cell migration, cells become polarized, change their shape, and move in response to various internal and external cues. Cell polarization is defined through the spatio-temporal organization of molecules such as PI3K or small GTPases, and is determined by intracellular signaling networks. It results in directional forces through actin polymerization and myosin contractions. Many existing mathematical models of cell polarization are formulated in terms of reaction-diffusion systems of interacting molecules, and are often defined in one or two spatial dimensions. In this paper, we introduce a 3D reaction-diffusion model of interacting molecules in a single cell, and find that cell geometry has an important role affecting the capability of a cell to polarize, or change polarization when an external signal changes direction. Our results suggest a geometrical argument why more roundish cells can repolarize more effectively than cells which are elongated along the direction of the original stimulus, and thus enable roundish cells to turn faster, as has been observed in experiments. On the other hand, elongated cells preferentially polarize along their main axis even when a gradient stimulus appears from another direction. Furthermore, our 3D model can accurately capture the effect of binding and unbinding of important regulators of cell polarization to and from the cell membrane. This spatial separation of membrane and cytosol, not possible to capture in 1D or 2D models, leads to marked differences of our model from comparable lower-dimensional models.

Where to Go: Breaking the Symmetry in Cell Motility

Cell migration in the “correct” direction is pivotal for many biological processes. Although most work is devoted to its molecular mechanisms, the cell’s preference for one direction over others, thus overcoming intrinsic random motility, epitomizes a profound principle that underlies all complex systems: the choice of one axis, in structure or motion, from a uniform or symmetric set of options. Explaining directional motility by an external chemo-attractant gradient does not solve but only shifts the problem of causation: whence the gradient? A new study in PLOS Biology shows cell migration in a self-generated gradient, offering an opportunity to take a broader look at the old dualism of extrinsic instruction versus intrinsic symmetry-breaking in cell biology.

Directional cell motility is enabled by chemoattractant gradient and symmetry-breaking. This Primer argues that the recent observation of cells generating a gradient in a uniformly distributed nutrient reveals the multilayered nature of symmetry-breaking in cell locomotion.

A Model for Direction Sensing in Dictyostelium discoideum: Ras Activity and Symmetry Breaking Driven by a Gβγ-Mediated, Gα2-Ric8 -- Dependent Signal Transduction Network

Chemotaxis is a dynamic cellular process, comprised of direction sensing, polarization and locomotion, that leads to the directed movement of eukaryotic cells along extracellular gradients. As a primary step in the response of an individual cell to a spatial stimulus, direction sensing has attracted numerous theoretical treatments aimed at explaining experimental observations in a variety of cell types. Here we propose a new model of direction sensing based on experiments using Dictyostelium discoideum (Dicty). The model is built around a reaction-diffusion-translocation system that involves three main component processes: a signal detection step based on G-protein-coupled receptors (GPCR) for cyclic AMP (cAMP), a transduction step based on a heterotrimetic G protein Gα2βγ, and an activation step of a monomeric G-protein Ras. The model can predict the experimentally-observed response of cells treated with latrunculin A, which removes feedback from downstream processes, under a variety of stimulus protocols. We show that [Formula: see text] cycling modulated by Ric8, a nonreceptor guanine exchange factor for [Formula: see text] in Dicty, drives multiple phases of Ras activation and leads to direction sensing and signal amplification in cAMP gradients. The model predicts that both [Formula: see text] and Gβγ are essential for direction sensing, in that membrane-localized [Formula: see text], the activated GTP-bearing form of [Formula: see text], leads to asymmetrical recruitment of RasGEF and Ric8, while globally-diffusing Gβγ mediates their activation. We show that the predicted response at the level of Ras activation encodes sufficient 'memory' to eliminate the 'back-of-the wave' problem, and the effects of diffusion and cell shape on direction sensing are also investigated. In contrast with existing LEGI models of chemotaxis, the results do not require a disparity between the diffusion coefficients of the Ras activator GEF and the Ras inhibitor GAP. Since the signal pathways we study are highly conserved between Dicty and mammalian leukocytes, the model can serve as a generic one for direction sensing.

A computational method for the coupled solution of reaction-diffusion equations on evolving domains and manifolds: Application to a model of cell migration and chemotaxis

In this paper, we devise a moving mesh finite element method for the approximate solution of coupled bulk-surface reaction-diffusion equations on an evolving two dimensional domain. Fundamental to the success of the method is the robust generation of bulk and surface meshes. For this purpose, we use a novel moving mesh partial differential equation (MMPDE) approach. The developed method is applied to model problems with known analytical solutions; these experiments indicate second-order spatial and temporal accuracy. Coupled bulk-surface problems occur frequently in many areas; in particular, in the modelling of eukaryotic cell migration and chemotaxis. We apply the method to a model of the two-way interaction of a migrating cell in a chemotactic field, where the bulk region corresponds to the extracellular region and the surface to the cell membrane.

Role of Polarized G Protein Signaling in Tracking Pheromone Gradients

Yeast cells track gradients of pheromones to locate mating partners. Intuition suggests that uniform distribution of pheromone receptors over the cell surface would yield optimal gradient sensing. However, yeast cells display polarized receptors. The benefit of such polarization was unknown. During gradient tracking, cell growth is directed by a patch of polarity regulators that wanders around the cortex. Patch movement is sensitive to pheromone dose, with wandering reduced on the up-gradient side of the cell, resulting in net growth in that direction. Mathematical modeling suggests that active receptors and associated G proteins lag behind the polarity patch and act as an effective drag on patch movement. In vivo, the polarity patch is trailed by a G protein-rich domain, and this polarized distribution of G proteins is required to constrain patch wandering. Our findings explain why G protein polarization is beneficial and illuminate a novel mechanism for gradient tracking.

Linking morphodynamics and directional persistence of T lymphocyte migration

T cells play a central role in the adaptive immune response, and their directed migration is essential for homing to sites of antigen presentation. Like neutrophils, T lymphocytes are rapidly moving cells that exhibit amoeboid movement, characterized by a definitive polarity with F-actin concentrated at the front and myosin II elsewhere. In this study, we used total internal reflection fluorescence (TIRF) microscopy to monitor the cells' areas of contact with a surface presenting adhesive ICAM-1 and the chemokine, CXCL12/SDF-1. Our analysis reveals that T-cell migration and reorientation are achieved by bifurcation and lateral separation of protrusions along the leading membrane edge, followed by cessation of one of the protrusions, which acts as a pivot for cell turning. We show that the distribution of bifurcation frequencies exhibits characteristics of a random, spontaneous process; yet, the waiting time between bifurcation events depends on whether or not the pivot point remains on the same side of the migration axis. Our analysis further suggests that switching of the dominant protrusion between the two sides of the migration axis is associated with persistent migration, whereas the opposite is true of cell turning. To help explain the bifurcation phenomenon and how distinct migration behaviours might arise, a spatio-temporal, stochastic model describing F-actin dynamics is offered.

Direct measurement of oscillatory RhoA activity in embryonic cortical neurons stimulated with the axon guidance cue netrin-1 using fluorescence resonance energy transfer

BACKGROUND INFORMATION

Rho GTPases play an essential role during the development of the nervous system. They induce cytoskeletal rearrangements that are critical for the regulation of axon outgrowth and guidance. It is generally accepted that Rac1 and Cdc42 are positive regulators of axon outgrowth and guidance, whereas RhoA is a negative regulator. However, spatiotemporal control of their activity can modify the function of Rho GTPases during axonal morphogenesis. Signalling downstream of the axon guidance cue netrin-1 and its receptor deleted in colorectal cancer (DCC) triggers the activation of Rac1 and the inhibition of RhoA to promote axon outgrowth. However, our previous work also suggests that netrin-1/DCC signalling can activate RhoA in a time- and region-specific manner.

RESULTS

Here, we visualised RhoA activation in response to netrin-1 in live embryonic cortical neurons using fluorescence resonance energy transfer. RhoA activity oscillated in unstimulated neurons and netrin-1 increased the amplitude of the oscillations in growth cones after 5 min of stimulation. Within this period of time, netrin-1 transiently increased RhoA activity and modulated the pattern of RhoA oscillations. We found that the timing of netrin-1-induced RhoA activation was different in whole neurons, cell bodies and growth cones.

CONCLUSIONS

We conclude that netrin-1 modulates the spatiotemporal activation of RhoA in embryonic cortical neurons.

SIGNIFICANCE

This study demonstrates for the first time the short-term localised activation of RhoA in neuronal growth cones by the axon guidance cue netrin-1.

Limits to the precision of gradient sensing with spatial communication and temporal integration

Gradient sensing requires at least two measurements at different points in space. These measurements must then be communicated to a common location to be compared, which is unavoidably noisy. Although much is known about the limits of measurement precision by cells, the limits placed by the communication are not understood. Motivated by recent experiments, we derive the fundamental limits to the precision of gradient sensing in a multicellular system, accounting for communication and temporal integration. The gradient is estimated by comparing a "local" and a "global" molecular reporter of the external concentration, where the global reporter is exchanged between neighboring cells. Using the fluctuation-dissipation framework, we find, in contrast to the case when communication is ignored, that precision saturates with the number of cells independently of the measurement time duration, because communication establishes a maximum length scale over which sensory information can be reliably conveyed. Surprisingly, we also find that precision is improved if the local reporter is exchanged between cells as well, albeit more slowly than the global reporter. The reason is that whereas exchange of the local reporter weakens the comparison, it decreases the measurement noise. We term such a model "regional excitation-global inhibition." Our results demonstrate that fundamental sensing limits are necessarily sharpened when the need to communicate information is taken into account.

Frequency and amplitude control of cortical oscillations by phosphoinositide waves

Rhythmicity is prevalent in the cortical dynamics of diverse single and multicellular systems. Current models of cortical oscillations focus primarily on cytoskeleton-based feedbacks, but information on signals upstream of the actin cytoskeleton is limited. In addition, inhibitory mechanisms--especially local inhibitory mechanisms, which ensure proper spatial and kinetic controls of activation--are not well understood. Here, we identified two phosphoinositide phosphatases, synaptojanin 2 and SHIP1, that function in periodic traveling waves of rat basophilic leukemia (RBL) mast cells. The local, phase-shifted activation of lipid phosphatases generates sequential waves of phosphoinositides. By acutely perturbing phosphoinositide composition using optogenetic methods, we showed that pulses of PtdIns(4,5)P2 regulate the amplitude of cyclic membrane waves while PtdIns(3,4)P2 sets the frequency. Collectively, these data suggest that the spatiotemporal dynamics of lipid metabolism have a key role in governing cortical oscillations and reveal how phosphatidylinositol 3-kinases (PI3K) activity could be frequency-encoded by a phosphatase-dependent inhibitory reaction.

Obituary: Hans Meinhardt (1938-2016)

Patrick Müller and Christiane Nüsslein-Volhard reflect on the life and career of their colleague Hans Meinhardt.

Energy dissipation drives the gradient signal amplification through an incoherent type-1 feed-forward loop

We present here the analytical relation between the gain of eukaryotic gradient sensing network and the associated thermodynamic cost. By analyzing a general incoherent type-1 feed-forward loop, we derive the gain function (G) through the reaction network and explicitly show that G depends on the nonequilibrium factor (0≤γ≤1 with γ=0 and 1 representing irreversible and equilibrium reaction systems, respectively), the Michaelis constant (K_{M}), and the turnover ratio (r_{cat}) of the participating enzymes. We further find the maximum possible gain is intrinsically determined by K_{M}/G_{max}=(1/K_{M}+2)/4. Our model also indicates that the dissipated energy (measured by -lnγ), from the intracellular energy-bearing bioparticles (e.g., ATP), is used to generate a force field F_{γ}∝(1-sqrt[γ]) that reshapes and disables the effective potential around the zero gain region, which leads to the ultrasensitive response to external chemical gradients.

Novel protein Callipygian defines the back of migrating cells

Asymmetric protein localization is essential for cell polarity and migration. We report a novel protein, Callipygian (CynA), which localizes to the lagging edge before other proteins and becomes more tightly restricted as cells polarize; additionally, it accumulates in the cleavage furrow during cytokinesis. CynA protein that is tightly localized, or "clustered," to the cell rear is immobile, but when polarity is disrupted, it disperses throughout the membrane and responds to uniform chemoattractant stimulation by transiently localizing to the cytosol. These behaviors require a pleckstrin homology-domain membrane tether and a WD40 clustering domain, which can also direct other membrane proteins to the back. Fragments of CynA lacking the pleckstrin homology domain, which are normally found in the cytosol, localize to the lagging edge membrane when coexpressed with full-length protein, showing that CynA clustering is mediated by oligomerization. Cells lacking CynA have aberrant lateral protrusions, altered leading-edge morphology, and decreased directional persistence, whereas those overexpressing the protein display exaggerated features of polarity. Consistently, actin polymerization is inhibited at sites of CynA accumulation, thereby restricting protrusions to the opposite edge. We suggest that the mutual antagonism between CynA and regions of responsiveness creates a positive feedback loop that restricts CynA to the rear and contributes to the establishment of the cell axis.

A hybrid computational model to predict chemotactic guidance of growth cones

The overall strategy used by growing axons to find their correct paths during the nervous system development is not yet completely understood. Indeed, some emergent and counterintuitive phenomena were recently described during axon pathfinding in presence of chemical gradients. Here, a novel computational model is presented together with its ability to reproduce both regular and counterintuitive axonal behaviours. In this model, the key role of intracellular calcium was phenomenologically modelled through a non standard Gierer-Meinhardt system, as a crucial factor influencing the growth cone behaviour both in regular and complex conditions. This model was able to explicitly reproduce neuritic paths accounting for the complex interplay between extracellular and intracellular environments, through the sensing capability of the growth cone. The reliability of this approach was proven by using quantitative metrics, numerically supporting the similarity between in silico and biological results in regular conditions (control and attraction). Finally, the model was able to qualitatively predict emergent and counterintuitive phenomena resulting from complex boundary conditions.

Alternative cell polarity behaviours arise from changes in G-protein spatial dynamics

Yeast cells form a single mating projection when exposed to mating pheromone, a classic example of cell polarity. Prolonged treatment with pheromone or specific mutations results in alternative cell polarity behaviours. The authors performed mathematical modelling to investigate these unusual cell morphologies from the perspective of balancing spatial amplification (i.e. positive feedback that localises components) with spatial tracking (i.e. negative feedback that allows sensing of gradient). First, they used generic models of cell polarity to explore different cell polarity behaviours that arose from changes in the model spatial dynamics. By exploring the positive and negative feedback loops in each stage of a two-stage model, they simulated a variety of cell morphologies including single bending projections, single straight projections, periodic multiple projections and simultaneous double projections. In the second half of the study, they used a two-stage mechanistic model of yeast cell polarity focusing on G-protein signalling to integrate the modelling results more closely with the authors' previously published experimental observations. In summary, the combination of modelling and experiments describes how yeast cells exhibit a diversity of cell morphologies arising from two-stage G-protein signalling dynamics modulated by positive and negative feedbacks.

Image based validation of dynamical models for cell reorientation

A key feature of directed cell movement is the ability of cells to reorient quickly in response to changes in the direction of an extracellular stimulus. Mathematical models have suggested quite different regulatory mechanisms to explain reorientation, raising the question of how we can validate these models in a rigorous way. In this study, we fit three reaction-diffusion models to experimental data of Dictyostelium amoebae reorienting in response to alternating gradients of mechanical shear flow. The experimental readouts we use to fit are spatio-temporal distributions of a fluorescent reporter for cortical F-actin labeling the cell front. Experiments performed under different conditions are fitted simultaneously to challenge the models with different types of cellular dynamics. Although the model proposed by Otsuji is unable to provide a satisfactory fit, those suggested by Meinhardt and Levchenko fit equally well. Further, we show that reduction of the three-variable Meinhardt model to a two-variable model also provides an excellent fit, but has the advantage of all parameters being uniquely identifiable. Our work demonstrates that model selection and identifiability analysis, commonly applied to temporal dynamics problems in systems biology, can be a powerful tool when extended to spatio-temporal imaging data.

Dynamic membrane patterning, signal localization and polarity in living cells

We review the molecular and physical aspects of the dynamic localization of signaling molecules on the plasma membranes of living cells. At the nanoscale, clusters of receptors and signaling proteins play an essential role in the processing of extracellular signals. At the microscale, "soft" and highly dynamic signaling domains control the interaction of individual cells with their environment. At the multicellular scale, individual polarity patterns control the forces that shape multicellular aggregates and tissues.

Moesin and myosin phosphatase confine neutrophil orientation in a chemotactic gradient

Jingsong Xu and colleagues investigate how neutrophils initiate polarized migration toward bacteria or chemoattractants. They find that attractant-induced activation of myosin phosphatase results in the deactivation of moesin at the prospective leading edge and its redistribution to the trailing edge, establishing polarity and directional pseudopod formation.

Neutrophils respond to invading bacteria by adopting a polarized morphology, migrating in the correct direction, and engulfing the bacteria. How neutrophils establish and precisely orient this polarity toward pathogens remains unclear. Here we report that in resting neutrophils, the ERM (ezrin, radixin, and moesin) protein moesin in its active form (phosphorylated and membrane bound) prevented cell polarization by inhibiting the small GTPases Rac, Rho, and Cdc42. Attractant-induced activation of myosin phosphatase deactivated moesin at the prospective leading edge to break symmetry and establish polarity. Subsequent translocation of moesin to the trailing edge confined the formation of a prominent pseudopod directed toward pathogens and prevented secondary pseudopod formation in other directions. Therefore, both moesin-mediated inhibition and its localized deactivation by myosin phosphatase are essential for neutrophil polarization and effective neutrophil tracking of pathogens.

Cell polarity: netrin calms an excitable system

In a tractable model for cell invasion, the Caenorhabditis elegans anchor cell migrates through basement membranes towards a polarity cue provided by netrin. A new study reveals that the anchor cell polarity network can break symmetry and oscillate in the absence of netrin, suggesting the presence of interlinked positive and negative feedback loops, which are common in polarity pathways.

Evolutionarily conserved coupling of adaptive and excitable networks mediates eukaryotic chemotaxis

Numerous models explain how cells sense and migrate towards shallow chemoattractant gradients. Studies show that an excitable signal transduction network acts as a pacemaker that controls the cytoskeleton to drive motility. Here we show that this network is required to link stimuli to actin polymerization and chemotactic motility and we distinguish the various models of chemotaxis. First, signalling activity is suppressed towards the low side in a gradient or following removal of uniform chemoattractant. Second, signalling activities display a rapid shut off and a slower adaptation during which responsiveness to subsequent test stimuli decline. Simulations of various models indicate that these properties require coupled adaptive and excitable networks. Adaptation involves a G-protein-independent inhibitor, as stimulation of cells lacking G-protein function suppresses basal activities. The salient features of the coupled networks were observed for different chemoattractants in Dictyostelium and in human neutrophils, suggesting an evolutionarily conserved mechanism for eukaryotic chemotaxis.

The directional response of chemotactic cells depends on a balance between cytoskeletal architecture and the external gradient

Polarized migrating cells display signal transduction events, such as activation of phosphatidylinositol 3-kinase (PI3K) and Scar/Wave, and respond more readily to chemotactic stimuli at the leading edge. We sought to determine the basis of this polarized sensitivity. Inhibiting actin polymerization leads to uniform sensitivity. However, when human neutrophils were "stalled" by simultaneously blocking actin and myosin dynamics, they maintained the gradient of responsiveness to chemoattractant and also displayed noise-driven PIP3 flashes on the basal membrane, localized toward the front. Thus, polarized sensitivity does not require migration or cytoskeletal dynamics. The threshold for response is correlated with the static F-actin distribution, but not cell shape or volume changes, membrane fluidity, or the preexisting distribution of PI3K. The kinetics of responses to temporal and spatial stimuli were consistent with the local excitation global inhibition model, but the overall direction of the response was biased by the internal axis of polarity.

Excitable signal transduction induces both spontaneous and directional cell asymmetries in the phosphatidylinositol lipid signaling system for eukaryotic chemotaxis

Intracellular asymmetry in the signaling network works as a compass to navigate eukaryotic chemotaxis in response to guidance cues. Although the compass variable can be derived from a self-organization dynamics, such as excitability, the responsible mechanism remains to be clarified. Here, we analyzed the spatiotemporal dynamics of the phosphatidylinositol 3,4,5-trisphosphate (PtdInsP3) pathway, which is crucial for chemotaxis. We show that spontaneous activation of PtdInsP3-enriched domains is generated by an intrinsic excitable system. Formation of the same signal domain could be triggered by various perturbations, such as short impulse perturbations that triggered the activation of intrinsic dynamics to form signal domains. We also observed the refractory behavior exhibited in typical excitable systems. We show that the chemotactic response of PtdInsP3 involves biasing the spontaneous excitation to orient the activation site toward the chemoattractant. Thus, this biased excitability embodies the compass variable that is responsible for both random cell migration and biased random walk. Our finding may explain how cells achieve high sensitivity to and robust coordination of the downstream activation that allows chemotactic behavior in the noisy environment outside and inside the cells.

Actin dynamics: cell migration takes a new turn with arpin

Accurate cell migration requires intricate control over the actin cytoskeleton. Recent work has identified an Arp2/3-interacting protein called Arpin, which restricts the rate of actin polymerization and is the latest component in the steadily expanding protein repertoire that controls cell migration.

Second messenger signaling for neuronal polarization: cell mechanics-dependent pattern formation

Neuronal polarization is a critical step in the neuronal morphogenesis. Despite the identification of several evolutionarily conserved factors for neural polarization, the exact mechanisms by which cells initiate and maintain polarity remain to be characterized. Here, we review the recent progress on the roles of second messengers, specifically the cyclic nucleotides and membrane-associated phospholipids, in the initiation, propagation, and integration of polarization signals, and propose an inhibitor-free model for neural polarization. The characteristic features of neuron polarization include the formation of single axon and multiple dendrites. These features involve chemical and mechanical mechanisms such as reaction-diffusion and tug-of-war, by which second messengers can act in concert to initiate and stabilize the cellular asymmetry. Nevertheless, biochemical factors eliciting the long-range inhibition remain ambiguous. Thus, we provide a simple, inhibitor-free model that can incorporate known cytochemical and cytomechanical factors, and produce features of neuronal polarization in environments provided with minimized extracellular regulators.

Mechanical feedback through E-cadherin promotes direction sensing during collective cell migration

E-cadherin is a major homophilic cell-cell adhesion molecule that inhibits motility of individual cells on matrix. However, its contribution to migration of cells through cell-rich tissues is less clear. We developed an in vivo sensor of mechanical tension across E-cadherin molecules, which we combined with cell-type-specific RNAi, photoactivatable Rac, and morphodynamic profiling, to interrogate how E-cadherin contributes to collective migration of cells between other cells. Using the Drosophila ovary as a model, we found that adhesion between border cells and their substrate, the nurse cells, functions in a positive feedback loop with Rac and actin assembly to stabilize forward-directed protrusion and directionally persistent movement. Adhesion between individual border cells communicates direction from the lead cell to the followers. Adhesion between motile cells and polar cells holds the cluster together and polarizes each individual cell. Thus, E-cadherin is an integral component of the guidance mechanisms that orchestrate collective chemotaxis in vivo.

Modeling self-organized spatio-temporal patterns of PIP₃ and PTEN during spontaneous cell polarization

During spontaneous cell polarization of Dictyostelium discoideum cells, phosphatidylinositol (3,4,5)-triphoshpate (PIP3) and PTEN (phosphatase tensin homolog) have been identified as key signaling molecules which govern the process of polarization in a self-organized manner. Recent experiments have quantified the spatio-temporal dynamics of these signaling components. Surprisingly, it was found that membrane-bound PTEN can be either in a high or low state, that PIP3 waves were initiated in areas lacking PTEN through an excitable mechanism, and that PIP3 was degraded even though the PTEN concentration remained low. Here we develop a reaction-diffusion model that aims to explain these experimental findings. Our model contains bistable dynamics for PTEN, excitable dynamics for PIP3, and postulates the existence of two species of PTEN with different dephosphorylation rates. We show that our model is able to produce results that are in good qualitative agreement with the experiments, suggesting that our reaction-diffusion model underlies the self-organized spatio-temporal patterns observed in experiments.

Synergistic effects of 3D ECM and chemogradients on neurite outgrowth and guidance: a simple modeling and microfluidic framework

During nervous system development, numerous cues within the extracellular matrix microenvironment (ECM) guide the growing neurites along specific pathways to reach their intended targets. Neurite motility is controlled by extracellular signal sensing through the growth cone at the neurite tip, including chemoattractive and repulsive cues. However, it is difficult to regenerate and restore neurite tracts, lost or degraded due to an injury or disease, in the adult central nervous system. Thus, it is important to evaluate the dynamic interplay between ECM and the concentration gradients of these cues, which would elicit robust neuritogenesis. Such information is critical in understanding the processes involved in developmental biology, and in developing high-fidelity neurite regenerative strategies post-injury, and in drug discovery and targeted therapeutics for neurodegenerative conditions. Here, we quantitatively investigated this relationship using a combination of mathematical modeling and in vitro experiments, and determined the synergistic role of guidance cues and ECM on neurite outgrowth and turning. Using a biomimetic microfluidic system, we have shown that cortical neurite outgrowth and turning under chemogradients (IGF-1 or BDNF) within 3D scaffolds is highly regulated by the source concentration of the guidance cue and the physical characteristics of the scaffold. A mechanistic-driven partial differential equation model of neurite outgrowth has been proposed, which could also be used prospectively as a predictive tool. The parameters for the chemotaxis term in the model are determined from the experimental data using our microfluidic assay. Resulting model simulations demonstrate how neurite outgrowth was critically influenced by the experimental variables, which was further supported by experimental data on cell-surface-receptor expressions. The model results are in excellent agreement with the experimental findings. This integrated approach represents a framework for further elucidation of biological mechanisms underlying neuronal responses of specialized cell types, during various stages of development, and under healthy or diseased conditions.

Intracellular encoding of spatiotemporal guidance cues in a self-organizing signaling system for chemotaxis in Dictyostelium cells

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

Moving towards a paradigm: common mechanisms of chemotactic signaling in Dictyostelium and mammalian leukocytes

Chemotaxis, or directed migration of cells along a chemical gradient, is a highly coordinated process that involves gradient sensing, motility, and polarity. Most of our understanding of chemotaxis comes from studies of cells undergoing amoeboid-type migration, in particular the social amoeba Dictyostelium discoideum and leukocytes. In these amoeboid cells the molecular events leading to directed migration can be conceptually divided into four interacting networks: receptor/G protein, signal transduction, cytoskeleton, and polarity. The signal transduction network occupies a central position in this scheme as it receives direct input from the receptor/G protein network, as well as feedback from the cytoskeletal and polarity networks. Multiple overlapping modules within the signal transduction network transmit the signals to the actin cytoskeleton network leading to biased pseudopod protrusion in the direction of the gradient. The overall architecture of the networks, as well as the individual signaling modules, is remarkably conserved between Dictyostelium and mammalian leukocytes, and the similarities and differences between the two systems are the subject of this review.

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.

Second messenger networks for accurate growth cone guidance

Growth cones are able to navigate over long distances to find their appropriate target by following guidance cues that are often presented to them in the form of an extracellular gradient. These external cues are converted into gradients of specific signaling molecules inside growth cones, while at the same time these internal signals are amplified. The amplified instruction is then used to generate asymmetric changes in the growth cone turning machinery so that one side of the growth cone migrates at a rate faster than the other side, and thus the growth cone turns toward or away from the external cue. This review examines how signal specification and amplification can be achieved inside the growth cone by multiple second messenger signaling pathways activated downstream of guidance cues. These include the calcium ion, cyclic nucleotide, and phosphatidylinositol signaling pathways.

An excitable signal integrator couples to an idling cytoskeletal oscillator to drive cell migration

It is generally believed that cytoskeletal activities drive random cell migration while signal transduction events initiated by receptors regulate the cytoskeleton to guide cells. However, we find that the cytoskeletal network, involving Scar/Wave, Arp 2/3, and actin binding proteins, is only capable of generating rapid oscillations and undulations of the cell boundary. The signal transduction network, comprising multiple pathways that include Ras GTPases, PI3K, and Rac GTPases, is required to generate the sustained protrusions of migrating cells. The signal transduction network is excitable, displaying wave propagation, refractoriness, and maximal response to suprathreshold stimuli, even in the absence of the cytoskeleton. We suggest that cell motility results from coupling of “pacemaker” signal transduction and “idling motor” cytoskeletal networks, and various guidance cues that modulate the threshold for triggering signal transduction events are integrated to control the mode and direction of migration.

Neuronal growth as diffusion in an effective potential

Current understanding of neuronal growth is mostly qualitative, as the staggering number of physical and chemical guidance cues involved prohibit a fully quantitative description of axonal dynamics. We report on a general approach that describes axonal growth in vitro, on poly-D-lysine-coated glass substrates, as diffusion in an effective external potential, representing the collective contribution of all causal influences on the growth cone. We use this approach to obtain effective growth rules that reveal an emergent regulatory mechanism for axonal pathfinding on these substrates.

Cellular polarization: interaction between extrinsic bounded noises and the wave-pinning mechanism

Cell polarization (cued or uncued) is a fundamental mechanism in cell biology. As an alternative to the classical Turing bifurcation, it has been proposed that the onset of cell polarity might arise by means of the well-known phenomenon of wave-pinning [Gamba et al., Proc. Natl. Acad. Sci. USA 102, 16927 (2005)]. A particularly simple and elegant deterministic model of cell polarization based on the wave-pinning mechanism has been proposed by Edelstein-Keshet and coworkers [Biophys. J. 94, 3684 (2008)]. This model consists of a small biomolecular network where an active membrane-bound factor interconverts into its inactive form that freely diffuses in the cell cytosol. However, biomolecular networks do communicate with other networks as well as with the external world. Thus, their dynamics must be considered as perturbed by extrinsic noises. These noises may have both a spatial and a temporal correlation, and in any case they must be bounded to preserve the biological meaningfulness of the perturbed parameters. Here we numerically show that the inclusion of external spatiotemporal bounded parametric perturbations in the above wave-pinning-based model of cellular polarization may sometimes destroy the polarized state. The polarization loss depends on both the extent of temporal and spatial correlations and on the kind of noise employed. For example, an increase of the spatial correlation of the noise induces an increase of the probability of cell polarization. However, if the noise is spatially homogeneous then the polarization is lost in the majority of cases. These phenomena are independent of the type of noise. Conversely, an increase of the temporal autocorrelation of the noise induces an effect that depends on the model of noise.

Spatial stochastic dynamics enable robust cell polarization

Although cell polarity is an essential feature of living cells, it is far from being well-understood. Using a combination of computational modeling and biological experiments we closely examine an important prototype of cell polarity: the pheromone-induced formation of the yeast polarisome. Focusing on the role of noise and spatial heterogeneity, we develop and investigate two mechanistic spatial models of polarisome formation, one deterministic and the other stochastic, and compare the contrasting predictions of these two models against experimental phenotypes of wild-type and mutant cells. We find that the stochastic model can more robustly reproduce two fundamental characteristics observed in wild-type cells: a highly polarized phenotype via a mechanism that we refer to as spatial stochastic amplification, and the ability of the polarisome to track a moving pheromone input. Moreover, we find that only the stochastic model can simultaneously reproduce these characteristics of the wild-type phenotype and the multi-polarisome phenotype of a deletion mutant of the scaffolding protein Spa2. Significantly, our analysis also demonstrates that higher levels of stochastic noise results in increased robustness of polarization to parameter variation. Furthermore, our work suggests a novel role for a polarisome protein in the stabilization of actin cables. These findings elucidate the intricate role of spatial stochastic effects in cell polarity, giving support to a cellular model where noise and spatial heterogeneity combine to achieve robust biological function.

Cell polarity is the fundamental process of breaking symmetry to create asymmetric cellular structures. It is an open question how randomness (stochasticity) in the cell hinders or helps cell polarity. In this work, we focus on the ability of yeast cells to sense a spatial gradient of mating pheromone and respond by forming a projection in the direction of the mating partner. A key element is the polarisome, which is at the tip of the mating projection. We introduce the first model of polarisome formation in yeast. The model is well-supported by experimental data. We perform modeling to explore the role of noise in the formation of the polarisome. By running simulations with and without noise, we arrive at the surprising conclusion, that gradient-dependent polarization is enhanced by stochasticity. Both the tight localization (amplification) and the ability to respond to directional change of the input (tracking) are enhanced by stochastic dynamics, resulting in a more robust behavior. Mutants in which key polarisome proteins have been deleted exhibit broader, noisier polarisome than the wild type. The mutant phenotype is accurately captured by our stochastic simulations. These results demonstrate the importance of stochasticity in the study of cell polarity.

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.

Excitable behavior in amoeboid chemotaxis

Chemotaxis, the directed motion of cells in response to chemical gradients, is a fundamental process. Eukaryotic cells detect spatial differences in chemoattractant receptor occupancy with high precision and use these differences to bias the location of actin-rich protrusions to guide their movement. Research into chemotaxis has benefitted greatly from a systems biology approach that combines novel experimental and computational tools to pose and test hypotheses. Recently, one such hypothesis has been postulated proposing that chemotaxis in eukaryotic cells is mediated by locally biasing the activity of an underlying excitable system. The excitable system hypothesis can account for a number of cellular behaviors related to chemotaxis, including the stochastic nature of the movement of unstimulated cells, the directional bias imposed by chemoattractant gradients, and the observed spatial and temporal distribution of signaling and cytoskeleton proteins.

Identifying network motifs that buffer front-to-back signaling in polarized neutrophils

Neutrophil polarity relies on local, mutual inhibition to segregate incompatible signaling circuits to the leading and trailing edges. Mutual inhibition alone should lead to cells having strong fronts and weak backs or vice versa. However, analysis of cell-to-cell variation in human neutrophils revealed that back polarity remains consistent despite changes in front strength. How is this buffering achieved? Pharmacological perturbations and mathematical modeling revealed a functional role for microtubules in buffering back polarity by mediating positive, long-range crosstalk from front to back; loss of microtubules inhibits buffering and results in anticorrelation between front and back signaling. Furthermore, a systematic, computational search of network topologies found that a long-range, positive front-to-back link is necessary for back buffering. Our studies suggest a design principle that can be employed by polarity networks: short-range mutual inhibition establishes distinct signaling regions, after which directed long-range activation insulates one region from variations in the other.