Orientation of chemotactic cells and growth cones: models and mechanisms

Persistent pseudopod splitting is an effective chemotaxis strategy in shallow gradients

Single-cell organisms and various cell types use a range of motility modes when following a chemical gradient, but it is unclear which mode is best suited for different gradients. Here, we model directional decision-making in chemotactic amoeboid cells as a stimulus-dependent actin recruitment contest. Pseudopods extending from the cell body compete for a finite actin pool to push the cell in their direction until one pseudopod wins and determines the direction of movement. Our minimal model provides a quantitative understanding of the strategies cells use to reach the physical limit of accurate chemotaxis, aligning with data without explicit gradient sensing or cellular memory for persistence. To generalize our model, we employ reinforcement learning optimization to study the effect of pseudopod suppression, a simple but effective cellular algorithm by which cells can suppress possible directions of movement. Different pseudopod-based chemotaxis strategies emerge naturally depending on the environment and its dynamics. For instance, in static gradients, cells can react faster at the cost of pseudopod accuracy, which is particularly useful in noisy, shallow gradients where it paradoxically increases chemotactic accuracy. In contrast, in dynamics gradients, cells form de novo pseudopods. Overall, our work demonstrates mechanical intelligence for high chemotaxis performance with minimal cellular regulation.

Traveling-wave chemotaxis of neutrophil-like HL-60 cells

The question of how changes in chemoattractant concentration translate into the chemotactic response of immune cells serves as a paradigm for the quantitative understanding of how cells perceive and process temporal and spatial information. Here, using a microfluidic approach, we analyzed the migration of neutrophil-like HL-60 cells to a traveling wave of the chemoattractants N-formyl-methionyl-leucyl-phenylalanine (fMLP) and leukotriene B4 (LTB4). We found that under a pulsatile wave that travels at a speed of 95 and 170 µm/min, cells move forward in the front of the wave but slow down and randomly orient at the back due to temporal decrease in the attractant concentration. Under a slower wave, cells reorient and migrate at the back of the wave; thus, cell displacement is canceled out or even becomes negative as cells chase the receding wave. Fluorescence resonance energy transfer (FRET)-based analysis indicated that these patterns of movement correlated well with spatiotemporal changes in Cdc42 activity. Furthermore, pharmacological perturbations showed that (re)orientation in front and back of the wave had different susceptibility to Cdc42 and ROCK inhibition. These results suggest that pulsatile attractant waves may recruit or disperse neutrophils, depending on their speed and degree of cell polarization.

A bulk-surface mechanobiochemical modelling approach for single cell migration in two-space dimensions

In this work, we present a mechanobiochemical model for two-dimensional cell migration which couples mechanical properties of the cell cytosol with biochemical processes taking place near or on the cell plasma membrane. The modelling approach is based on a recently developed mathematical formalism of evolving bulk-surface partial differential equations of reaction-diffusion type. We solve these equations using finite element methods within a moving-mesh framework derived from the weak formulation of the evolving bulk-surface PDEs. In the present work, the cell cytosol interior (bulk) dynamics are coupled to the cell membrane (surface) dynamics through non-homogeneous Dirichlet boundary conditions. The modelling approach exhibits both directed cell migration in response to chemical cues as well as spontaneous migration in the absence of such cues. As a by-product, the approach shows fundamental characteristics associated with single cell migration such as: (i) cytosolic and membrane polarisation, (ii) actin dependent protrusions, and (iii) continuous shape deformation of the cell during migration. Cell migration is an ubiquitous process in life that is mainly triggered by the dynamics of the actin cytoskeleton and therefore is driven by both mechanical and biochemical processes. It is a multistep process essential for mammalian organisms and is closely linked to a vast diversity of processes; from embryonic development to cancer invasion. Experimental, theoretical and computational studies have been key to elucidate the mechanisms underlying cell migration. On one hand, rapid advances in experimental techniques allow for detailed experimental measurements of cell migration pathways, while, on the other, computational approaches allow for the modelling, analysis and understanding of such observations. The bulk-surface mechanobiochemical modelling approach presented in this work, set premises to study single cell migration through complex non-isotropic environments in two- and three-space dimensions.

Receptor polarization through localized activity and global sensitization

Eukaryotic cells chemosense concentration gradients of extracellular ligands using membrane-bound receptors that polarize their activity. Receptors from several chemosensing families are preferentially degraded after activation and undergo significant lateral diffusion, both of which may blunt their polarization. To explore the combined role of these two seemingly detrimental phenomena on active receptor polarization, we use a reaction/diffusion model. The model elucidates a counterintuitive principle that governs receptor polarization under external gradients: Localized Activity and Global Sensitization (LAGS). In LAGS, receptor activity is localized through receptor degradation or ligand unbinding. In contrast, uniform sensitivity to ligands is maintained over the plasma membrane through lateral receptor diffusion. Surprisingly, increasing preferential degradation of active receptors and increasing lateral diffusion of all receptors both sharpen active receptor polarization. Additionally, when combined with receptor oligomerization, an increase in preferential degradation allows cells to sense relative ligand gradients over a larger range of background ligand concentrations. An analytical model identifies parameter regimes that dictate which processes dominate receptor polarization. A survey of kinetic parameters suggests that receptor polarization in many mammalian pathways can be modeled using LAGS.

Chemo-mechanical model of cell polarization initiated by structural polarity

Cell polarization is crucial in most physiological functions. Living cells at the extracellular matrix (ECM) actively coordinate a polarized morphology to target the preferred signals. In particular, the initial heterogeneity of subcellular components, termed as structural polarity, has been discovered to mediate the early attachment and transmigration of cells in tumour metastasis. However, how heterogeneous cells initiate the early polarization remains incompletely discovered. Here, we establish a multiscale model of a cell to explore the chemo-mechanical mechanisms of cell polarization initiated by structural polarity. The two-dimensional vertex model of the cell is built with the main mechanical components of eukaryotic cells. The initial structural polarity of the modeled cell is introduced by seeding heterogeneous actin filaments at the cell cortex and quantified by the ratio of the filamentous forces at the vertices. Then, the structural polarity is integrated in the reaction-diffusion system of Rho GTPase (Cdc42) at the cell cortex to obtain the traction forces at the leading vertices. Finally, the modeled cell is actuated to spread under the traction forces and discovered to develop into a characteristic polarized morphology. The results indicate that the cell polarization is initiated and dynamically developed by structural polarity through the reaction-diffusion system of Cdc42. In addition, the bistability of Cdc42 activation at the cell cortex is defined and discovered to dominate the polarization status of the cell. Furthermore, biphasic (i.e., positive and negative) durotaxis of the cell is successfully modeled at an ECM with a stiffness gradient, and concluded to be codetermined by the chemo-mechanical coupling of the initial structural polarity and ECM stiffness gradient. The proposed multiscale model provides a quantitative way to probe cell polarization coupled with mechanical stimuli, biochemical reaction and cytoskeletal reorganization, and holds the potential to guide studies of cell polarization under multiple stimuli.

Long range mutual activation establishes Rho and Rac polarity during cell migration

In migrating cells, the GTPase Rac organizes a protrusive front, whereas Rho organizes a contractile back. How these GTPases are appropriately positioned at the opposite poles of a migrating cell is unknown. Here we leverage optogenetics, manipulation of cell mechanics, and mathematical modeling to reveal a surprising long-range mutual activation of the front and back polarity programs that complements their well-known local mutual inhibition. This long-range activation is rooted in two distinct modes of mechanochemical crosstalk. Local Rac-based protrusion stimulates Rho activation at the opposite side of the cell via membrane tension-based activation of mTORC2. Conversely, local Rho-based contraction induces cortical-flow-based remodeling of membrane-to-cortex interactions leading to PIP2 release, PIP3 generation, and Rac activation at the opposite side of the cell. We develop a minimal unifying mechanochemical model of the cell to explain how this long-range mechanical facilitation complements local biochemical inhibition to enable robust global Rho and Rac partitioning. Finally, we validate the importance of this long-range facilitation in the context of chemoattractant-based cell polarization and migration in primary human lymphocytes. Our findings demonstrate that the actin cortex and plasma membrane function as an integrated mechanochemical system for long-range partitioning of Rac and Rho during cell migration and likely other cellular contexts.

Local negative feedback of Rac activity at the leading edge underlies a pilot pseudopod-like program for amoeboid cell guidance

To migrate efficiently, neutrophils must polarize their cytoskeletal regulators along a single axis of motion. This polarization process is thought to be mediated through local positive feedback that amplifies leading edge signals and global negative feedback that enables sites of positive feedback to compete for dominance. Though this two-component model efficiently establishes cell polarity, it has potential limitations, including a tendency to "lock" onto a particular direction, limiting the ability of cells to reorient. We use spatially defined optogenetic control of a leading edge organizer (PI3K) to probe how neutrophil-like HL-60 cells balance "decisiveness" needed to polarize in a single direction with the flexibility needed to respond to new cues. Underlying this balancing act is a local Rac inhibition process that destabilizes the leading edge to promote exploration. We show that this local inhibition enables cells to process input signal dynamics, linking front stability and orientation to local temporal increases in input signals.

Leading edge competition promotes context-dependent responses to receptor inputs to resolve directional dilemmas in neutrophil migration

Maintaining persistent migration in complex environments is critical for neutrophils to reach infection sites. Neutrophils avoid getting trapped, even when obstacles split their front into multiple leading edges. How they re-establish polarity to move productively while incorporating receptor inputs under such conditions remains unclear. Here, we challenge chemotaxing HL60 neutrophil-like cells with symmetric bifurcating microfluidic channels to probe cell-intrinsic processes during the resolution of competing fronts. Using supervised statistical learning, we demonstrate that cells commit to one leading edge late in the process, rather than amplifying structural asymmetries or early fluctuations. Using optogenetic tools, we show that receptor inputs only bias the decision similarly late, once mechanical stretching begins to weaken each front. Finally, a retracting edge commits to retraction, with ROCK limiting sensitivity to receptor inputs until the retraction completes. Collectively, our results suggest that cell edges locally adopt highly stable protrusion/retraction programs that are modulated by mechanical feedback.

Oligomerization of peripheral membrane proteins provides tunable control of cell surface polarity

Asymmetric distributions of peripheral membrane proteins define cell polarity across all kingdoms of life. Non-linear positive feedback on membrane binding is essential to amplify and stabilize these asymmetries, but how specific molecular sources of non-linearity shape polarization dynamics remains poorly understood. Here we show that the ability to oligomerize, which is common to many peripheral membrane proteins, can play a profound role in shaping polarization dynamics in simple feedback circuits. We show that size-dependent binding avidity and mobility of membrane-bound oligomers endow polarity circuits with several key properties. Size-dependent membrane binding avidity confers a form of positive feedback on the accumulation of oligomer subunits. Although insufficient by itself, this sharply reduces the amount of additional feedback required for spontaneous emergence and stable maintenance of polarized states. Size-dependent oligomer mobility makes symmetry breaking and stable polarity more robust with respect to variation in subunit diffusivities and cell sizes, and slows the approach to a final stable spatial distribution, allowing cells to "remember" polarity boundaries imposed by transient external cues. Together, these findings reveal how oligomerization of peripheral membrane proteins can provide powerful and highly tunable sources of non-linear feedback in biochemical circuits that govern cell surface polarity. Given its prevalence and widespread involvement in cell polarity, we speculate that self-oligomerization may have provided an accessible path to evolving simple polarity circuits.

Cell Repolarization: A Bifurcation Study of Spatio-Temporal Perturbations of Polar Cells

The intrinsic polarity of migrating cells is regulated by spatial distributions of protein activity. Those proteins (Rho-family GTPases, such as Rac and Rho) redistribute in response to stimuli, determining the cell front and back. Reaction-diffusion equations with mass conservation and positive feedback have been used to explain initial polarization of a cell. However, the sensitivity of a polar cell to a reversal stimulus has not yet been fully understood. We carry out a PDE bifurcation analysis of two polarity models to investigate routes to repolarization: (1) a single-GTPase ("wave-pinning") model and (2) a mutually antagonistic Rac-Rho model. We find distinct routes to reversal in (1) vs. (2). We show numerical simulations of full PDE solutions for the RD equations, demonstrating agreement with predictions of the bifurcation results. Finally, we show that simulations of the polarity models in deforming 1D model cells are consistent with biological experiments.

Cortical waves mediate the cellular response to electric fields

Electrotaxis, the directional migration of cells in a constant electric field, is important in regeneration, development, and wound healing. Electrotaxis has a slower response and a smaller dynamic range than guidance by other cues, suggesting that the mechanism of electrotaxis shares both similarities and differences with chemical-gradient-sensing pathways. We examine a mechanism centered on the excitable system consisting of cortical waves of biochemical signals coupled to cytoskeletal reorganization, which has been implicated in random cell motility. We use electro-fused giant Dictyostelium discoideum cells to decouple waves from cell motion and employ nanotopographic surfaces to limit wave dimensions and lifetimes. We demonstrate that wave propagation in these cells is guided by electric fields. The wave area and lifetime gradually increase in the first 10 min after an electric field is turned on, leading to more abundant and wider protrusions in the cell region nearest the cathode. The wave directions display 'U-turn' behavior upon field reversal, and this switch occurs more quickly on nanotopography. Our results suggest that electric fields guide cells by controlling waves of signal transduction and cytoskeletal activity, which underlie cellular protrusions. Whereas surface receptor occupancy triggers both rapid activation and slower polarization of signaling pathways, electric fields appear to act primarily on polarization, explaining why cells respond to electric fields more slowly than to other guidance cues.

Oscillations and bifurcation structure of reaction-diffusion model for cell polarity formation

We investigate the oscillatory dynamics and bifurcation structure of a reaction-diffusion system with bistable nonlinearity and mass conservation, which was proposed by (Otsuji et al., PLoS Comp Biol 3:e108, 2007). The system is a useful model for understanding cell polarity formation. We show that this model exhibits four different spatiotemporal patterns including two types of oscillatory patterns, which can be regarded as cell polarity oscillations with the reversal and non-reversal of polarity, respectively. The trigger causing these patterns is a diffusion-driven (Turing-like) instability. Moreover, we investigate the effects of extracellular signals on the cell polarity oscillations.

Orientation of Cell Polarity by Chemical Gradients

Accurate decoding of spatial chemical landscapes is critical for many cell functions. Eukaryotic cells decode local chemical gradients to orient growth or movement in productive directions. Recent work on yeast model systems, whose gradient sensing pathways display much less complexity than those in animal cells, has suggested new paradigms for how these very small cells successfully exploit information in noisy and dynamic pheromone gradients to identify their mates. Pheromone receptors regulate a polarity circuit centered on the conserved Rho-family GTPase, Cdc42. The polarity circuit contains both positive and negative feedback pathways, allowing spontaneous symmetry breaking and also polarity site disassembly and relocation. Cdc42 orients the actin cytoskeleton, leading to focused vesicle traffic that promotes movement of the polarity site and also reshapes the cortical distribution of receptors at the cell surface. In this article, we review the advances from work on yeasts and compare them with the excitable signaling pathways that have been revealed in chemotactic animal cells. Expected final online publication date for the Annual Review of Biophysics, Volume 51 is May 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

A systems approach to investigate GPCR-mediated Ras signaling network in chemoattractant sensing

A GPCR-mediated signaling network enables a chemotactic cell to generate adaptative Ras signaling in response to a large range of concentrations of a chemoattractant. To explore potential regulatory mechanisms of GPCR-controlled Ras signaling in chemosensing, we applied a software package, Simmune, to construct detailed spatiotemporal models simulating responses of the cAR1-mediated Ras signaling network. We first determined the dynamics of G-protein activation and Ras signaling in Dictyostelium cells in response to cAMP stimulations using live-cell imaging and then constructed computation models by incorporating potential mechanisms. Using simulations, we validated the dynamics of signaling events and predicted the dynamic profiles of those events in the cAR1-mediated Ras signaling networks with defective Ras inhibitory mechanisms, such as without RasGAP, with RasGAP overexpression, or with RasGAP hyperactivation. We describe a method of using Simmune to construct spatiotemporal models of a signaling network and run computational simulations without writing mathematical equations. This approach will help biologists to develop and analyze computational models that parallel live-cell experiments.

Three-dimensional morphodynamic simulations of macropinocytic cups

Macropinocytosis refers to the non-specific uptake of extracellular fluid, which plays ubiquitous roles in cell growth, immune surveillance, and virus entry. Despite its widespread occurrence, it remains unclear how its initial cup-shaped plasma membrane extensions form without any external solid support, as opposed to the process of particle uptake during phagocytosis. Here, by developing a computational framework that describes the coupling between the bistable reaction-diffusion processes of active signaling patches and membrane deformation, we demonstrated that the protrusive force localized to the edge of the patches can give rise to a self-enclosing cup structure, without further assumptions of local bending or contraction. Efficient uptake requires a balance among the patch size, magnitude of protrusive force, and cortical tension. Furthermore, our model exhibits cyclic cup formation, coexistence of multiple cups, and cup-splitting, indicating that these complex morphologies self-organize via a common mutually-dependent process of reaction-diffusion and membrane deformation.

Using Live-Cell Imaging and Synthetic Biology to Probe Directed Migration in Dictyostelium

For decades, the social amoeba Dictyostelium discoideum has been an invaluable tool for dissecting the biology of eukaryotic cells. Its short growth cycle and genetic tractability make it ideal for a variety of biochemical, cell biological, and biophysical assays. Dictyostelium have been widely used as a model of eukaryotic cell motility because the signaling and mechanical networks which they use to steer and produce forward motion are highly conserved. Because these migration networks consist of hundreds of interconnected proteins, perturbing individual molecules can have subtle effects or alter cell morphology and signaling in major unpredictable ways. Therefore, to fully understand this network, we must be able to quantitatively assess the consequences of abrupt modifications. This ability will allow us better control cell migration, which is critical for development and disease, in vivo. Here, we review recent advances in imaging, synthetic biology, and computational analysis which enable researchers to tune the activity of individual molecules in single living cells and precisely measure the effects on cellular motility and signaling. We also provide practical advice and resources to assist in applying these approaches in Dictyostelium.

Spatiotemporal development of coexisting wave domains of Rho activity in the cell cortex

The Rho family GTPases are molecular switches that regulate cytoskeletal dynamics and cell movement through a complex spatiotemporal organization of their activity. In Patiria miniata (starfish) oocytes under in vitro experimental conditions (with overexpressed Ect2, induced expression of Δ90 cyclin B, and roscovitine treatment), such activity generates multiple co-existing regions of coherent propagation of actin waves. Here we use computational modeling to investigate the development and properties of such wave domains. The model reveals that the formation of wave domains requires a balance between the activation and inhibition in the Rho signaling motif. Intriguingly, the development of the wave domains is preceded by a stage of low-activity quasi-static patterns, which may not be readily observed in experiments. Spatiotemporal patterns of this stage and the different paths of their destabilization define the behavior of the system in the later high-activity (observable) stage. Accounting for a strong intrinsic noise allowed us to achieve good quantitative agreement between simulated dynamics in different parameter regimes of the model and different wave dynamics in Patiria miniata and wild type Xenopus laevis (frog) data. For quantitative comparison of simulated and experimental results, we developed an automated method of wave domain detection, which revealed a sharp reversal in the process of pattern formation in starfish oocytes. Overall, our findings provide an insight into spatiotemporal regulation of complex and diverse but still computationally reproducible cell-level actin dynamics.

CYRI-A limits invasive migration through macropinosome formation and integrin uptake regulation

The Scar/WAVE complex drives actin nucleation during cell migration. Interestingly, the same complex is important in forming membrane ruffles during macropinocytosis, a process mediating nutrient uptake and membrane receptor trafficking. Mammalian CYRI-B is a recently described negative regulator of the Scar/WAVE complex by RAC1 sequestration, but its other paralogue, CYRI-A, has not been characterized. Here, we implicate CYRI-A as a key regulator of macropinosome formation and integrin internalization. We find that CYRI-A is transiently recruited to nascent macropinosomes, dependent on PI3K and RAC1 activity. CYRI-A recruitment precedes RAB5A recruitment but follows sharply after RAC1 and actin signaling, consistent with it being a local inhibitor of actin polymerization. Depletion of both CYRI-A and -B results in enhanced surface expression of the α5β1 integrin via reduced internalization. CYRI depletion enhanced migration, invasion, and anchorage-independent growth in 3D. Thus, CYRI-A is a dynamic regulator of macropinocytosis, functioning together with CYRI-B to regulate integrin trafficking.

Cytoskeletal symmetry breaking in animal cells

Symmetry breaking is a crucial step in structure formation and function of all cells, necessary for cell movement, cell division, and polarity establishment. Although the mechanisms of symmetry breaking are diverse, they often share common characteristics. Here we review examples of nematic, polar, and chiral cytoskeletal symmetry breaking in animal cells, and analogous processes in simplified reconstituted systems. We discuss the origins of symmetry breaking, which can arise spontaneously, or involve amplification of a pre-existing external or internal bias to the whole cell level. The underlying mechanisms often involve both chemical and mechanical processes that cooperate to break symmetry in a robust manner, and typically depend on the shape, size, or properties of the cell's boundary.

A novel stochastic simulation approach enables exploration of mechanisms for regulating polarity site movement

Cells polarize their movement or growth toward external directional cues in many different contexts. For example, budding yeast cells grow toward potential mating partners in response to pheromone gradients. Directed growth is controlled by polarity factors that assemble into clusters at the cell membrane. The clusters assemble, disassemble, and move between different regions of the membrane before eventually forming a stable polarity site directed toward the pheromone source. Pathways that regulate clustering have been identified but the molecular mechanisms that regulate cluster mobility are not well understood. To gain insight into the contribution of chemical noise to cluster behavior we simulated clustering using the reaction-diffusion master equation (RDME) framework to account for molecular-level fluctuations. RDME simulations are a computationally efficient approximation, but their results can diverge from the underlying microscopic dynamics. We implemented novel concentration-dependent rate constants that improved the accuracy of RDME-based simulations, allowing us to efficiently investigate how cluster dynamics might be regulated. Molecular noise was effective in relocating clusters when the clusters contained low numbers of limiting polarity factors, and when Cdc42, the central polarity regulator, exhibited short dwell times at the polarity site. Cluster stabilization occurred when abundances or binding rates were altered to either lengthen dwell times or increase the number of polarity molecules in the cluster. We validated key results using full 3D particle-based simulations. Understanding the mechanisms cells use to regulate the dynamics of polarity clusters should provide insights into how cells dynamically track external directional cues.

Cells localize polarity molecules in a small region of the plasma membrane forming a polarity cluster that directs functions such as migration, reproduction, and growth. Guided by external signals, these clusters move across the membrane allowing cells to reorient growth or motion. The polarity molecules continuously and randomly shuttle between the cluster and the cell cytosol and, as a result, the number and distribution of molecules at the cluster constantly changes. Here we present an improved stochastic simulation algorithm to investigate how such molecular-scale fluctuations induce cluster movement across the cell membrane. Unexpectedly, cluster mobility does not correlate with variations in total molecule abundance within the cluster, but rather with changes in the spatial distribution of molecules that form the cluster. Cluster motion is faster when polarity molecules are scarce and when they shuttle rapidly between the cluster and the cytosol. Our results suggest that cells control cluster mobility by regulating the abundance of polarity molecules and biochemical reactions that affect the time molecules spend at the cluster. We provide insights into how cells harness random molecular behavior to perform functions important for survival, such as detecting the direction of external signals.

Chemotactic movement of a polarity site enables yeast cells to find their mates

How small eukaryotic cells can interpret dynamic, noisy, and spatially complex chemical gradients to orient growth or movement is poorly understood. We address this question using Saccharomyces cerevisiae, where cells orient polarity up pheromone gradients during mating. Initial orientation is often incorrect, but polarity sites then move around the cortex in a search for partners. We find that this movement is biased by local pheromone gradients across the polarity site: that is, movement of the polarity site is chemotactic. A bottom-up computational model recapitulates this biased movement. The model reveals how even though pheromone-bound receptors do not mimic the shape of external pheromone gradients, nonlinear and stochastic effects combine to generate effective gradient tracking. This mechanism for gradient tracking may be applicable to any cell that searches for a target in a complex chemical landscape.

Mathematical modeling of chemotaxis guided amoeboid cell swimming

Cells and microorganisms adopt various strategies to migrate in response to different environmental stimuli. To date, many modeling research has focused on the crawling-basedDictyostelium discoideum(Dd) cells migration induced by chemotaxis, yet recent experimental results reveal that even without adhesion or contact to a substrate, Dd cells can still swim to follow chemoattractant signals. In this paper, we develop a modeling framework to investigate the chemotaxis induced amoeboid cell swimming dynamics. A minimal swimming system consists of one deformable Dd amoeboid cell and a dilute suspension of bacteria, and the bacteria produce chemoattractant signals that attract the Dd cell. We use themathematical amoeba modelto generate Dd cell deformation and solve the resulting low Reynolds number flows, and use a moving mesh based finite volume method to solve the reaction-diffusion-convection equation. Using the computational model, we show that chemotaxis guides a swimming Dd cell to follow and catch bacteria, while on the other hand, bacterial rheotaxis may help the bacteria to escape from the predator Dd cell.

Self-organized cell migration across scales - from single cell movement to tissue formation

Self-organization is a key feature of many biological and developmental processes, including cell migration. Although cell migration has traditionally been viewed as a biological response to extrinsic signals, advances within the past two decades have highlighted the importance of intrinsic self-organizing properties to direct cell migration on multiple scales. In this Review, we will explore self-organizing mechanisms that lay the foundation for both single and collective cell migration. Based on in vitro and in vivo examples, we will discuss theoretical concepts that underlie the persistent migration of single cells in the absence of directional guidance cues, and the formation of an autonomous cell collective that drives coordinated migration. Finally, we highlight the general implications of self-organizing principles guiding cell migration for biological and medical research.

Mathematical modelling in cell migration: tackling biochemistry in changing geometries

Directed cell migration poses a rich set of theoretical challenges. Broadly, these are concerned with (1) how cells sense external signal gradients and adapt; (2) how actin polymerisation is localised to drive the leading cell edge and Myosin-II molecular motors retract the cell rear; and (3) how the combined action of cellular forces and cell adhesion results in cell shape changes and net migration. Reaction-diffusion models for biological pattern formation going back to Turing have long been used to explain generic principles of gradient sensing and cell polarisation in simple, static geometries like a circle. In this minireview, we focus on recent research which aims at coupling the biochemistry with cellular mechanics and modelling cell shape changes. In particular, we want to contrast two principal modelling approaches: (1) interface tracking where the cell membrane, interfacing cell interior and exterior, is explicitly represented by a set of moving points in 2D or 3D space and (2) interface capturing. In interface capturing, the membrane is implicitly modelled analogously to a level line in a hilly landscape whose topology changes according to forces acting on the membrane. With the increased availability of high-quality 3D microscopy data of complex cell shapes, such methods will become increasingly important in data-driven, image-based modelling to better understand the mechanochemistry underpinning cell motion.

Tools for computational analysis of moving boundary problems in cellular mechanobiology

A cell's ability to change shape is one of the most fundamental biological processes and is essential for maintaining healthy organisms. When the ability to control shape goes awry, it often results in a diseased system. As such, it is important to understand the mechanisms that allow a cell to sense and respond to its environment so as to maintain cellular shape homeostasis. Because of the inherent complexity of the system, computational models that are based on sound theoretical understanding of the biochemistry and biomechanics and that use experimentally measured parameters are an essential tool. These models involve an inherent feedback, whereby shape is determined by the action of regulatory signals whose spatial distribution depends on the shape. To carry out computational simulations of these moving boundary problems requires special computational techniques. A variety of alternative approaches, depending on the type and scale of question being asked, have been used to simulate various biological processes, including cell motility, division, mechanosensation, and cell engulfment. In general, these models consider the forces that act on the system (both internally generated, or externally imposed) and the mechanical properties of the cell that resist these forces. Moving forward, making these techniques more accessible to the non-expert will help improve interdisciplinary research thereby providing new insight into important biological processes that affect human health. This article is categorized under: Cancer > Cancer>Computational Models Cancer > Cancer>Molecular and Cellular Physiology.

Membrane Tension Can Enhance Adaptation to Maintain Polarity of Migrating Cells

Migratory cells are known to adapt to environments that contain wide-ranging levels of chemoattractant. Although biochemical models of adaptation have been previously proposed, here, we discuss a different mechanism based on mechanosensing, in which the interaction between biochemical signaling and cell tension facilitates adaptation. We describe and analyze a model of mechanochemical-based adaptation coupling a mechanics-based physical model of cell tension coupled with the wave-pinning reaction-diffusion model for Rac GTPase activity. The mathematical analysis of this model, simulations of a simplified one-dimensional cell geometry, and two-dimensional finite element simulations of deforming cells reveal that as a cell protrudes under the influence of high stimulation levels, tension-mediated inhibition of Rac signaling causes the cell to polarize even when initially overstimulated. Specifically, tension-mediated inhibition of Rac activation, which has been experimentally observed in recent years, facilitates this adaptation by countering the high levels of environmental stimulation. These results demonstrate how tension-related mechanosensing may provide an alternative (and potentially complementary) mechanism for cell adaptation.

A computational study of amoeboid motility in 3D: the role of extracellular matrix geometry, cell deformability, and cell-matrix adhesion

Amoeboid cells often migrate using pseudopods, which are membrane protrusions that grow, bifurcate, and retract dynamically, resulting in a net cell displacement. Many cells within the human body, such as immune cells, epithelial cells, and even metastatic cancer cells, can migrate using the amoeboid phenotype. Amoeboid motility is a complex and multiscale process, where cell deformation, biochemistry, and cytosolic and extracellular fluid motions are coupled. Furthermore, the extracellular matrix (ECM) provides a confined, complex, and heterogeneous environment for the cells to navigate through. Amoeboid cells can migrate without significantly remodeling the ECM using weak or no adhesion, instead utilizing their deformability and the microstructure of the ECM to gain enough traction. While a large volume of work exists on cell motility on 2D substrates, amoeboid motility is 3D in nature. Despite recent progress in modeling cellular motility in 3D, there is a lack of systematic evaluations of the role of ECM microstructure, cell deformability, and adhesion on 3D motility. To fill this knowledge gap, here we present a multiscale, multiphysics modeling study of amoeboid motility through 3D-idealized ECM. The model is a coupled fluid‒structure and coarse-grain biochemistry interaction model that accounts for large deformation of cells, pseudopod dynamics, cytoplasmic and extracellular fluid motion, stochastic dynamics of cell-ECM adhesion, and microstructural (pore-scale) geometric details of the ECM. The key finding of the study is that cell deformation and matrix porosity strongly influence amoeboid motility, while weak adhesion and microscale structural details of the ECM have secondary but subtle effects.

Traveling and standing waves mediate pattern formation in cellular protrusions

The mechanisms regulating protrusions during amoeboid migration exhibit excitability. Theoretical studies have suggested the possible coexistence of traveling and standing waves in excitable systems. Here, we demonstrate the direct transformation of a traveling into a standing wave and establish conditions for the stability of this conversion. This theory combines excitable wave stopping and the emergence of a family of standing waves at zero velocity, without altering diffusion parameters. Experimentally, we show the existence of this phenomenon on the cell cortex of some Dictyostelium and mammalian mutant strains. We further predict a template that encompasses a spectrum of protrusive phenotypes, including pseudopodia and filopodia, through transitions between traveling and standing waves, allowing the cell to switch between excitability and bistability. Overall, this suggests that a previously-unidentified method of pattern formation, in which traveling waves spread, stop, and turn into standing waves that rearrange to form stable patterns, governs cell motility.

CompuCell3D Simulations Reproduce Mesenchymal Cell Migration on Flat Substrates

Mesenchymal cell crawling is a critical process in normal development, in tissue function, and in many diseases. Quantitatively predictive numerical simulations of cell crawling thus have multiple scientific, medical, and technological applications. However, we still lack a low-computational-cost approach to simulate mesenchymal three-dimensional (3D) cell crawling. Here, we develop a computationally tractable 3D model (implemented as a simulation in the CompuCell3D simulation environment) of mesenchymal cells crawling on a two-dimensional substrate. The Fürth equation, the usual characterization of mean-squared displacement (MSD) curves for migrating cells, describes a motion in which, for increasing time intervals, cell movement transitions from a ballistic to a diffusive regime. Recent experiments have shown that for very short time intervals, cells exhibit an additional fast diffusive regime. Our simulations' MSD curves reproduce the three experimentally observed temporal regimes, with fast diffusion for short time intervals, slow diffusion for long time intervals, and intermediate time -interval-ballistic motion. The resulting parameterization of the trajectories for both experiments and simulations allows the definition of time- and length scales that translate between computational and laboratory units. Rescaling by these scales allows direct quantitative comparisons among MSD curves and between velocity autocorrelation functions from experiments and simulations. Although our simulations replicate experimentally observed spontaneous symmetry breaking, short-timescale diffusive motion, and spontaneous cell-motion reorientation, their computational cost is low, allowing their use in multiscale virtual-tissue simulations. Comparisons between experimental and simulated cell motion support the hypothesis that short-time actomyosin dynamics affects longer-time cell motility. The success of the base cell-migration simulation model suggests its future application in more complex situations, including chemotaxis, migration through complex 3D matrices, and collective cell motion.

Cell confinement reveals a branched-actin independent circuit for neutrophil polarity

Migratory cells use distinct motility modes to navigate different microenvironments, but it is unclear whether these modes rely on the same core set of polarity components. To investigate this, we disrupted actin-related protein 2/3 (Arp2/3) and the WASP-family verprolin homologous protein (WAVE) complex, which assemble branched actin networks that are essential for neutrophil polarity and motility in standard adherent conditions. Surprisingly, confinement rescues polarity and movement of neutrophils lacking these components, revealing a processive bleb-based protrusion program that is mechanistically distinct from the branched actin-based protrusion program but shares some of the same core components and underlying molecular logic. We further find that the restriction of protrusion growth to one site does not always respond to membrane tension directly, as previously thought, but may rely on closely linked properties such as local membrane curvature. Our work reveals a hidden circuit for neutrophil polarity and indicates that cells have distinct molecular mechanisms for polarization that dominate in different microenvironments.

Cells display a high degree of plasticity in migration, but how polarity is organized in different microenvironments has remained unclear. This study uses mechanical perturbations to reveal that migration using actin-rich or bleb-based protrusions are both organized around Rac GTPase.

CYRI/ Fam49 Proteins Represent a New Class of Rac1 Interactors

Fam49 proteins, now referred to as CYRI (CYFIP-related Rac Interactor), are evolutionarily conserved across many phyla. Their closest relative by amino acid sequence is CYFIP, as both proteins contain a domain of unknown function DUF1394. We recently showed that CYRI and the DUF1394 can mediate binding to Rac1 and evidence is building to suggest that CYRI plays important roles in cell migration, chemotaxis and pathogen entry into cells. Here we discuss how CYRI proteins fit into the current framework of the control of actin dynamics by positive and negative feedback loops containing Rac1, the Scar/WAVE Complex, the Arp2/3 Complex and branched actin. We also provide data regarding the interaction between Rac1 and CYRI in an unbiassed mass spectrometry screen for interactors of an active mutant of Rac1.

Small GTPase patterning: How to stabilise cluster coexistence

Many biological processes have to occur at specific locations on the cell membrane. These locations are often specified by the localised activity of small GTPase proteins. Some processes require the formation of a single cluster of active GTPase, also called unipolar polarisation (here “polarisation”), whereas others need multiple coexisting clusters. Moreover, sometimes the pattern of GTPase clusters is dynamically regulated after its formation. This raises the question how the same interacting protein components can produce such a rich variety of naturally occurring patterns. Most currently used models for GTPase-based patterning inherently yield polarisation. Such models may at best yield transient coexistence of at most a few clusters, and hence fail to explain several important biological phenomena. These existing models are all based on mass conservation of total GTPase and some form of direct or indirect positive feedback. Here, we show that either of two biologically plausible modifications can yield stable coexistence: including explicit GTPase turnover, i.e., breaking mass conservation, or negative feedback by activation of an inhibitor like a GAP. Since we start from two different polarising models our findings seem independent of the precise self-activation mechanism. By studying the net GTPase flows among clusters, we provide insight into how these mechanisms operate. Our coexistence models also allow for dynamical regulation of the final pattern, which we illustrate with examples of pollen tube growth and the branching of fungal hyphae. Together, these results provide a better understanding of how cells can tune a single system to generate a wide variety of biologically relevant patterns.

Excitable dynamics of Ras triggers spontaneous symmetry breaking of PIP3 signaling in motile cells

Spontaneous cell movement is underpinned by an asymmetric distribution of signaling molecules including small G proteins and phosphoinositides on the cell membrane. However, the molecular network necessary for spontaneous symmetry breaking has not been fully elucidated. Here, we report that, in Dictyostelium discoideum, the spatiotemporal dynamics of GTP bound Ras (Ras-GTP) breaks the symmetry due its intrinsic excitability even in the absence of extracellular spatial cues and downstream signaling activities. A stochastic excitation of local and transient Ras activation induced phosphatidylinositol (3,4,5)-trisphosphate (PIP3) accumulation via direct interaction with Phosphoinositide 3-kinase (PI3K), causing tightly coupled traveling waves that propagated along the membrane. Comprehensive phase analysis of the waves of Ras-GTP and PIP3 metabolism-related molecules revealed the network structure of the excitable system including positive-feedback regulation of Ras-GTP by the downstream PIP3. A mathematical model reconstituted a series of the observed symmetry-breaking phenomena, illustrating the essential involvement of Ras excitability in the cellular decision-making process.

Theoretical Models of Neural Development

Constructing a functioning nervous system requires the precise orchestration of a vast array of mechanical, molecular, and neural-activity-dependent cues. Theoretical models can play a vital role in helping to frame quantitative issues, reveal mathematical commonalities between apparently diverse systems, identify what is and what is not possible in principle, and test the abilities of specific mechanisms to explain the data. This review focuses on the progress that has been made over the last decade in our theoretical understanding of neural development.

Fam49/CYRI interacts with Rac1 and locally suppresses protrusions

Actin-based protrusions are reinforced through positive feedback, but it is unclear what restricts their size, or limits positive signals when they retract or split. We identify an evolutionarily conserved regulator of actin-based protrusion: CYRI (CYFIP-related Rac interactor) also known as Fam49 (family of unknown function 49). CYRI binds activated Rac1 via a domain of unknown function (DUF1394) shared with CYFIP, defining DUF1394 as a Rac1-binding module. CYRI-depleted cells have broad lamellipodia enriched in Scar/WAVE, but reduced protrusion-retraction dynamics. Pseudopods induced by optogenetic Rac1 activation in CYRI-depleted cells are larger and longer lived. Conversely, CYRI overexpression suppresses recruitment of active Scar/WAVE to the cell edge, resulting in short-lived, unproductive protrusions. CYRI thus focuses protrusion signals and regulates pseudopod complexity by inhibiting Scar/WAVE-induced actin polymerization. It thus behaves like a 'local inhibitor' as predicted in widely accepted mathematical models, but not previously identified in cells. CYRI therefore regulates chemotaxis, cell migration and epithelial polarization by controlling the polarity and plasticity of protrusions.

Mutually inhibitory Ras-PI(3,4)P2 feedback loops mediate cell migration

Signal transduction and cytoskeleton networks in a wide variety of cells display excitability, but the mechanisms are poorly understood. Here, we show that during random migration and in response to chemoattractants, cells maintain complementary spatial and temporal distributions of Ras activity and phosphatidylinositol (3,4)-bisphosphate [PI(3,4)P₂]. In addition, depletion of PI(3,4)P₂ by disruption of the 5-phosphatase, Dd5P4, or by recruitment of 4-phosphatase INPP4B to the plasma membrane, leads to elevated Ras activity, cell spreading, and altered migratory behavior. Furthermore, RasGAP2 and RapGAP3 bind to PI(3,4)P₂, and the phenotypes of cells lacking these genes mimic those with low PI(3,4)P₂ levels, providing a molecular mechanism. These findings suggest that Ras activity drives PI(3,4)P₂ down, causing the PI(3,4)P₂-binding GAPs to dissociate from the membrane, further activating Ras, completing a positive-feedback loop essential for excitability. Consistently, a computational model incorporating such a feedback loop in an excitable network model accurately simulates the dynamic distributions of active Ras and PI(3,4)P₂ as well as cell migratory behavior. The mutually inhibitory Ras-PI(3,4)P₂ mechanisms we uncovered here provide a framework for Ras regulation that may play a key role in many physiological processes.

Exploration and stabilization of Ras1 mating zone: A mechanism with positive and negative feedbacks

In mating fission yeast cells, sensing and response to extracellular pheromone concentrations occurs through an exploratory Cdc42 patch that stochastically samples the cell cortex before stabilizing towards a mating partner. Active Ras1 (Ras1-GTP), an upstream regulator of Cdc42, and Gap1, the GTPase-activating protein for Ras1, localize at the patch. We developed a reaction-diffusion model of Ras1 patch appearance and disappearance with a positive feedback by a Guanine nucleotide Exchange Factor (GEF) and Gap1 inhibition. The model is based on new estimates of Ras1-GDP, Ras1-GTP and Gap1 diffusion coefficients and rates of cytoplasmic exchange studied by FRAP. The model reproduces exploratory patch behavior and lack of Ras1 patch in cells lacking Gap1. Transition to a stable patch can occur by change of Gap1 rates constants or local increase of the positive feedback rate constants. The model predicts that the patch size and number of patches depend on the strength of positive and negative feedbacks. Measurements of Ras1 patch size and number in cells overexpressing the Ras1 GEF or Gap1 are consistent with the model.

Unicellular fission yeasts mate by fusing with partners of the opposite mating type. Each pair member grows towards its selected partner that signals its presence through secreted pheromone. The process of partner selection occurs through an exploratory patch (containing activated signaling protein Cdc42 and upstream regulator Ras1) that assembles and disassembles on the cell cortex, stabilizing in regions of higher opposite pheromone concentration. We present a computational model of the molecular mechanisms driving the dynamical pattern of patch exploration and stabilization. The model is based on reaction and diffusion along the curved cell membrane, with diffusion coefficients measured experimentally. In the model, a positive Ras1 activation feedback loop generates a patch containing most of the activating protein (Ras1 GEF). The fast diffusing inhibitor Gap1 that is recruited locally from the cytoplasm spreads on the cell membrane, limiting patch size and causing its decay. Spontaneous reinitiation of Ras1 activation elsewhere on the cortex provides a mechanism for exploration. Transition of the system’s behavior to that of a single stable patch is possible upon simulated pheromone sensing. The computational model provides predictions for the number of patches and patch size dependence on parameters that we tested experimentally.

Eukaryotic Cell Dynamics from Crawlers to Swimmers

Movement requires force transmission to the environment, and motile cells are robustly, though not elegantly, designed nanomachines that often can cope with a variety of environmental conditions by altering the mode of force transmission used. As with humans, the available modes range from momentary attachment to a substrate when crawling, to shape deformations when swimming, and at the cellular level this involves sensing the mechanical properties of the environment and altering the mode appropriately. While many types of cells can adapt their mode of movement to their microenvironment (ME), our understanding of how they detect, transduce and process information from the ME to determine the optimal mode is still rudimentary. The shape and integrity of a cell is determined by its cytoskeleton (CSK), and thus the shape changes that may be required to move involve controlled remodeling of the CSK. Motion in vivo is often in response to extracellular signals, which requires the ability to detect such signals and transduce them into the shape changes and force generation needed for movement. Thus the nanomachine is complex, and while much is known about individual components involved in movement, an integrated understanding of motility in even simple cells such as bacteria is not at hand. In this review we discuss recent advances in our understanding of cell motility and some of the problems remaining to be solved.

Dynamic seesaw model for rapid signaling responses in eukaryotic chemotaxis

Directed movement of eukaryotic cells toward spatiotemporally varied chemotactic stimuli enables rapid intracellular signaling responses. While macroscopic cellular manifestation is shaped by balancing external stimuli strength with finite internal delays, the organizing principles of the underlying molecular mechanisms remain to be clarified. Here, we developed a novel modeling framework based on a simple seesaw mechanism to elucidate how cells repeatedly reverse polarity. As a key feature of the modeling, the bottom module of bidirectional molecular transport is successively controlled by three upstream modules of signal reception, initial signal processing, and Rho GTPase regulation. Our simulations indicated that an isotropic cell is polarized in response to a graded input signal. By applying a reversal gradient to a chemoattractant signal, lamellipod-specific molecules (i.e. PIP₃ and PI3K) disappear, first from the cell front, and then they redistribute at the opposite side, whereas functional molecules at the rear of the cell (i.e. PIP₂ and PTEN) act oppositely. In particular, the model cell exhibits a seesaw-like spatiotemporal pattern for the establishment of front and rear and interconversion, consistent with those related experimental observations. Increasing the switching frequency of the chemotactic gradient causes the cell to stay in a trapped state, further supporting the proposed dynamics of eukaryotic chemotaxis with the underlying cytoskeletal remodeling.

A G-protein-coupled chemoattractant receptor recognizes lipopolysaccharide for bacterial phagocytosis

Phagocytes locate microorganisms via chemotaxis and then consume them using phagocytosis. Dictyostelium amoebas are stereotypical phagocytes that prey on diverse bacteria using both processes. However, as typical phagocytic receptors, such as complement receptors or Fcγ receptors, have not been found in Dictyostelium, it remains mysterious how these cells recognize bacteria. Here, we show that a single G-protein-coupled receptor (GPCR), folic acid receptor 1 (fAR1), simultaneously recognizes the chemoattractant folate and the phagocytic cue lipopolysaccharide (LPS), a major component of bacterial surfaces. Cells lacking fAR1 or its cognate G-proteins are defective in chemotaxis toward folate and phagocytosis of Klebsiella aerogenes. Computational simulations combined with experiments show that responses associated with chemotaxis can also promote engulfment of particles coated with chemoattractants. Finally, the extracellular Venus-Flytrap (VFT) domain of fAR1 acts as the binding site for both folate and LPS. Thus, fAR1 represents a new member of the pattern recognition receptors (PRRs) and mediates signaling from both bacterial surfaces and diffusible chemoattractants to reorganize actin for chemotaxis and phagocytosis.

A computational model for how cells choose temporal or spatial sensing during chemotaxis

Cell size is thought to play an important role in choosing between temporal and spatial sensing in chemotaxis. Large cells are thought to use spatial sensing due to large chemical difference at its ends whereas small cells are incapable of spatial sensing due to rapid homogenization of proteins within the cell. However, small cells have been found to polarize and large cells like sperm cells undergo temporal sensing. Thus, it remains an open question what exactly governs spatial versus temporal sensing. Here, we identify the factors that determines sensing choices through mathematical modeling of chemotactic circuits. Comprehensive computational search of three-node signaling circuits has identified the negative integral feedback (NFB) and incoherent feedforward (IFF) circuits as capable of adaptation, an important property for chemotaxis. Cells are modeled as one-dimensional circular system consisting of diffusible activator, inactivator and output proteins, traveling across a chemical gradient. From our simulations, we find that sensing outcomes are similar for NFB or IFF circuits. Rather than cell size, the relevant parameters are the 1) ratio of cell speed to the product of cell diameter and rate of signaling, 2) diffusivity of the output protein and 3) ratio of the diffusivities of the activator to inactivator protein. Spatial sensing is favored when all three parameters are low. This corresponds to a cell moving slower than the time it takes for signaling to propagate across the cell diameter, has an output protein that is polarizable and has a local-excitation global-inhibition system to amplify the chemical gradient. Temporal sensing is favored otherwise. We also find that temporal sensing is more robust to noise. By performing extensive literature search, we find that our prediction agrees with observation in a wide range of species and cell types ranging from E. coli to human Fibroblast cells and propose that our result is universally applicable.

Unicellular organisms and other single cells often have to migrate towards food sources or away from predators by sensing chemicals present in the environment. There are two ways for a cell to sense these external chemicals: temporal sensing, where the cell senses the external chemical at two different time points after it has moved through a certain distance, or spatial sensing, where the cell senses the external chemical at two different locations on its cellular surface (e.g., the front and rear of the cell) simultaneously. It has been thought that small unicellular organisms employ temporal sensing as their small size prohibits sensing at two different locations on the cellular surface. Using computational modeling, we find that the choice between temporal and spatial sensing is determined by the ratio of cell velocity to the product of cell diameter and rate of signaling, as well as the diffusivities of the signaling proteins. Predictions from our model agree with experimental observations over a wide range of cells, where a fast-moving, small cell performs better comparing the chemoattractant at different times in its trajectory; whereas, a slow-moving, big cell performs better by comparing the chemoattractant concentration at its two ends.

Migrating Myeloid Cells Sense Temporal Dynamics of Chemoattractant Concentrations

Chemoattractant-mediated recruitment of hematopoietic cells to sites of pathogen growth or tissue damage is critical to host defense and organ homeostasis. Chemotaxis is typically considered to rely on spatial sensing, with cells following concentration gradients as long as these are present. Utilizing a microfluidic approach, we found that stable gradients of intermediate chemokines (CCL19 and CXCL12) failed to promote persistent directional migration of dendritic cells or neutrophils. Instead, rising chemokine concentrations were needed, implying that temporal sensing mechanisms controlled prolonged responses to these ligands. This behavior was found to depend on G-coupled receptor kinase-mediated negative regulation of receptor signaling and contrasted with responses to an end agonist chemoattractant (C5a), for which a stable gradient led to persistent migration. These findings identify temporal sensing as a key requirement for long-range myeloid cell migration to intermediate chemokines and provide insights into the mechanisms controlling immune cell motility in complex tissue environments.

A Reaction-Diffusion Model Explains Amplification of the PLC/PKC Pathway in Fibroblast Chemotaxis

During the proliferative phase of cutaneous wound healing, dermal fibroblasts are recruited into the clotted wound by a concentration gradient of platelet-derived growth factor (PDGF), together with other spatial cues. Despite the importance of this chemotactic process, the mechanisms controlling the directed migration of slow-moving mesenchymal cells such as fibroblasts are not well understood. Here, we develop and analyze a reaction-diffusion model of phospholipase C/protein kinase C (PKC) signaling, which was recently identified as a requisite PDGF-gradient-sensing pathway, with the goal of identifying mechanisms that can amplify its sensitivity in the shallow external gradients typical of chemotaxis experiments. We show that phosphorylation of myristoylated alanine-rich C kinase substrate by membrane-localized PKC constitutes a positive feedback that is sufficient for local pathway amplification. The release of phosphorylated myristoylated alanine-rich C kinase substrate and its subsequent diffusion and dephosphorylation in the cytosol also serves to suppress the pathway in down-gradient regions of the cell. By itself, this mechanism only weakly amplifies signaling in a shallow PDGF gradient, but it synergizes with other feedback mechanisms to enhance amplification. This model offers a framework for a mechanistic understanding of phospholipase C/PKC signaling in chemotactic gradient sensing and can guide the design of experiments to assess the roles of putative feedback loops.

Excitable Signal Transduction Networks in Directed Cell Migration

Although directed migration of eukaryotic cells may have evolved to escape nutrient depletion, it has been adopted for an extensive range of physiological events during development and in the adult organism. The subversion of these movements results in disease, such as cancer. Mechanisms of propulsion and sensing are extremely diverse, but most eukaryotic cells move by extending actin-filled protrusions termed macropinosomes, pseudopodia, or lamellipodia or by extension of blebs. In addition to motility, directed migration involves polarity and directional sensing. The hundreds of gene products involved in these processes are organized into networks of parallel and interconnected pathways. Many of these components are activated or inhibited coordinately with stimulation and on each spontaneously extended protrusion. Moreover, these networks display hallmarks of excitability, including all-or-nothing responsiveness and wave propagation. Cellular protrusions result from signal transduction waves that propagate outwardly from an origin and drive cytoskeletal activity. The range of the propagating waves and hence the size of the protrusions can be altered by lowering or raising the threshold for network activation, with larger and wider protrusions favoring gliding or oscillatory behavior over amoeboid migration. Here, we evaluate the variety of models of excitable networks controlling directed migration and outline critical tests. We also discuss the utility of this emerging view in producing cell migration and in integrating the various extrinsic cues that direct migration.

Collective cell migration: a physics perspective

Cells have traditionally been viewed either as independently moving entities or as somewhat static parts of tissues. However, it is now clear that in many cases, multiple cells coordinate their motions and move as collective entities. Well-studied examples comprise development events, as well as physiological and pathological situations. Different ex vivo model systems have also been investigated. Several recent advances have taken place at the interface between biology and physics, and have benefitted from progress in imaging and microscopy, from the use of microfabrication techniques, as well as from the introduction of quantitative tools and models. We review these interesting developments in quantitative cell biology that also provide rich examples of collective out-of-equilibrium motion.

A critical-like collective state leads to long-range cell communication in Dictyostelium discoideum aggregation

The transition from single-cell to multicellular behavior is important in early development but rarely studied. The starvation-induced aggregation of the social amoeba Dictyostelium discoideum into a multicellular slug is known to result from single-cell chemotaxis towards emitted pulses of cyclic adenosine monophosphate (cAMP). However, how exactly do transient, short-range chemical gradients lead to coherent collective movement at a macroscopic scale? Here, we developed a multiscale model verified by quantitative microscopy to describe behaviors ranging widely from chemotaxis and excitability of individual cells to aggregation of thousands of cells. To better understand the mechanism of long-range cell—cell communication and hence aggregation, we analyzed cell—cell correlations, showing evidence of self-organization at the onset of aggregation (as opposed to following a leader cell). Surprisingly, cell collectives, despite their finite size, show features of criticality known from phase transitions in physical systems. By comparing wild-type and mutant cells with impaired aggregation, we found the longest cell—cell communication distance in wild-type cells, suggesting that criticality provides an adaptive advantage and optimally sized aggregates for the dispersal of spores.

A multiscale model and imaging data show that cells of the slime mold Dictyostelium discoideum maximize their cell—cell communication range during aggregation by a critical-like state known from phase transitions in physical systems.

Cells are often coupled to each other in cell collectives, such as aggregates during early development, tissues in the developed organism, and tumors in disease. How do cells communicate over macroscopic distances much larger than the typical cell—cell distance to decide how they should behave? Here, we developed a multiscale model of social amoeba, spanning behavior from individuals to thousands of cells. We show that local cell—cell coupling via secreted chemicals may be tuned to a critical value, resulting in emergent long-range communication and heightened sensitivity. Hence, these aggregates are remarkably similar to bacterial biofilms and neuronal networks, all communicating in a pulselike fashion. Similar organizing principles may also aid our understanding of the remarkable robustness in cancer development.

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.

Spatial and temporal signal processing and decision making by MAPK pathways

Mitogen-activated protein kinase (MAPK) pathways are conserved from yeast to man and regulate a variety of cellular processes, including proliferation and differentiation. Recent developments show how MAPK pathways perform exquisite spatial and temporal signal processing and underscores the importance of studying the dynamics of signaling pathways to understand their physiological response. The importance of dynamic mechanisms that process input signals into graded downstream responses has been demonstrated in the pheromone-induced and osmotic stress-induced MAPK pathways in yeast and in the mammalian extracellular signal-regulated kinase MAPK pathway. Particularly, recent studies in the yeast pheromone response have shown how positive feedback generates switches, negative feedback enables gradient detection, and coherent feedforward regulation underlies cellular memory. More generally, a new wave of quantitative single-cell studies has begun to elucidate how signaling dynamics determine cell physiology and represents a paradigm shift from descriptive to predictive biology.