Ordered patterns of cell shape and orientational correlation during spontaneous cell migration

Rigidity percolation and active advection synergize in the actomyosin cortex to drive amoeboid cell motility

Spontaneous locomotion is a common feature of most metazoan cells, generally attributed to the properties of actomyosin networks. This force-producing machinery has been studied down to the most minute molecular details, especially in lamellipodium-driven migration. Nevertheless, how actomyosin networks work inside contraction-driven amoeboid cells still lacks unifying principles. Here, using stable motile blebs from HeLa cells as a model amoeboid motile system, we imaged the dynamics of the actin cortex at the single filament level and revealed the co-existence of three distinct rheological phases. We introduce "advected percolation," a process where rigidity percolation and active advection synergize, spatially organizing the actin network's mechanical properties into a minimal and generic locomotion mechanism. Expanding from our observations on simplified systems, we speculate that this model could explain, down to the single actin filament level, how amoeboid cells, such as cancer or immune cells, can propel efficiently through complex 3D environments.

The Genetic Background of Abnormalities in Metabolic Pathways of Phosphoinositides and Their Linkage with the Myotubular Myopathies, Neurodegenerative Disorders, and Carcinogenesis

Myo-inositol belongs to one of the sugar alcohol groups known as cyclitols. Phosphatidylinositols are one of the derivatives of Myo-inositol, and constitute important mediators in many intracellular processes such as cell growth, cell differentiation, receptor recycling, cytoskeletal organization, and membrane fusion. They also have even more functions that are essential for cell survival. Mutations in genes encoding phosphatidylinositols and their derivatives can lead to many disorders. This review aims to perform an in-depth analysis of these connections. Many authors emphasize the significant influence of phosphatidylinositols and phosphatidylinositols' phosphates in the pathogenesis of myotubular myopathies, neurodegenerative disorders, carcinogenesis, and other less frequently observed diseases. In our review, we have focused on three of the most often mentioned groups of disorders. Inositols are the topic of many studies, and yet, there are no clear results of successful clinical trials. Analysis of the available literature gives promising results and shows that further research is still needed.

Coordinates in low-dimensional cell shape-space discriminate migration dynamics from single static cell images

Cell shape has long been used to discern cell phenotypes and states, but the underlying premise has not been quantitatively tested. Here, we show that a single cell image can be used to discriminate its migration behavior by analyzing a large number of cell migration data in vitro. We analyzed a large number of two-dimensional cell migration images over time and found that the cell shape variation space has only six dimensions, and migration behavior can be determined by the coordinates of a single cell image in this 6-dimensional shape-space. We further show that this is possible because persistent cell migration is characterized by spatial-temporally coordinated protrusion and contraction, and a distribution signature in the shape-space. Our findings provide a quantitative underpinning for using cell morphology to differentiate cell dynamical behavior.

Physical biomarkers for human hematopoietic stem and progenitor cells

Adhesion of hematopoietic stem and progenitor cells (HSPCs) to the bone marrow niche plays critical roles in the maintenance of the most primitive HSPCs. The interactions of HSPC-niche interactions are clinically relevant in acute myeloid leukemia (AML), because (i) leukemia-initiating cells adhered to the marrow niche are protected from the cytotoxic effect by chemotherapy and (ii) mobilization of HSPCs from healthy donors' bone marrow is crucial for the effective stem cell transplantation. However, although many clinical agents have been developed for the HSPC mobilization, the effects caused by the extrinsic molecular cues were traditionally evaluated based on phenomenological observations. This review highlights the recent interdisciplinary challenges of hematologists, biophysicists and cell biologists towards the design of defined in vitro niche models and the development of physical biomarkers for quantitative indexing of differential effects of clinical agents on human HSPCs.

Mechanochemical subcellular-element model of crawling cells

Constructing physical models of living cells and tissues is an extremely challenging task because of the high complexities of both intra- and intercellular processes. In addition, the force that a single cell generates vanishes in total due to the law of action and reaction. The typical mechanics of cell crawling involve periodic changes in the cell shape and in the adhesion characteristics of the cell to the substrate. However, the basic physical mechanisms by which a single cell coordinates these processes cooperatively to achieve autonomous migration are not yet well understood. To obtain a clearer grasp of how the intracellular force is converted to directional motion, we develop a basic mechanochemical model of a crawling cell based on subcellular elements with the focus on the dependence of the protrusion and contraction as well as the adhesion and de-adhesion processes on intracellular biochemical signals. By introducing reaction-diffusion equations that reproduce traveling waves of local chemical concentrations, we clarify that the chemical dependence of the cell-substrate adhesion dynamics determines the crawling direction and distance with one chemical wave. Finally, we also perform multipole analysis of the traction force to compare it with the experimental results. Our present work sheds light on how intracellular chemical reactions are converted to a directional cell migration under the force-free condition. Although the detailed mechanisms of actual cells are far more complicated than our simple model, we believe that this mechanochemical model is a good prototype for more realistic models.

Morphological growth dynamics, mechanical stability, and active microtubule mechanics underlying spindle self-organization

The spindle is a dynamic intracellular structure self-organized from microtubules and microtubule-associated proteins. The spindle’s bipolar morphology is essential for the faithful segregation of chromosomes during cell division, and it is robustly maintained by multifaceted mechanisms. However, abnormally shaped spindles, such as multipolar spindles, can stochastically arise in a cell population and cause chromosome segregation errors. The physical basis of how microtubules fail in bipolarization and occasionally favor nonbipolar assembly is poorly understood. Here, using live fluorescence imaging and quantitative shape analysis in Xenopus egg extracts, we find that spindles of varied shape morphologies emerge through nonrandom, bistable self-organization paths, one leading to a bipolar and the other leading to a multipolar phenotype. The bistability defines the spindle’s unique morphological growth dynamics linked to each shape phenotype and can be promoted by a locally distorted microtubule flow that arises within premature structures. We also find that bipolar and multipolar spindles are stable at the steady-state in bulk but can infrequently switch between the two phenotypes. Our microneedle-based physical manipulation further demonstrates that a transient force perturbation applied near the assembled pole can trigger the phenotypic switching, revealing the mechanical plasticity of the spindle. Together with molecular perturbation of kinesin-5 and augmin, our data propose the physical and molecular bases underlying the emergence of spindle-shape variation, which influences chromosome segregation fidelity during cell division.

Collective motion of epithelial cells along a wrinkled 3D-buckled hydrogel

Epithelial cells migrate autonomously by aligning and inducing a collective motion. Controlling the collective motion of epithelial cells in geometrically confined environments is important for understanding physiological processes such as wound healing and self-organized morphogenesis. However, collective migration under a three-dimensional (3D) curved surface resembling living epithelial tissue has not yet been explored. In this study, we investigated the collective motion of a 3D-buckled polyacrylamide (PAAm) gel that mimics the shape of folds and wrinkles of epithelial tissue to understand the geometric effects of collective motion. We found that the velocity correlation in the space near the hydrogel boundary showed a periodic change that correlated with the wrinkled folding of the hydrogel pattern. Furthermore, the characteristic length of the velocity correlation increased proportionally with the wavelength of wrinkled folding. These observations indicated that the hydrogel pattern could steer the collective motion of epithelial cells over long distances. Our study also suggests that the wrinkled design of the hydrogel is a versatile platform for studying the geometric effect of a curved surface on complex epithelial cell dynamics.

Combined Effect of Matrix Topography and Stiffness on Neutrophil Shape and Motility

The crawling behavior of leukocytes is driven by the cell morphology transition, which is a direct manifestation of molecular motor machinery. The topographical anisotropy and mechanical stiffness of the substrates are the main physical cues that affect leukocytes' shape generation and migratory responses. However, their combined effects on the cell morphology and motility have been poorly understood, particularly for neutrophils, which are the fastest reacting leukocytes against infections and wounds. Here, spatiotemporally correlated physical parameters are shown, which determine the neutrophil shape change during migratory processes, in response to surface topography and elasticity. Guided crawling and shape generation of individual neutrophils, activated by a uniform concentration of a chemoattractant, are analyzed by adopting elasticity-tunable micropatterning and live cell imaging techniques. Whole cell-level image analysis is performed based on a planar geometric quantification of cell shape and motility. The findings show that the pattern anisotropy and elastic modulus of the substrate induce synergic effects on the shape anisotropy, deformability, and polarization/alignment of crawling neutrophils. How the morphology-motility relationship is affected by different surface microstructures and stiffness is demonstrated. These results imply that the neutrophil shape-motility correlations can be utilized for controlling the immune cell functions with predefined physical microenvironments.

Alignment interactions drive structural transitions in biological tissues

Experimental evidence shows that there is a feedback between cell shape and cell motion. How this feedback impacts the collective behavior of dense cell monolayers remains an open question. We investigate the effect of a feedback that tends to align the cell crawling direction with cell elongation in a biological tissue model. We find that the alignment interaction promotes nematic patterns in the fluid phase that eventually undergo a nonequilibrium phase transition into a quasihexagonal solid. Meanwhile, highly asymmetric cells do not undergo the liquid-to-solid transition for any value of the alignment coupling. In this regime, the dynamics of cell centers and shape fluctuation show features typical of glassy systems.

Neighbor-enhanced diffusivity in dense, cohesive cell populations

The dispersal or mixing of cells within cellular tissue is a crucial property for diverse biological processes, ranging from morphogenesis, immune action, to tumor metastasis. With the phenomenon of ‘contact inhibition of locomotion,’ it is puzzling how cells achieve such processes within a densely packed cohesive population. Here we demonstrate that a proper degree of cell-cell adhesiveness can, intriguingly, enhance the super-diffusive nature of individual cells. We systematically characterize the migration trajectories of crawling MDA-MB-231 cell lines, while they are in several different clustering modes, including freely crawling singles, cohesive doublets of two cells, quadruplets, and confluent population on two-dimensional substrate. Following data analysis and computer simulation of a simple cellular Potts model, which faithfully recapitulated all key experimental observations such as enhanced diffusivity as well as periodic rotation of cell-doublets and cell-quadruplets with mixing events, we found that proper combination of active self-propelling force and cell-cell adhesion is sufficient for generating the observed phenomena. Additionally, we found that tuning parameters for these two factors covers a variety of different collective dynamic states.

Dispersal or movement of cells within dense biological tissue is essential for diverse biological processes, ranging from pattern formation, immune action, to tumor metastasis. However, it is quite puzzling how cells acquire such ability when they are supposedly “caged” by neighboring cells. Here, we report an unusual property of (MDA-MB-231) breast cancer cells that diffuse more persistently within a densely packed population than when they are free to crawl around with little interference. This property is rather surprising since they prefer to stick together, forming clusters. Interestingly, however, we find that having sticky neighbors not only makes two active cells in contact periodically rotate, reminiscent of a ballroom dance, but also enhances the persistence of the cells within a dense population. These intriguing phenomena appear to be universal as they can be generated by a simple cellular Potts model with appropriate combination of active self-propulsion and cell-cell adhesion force.

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.

Critical role of lipid membranes in polarization and migration of cells: a biophysical view

Cell migration plays vital roles in many biologically relevant processes such as tissue morphogenesis and cancer metastasis, and it has fascinated biophysicists over the past several decades. However, despite an increasing number of studies highlighting the orchestration of proteins involved in different signaling pathways, the functional roles of lipid membranes have been essentially overlooked. Lipid membranes are generally considered to be a functionless two-dimensional matrix of proteins, although many proteins regulating cell migration gain functions only after they are recruited to the membrane surface and self-organize their functional domains. In this review, we summarize how the logistical recruitment and release of proteins to and from lipid membranes coordinates complex spatiotemporal molecular processes. As predicted from the classical framework of the Smoluchowski equation of diffusion, lipid/protein membranes serve as a 2D reaction hub that contributes to the effective and robust regulation of polarization and migration of cells involving several competing pathways.

OrgDyn: feature- and model-based characterization of spatial and temporal organoid dynamics

SUMMARY

Organoid model systems recapitulate key features of mammalian tissues and enable high throughput experiments. However, the impact of these experiments may be limited by manual, non-standardized, static or qualitative phenotypic analysis. OrgDyn is an open-source and modular pipeline to quantify organoid shape dynamics using a combination of feature- and model-based approaches on time series of 2D organoid contour images. Our pipeline consists of (i) geometrical and signal processing feature extraction, (ii) dimensionality reduction to differentiate dynamical paths, (iii) time series clustering to identify coherent groups of organoids and (iv) dynamical modeling using point distribution models to explain temporal shape variation. OrgDyn can characterize, cluster and model differences among unique dynamical paths that define diverse final shapes, thus enabling quantitative analysis of the molecular basis of tissue development and disease.

AVAILABILITY AND IMPLEMENTATION

https://github.com/zakih/organoidDynamics (BSD 3-Clause License).

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Control of cell colony growth by contact inhibition

Contact inhibition is a cell property that limits the migration and proliferation of cells in crowded environments. Here we investigate the growth dynamics of a cell colony composed of migrating and proliferating cells on a substrate using a minimal model that incorporates the mechanisms of contact inhibition of locomotion and proliferation. We find two distinct regimes. At early times, when contact inhibition is weak, the colony grows exponentially in time, fully characterised by the proliferation rate. At long times, the colony boundary moves at a constant speed, determined only by the migration speed of a single cell and independent of the proliferation rate. Further, the model demonstrates how cell-cell alignment speeds up colony growth. Our model illuminates how simple local mechanical interactions give rise to contact inhibition, and from this, how cell colony growth is self-organised and controlled on a local level.

Dynamic spherical harmonics approach for shape classification of migrating cells

Cell migration involves dynamic changes in cell shape. Intricate patterns of cell shape can be analyzed and classified using advanced shape descriptors, including spherical harmonics (SPHARM). Though SPHARM have been used to analyze and classify migrating cells, such classification did not exploit SPHARM spectra in their dynamics. Here, we examine whether additional information from dynamic SPHARM improves classification of cell migration patterns. We combine the static and dynamic SPHARM approach with a support-vector-machine classifier and compare their classification accuracies. We demonstrate that the dynamic SPHARM analysis classifies cell migration patterns more accurately than the static one for both synthetic and experimental data. Furthermore, by comparing the computed accuracies with that of a naive classifier, we can identify the experimental conditions and model parameters that significantly affect cell shape. This capability should – in the future – help to pinpoint factors that play an essential role in cell migration.

Cell body shape and directional movement stability in human-induced pluripotent stem cell-derived dopaminergic neurons

Neuronal migration is necessary in the process of the formation of brain architecture. Recently, we demonstrated that human induced pluripotent stem cell (iPSC)-derived dopaminergic neurons exhibit directional migration in vitro. However, it remains unclear how the cell shape is involved in their migration. In this study, we performed live imaging analyses using human iPSC-derived dopaminergic neurons. Our automated method, which can automatically identify the cell body shape and the cell position at specific time points, revealed that healthy iPSC-derived dopaminergic neurons migrate according to their shape. This migration behavior was out of accord in neurons derived from iPSCs carrying an RELN deletion. Our findings provide a novel theory that cell body orientation is related to the stability of movement direction for human dopaminergic neurons, under the regulation of RELN.

A hybrid camphor-camphene wax material for studies on self-propelled motion

A new material that combines the self-propelling properties of camphor with the malleability of camphene is reported. It has wax-like mechanical properties at room temperature and can be formed into required shapes. The speed of the self-propelled objects and the trajectory depend on the shape and camphor-camphene weight ratio.

Sensing of substratum rigidity and directional migration by fast-crawling cells

Living cells sense the mechanical properties of their surrounding environment and respond accordingly. Crawling cells detect the rigidity of their substratum and migrate in certain directions. They can be classified into two categories: slow-moving and fast-moving cell types. Slow-moving cell types, such as fibroblasts, smooth muscle cells, mesenchymal stem cells, etc., move toward rigid areas on the substratum in response to a rigidity gradient. However, there is not much information on rigidity sensing in fast-moving cell types whose size is ∼10 μm and migration velocity is ∼10 μm/min. In this study, we used both isotropic substrata with different rigidities and an anisotropic substratum that is rigid on the x axis but soft on the y axis to demonstrate rigidity sensing by fast-moving Dictyostelium cells and neutrophil-like differentiated HL-60 cells. Dictyostelium cells exerted larger traction forces on a more rigid isotropic substratum. Dictyostelium cells and HL-60 cells migrated in the "soft" direction on the anisotropic substratum, although myosin II-null Dictyostelium cells migrated in random directions, indicating that rigidity sensing of fast-moving cell types differs from that of slow types and is induced by a myosin II-related process.

HIV-1 Nef Disrupts CD4+ T Lymphocyte Polarity, Extravasation, and Homing to Lymph Nodes via Its Nef-Associated Kinase Complex Interface

HIV-1 Nef is a multifunctional protein that optimizes virus spread and promotes immune evasion of infected cells to accelerate disease progression in AIDS patients. As one of its activities, Nef reduces the motility of infected CD4⁺ T lymphocytes in confined space. In vivo, Nef restricts T lymphocyte homing to lymph nodes as it reduces the ability for extravasation at the diapedesis step. Effects of Nef on T lymphocyte motility are typically mediated by its ability to reduce actin remodeling. However, interference with diapedesis does not depend on residues in Nef required for inhibition of host cell actin dynamics. In search for an alternative mechanism by which Nef could alter T lymphocyte extravasation, we noted that the viral protein interferes with the polarization of primary human CD4⁺ T lymphocytes upon infection with HIV-1. Expression of Nef alone is sufficient to disrupt T cell polarization, and this effect is conserved among lentiviral Nef proteins. Nef acts by arresting the oscillation of CD4⁺ T cells between polarized and nonpolarized morphologies. Mapping studies identified the binding site for the Nef-associated kinase complex (NAKC) as critical determinant of this Nef activity and a NAKC-binding-deficient Nef variant fails to impair CD4⁺ T lymphocyte extravasation and homing to lymph nodes. These results thus imply the disruption of T lymphocyte polarity via its NAKC binding site as a novel mechanism by which lentiviral Nef proteins alter T lymphocyte migration in vivo.

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

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

Profiling cellular morphodynamics by spatiotemporal spectrum decomposition

Cellular morphology and associated morphodynamics are widely used for qualitative and quantitative assessments of cell state. Here we implement a framework to profile cellular morphodynamics based on an adaptive decomposition of local cell boundary motion into instantaneous frequency spectra defined by the Hilbert-Huang transform (HHT). Our approach revealed that spontaneously migrating cells with approximately homogeneous molecular makeup show remarkably consistent instantaneous frequency distributions, though they have markedly heterogeneous mobility. Distinctions in cell edge motion between these cells are captured predominantly by differences in the magnitude of the frequencies. We found that acute photo-inhibition of Vav2 guanine exchange factor, an activator of the Rho family of signaling proteins coordinating cell motility, produces significant shifts in the frequency distribution, but does not affect frequency magnitude. We therefore concluded that the frequency spectrum encodes the wiring of the molecular circuitry that regulates cell boundary movements, whereas the magnitude captures the activation level of the circuitry. We also used HHT spectra as multi-scale spatiotemporal features in statistical region merging to identify subcellular regions of distinct motion behavior. In line with our conclusion that different HHT spectra relate to different signaling regimes, we found that subcellular regions with different morphodynamics indeed exhibit distinct Rac1 activities. This algorithm thus can serve as an accurate and sensitive classifier of cellular morphodynamics to pinpoint spatial and temporal boundaries between signaling regimes.

Many studies in cell biology employ global shape descriptors to probe mechanisms of cell morphogenesis. Here, we implement a framework in this paper to profile cellular morphodynamics very locally. We employ the Hilbert-Huang transform (HHT) to extract along the entire cell edge spectra of instantaneous edge motion frequency and magnitude and use them to classify overall cell behavior as well as subcellular edge sectors of distinct dynamics. We find in fibroblast-like COS7 cells that the marked heterogeneity in mobility of an unstimulated population is fully captured by differences in the magnitude spectra, while the frequency spectra are conserved between cells. Using optogenetics to acutely inhibit morphogenetic signaling pathways we find that these molecular shifts are reflected by changes in the frequency spectra but not in the magnitude spectra. After clustering cell edge sectors with distinct morphodynamics we observe in cells expressing a Rac1 activity biosensor that the sectors with different frequency spectra associate with different signaling intensity and dynamics. Together, these observations let us conclude that the frequency spectrum encodes the wiring of the molecular circuitry that regulates edge movements, whereas the magnitude captures the activation level of the circuitry.

Simple Physical Model Unravels Influences of Chemokine on Shape Deformation and Migration of Human Hematopoietic Stem Cells

We studied the dynamic behavior of human hematopoietic stem cells (HSC) on the in vitro model of bone marrow surfaces in the absence and presence of chemokine (SDF1α). The deformation and migration of cells were investigated by varying the chemokine concentration and surface density of ligand molecules. Since HSC used in this study were primary cells extracted from the human umbilical cord blood, it is not possible to introduce molecular reporter systems before or during the live cell imaging. To account for the experimental observations, we propose a simple and general theoretical model for cell crawling. In contrast to other theoretical models reported previously, our model focuses on the nonlinear coupling between shape deformation and translational motion and is free from any molecular-level process. Therefore, it is ideally suited for the comparison with our experimental results. We have demonstrated that the results in the absence of SDF1α were well recapitulated by the linear model, while the nonlinear model is necessary to reproduce the elongated migration observed in the presence of SDF1α. The combination of the simple theoretical model and the label-free, live cell observations of human primary cells opens a large potential to numerically identify the differential effects of extrinsic factors such as chemokines, growth factors, and clinical drugs on dynamic phenotypes of primary cells.

Persistent random deformation model of cells crawling on a gel surface

In general, cells move on a substrate through extension and contraction of the cell body. Though cell movement should be explained by taking into account the effect of such shape fluctuations, past approaches to formulate cell-crawling have not sufficiently quantified the relationship between cell movement (velocity and trajectory) and shape fluctuations based on experimental data regarding actual shaping dynamics. To clarify this relationship, we experimentally characterized cell-crawling in terms of shape fluctuations, especially extension and contraction, by using an elasticity-tunable gel substrate to modulate cell shape. As a result, an amoeboid swimmer-like relation was found to arise between the cell velocity and cell-shape dynamics. To formulate this experimentally-obtained relationship between cell movement and shaping dynamics, we established a persistent random deformation (PRD) model based on equations of a deformable self-propelled particle adopting an amoeboid swimmer-like velocity-shape relationship. The PRD model successfully explains the statistical properties of velocity, trajectory and shaping dynamics of the cells including back-and-forth motion, because the velocity equation exhibits time-reverse symmetry, which is essentially different from previous models. We discuss the possible application of this model to classify the phenotype of cell migration based on the characteristic relation between movement and shaping dynamics.

Swinging motion of active deformable particles in Poiseuille flow

Dynamics of active deformable particles in an external Poiseuille flow is investigated. To make the analysis general, we employ time-evolution equations derived from symmetry considerations that take into account an elliptical shape deformation. First, we clarify the relation of our model to that of rigid active particles. Then, we study the dynamical modes that active deformable particles exhibit by changing the strength of the external flow. We emphasize the difference between the active particles that tend to self-propel parallel to the elliptical shape deformation and those self-propelling perpendicularly. In particular, a swinging motion around the centerline far from the channel walls is discussed in detail.

Collective motion of cells crawling on a substrate: roles of cell shape and contact inhibition

Contact inhibition plays a crucial role in cell motility, wound healing, and tumour formation. By mimicking the mechanical motion of cells crawling on a substrate, we constructed a minimal model of migrating cells that naturally gives rise to contact inhibition of locomotion (CIL). The model cell consists of two disks, a front disk (a pseudopod) and a back disk (cell body), which are connected by a finite extensible spring. Despite the simplicity of the model, the collective behaviour of the cells is highly non-trivial and depends on both the shape of the cells and whether CIL is enabled. Cells with a small front disk (i.e., a narrow pseudopod) form immobile colonies. In contrast, cells with a large front disk (e.g., a lamellipodium) exhibit coherent migration without any explicit alignment mechanism in the model. This result suggests that crawling cells often exhibit broad fronts because this helps facilitate alignment. After increasing the density, the cells develop density waves that propagate against the direction of cell migration and finally stop at higher densities.

Challenges in tissue engineering - towards cell control inside artificial scaffolds

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

Getting drowned in a swirl: Deformable bead-spring model microswimmers in external flow fields

Deformability is a central feature of many types of microswimmers, e.g., for artificially generated self-propelled droplets. Here, we analyze deformable bead-spring microswimmers in an externally imposed solvent flow field as simple theoretical model systems. We focus on their behavior in a circular swirl flow in two spatial dimensions. Linear (straight) two-bead swimmers are found to circle around the swirl with a slight drift to the outside with increasing activity. In contrast to that, we observe for triangular three-bead or squarelike four-bead swimmers a tendency of being drawn into the swirl and finally getting drowned, although a radial inward component is absent in the flow field. During one cycle around the swirl, the self-propulsion direction of an active triangular or squarelike swimmer remains almost constant, while their orbits become deformed exhibiting an "egglike" shape. Over time, the swirl flow induces slight net rotations of these swimmer types, which leads to net rotations of the egg-shaped orbits. Interestingly, in certain cases, the orbital rotation changes sense when the swimmer approaches the flow singularity. Our predictions can be verified in real-space experiments on artificial microswimmers.

Distinct predictive performance of Rac1 and Cdc42 in cell migration

We propose a new computation-based approach for elucidating how signaling molecules are decoded in cell migration. In this approach, we performed FRET time-lapse imaging of Rac1 and Cdc42, members of Rho GTPases which are responsible for cell motility, and quantitatively identified the response functions that describe the conversion from the molecular activities to the morphological changes. Based on the identified response functions, we clarified the profiles of how the morphology spatiotemporally changes in response to local and transient activation of Rac1 and Cdc42, and found that Rac1 and Cdc42 activation triggers laterally propagating membrane protrusion. The response functions were also endowed with property of differentiator, which is beneficial for maintaining sensitivity under adaptation to the mean level of input. Using the response function, we could predict the morphological change from molecular activity, and its predictive performance provides a new quantitative measure of how much the Rho GTPases participate in the cell migration. Interestingly, we discovered distinct predictive performance of Rac1 and Cdc42 depending on the migration modes, indicating that Rac1 and Cdc42 contribute to persistent and random migration, respectively. Thus, our proposed predictive approach enabled us to uncover the hidden information processing rules of Rho GTPases in the cell migration.

Directing and Boosting of Cell Migration by the Entropic Force Gradient in Polymer Solution

Noncontact manipulation of nano/micromaterials presents a great challenge in fields ranging from biotechnology to nanotechnology. In this study we developed a new strategy for the manipulation of molecules and cells based on diffusiophoresis driven by a concentration gradient of a polymer solute. By using laser focusing in a microfluidic device, we created a sharp concentration gradient of poly(ethylene glycol) (PEG) in a solution of this polymer. Because diffusiophoresis essentially depends on solute gradients alone, PEG solute contrast resulted in trapping of DNA and eukaryotic cells with little material dependence. Furthermore, quantitative analysis revealed that the motility of migrating cells was enhanced with the PEG concentration, consistent with a theoretical model of boosted cell migration. Our results support that a solute contrast of polymer can exert an interfacial force gradient that physically propels objects and may have application for the manipulation of soft materials.

Coordinated Behaviour in Pigeon Flocks

We analysed pigeon flock flights using GPS trajectory data to reveal the most important kinematic aspects of flocking behaviour. We quantitatively investigated the internal motion of the flock based on pairwise statistics and found the following general relationships in all datasets: i) the temporal order of decisions characterised by the delay between directional changes is strictly related to the spatial order characterised by the longitudinal relative position within the flock; ii) during circling motion, pigeons use a mixture of two idealised and fundamentally different turning strategies, namely, parallel-path and equal-radius type turning. While pigeons tend to maintain their relative position within the flock on average, as in the parallel-path approximation, those who turn later also get behind as in the equal-radius case. Equal-radius type turning also tends to be expressed more during smaller radius turns.

Quantifying adhesion mechanisms and dynamics of human hematopoietic stem and progenitor cells

Using planar lipid membranes with precisely defined concentrations of specific ligands, we have determined the binding strength between human hematopoietic stem cells (HSC) and the bone marrow niche. The relative significance of HSC adhesion to the surrogate niche models via SDF1α-CXCR4 or N-cadherin axes was quantified by (a) the fraction of adherent cells, (b) the area of tight adhesion, and (c) the critical pressure for cell detachment. We have demonstrated that the binding of HSC to the niche model is a cooperative process, and the adhesion mediated by the CXCR4- SDF1α axis is stronger than that by homophilic N-cadherin binding. The statistical image analysis of stochastic morphological dynamics unraveled that HSC dissipated energy by undergoing oscillatory deformation. The combination of an in vitro niche model and novel physical tools has enabled us to quantitatively determine the relative significance of binding mechanisms between normal HSC versus leukemia blasts to the bone marrow niche.

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

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

Collision dynamics of traveling bands in systems of deformable self-propelled particles

We study the soliton-like character of traveling bands in systems of interacting deformable self-propelled particles in two dimensions. The collision dynamics of the model in which migration velocity increases with increasing local density is investigated numerically by changing the relaxation rate of deformations. The bands are unstable upon head-on collisions for larger relaxation rates. This clearly indicates that deformability plays a crucial role of the soliton-like behavior.

PTEN redundancy: overexpressing lpten, a homolog of Dictyostelium discoideum ptenA, the ortholog of human PTEN, rescues all behavioral defects of the mutant ptenA-

Mutations in the tumor suppressor gene PTEN are associated with a significant proportion of human cancers. Because the human genome also contains several homologs of PTEN, we considered the hypothesis that if a homolog, functionally redundant with PTEN, can be overexpressed, it may rescue the defects of a PTEN mutant. We have performed an initial test of this hypothesis in the model system Dictyostelium discoideum, which contains an ortholog of human PTEN, ptenA. Deletion of ptenA results in defects in motility, chemotaxis, aggregation and multicellular morphogenesis. D. discoideum also contains lpten, a newly discovered homolog of ptenA. Overexpressing lpten completely rescues all developmental and behavioral defects of the D. discoideum mutant ptenA⁻. This hypothesis must now be tested in human cells.

A simple force-motion relation for migrating cells revealed by multipole analysis of traction stress

For biophysical understanding of cell motility, the relationship between mechanical force and cell migration must be uncovered, but it remains elusive. Since cells migrate at small scale in dissipative circumstances, the inertia force is negligible and all forces should cancel out. This implies that one must quantify the spatial pattern of the force instead of just the summation to elucidate the force-motion relation. Here, we introduced multipole analysis to quantify the traction stress dynamics of migrating cells. We measured the traction stress of Dictyostelium discoideum cells and investigated the lowest two moments, the force dipole and quadrupole moments, which reflect rotational and front-rear asymmetries of the stress field. We derived a simple force-motion relation in which cells migrate along the force dipole axis with a direction determined by the force quadrupole. Furthermore, as a complementary approach, we also investigated fine structures in the stress field that show front-rear asymmetric kinetics consistent with the multipole analysis. The tight force-motion relation enables us to predict cell migration only from the traction stress patterns.

UNC-6 (netrin) stabilizes oscillatory clustering of the UNC-40 (DCC) receptor to orient polarity

The receptor deleted in colorectal cancer (DCC) directs dynamic polarizing activities in animals toward its extracellular ligand netrin. How DCC polarizes toward netrin is poorly understood. By performing live-cell imaging of the DCC orthologue UNC-40 during anchor cell invasion in Caenorhabditis elegans, we have found that UNC-40 clusters, recruits F-actin effectors, and generates F-actin in the absence of UNC-6 (netrin). Time-lapse analyses revealed that UNC-40 clusters assemble, disassemble, and reform at periodic intervals in different regions of the cell membrane. This oscillatory behavior indicates that UNC-40 clusters through a mechanism involving interlinked positive (formation) and negative (disassembly) feedback. We show that endogenous UNC-6 and ectopically provided UNC-6 orient and stabilize UNC-40 clustering. Furthermore, the UNC-40-binding protein MADD-2 (a TRIM family protein) promotes ligand-independent clustering and robust UNC-40 polarization toward UNC-6. Together, our data suggest that UNC-6 (netrin) directs polarized responses by stabilizing UNC-40 clustering. We propose that ligand-independent UNC-40 clustering provides a robust and adaptable mechanism to polarize toward netrin.

Intrinsic fluctuations of cell migration under different cellular densities

The motility of the Dictyostelium discoideum (DD) cell is studied by video microscopy when the cells are plated on top of an agar plate at different densities, n. It is found that the fluctuating kinetics of the cells can be divided into two normal directions: the cell's forward-moving direction and its normal direction. Along the forward-moving direction, the slope of the amplitude of fluctuation vs. velocity (R||(v)) increases with n, while along the normal direction the slope of R⊥ is independent of n. Both R|| and R⊥ are functions of the cell speed v. The observed linearity in R⊥(v) indicated that the amplitude of orientational fluctuation (κ) of DD cells is a constant independent of v. The independence of the slope of R⊥(v) on n indicated that κ is also not affected by cellular interactions. The independence of κ on both v and n suggests that orientational fluctuation originates from the intrinsic property of motion fluctuations in DD.

Migration of dendritic cells: physical principles, molecular mechanisms, and functional implications

Dendritic cells (DCs) constitute a complex cell population that resides in both peripheral tissues and lymphoid organs. Their major function in tissues is to patrol their environment in search of danger-associated antigens to transport to lymph nodes and present to T lymphocytes. This process constitutes the first step of the adaptive immune response and relies on specific DC properties, including a high endocytic capacity as well as efficient motility in confined three-dimensional environments. Although cell motility has been widely studied, little is known on how the geometric characteristics of the environment influence DC migration and function. In this review, we give an overview of the basic physical principles and molecular mechanisms that control DC migration under confinement and discuss how such mechanisms impact the environment-patrolling capacity of DCs.

Distinct cell shapes determine accurate chemotaxis

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

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.

Spontaneous motion and deformation of a self-propelled droplet

The time evolution equation of motion and shape are derived for a self-propelled droplet driven by a chemical reaction. The coupling between the chemical reaction and motion makes an inhomogeneous concentration distribution as well as a surrounding flow leading to the instability of a stationary state. The instability results in spontaneous motion by which the shape of the droplet deforms from a sphere. We found that the self-propelled droplet is elongated perpendicular to the direction of motion and is characterized as a pusher.

Non-overlapping activities of ADF and cofilin-1 during the migration of metastatic breast tumor cells

BACKGROUND

ADF/cofilin proteins are key modulators of actin dynamics in metastasis and invasion of cancer cells. Here we focused on the roles of ADF and cofilin-1 individually in the development of polarized migration of rat mammary adenocarcinoma (MTLn3) cells, which express nearly equal amounts of each protein. Small interference RNA (siRNA) technology was used to knockdown (KD) the expression of ADF and cofilin-1 independently.

RESULTS

Either ADF KD or cofilin KD caused cell elongation, a reduction in cell area, a decreased ability to form invadopodia, and a decreased percentage of polarized cells after 180 s of epidermal growth factor stimulation. Moreover, ADF KD or cofilin KD increased the rate of cell migration and the time of lamellipodia protrusion but through different mechanisms: lamellipodia protrude more frequently in ADF KD cells and are more persistent in cofilin KD cells. ADF KD cells showed a significant increase in F-actin aggregates, whereas cofilin KD cells showed a significant increase in prominent F-actin bundles and increased cell adhesion. Focal adhesion area and cell adhesion in cofilin KD cells were returned to control levels by expressing exogenous cofilin but not ADF. Return to control rates of cell migration in ADF KD cells was achieved by expression of exogenous ADF but not cofilin, whereas in cofilin KD cells, expression of cofilin efficiently rescued control migration rates.

CONCLUSION

Although ADF and cofilin have many redundant functions, each of these isoforms has functional differences that affect F-actin structures, cell adhesion and lamellipodial dynamics, all of which are important determinants of cell migration.

Interaction of motility, directional sensing, and polarity modules recreates the behaviors of chemotaxing cells

Chemotaxis involves the coordinated action of separable but interrelated processes: motility, gradient sensing, and polarization. We have hypothesized that these are mediated by separate modules that account for these processes individually and that, when combined, recreate most of the behaviors of chemotactic cells. Here, we describe a mathematical model where the modules are implemented in terms of reaction-diffusion equations. Migration and the accompanying changes in cellular morphology are demonstrated in simulations using a mechanical model of the cell cortex implemented in the level set framework. The central module is an excitable network that accounts for random migration. The response to combinations of uniform stimuli and gradients is mediated by a local excitation, global inhibition module that biases the direction in which excitability is directed. A polarization module linked to the excitable network through the cytoskeleton allows unstimulated cells to move persistently and, for cells in gradients, to gradually acquire distinct sensitivity between front and back. Finally, by varying the strengths of various feedback loops in the model we obtain cellular behaviors that mirror those of genetically altered cell lines.

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

Excitable behavior in amoeboid chemotaxis

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

Oscillatory motions of an active deformable particle

We investigate dynamics of an active particle in which shape deformations occur spontaneously. In two dimensions, the deformations are expanded in terms of the Fourier series and the couplings of different modes are taken into consideration truncated up to lower orders. We focus our attention on the special symmetrical structure between the coupled equations of n- and 2n-mode deformations for n=1, and those for n=2. We show that an oscillatory bifurcation occurs for n=2, which corresponds mathematically to the bifurcation for n=1 where a straight motion becomes unstable and a circular motion appears. At the oscillatory state, the particle undergoes either a spinning motion or a standing oscillation of shape deformations.

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

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

Theoretical model for cell migration with gradient sensing and shape deformation

Amoeboid cells take various shapes during migration, depending on the cell type and its environment. Deformability of the cell shape can then affect the migrating behavior. In this article, we introduce a theoretical model of chemotactic cell migration with elliptical shape deformation. Based on the model, we calculate the stationary distributions of the migration directions analytically. As a result, we find that the distributions show different characteristics depending on the difference in the interdependence of the internal polarity, cell morphology and gradient sensing.