Cell movement has essential functions in development, immunity, and cancer. Various cell migration patterns have been reported, but no general rule has emerged so far. Here, we show on the basis of experimental data in vitro and in vivo that cell persistence, which quantifies the straightness of trajectories, is robustly coupled to cell migration speed. We suggest that this universal coupling constitutes a generic law of cell migration, which originates in the advection of polarity cues by an actin cytoskeleton undergoing flows at the cellular scale. Our analysis relies on a theoretical model that we validate by measuring the persistence of cells upon modulation of actin flow speeds and upon optogenetic manipulation of the binding of an actin regulator to actin filaments. Beyond the quantitative prediction of the coupling, the model yields a generic phase diagram of cellular trajectories, which recapitulates the full range of observed migration patterns.

Although collective cell motion plays an important role, for example during wound healing, embryogenesis, or cancer progression, the fundamental rules governing this motion are still not well understood, in particular at high cell density. We study here the motion of human bronchial epithelial cells within a monolayer, over long times. We observe that, as the monolayer ages, the cells slow down monotonously, while the velocity correlation length first increases as the cells slow down but eventually decreases at the slowest motions. By comparing experiments, analytic model, and detailed particle-based simulations, we shed light on this biological amorphous solidification process, demonstrating that the observed dynamics can be explained as a consequence of the combined maturation and strengthening of cell−cell and cell−substrate adhesions. Surprisingly, the increase of cell surface density due to proliferation is only secondary in this process. This analysis is confirmed with two other cell types. The very general relations between the mean cell velocity and velocity correlation lengths, which apply for aggregates of self-propelled particles, as well as motile cells, can possibly be used to discriminate between various parameter changes in vivo, from noninvasive microscopy data.collective cell migration | jamming | glass transition | dynamic inhomogeneity | cell−cell adhesion C ollective motion of cells is crucial in many biological phenomena, including embryonic development (1), wound healing (2, 3), tissue repair (1, 4), and cancer (1, 4). Therefore, understanding the physics underlying how individually migrating cells combine their motion to collectively migrate is presently a matter of intense study. In this context, several studies have recently shown, by numerical simulations, that local alignment rules can result in the emergence of strongly correlated cellular motions in a confluent monolayer (5-9).As time passes, these cell movements in the monolayer slow down. This classic observation is usually associated with the socalled "density-mediated contact inhibition of locomotion" (10, 11). To go further in the analysis of this phenomenon, several observations (6, 12, 13) and simulations (7,14,15) give an interesting new angle by emphasizing the analogy between a cell monolayer and a bidimensional "jammed" colloidal system, where the individual motions of the particles are confined in "cages" of the size of the particles, and where the whole system behaves as a solid (16)(17)(18)(19). In particular, the increase in the characteristic length scales describing the velocity field as well as the presence of "giant" density fluctuations (20, 21) appear to validate this analogy. As a consequence, several theoretical descriptions have been proposed for these cell assemblies within the conceptual framework used to describe jamming in active systems (6,12,13,(22)(23)(24).Cellular density (the equivalent of the packing fraction in colloidal systems) is often assumed to be the principal control parameter in these system...

The biological function of transmembrane proteins is closely related to their insertion, which has most often been studied through their lateral mobility. For >30 years, it has been thought that hardly any information on the size of the diffusing object can be extracted from such experiments. Indeed, the hydrodynamic model developed by Saffman and Delbrü ck predicts a weak, logarithmic dependence of the diffusion coefficient D with the radius R of the protein. Despite widespread use, its validity has never been thoroughly investigated. To check this model, we measured the diffusion coefficients of various peptides and transmembrane proteins, incorporated into giant unilamellar vesicles of 1-stearoyl-2-oleoylsn-glycero-3-phosphocholine (SOPC) or in model bilayers of tunable thickness. We show in this work that, for several integral proteins spanning a large range of sizes, the diffusion coefficient is strongly linked to the protein dimensions. A heuristic model results in a Stokes-like expression for D, (D ؔ 1͞R), which fits literature data as well as ours. Diffusion measurement is then a fast and fruitful method; it allows determining the oligomerization degree of proteins or studying lipid-protein and protein-protein interactions within bilayers.bilayers ͉ transmembrane proteins ͉ diffusion ͉ peptides ͉ sponge phase I n the hydrodynamic model of Saffman and Delbrück (1), transmembrane peptides and proteins are described as diffusing in a perfectly continuous medium, ignoring the finite size of the lipids. This model predicts that the diffusion coefficient D of a simple cylinder embedded in a thin sheet of fluid matching its height ( Fig. 1) is given byIn this expression, the adjustable parameters are by order of importance: the thickness h and viscosity m of the liquid membrane, the radius R of the diffusing cylinder, and the viscosity of the surrounding aqueous phase w . This result follows from solving the flow field in the membrane and in the surrounding fluid, assuming no-slip boundary conditions at the surface of the cylinder, which is considered as large compared with the bilayer components (i.e., R Ͼ h). Numerous biological studies, both in model systems (2-4) and living cells (5, 6), refer to this continuum approach (7). Because D depends only weakly on R, the characterization of protein or rafts radii is delicate (8); for example, increasing the radius from 10 to 100 Å changes the mobility by a mere 30% [for h ϭ 30 Å and m ϭ 10 poise (P; 1 P ϭ 0.1 Pa⅐s)].To check the applicability of the Saffman-Delbrück formula (Eq. 1), we have used fringe pattern photobleaching under the microscope (9) to measure precisely the self-diffusion of transmembrane peptides and proteins of well characterized dimensions. Results and DiscussionThe weight of the bilayer thickness, h, has never been investigated. Rather than using lipids of various lengths, we opted for a unique system where the bilayer thickness can be continuously tuned, leaving the bilayer viscosity constant.We use a phase of model bilayers made of nonionic ...

The remarkable deformability of the human red blood cell (RBC) results from the coupled dynamic response of the phospholipid bilayer and the spectrin molecular network. Here we present quantitative connections between spectrin morphology and membrane fluctuations of human RBCs by using dynamic full-field laser interferometry techniques. We present conclusive evidence that the presence of adenosine 5′-triphosphate (ATP) facilitates nonequilibrium dynamic fluctuations in the RBC membrane that are highly correlated with the biconcave shape of RBCs. Spatial analysis of the fluctuations reveals that these non-equilibrium membrane vibrations are enhanced at the scale of spectrin mesh size. Our results indicate that the dynamic remodeling of the coupled membranes powered by ATP results in non-equilibrium membrane fluctuations manifesting from both metabolic and thermal energies and also maintains the biconcave shape of RBCs.ATP | imaging technique | membrane fluctuation | RBC | spectrin A s they travel through small blood vessels and organs, RBCs undergo repeated severe deformation. The coupling and interactions between the phospholipid bilayer and the spectrin network govern the deformability of RBCs (1). The fluid-like lipid bilayer is coupled to the two-dimensional spectrin network that comprises an approximately hexagonal lattice via protein junctional complexes. The RBC membrane is remarkably soft and elastic, and thus exhibits fluctuations with amplitudes of the order of tens of nanometers. The dynamics of the RBC membrane is strongly related to the membrane structure and mechanical properties and has been explored extensively (2-6). However, experimental results available to date on RBC membrane fluctuations have provided only limited information on select regions of the cell membrane with limited spatial and/or temporal resolution (7-9). No full-field measurements of membrane fluctuations in the entire RBC arising in response to well-controlled metabolic activity have been made so far and, consequently, different techniques have led to different interpretations of the mechanistic origins of dynamic RBC membrane fluctuations with and without metabolic activity (7-9).The RBC membrane is not a static but a metabolically regulated active structure. It is known that biochemical energy controls its static and dynamic characteristics. The presence of ATP is not only crucial in maintaining the biconcave shape of the RBC membrane (10), but was also shown to increase the dynamic membrane fluctuations (7, 9). However, the regulatory mechanism of ATP in RBC membranes still remains elusive. Furthermore, these static and dynamic effects of ATP on RBC membrane fluctuations have hitherto been regarded as separate phenomena and have never been explored simultaneously.Here, we present dynamic, full-field, and quantitative measurements of ATP effects on RBC membrane morphology and fluctuations. We show that in the presence of ATP, the RBC membrane fluctuations have a non-equilibrium, metabolic component in addition to a thermal o...

We show theoretically how adenosine 5'-triphosphate (ATP)-induced dynamic dissociations of spectrin filaments (from each other and from the membrane) in the cytoskeleton network of red blood cells (RBC) can explain in a unified manner both the measured fluctuation amplitude as well as the observed shape transformations as a function of intracellular ATP concentration. Static defects can be induced by external stresses such as those present when RBCs pass through small capillaries. We suggest that the partially freed actin at these defect sites may explain the activation of the CFTR membrane-bound protein and the subsequent release of ATP by RBCs subjected to deformations. Our theoretical predictions can be tested by experiments that measure the correlation between variations in the binding of actin to spectrin, the activity of CFTR, and the amount of ATP released.

Collective behavior refers to the emergence of complex migration patterns over scales larger than those of the individual elements constituting a system. It plays a pivotal role in biological systems in regulating various processes such as gastrulation, morphogenesis and tissue organization. Here, by combining experimental approaches and numerical modeling, we explore the role of cell density ('crowding'), strength of intercellular adhesion ('cohesion') and boundary conditions imposed by extracellular matrix (ECM) proteins ('constraints') in regulating the emergence of collective behavior within epithelial cell sheets. Our results show that the geometrical confinement of cells into well-defined circles induces a persistent, coordinated and synchronized rotation of cells that depends on cell density. The speed of such rotating large-scale movements slows down as the density increases. Furthermore, such collective rotation behavior depends on the size of the micropatterned circles: we observe a rotating motion of the overall cell population in the same direction for sizes of up to 200 μm. The rotating cells move as a solid body, with a uniform angular velocity. Interestingly, this upper limit leads to length scales that are similar to the natural correlation length observed for unconfined epithelial cell sheets. This behavior is strongly altered in cells that present a downregulation of adherens junctions and in cancerous cell types. We anticipate that our system provides a simple and easy approach to investigate collective cell behavior in a well-controlled and systematic manner.

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In somatic cells, the position of the cell centroid is dictated by the centrosome. The centrosome is instrumental in nucleus positioning, the two structures being physically connected. Mouse oocytes have no centrosomes, yet harbour centrally located nuclei. We demonstrate how oocytes define their geometric centre in the absence of centrosomes. Using live imaging of oocytes, knockout for the formin 2 actin nucleator, with off-centred nuclei, together with optical trapping and modelling, we discover an unprecedented mode of nucleus positioning. We document how active diffusion of actin-coated vesicles, driven by myosin Vb, generates a pressure gradient and a propulsion force sufficient to move the oocyte nucleus. It promotes fluidization of the cytoplasm, contributing to nucleus directional movement towards the centre. Our results highlight the potential of active diffusion, a prominent source of intracellular transport, able to move large organelles such as nuclei, providing in vivo evidence of its biological function.