Phosphoinositides and Rho proteins spatially regulate actin polymerization to initiate and maintain directed movement in a one-dimensional model of a motile cell

Mesenchymal cell migration on one-dimensional micropatterns

Quantitative studies of mesenchymal cell motion are important to elucidate cytoskeleton function and mechanisms of cell migration. To this end, confinement of cell motion to one dimension (1D) significantly simplifies the problem of cell shape in experimental and theoretical investigations. Here we review 1D migration assays employing micro-fabricated lanes and reflect on the advantages of such platforms. Data are analyzed using biophysical models of cell migration that reproduce the rich scenario of morphodynamic behavior found in 1D. We describe basic model assumptions and model behavior. It appears that mechanical models explain the occurrence of universal relations conserved across different cell lines such as the adhesion-velocity relation and the universal correlation between speed and persistence (UCSP). We highlight the unique opportunity of reproducible and standardized 1D assays to validate theory based on statistical measures from large data of trajectories and discuss the potential of experimental settings embedding controlled perturbations to probe response in migratory behavior.

On multistability and constitutive relations of cell motion on fibronectin lanes

Cell motility on flat substrates exhibits coexisting steady and oscillatory morphodynamics, the biphasic adhesion-velocity relation, and the universal correlation between speed and persistence (UCSP) as simultaneous observations common to many cell types. Their universality and concurrency suggest a unifying mechanism causing all three of them. Stick-slip models for cells on one-dimensional lanes suggest multistability to arise from the nonlinear friction of retrograde flow. This study suggests a mechanical mechanism controlled by integrin signaling on the basis of a biophysical model and analysis of trajectories of MDA-MB-231 cells on fibronectin lanes, which additionally explains the constitutive relations. The experiments exhibit cells with steady or oscillatory morphodynamics and either spread or moving with spontaneous transitions between the dynamic regimes, spread and moving, and spontaneous direction reversals. Our biophysical model is based on the force balance at the protrusion edge, the noisy clutch of retrograde flow, and a response function of friction and membrane drag to integrin signaling. The theory reproduces the experimentally observed cell states, characteristics of oscillations, and state probabilities. Analysis of experiments with the biophysical model establishes a stick-slip oscillation mechanism, and explains multistability of cell states and the statistics of state transitions. It suggests protrusion competition to cause direction reversal events, the statistics of which explain the UCSP. The effect of integrin signaling on drag and friction explains the adhesion-velocity relation and cell behavior at fibronectin density steps. The dynamics of our mechanism are nonlinear flow mechanics driven by F-actin polymerization and shaped by the noisy clutch of retrograde flow friction, protrusion competition via membrane tension, and drag forces. Integrin signaling controls the parameters of the mechanical system.

How do cells stiffen?

Cell stiffness is an important characteristic of cells and their response to external stimuli. In this review, we survey methods used to measure cell stiffness, summarize stimuli that alter cell stiffness, and discuss signaling pathways and mechanisms that control cell stiffness. Several pathological states are characterized by changes in cell stiffness, suggesting this property can serve as a potential diagnostic marker or therapeutic target. Therefore, we consider the effect of cell stiffness on signaling and growth processes required for homeostasis and dysfunction in healthy and pathological states. Specifically, the composition and structure of the cell membrane and cytoskeleton are major determinants of cell stiffness, and studies have identified signaling pathways that affect cytoskeletal dynamics both directly and by altered gene expression. We present the results of studies interrogating the effects of biophysical and biochemical stimuli on the cytoskeleton and other cellular components and how these factors determine the stiffness of both individual cells and multicellular structures. Overall, these studies represent an intersection of the fields of polymer physics, protein biochemistry, and mechanics, and identify specific mechanisms involved in mediating cell stiffness that can serve as therapeutic targets.

Manipulating oligodendrocyte intrinsic regeneration mechanism to promote remyelination

In demyelinated lesions, astrocytes, activated microglia and infiltrating macrophages secrete several factors regulating oligodendrocyte precursor cells' behaviour. What appears to be the initiation of an intrinsic mechanism of myelin repair is only leading to partial recovery and inefficient remyelination, a process worsening over the course of the disease. This failure is largely due to the concomitant accumulation of inhibitory cues in and around the lesion sites opposing to growth promoting factors. Here starts a complex game of interactions between the signalling pathways controlling oligodendrocytes migration or differentiation. Receptors of positive or negative cues are modulating Ras, PI3K or RhoGTPases pathways acting on oligodendrocyte cytoskeleton remodelling. From the description of this intricate signalling network, this review addresses the extent to which the modulation of the global response to inhibitory cues may pave the route towards novel therapeutic approaches for myelin repair.

Describing the movement of molecules in reduced-dimension models

When addressing spatial biological questions using mathematical models, symmetries within the system are often exploited to simplify the problem by reducing its physical dimension. In a reduced-dimension model molecular movement is restricted to the reduced dimension, changing the nature of molecular movement. This change in molecular movement can lead to quantitatively and even qualitatively different results in the full and reduced systems. Within this manuscript we discuss the condition under which restricted molecular movement in reduced-dimension models accurately approximates molecular movement in the full system. For those systems which do not satisfy the condition, we present a general method for approximating unrestricted molecular movement in reduced-dimension models. We will derive a mathematically robust, finite difference method for solving the 2D diffusion equation within a 1D reduced-dimension model. The methods described here can be used to improve the accuracy of many reduced-dimension models while retaining benefits of system simplification.

A phosphoinositide-based model of actin waves in frustrated phagocytosis

Phagocytosis is a complex process by which phagocytes such as lymphocytes or macrophages engulf and destroy foreign bodies called pathogens in a tissue. The process is triggered by the detection of antibodies that trigger signaling mechanisms that control the changes of the cellular cytoskeleton needed for engulfment of the pathogen. A mathematical model of the entire process would be extremely complicated, because the signaling and cytoskeletal changes produce large mechanical deformations of the cell. Recent experiments have used a confinement technique that leads to a process called frustrated phagocytosis, in which the membrane does not deform, but rather, signaling triggers actin waves that propagate along the boundary of the cell. This eliminates the large-scale deformations and facilitates modeling of the wave dynamics. Herein we develop a model of the actin dynamics observed in frustrated phagocytosis and show that it can replicate the experimental observations. We identify the key components that control the actin waves and make a number of experimentally-testable predictions. In particular, we predict that diffusion coefficients of membrane-bound species must be larger behind the wavefront to replicate the internal structure of the waves. Our model is a first step toward a more complete model of phagocytosis, and provides insights into circular dorsal ruffles as well.

On the influence of cell shape on dynamic reaction-diffusion polarization patterns

The distribution of signaling molecules following mechanical or chemical stimulation of a cell defines cell polarization, with regions of high active Cdc42 at the front and low active Cdc42 at the rear. As reaction-diffusion phenomena between signaling molecules, such as Rho GTPases, define the gradient dynamics, we hypothesize that the cell shape influences the maintenance of the “front-to-back” cell polarization patterns. We investigated the influence of cell shape on the Cdc42 patterns using an established computational polarization model. Our simulation results showed that not only cell shape but also Cdc42 and Rho-related (in)activation parameter values affected the distribution of active Cdc42. Despite an initial Cdc42 gradient, the in silico results showed that the maximal Cdc42 concentration shifts in the opposite direction, a phenomenon we propose to call “reverse polarization”. Additional in silico analyses indicated that “reverse polarization” only occurred in a particular parameter value space that resulted in a balance between inactivation and activation of Rho GTPases. Future work should focus on a mathematical description of the underpinnings of reverse polarization, in combination with experimental validation using, for example, dedicated FRET-probes to spatiotemporally track Rho GTPase patterns in migrating cells. In summary, the findings of this study enhance our understanding of the role of cell shape in intracellular signaling.

Modeling of Mechanosensing Mechanisms Reveals Distinct Cell Migration Modes to Emerge From Combinations of Substrate Stiffness and Adhesion Receptor-Ligand Affinity

Mesenchymal cell migration is an integral process in development and healing. The process is regulated by both mechanical and biochemical properties. Mechanical properties of the environment are sensed through mechanosensing, which consists of molecular responses mediated by mechanical signals. We developed a computational model of a deformable 3D cell on a flat substrate using discrete element modeling. The cell is polarized in a single direction and thus moves along the long axis of the substrate. By modeling discrete focal adhesions and stress fibers, we implement two mechanosensing mechanisms: focal adhesion stabilization by force and stress fiber strengthening upon contraction stalling. Two substrate-associated properties, substrate (ligand) stiffness and adhesion receptor–ligand affinity (in the form of focal adhesion disassembly rate), were varied for different model setups in which the mechanosensing mechanisms are set as active or inactive. Cell displacement, focal adhesion number, and cellular traction were quantified and tracked in time. We found that varying substrate stiffness (a mechanical property) and adhesion receptor–ligand affinity (a biochemical property) simultaneously dictate the mode in which cells migrate; cells either move in a smooth manner reminiscent of keratocytes or in a cyclical manner reminiscent of epithelial cells. Mechanosensing mechanisms are responsible for the range of conditions in which a cell adopts a particular migration mode. Stress fiber strengthening, specifically, is responsible for cyclical migration due to build-up of enough force to elicit rupture of focal adhesions and retraction of the cellular rear. Together, both mechanisms explain bimodal dependence of cell migration on substrate stiffness observed in the literature.

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.

Multiscale modelling of motility wave propagation in cell migration

The collective motion of cell monolayers within a tissue is a fundamental biological process that occurs during tissue formation, wound healing, cancerous invasion, and viral infection. Experiments have shown that at the onset of migration, the motility is self-generated as a polarisation wave starting from the leading edge of the monolayer and progressively propagates into the bulk. However, it is unclear how the propagation of this motility wave is influenced by cellular properties. Here, we investigate this question using a computational model based on the Potts model coupled to the dynamics of intracellular polarisation. The model captures the propagation of the polarisation wave and suggests that the cells cortex can regulate the migration modes: strongly contractile cells may depolarise the monolayer, whereas less contractile cells can form swirling movement. Cortical contractility is further found to limit the cells motility, which (i) decelerates the wave speed and the leading edge progression, and (ii) destabilises the leading edge. Together, our model describes how different mechanical properties of cells can contribute to the regulation of collective cell migration.

Tuning Cell Motility via Cell Tension with a Mechanochemical Cell Migration Model

Cell migration is orchestrated by a complicated mechanochemical system. However, few cell migration models take into account the coupling between the biochemical network and mechanical factors. Here, we construct a mechanochemical cell migration model to study the cell tension effect on cell migration. Our model incorporates the interactions between Rac-GTP, Rac-GDP, F-actin, myosin, and cell tension, and it is very convenient in capturing the change of cell shape by taking the phase field approach. This model captures the characteristic features of cell polarization, cell shape change, and cell migration modes. It shows that cell tension inhibits migration ability monotonically when cells are applied with persistent external stimuli. On the other hand, if random internal noise is significant, the regulation of cell tension exerts a nonmonotonic effect on cell migration. Because the increase of cell tension hinders the formation of multiple protrusions, migration ability could be maximized at intermediate cell tension under random internal noise. These model predictions are consistent with our single-cell experiments and other experimental results.

The bioenergetics of integrin-based adhesion, from single molecule dynamics to stability of macromolecular complexes

The forces actively generated by motile cells must be transmitted to their environment in a spatiotemporally regulated manner, in order to produce directional cellular motion. This task is accomplished through integrin-based adhesions, large macromolecular complexes that link the actin-cytoskelton inside the cell to its external environment. Despite their relatively large size, adhesions exhibit rapid dynamics, switching between assembly and disassembly in response to chemical and mechanical cues exerted by cytoplasmic biochemical signals, and intracellular/extracellular forces, respectively. While in material science, force typically disrupts adhesive contact, in this biological system, force has a more nuanced effect, capable of causing assembly or disassembly. This initially puzzled experimentalists and theorists alike, but investigation into the mechanisms regulating adhesion dynamics have progressively elucidated the origin of these phenomena. This review provides an overview of recent studies focused on the theoretical understanding of adhesion assembly and disassembly as well as the experimental studies that motivated them. We first concentrate on the kinetics of integrin receptors, which exhibit a complex response to force, and then investigate how this response manifests itself in macromolecular adhesion complexes. We then turn our attention to studies of adhesion plaque dynamics that link integrins to the actin-cytoskeleton, and explain how force can influence the assembly/disassembly of these macromolecular structure. Subsequently, we analyze the effect of force on integrins populations across lengthscales larger than single adhesions. Finally, we cover some theoretical studies that have considered both integrins and the adhesion plaque and discuss some potential future avenues of research.

Cell Size, Mechanical Tension, and GTPase Signaling in the Single Cell

Cell polarization requires redistribution of specific proteins to the nascent front and back of a eukaryotic cell. Among these proteins are Rac and Rho, members of the small GTPase family that regulate the actin cytoskeleton. Rac promotes actin assembly and protrusion of the front edge, whereas Rho activates myosin-driven contraction at the back. Mathematical models of cell polarization at many levels of detail have appeared. One of the simplest based on "wave-pinning" consists of a pair of reaction-diffusion equations for a single GTPase. Mathematical analysis of wave-pinning so far is largely restricted to static domains in one spatial dimension. Here, we extend the analysis to cells that change in size, showing that both shrinking and growing cells can lose polarity. We further consider the feedback between mechanical tension, GTPase activation, and cell deformation in both static, growing, shrinking, and moving cells. Special cases (spatially uniform cell chemistry, the absence or presence of mechanical feedback) are analyzed, and the full model is explored by simulations in 1D. We find a variety of novel behaviors, including "dilution-induced" oscillations of Rac activity and cell size, as well as gain or loss of polarization and motility in the model cell.

Effects of miR-181a-5p abnormal expression on zebrafish (Danio rerio) vascular development following triclosan exposure

Triclosan (TCS), one of the important bactericides, is widely used in personal care products, and its chronic exposure leads to severe toxic effects on the growth and development of blood vessels in zebrafish (Danio rerio). Herein, we screened out three differentially expressed miRNAs (miR-181a-5p, miR-132-3p and miR-128-3p) by sequencing and qRT-PCR analyses of 4-96-hpf TCS-exposed zebrafish, among which miR-181a-5p was found to regulate many signaling pathways involved in fatty acid biosynthesis and phosphatidylimositol signaling systems. By O-dianisidine staining, TCS-exposure resulted in decreased distribution of red blood cells and induced blood hypercoagulable state and thrombotic effects. Defective subintestinal veins (SIVs), and decreased branching and curvature of blood vessels were observed with increasing TCS-exposure concentrations. After microinjection of miR-181a-5p mimic and inhibitor, zebrafish malformation type and percentage were prominently increased such as distorted SIV vessels along with reduced venation and abnormal branches by ALP staining. Overexpressed miR-181a-5p had a greater effect on development and branching patterns of arteries and veins than its knockdown. By laser confocal microscopy observation, the 72-hpf Tg (flk1: mCherry) zebrafish obviously displayed vascular proliferation and ablation in the miR-181a-5p mimic group. Microinjection of miR-181a-5p mimics and inhibitors led to abnormal expressions (20-50%) of two key target genes (pax2a and vash2) by WISH, and increased malformation percentages (18-45%) by IOD analysis. Overexpression of vash2 led to the inhibitory or promoting effects on the expression of PI3K signaling pathway-related genes, proving that the effect of vash2 on development of blood vessels could be realized by inhibiting PI3K signaling pathway. These observations lay theoretical foundation for deep insight into the molecular mechanisms on TCS-induced cardiovascular diseases.

Mechanochemical modeling of neutrophil migration based on four signaling layers, integrin dynamics, and substrate stiffness

Directional neutrophil migration during human immune responses is a highly coordinated process regulated by both biochemical and biomechanical environments. In this paper, we developed an integrative mathematical model of neutrophil migration using a lattice Boltzmann-particle method built in-house to solve the moving boundary problem with spatiotemporal regulation of biochemical components. The mechanical features of the cell cortex are modeled by a series of spring-connected nodes representing discrete cell-substrate adhesive sites. The intracellular signaling cascades responsible for cytoskeletal remodeling [e.g., small GTPases, phosphoinositide-3-kinase (PI3K), and phosphatase and tensin homolog] are built based on our previous four-layered signaling model centered on the bidirectional molecular transport mechanism and implemented as reaction-diffusion equations. Focal adhesion dynamics are determined by force-dependent integrin-ligand binding kinetics and integrin recycling and are thus integrated with cell motion. Using numerical simulations, the model reproduces the major features of cell migration in response to uniform and gradient biochemical stimuli based on the quantitative spatiotemporal regulation of signaling molecules, which agree with experimental observations. The existence of multiple types of integrins with different binding kinetics could act as an adaptation mechanism for substrate stiffness. Moreover, cells can perform reversal, U-turn, or lock-on behaviors depending on the steepness of the reversal biochemical signals received. Finally, this model is also applied to predict the responses of mutants in which PTEN is overexpressed or disrupted.

Computational Modeling of the Dynamics of Spatiotemporal Rho GTPase Signaling: A Systematic Review

The Rho family of GTPases are known to play pivotal roles in the regulation of fundamental cellular processes, ranging from cell migration and polarity to wound healing and regulation of actin cytoskeleton. Over the past decades, accumulating experimental work has increasingly mapped out the mechanistic details and interactions between members of the family and their regulators, establishing detailed interaction circuits within the Rho GTPase signaling network. These circuits have served as a vital foundation based on which a multitude of mathematical models have been developed to explain experimental data, gain deeper insights into the biological phenomenon they describe, as well as make new testable predictions and hypotheses. Due to the diverse nature and purpose of these models, they often vary greatly in size, scope, complexity, and formulation. Here, we provide a systematic, categorical, and comprehensive account of the recent modeling studies of Rho family GTPases, with an aim to offer a broad perspective of the field. The modeling limitations and possible future research directions are also discussed.

Intestinal mucosal barrier dysfunction in SAP patients with MODS ameliorated by continuous blood purification

BACKGROUND

Dysfunction of the intestinal mucosal barrier plays an important role in the pathophysiology of severe acute pancreatitis (SAP). Continuous blood purification (CBP) has been shown to improve the prognosis of SAP patients. In order to investigate the effect of CBP on intestinal mucosal barrier dysfunction in SAP patients with MODS, we conducted in vivo and in vitro experiments to explore the underlying mechanisms.

METHODS

The markers for the assessment of intestinal mucosal barrier function including serum diamine oxidase (DAO), endotoxin and intestinal epithelial monolayer permeability were detected during CBP therapy. The distribution and expression of cytoskeleton protein F-actin and tight junction proteins claudin-1 were observed. In addition, Rho kinase (ROCK) mRNA expression and serum tumor necrosis factor-alpha (TNF-α) levels during CBP were determined.

RESULTS

SAP patients with MODS had increased levels of serum DAO, endotoxin and intestinal epithelial monolayer permeability when compared with normal controls. While the distribution of F-actin and claudin-1 was rearranged, and the expression of claudin-1 significantly decreased, but F-actin had no change. Meanwhile, ROCK mRNA expression and serum TNF-α level were increased. However, after CBP treatment, levels of serum DAO, endotoxin and intestinal epithelial monolayer permeability decreased. The F-actin and claudin-1 reorganization attenuated and the expression of claudin-1 increased. At the same time, ROCK mRNA expression and serum TNF-α level were decreased.

CONCLUSIONS

CBP can effectively improve intestinal mucosal barrier dysfunction. The beneficial effect is associated with the improvement of cytoskeleton and tight junction proteins in stability by downregulation of ROCK mRNA expression through the removal of excess proinflammatory factors.

A Computational Model of YAP/TAZ Mechanosensing

In cell proliferation, stem cell differentiation, chemoresistance, and tissue organization, the ubiquitous role of YAP/TAZ continues to impact our fundamental understanding in numerous physiological and disease systems. YAP/TAZ is an important signaling nexus integrating diverse mechanical and biochemical signals, such as ECM stiffness, adhesion ligand density, or cell-cell contacts, and thus strongly influences cell fate. Recent studies show that YAP/TAZ mechanical sensing is dependent on RhoA-regulated stress fibers. However, current understanding of YAP/TAZ remains limited due to the unknown interaction between the canonical Hippo pathway and cell tension. Furthermore, the multiscale relationship connecting adhesion signaling to YAP/TAZ activity through cytoskeleton dynamics remains poorly understood. To identify the roles of key signaling molecules in mechanical signal sensing and transduction, we present a, to our knowledge, novel computational model of the YAP/TAZ signaling pathway. This model converts extracellular-matrix mechanical properties to biochemical signals via adhesion, and integrates intracellular signaling cascades associated with cytoskeleton dynamics. We perform perturbations of molecular levels and sensitivity analyses to predict how various signaling molecules affect YAP/TAZ activity. Adhesion molecules, such as FAK, are predicted to rescue YAP/TAZ activity in soft environments via the RhoA pathway. We also found that changes of molecule concentrations result in different patterns of YAP/TAZ stiffness response. We also investigate the sensitivity of YAP/TAZ activity to ECM stiffness, and compare with that of SRF/MAL, which is another important regulator of differentiation. In addition, the model shows that the unresolved synergistic effect of YAP/TAZ activity between the mechanosensing and the Hippo pathways can be explained by the interaction of LIM-kinase and LATS. Overall, our model provides a, to our knowledge, novel platform for studying YAP/TAZ activity in the context of integrating different signaling pathways. This platform can be used to gain, to our knowledge, new fundamental insights into roles of key molecular and mechanical regulators on development, tissue engineering, or tumor progression.

Crosstalk of cell polarity signaling pathways

Cell polarity, the asymmetric organization of cellular components along one or multiple axes, is present in most cells. From budding yeast cell polarization induced by pheromone signaling, oocyte polarization at fertilization to polarized epithelia and neuronal cells in multicellular organisms, similar mechanisms are used to determine cell polarity. Crucial role in this process is played by signaling lipid molecules, small Rho family GTPases and Par proteins. All these signaling circuits finally govern the cytoskeleton, which is responsible for oriented cell migration, cell shape changes, and polarized membrane and organelle trafficking. Thus, typically in the process of cell polarization, most cellular constituents become polarized, including plasma membrane lipid composition, ion concentrations, membrane receptors, and proteins in general, mRNA, vesicle trafficking, or intracellular organelles. This review gives a brief overview how these systems talk to each other both during initial symmetry breaking and within the signaling feedback loop mechanisms used to preserve the polarized state.

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.

Emergence of collective dynamical chirality for achiral active particles

Emergence of collective dynamical chirality (CDC) at mesoscopic scales plays a key role in many formation processes of chiral structures in nature, which may also provide possible routines for people to fabricate complex chiral architectures. So far, most of the reported CDCs have been found in systems of active objects with individual structure chirality or/and dynamical chirality, and whether CDC can arise from simple and achiral units is still an attractive mystery. Here, we report a spontaneous formation of CDC in a system of both dynamically and structurally achiral particles motivated by active motion of cells adhered onto a substrate. Active motion, confinement and hydrodynamic interaction are found to be the three key factors. Detailed analysis shows that the system can support abundant collective dynamical behaviors, including rotating droplets, rotating bubbles, CDC oscillations, arrays of collective rotations, and interesting transitions such as chirality transition, structure transition and state reentrance.

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.

Single-Cell Migration in Complex Microenvironments: Mechanics and Signaling Dynamics

Cells are highly dynamic and mechanical automata powered by molecular motors that respond to external cues. Intracellular signaling pathways, either chemical or mechanical, can be activated and spatially coordinated to induce polarized cell states and directional migration. Physiologically, cells navigate through complex microenvironments, typically in three-dimensional (3D) fibrillar networks. In diseases, such as metastatic cancer, they invade across physiological barriers and remodel their local environments through force, matrix degradation, synthesis, and reorganization. Important external factors such as dimensionality, confinement, topographical cues, stiffness, and flow impact the behavior of migrating cells and can each regulate motility. Here, we review recent progress in our understanding of single-cell migration in complex microenvironments.

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.

Cholesterol-Dependent Phase-Demixing in Lipid Bilayers as a Switch for the Activity of the Phosphoinositide-Binding Cytoskeletal Protein Gelsolin

The lateral distribution of phosphatidylinositol 4,5-bisphosphate (PIP2) in lipid bilayers is affected both by divalent cation-mediated attractions and cholesterol-dependent phase demixing. The effects of lateral redistribution of PIP2 within a membrane on PIP2-protein interactions are explored with an N-terminal fragment of gelsolin (NtGSN) that severs actin in a Ca(2+)-insensitive manner. The extent of NtGSN inhibition by PIP2-containing large unilamellar vesicles (LUVs) depends on the lateral organization of the membrane as quantified by an actin-severing assay. At a fixed PIP2 mole fraction, the inhibition is largely enhanced by the segregation of liquid ordered/liquid disordered (Lo/Ld) phases that is induced by altering either cholesterol content or temperature, whereas the presence of Ca(2+) only slightly improves the inhibition. Inhibition of gelsolin induced by demixed LUVs is more effective with decreasing temperature, coincident with increasing membrane order as determined by Laurdan generalized polarization and is reversible as the temperature increases. This result suggests that PIP2-mediated inhibition of gelsolin function depends not only on changes in global concentration but also on lateral distribution of PIP2. These observations imply that gelsolin, and perhaps other PIP2-regulated proteins, can be activated or inactivated by the formation of nanodomains or clusters without changing PIP2 bulk concentration in the cell membrane.

EphrinB2/EphA4-mediated activation of endothelial cells increases monocyte adhesion

The membrane anchored ligand ephrinB2 belongs to the broad Eph/ephrin system and is able to activate different Eph receptors. The Eph receptors belong to the huge group of receptor-tyrosine kinases. Eph receptors as well as their corresponding ephrin ligands are cell-membrane attached proteins. Therefore, direct cell-cell contact is essentially for interaction. It is known that ephrinB2 plays a pivotal role in developmental and in tumour angiogenesis. Previous studies point to a crucial role of the EphA4-receptor in the process of monocyte adhesion. Since ephrinB2 is known as an interaction partner of EphA4, the aim of the present study was to investigate a possible interplay of EphA4-receptor with ephrinB2 during monocyte adhesion to the endothelium. As verified by bulk adhesion assays and atomic-force microscopy based single-cell force spectroscopy, temporary stimulation of endothelial cells from different sources with the soluble ligand ephrinB2 increased monocyte adhesion to endothelial cells. The proadhesive effect of ephrinB2 was independent of an active transcription, but is mediated via the Rho signaling pathway with subsequent modulation of the actin cytoskeleton. Furthermore, ephrinB2 mediated its impact on monocyte adhesion via the receptor EphA4 as shown by siRNA-mediated silencing. Interestingly, ephrinB2 was induced by TNF-α treatment. Silencing of ephrinB2 led to a lowering of the TNF-α mediated monocyte adhesion to endothelial cells. Furthermore, immunohistochemical staining of human atherosclerotic plaque revealed expression of ephrinB2 in macrophages. The results of the present study point to a crucial role of ephrinB2 induced EphA4 forward signaling in the context of monocyte adhesion to endothelial cells. This transcription-independent effect is mediated by Rho signaling induced actin-filament polymerization.

The mechanisms of spatial and temporal patterning of cell-edge dynamics

Adherent cells migrate and change their shape by means of protrusion and retraction at their edges. When and where these activities occur defines the shape of the cell and the way it moves. Despite a great deal of knowledge about the structural organization, components, and biochemical reactions involved in protrusion and retraction, the origins of their spatial and temporal patterns are still poorly understood. Chemical signaling circuitry is believed to be an important source of patterning, but recent studies highlighted mechanisms based on physical forces, motion, and mechanical feedback.

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.

Anomalous segregation dynamics of self-propelled particles

A number of novel experimental and theoretical results have recently been obtained on active soft matter, demonstrating the various interesting universal and anomalous features of this kind of driven systems. Here we consider the adhesion difference-driven segregation of actively moving units, a fundamental but still poorly explored aspect of collective motility. In particular, we propose a model in which particles have a tendency to adhere through a mechanism which makes them both stay in touch and synchronize their direction of motion - but the interaction is limited to particles of the same kind. The calculations corresponding to the related differential equations can be made in parallel, thus a powerful GPU card allows large scale simulations. We find that in a very large system of particles, interacting without explicit alignment rule, three basic segregation regimes seem to exist as a function of time: i) at the beginning the time dependence of the correlation length is analogous to that predicted by the Cahn-Hillard theory, ii) next rapid segregation occurs characterized with a separation of the different kinds of units being faster than any previously suggested speed, finally, iii) the growth of the characteristic sizes in the system slows down due to a new regime in which self-confined, rotating, splitting and re-joining clusters appear. Our results can explain recent observations of segregating tissue cells in vitro.

Modeling large-scale dynamic processes in the cell: polarization, waves, and division

The past decade has witnessed significant developments in molecular biology techniques, fluorescent labeling, and super-resolution microscopy, and together these advances have vastly increased our quantitative understanding of the cell. This detailed knowledge has concomitantly opened the door for biophysical modeling on a cellular scale. There have been comprehensive models produced describing many processes such as motility, transport, gene regulation, and chemotaxis. However, in this review we focus on a specific set of phenomena, namely cell polarization, F-actin waves, and cytokinesis. In each case, we compare and contrast various published models, highlight the relevant aspects of the biology, and provide a sense of the direction in which the field is moving.

Local perturbation analysis: a computational tool for biophysical reaction-diffusion models

Diffusion and interaction of molecular regulators in cells is often modeled using reaction-diffusion partial differential equations. Analysis of such models and exploration of their parameter space is challenging, particularly for systems of high dimensionality. Here, we present a relatively simple and straightforward analysis, the local perturbation analysis, that reveals how parameter variations affect model behavior. This computational tool, which greatly aids exploration of the behavior of a model, exploits a structural feature common to many cellular regulatory systems: regulators are typically either bound to a membrane or freely diffusing in the interior of the cell. Using well-documented, readily available bifurcation software, the local perturbation analysis tracks the approximate early evolution of an arbitrarily large perturbation of a homogeneous steady state. In doing so, it provides a bifurcation diagram that concisely describes various regimes of the model's behavior, reducing the need for exhaustive simulations to explore parameter space. We explain the method and provide detailed step-by-step guides to its use and application.

Feedback mechanisms in a mechanical model of cell polarization

Directed cell migration requires a spatially polarized distribution of polymerized actin. We develop and treat a mechanical model of cell polarization based on polymerization and depolymerization of actin filaments at the two ends of a cell, modulated by forces at either end that are coupled by the cell membrane. We solve this model using both a simulation approach that treats filament nucleation, polymerization, and depolymerization stochastically, and a rate-equation approach based on key properties such as the number of filaments N and the number of polymerized subunits F at either end of the cell. The rate-equation approach agrees closely with the stochastic approach at steady state and, when appropriately generalized, also predicts the dynamic behavior accurately. The calculated transitions from symmetric to polarized states show that polarization is enhanced by a high free-actin concentration, a large pointed-end off-rate, a small barbed-end off-rate, and a small spontaneous nucleation rate. The rate-equation approach allows us to perform a linear-stability analysis to pin down the key interactions that drive the polarization. The polarization is driven by a positive-feedback loop having two interactions. First, an increase in F at one side of the cell lengthens the filaments and thus reduces the decay rate of N (increasing N); second, increasing N enhances F because the force per growing filament tip is reduced. We find that the transitions induced by changing system properties result from supercritical pitchfork bifurcations. The filament lifetime depends strongly on the average filament length, and this effect is crucial for obtaining polarization correctly.

Covalent modification cycles through the spatial prism

Covalent modification cycles are basic units and building blocks of posttranslational modification and cellular signal transduction. We systematically explore different spatial aspects of signal transduction in covalent modification cycles by starting with a basic temporal cycle as a reference and focusing on steady-state signal transduction. We consider, in turn, the effect of diffusion on spatial signal transduction, spatial analogs of ultrasensitive behavior, and the interplay between enzyme localization and substrate diffusion. Our analysis reveals the need to explicitly account for kinetics and diffusional transport (and localization) of enzymes, substrates, and complexes. It demonstrates a complex and subtle interplay between spatial heterogeneity, diffusion, and localization. Overall, examining the spatial dimension of covalent modification reveals that 1), there are important differences between spatial and temporal signal transduction even in this cycle; and 2), spatial aspects may play a substantial role in affecting and distorting information transfer in modules/networks that are usually studied in purely temporal terms. This has important implications for the systematic understanding of signaling in covalent modification cycles, pathways, and networks in multiple cellular contexts.

Transduction of extracellular cues into cell polarity: the role of the transmembrane proteoglycan NG2

Resident progenitor cells expressing nerve/glial antigen 2 (NG2) such as oligodendrocyte precursor cells (OPC) and pericytes persist in the adult brain. The transmembrane proteoglycan NG2 regulates migration of both these cell types in response to growth factors or specific components of the extracellular matrix. This role of NG2 is linked to the control of cell polarity. The polarization of OPC toward an acute lesion in the brain is impaired in NG2-deficient mice, supporting this concept. A review of the signaling pathways impinged on by NG2 reveals key proteins of cell polarity: phosphatidylinositol 3-kinase, focal adhesion kinase, Rho GTPases, and polarity complex proteins. In the scope of cell migration, I discuss here how the interplay of NG2 with signaling transmitted by extracellular cues can control the establishment of cell polarity, and I propose a model to integrate the apparent opposite effects of NG2 on cellular dynamics.

Chlamydia pneumoniae infection induces vascular smooth muscle cell migration via Rac1 activation

Chlamydia pneumoniae infection has been shown to be associated with the development of atherosclerosis by promoting the migration of vascular smooth muscle cells (VSMCs). However, how C. pneumoniae infection induces VSMC migration is not fully understood. A primary role of Ras-related C3 botulinum toxin substrate 1 (Rac1) is to generate a protrusive force at the leading edge that contributes to cell migration. Whether Rac1 activation plays a role in C. pneumoniae infection-induced VSMC migration is not well defined. In the present study, we therefore examined Rac1 activation in C. pneumoniae-infected rat primary VSMCs and the role of Rac1 activation in C. pneumoniae infection-induced VSMC migration. Glutathione S-transferase pull-down assay results showed that Rac1 was activated in C. pneumoniae-infected rat primary VSMCs. A Rac1 inhibitor, NSC23766 (50 µM,) suppressed Rac1 activation stimulated by C. pneumoniae infection, and thereby inhibited C. pneumoniae infection-induced VSMC migration. In addition, C. pneumoniae infection-induced Rac1 activation in the VSMCs was blocked by LY294002 (25 µM), an inhibitor of phosphatidylinositol 3-kinase (PI3K). Taken together, these data suggest that C. pneumoniae infection promotes VSMC migration, possibly through activating Rac1 via PI3K.

Mechanotransduction channels of the trabecular meshwork

PURPOSE

To determine whether the trabecular meshwork (TM), like the other organs engaged in filter like activities (such as kidneys), show the expression of known mechanotransduction channels at protein level.

METHODS

Human donor eye globes (n = 20), Donor eye derived TM tissue and primary TM cells were utilized for these studies. Commercially available antibodies to channels, immunohisto- and immunocytochemistry, Western blot and mass spectrometric analyses were performed to determine the presence of mechanosensitive channels at protein level. The study was performed adhering to tenets of declaration of Helsinki.

RESULTS

We demonstrate here the presence of 11 mechanotransduction channels (Piezo1, Piezo2, TASK1, TREK1, TRPA1, TRPC1, TRPC2, TRPC3, TRPC6, TRPM2, TRPP2) as expressed protein in the TM tissue and at the isolated TM cell level. Presence of at least one known isoform of these channels was demonstrated using Western blot analyses.

CONCLUSIONS

We demonstrated the presence of 11 mechanotransduction channels in the TM and in isolated TM cells at protein level. Demonstration of these channels as proteins at tissue and cellular level will pave the way for further experimentation.

An efficient, nonlinear stability analysis for detecting pattern formation in reaction diffusion systems

Reaction diffusion systems are often used to study pattern formation in biological systems. However, most methods for understanding their behavior are challenging and can rarely be applied to complex systems common in biological applications. I present a relatively simple and efficient, nonlinear stability technique that greatly aids such analysis when rates of diffusion are substantially different. This technique reduces a system of reaction diffusion equations to a system of ordinary differential equations tracking the evolution of a large amplitude, spatially localized perturbation of a homogeneous steady state. Stability properties of this system, determined using standard bifurcation techniques and software, describe both linear and nonlinear patterning regimes of the reaction diffusion system. I describe the class of systems this method can be applied to and demonstrate its application. Analysis of Schnakenberg and substrate inhibition models is performed to demonstrate the methods capabilities in simplified settings and show that even these simple models have nonlinear patterning regimes not previously detected. The real power of this technique, however, is its simplicity and applicability to larger complex systems where other nonlinear methods become intractable. This is demonstrated through analysis of a chemotaxis regulatory network comprised of interacting proteins and phospholipids. In each case, predictions of this method are verified against results of numerical simulation, linear stability, asymptotic, and/or full PDE bifurcation analyses.

Improving RhoA-mediated intestinal epithelial permeability by continuous blood purification in patients with severe acute pancreatitis

BACKGROUND

Early dysfunction of the intestinal mucosal barrier contributes to increasing intestinal permeability. It may play an important role in the pathophysiology of severe acute pancreatitis (SAP). A rising number of clinical data have showed that continuous blood purification (CBP) may improve the prognosis of SAP. However, the therapeutic effects of CBP on intestinal epithelial permeability have been rarely reported.

METHODS

Intestinal epithelial monolayer (Caco-2) was incubated with serum samples collected at specific time points from SAP patients during CBP. Changes in intestinal epithelial monolayer permeability and configuration, and levels of cellular tight junction structural proteins including occludin and ZO-1, and RhoA mRNA expression level were recorded, respectively. In addition, serum tumor necrosis factor-alpha (TNF-α) levels at specific time points during CBP were determined.

RESULTS

Before CBP initiation, intestinal epithelial permeability was increased and tight junction structural protein level was decreased and reorganized, but RhoA mRNA expression and serum TNF-α were increased. However, after CBP treatment, intestinal epithelial permeability was reduced and tight junction protein levels were increased, with reorganization attenuated. Meanwhile, RhoA mRNA expression and serum TNF-α level was decreased.

CONCLUSIONS

After CBP treatment, intestinal epithelial permeability was reduced by increasing occludin and ZO-1 protein level and attenuating reorganization. This beneficial effect of CBP on intestinal epithelial permeability is associated with down-regulation of RhoA mRNA expression, and it may be related to the removal of TNF-α by CBP.

From simple to detailed models for cell polarization

Many mathematical models have been proposed for the process of cell polarization. Some of these are 'functional models' that capture a class of dynamical behaviour, whereas others are derived from features of signalling molecules. Some mechanistic models are detailed, and therefore complex, whereas others are simplified. Each type contributes to our understanding of cell polarization. However, the huge variety at different levels of detail makes comparisons challenging. Here, we provide examples of both elementary and more detailed models for polarization. We also display how a recent mathematical method, local perturbation analysis, can provide an appropriate tool for such comparisons. This technique simplifies and speeds up the model development process by revealing the effect of model extensions, parameter variations and in silico manipulations such as knock-out or over-expression of key molecules. Finally, simulations in both one dimension and two dimensions, and particularly in deforming two-dimensional 'cells', can highlight behaviour not captured by traditional simulation methods.

Continuous blood purification ameliorates endothelial hyperpermeability in SAP patients with MODS by regulating tight junction proteins via ROCK

BACKGROUND

Excessive activation of inflammatory mediator cascade during severe acute pancreatitis (SAP) is a major cause of multiple organ dysfunction and is associated with a high mortality. Recently, more and more studies have shown that continuous blood purification (CBP) could improve the prognosis of patients with multiple organ dysfunction syndrome (MODS), but the exact mechanism is still unclear. Many researchers have found that the disruption of tight junction barrier was an important factor for endothelial hyperpermeability, which played a key role in the pathogenesis of MODS. Previously, we found CBP could attenuate endothelial hyperpermeability in SAP patients with lung injury through regulating cytoskeleton reorganization mediated by RhoA/ROCK. However, the effect of CBP on the change of tight junction proteins in SAP patients with MODS was still unknown. This study aimed to investigate the role of tight junctions in endothelial hyperpermeability in SAP patients with MODS using an in vitro model, and the effect of CBP on tight junction barrier.


METHODS

Before CBP and after CBP, blood samples were collected to observe hepatic and renal function, and arterial blood gas, while the APACHE II score was calculated to evaluate the severity of patients. To test whether RhoA/ROCK signaling pathway was involved, human umbilical vein endothelial cells (HUVECs) were exposed to serum samples taken from patients at specific time points during CBP, or preincubated with ROCK inhibitor, Y-27632, followed by treatment with serum. Then, the changes in endothelial cell permeability and the expression and distribution of tight junction proteins occludin and claudin-1 were observed. 


RESULTS

Compared with before CBP, the APACHE II score, serum creatinine and alanine aminotransferase decreased significantly, while PaO2/FiO2 increased significantly after CBP. Meanwhile, endothelial permeability induced by serum from patients significantly increased, while the expression of tight junction proteins occludin and claudin-1 significantly decreased, and severe disruption of occludin and claudin-1 was found in these cells. However, pretreated with Rho-kinase inhibitor, Y-27632 could lessen all of these abnormalities, and in a dose-dependent way. Endothelial hyperpermeability, the abnormal expression and distribution of occludin and claudin-1 were attenuated in HUVECs treated with serum from patients after CBP treatment. 


CONCLUSIONS

The abnormality of tight junctions mediated by ROCK was an important mechanism for endothelial hyperpermeability induced by serum from SAP patients with MODS. CBP could ameliorate the disorganization and redistribution of tight junction proteins, hence improve the endothelial permeability.

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.

Endothelial cell motility, coordination and pattern formation during vasculogenesis

How vascular networks assemble is a fundamental problem of developmental biology that also has medical importance. To explain the organizational principles behind vascular patterning, we must understand how can tissue level structures be controlled through cell behavior patterns like motility and adhesion that, in turn, are determined by biochemical signal transduction processes? We discuss the various ideas that have been proposed as mechanisms for vascular network assembly: cell motility guided by extracellular matrix alignment (contact guidance), chemotaxis guided by paracrine and autocrine morphogens, and multicellular sprouting guided by cell-cell contacts. All of these processes yield emergent patterns, thus endothelial cells can form an interconnected structure autonomously, without guidance from an external pre-pattern.

A model for intracellular actin waves explored by nonlinear local perturbation analysis

Waves and dynamic patterns in chemical and physical systems have long interested experimentalists and theoreticians alike. Here we investigate a recent example within the context of cell biology, where waves of actin (a major component of the cytoskeleton) and its regulators (nucleation promoting factors, NPFs) are observed experimentally. We describe and analyze a minimal reaction diffusion model depicting the feedback between signalling proteins and filamentous actin (F-actin). Using numerical simulation, we show that this model displays a rich variety of patterning regimes. A relatively recent nonlinear stability method, the Local Perturbation Analysis (LPA), is used to map the parameter space of this model and explain the genesis of patterns in various linear and nonlinear patterning regimes. We compare our model for actin waves to others in the literature, and focus on transitions between static polarization, transient waves, periodic wave trains, and reflecting waves. We show, using LPA, that the spatially distributed model gives rise to dynamics that are absent in the kinetics alone. Finally, we show that the width and speed of the waves depend counter-intuitively on parameters such as rates of NPF activation, negative feedback, and the F-actin time scale.

Collective cell streams in epithelial monolayers depend on cell adhesion

We report a spontaneously emerging, randomly oriented, collective streaming behavior within a monolayer culture of a human keratinocyte cell line, and explore the effect of modulating cell adhesions by perturbing the function of calcium-dependent cell adhesion molecules. We demonstrate that decreasing cell adhesion induces narrower and more anisotropic cell streams, reminiscent of decreasing the Taylor scale of turbulent liquids. To explain our empirical findings, we propose a cell-based model that represents the dual nature of cell-cell adhesions. Spring-like connections provide mechanical stability, while a cellular Potts model formalism represents surface-tension driven attachment. By changing the relevance and persistence of mechanical links between cells, we are able to explain the experimentally observed changes in emergent flow patterns.

Ephrin-A1/EphA4-mediated adhesion of monocytes to endothelial cells

The Eph receptors represent the largest family of receptor tyrosine kinases. Both Eph receptors and their ephrin ligands are cell-surface proteins, and they typically mediate cell-to-cell communication by interacting at sites of intercellular contact. The major aim of the present study was to investigate the involvement of EphA4-ephrin-A1 interaction in monocyte adhesion to endothelial cells, as this process is a crucial step during the initiation and progression of the atherosclerotic plaque. Immunohistochemical analysis of human atherosclerotic plaques revealed expression of EphA4 receptor and ephrin-A1 ligand in major cell types within the plaque. Short-time stimulation of endothelial cells with the soluble ligand ephrin-A1 leads to a fourfold increase in adhesion of human monocytes to endothelial cells. In addition, ephrin-A1 further increases monocyte adhesion to already inflamed endothelial cells. EphrinA1 mediates its effect on monocyte adhesion via the activated receptor EphA4. This ephrinA1/EphA4 induced process involves the activation of the Rho signaling pathway and does not require active transcription. Rho activation downstream of EphA4 leads to increased polymerization of actin filaments in endothelial cells. This process was shown to be crucial for the proadhesive effect of ephrin-A1. The results of the present study show that ephrin-A1-induced EphA4 forward signaling promotes monocyte adhesion to endothelial cells via activation of RhoA and subsequent stress-fiber formation by a non-transcriptional mechanism.

Synthetic spatially graded Rac activation drives cell polarization and movement

Migrating cells possess intracellular gradients of active Rho GTPases, which serve as central hubs in transducing signals from extracellular receptors to cytoskeletal and adhesive machinery. However, it is unknown whether shallow exogenously induced intracellular gradients of Rho GTPases are sufficient to drive cell polarity and motility. Here, we use microfluidic control to generate gradients of a small molecule and thereby directly induce linear gradients of active, endogenous Rac without activation of chemotactic receptors. Gradients as low as 15% were sufficient not only to trigger cell migration up the chemical gradient but to induce both cell polarization and repolarization. Cellular response times were inversely proportional to the steepness of Rac inducer gradient in agreement with a mathematical model, suggesting a function for chemoattractant gradient amplification upstream of Rac. Increases in activated Rac levels beyond a well-defined threshold augmented polarization and decreased sensitivity to the imposed gradient. The threshold was governed by initial cell polarity and PI3K activity, supporting a role for both in defining responsiveness to Rac activation. Our results reveal that Rac can serve as a starting point in defining cell polarity. Furthermore, our methodology may serve as a template to investigate processes regulated by intracellular signaling gradients.