Spontaneous shear flow in confined cellular nematics.

In embryonic development or tumor evolution, cells often migrate collectively within confining tracks defined by their microenvironment 1,2. In some of these situations, the displacements within a cell strand are antiparallel 3, giving rise to shear flows. However, the mechanisms underlying these spontaneous flows remain poorly understood. Here, we show that an ensemble of spindle-shaped cells plated in a well-defined stripe spontaneously develop a shear flow whose characteristics depend on the width of the stripe. On wide stripes, the cells self-organize in a nematic phase with a director at a well-defined angle with the stripe's direction, and develop a shear flow close to the stripe's edges. However, on stripes narrower than a critical width, the cells perfectly align with the stripe's direction and the net flow vanishes. A hydrodynamic active gel theory provides an understanding of these observations and identifies the transition between the non-flowing phase oriented along the stripe and the tilted phase exhibiting shear flow as a Fréedericksz transition driven by the activity of the cells. This physical theory is grounded in the active nature of the cells and based on symmetries and conservation laws, providing a generic mechanism to interpret in vivo antiparallel cell displacements.

Turbulent Dynamics of Epithelial Cell Cultures.

We investigate the large length and long time scales collective flows and structural rearrangements within in vitro human bronchial epithelial cell (HBEC) cultures. Activity-driven collective flows result in ensembles of vortices randomly positioned in space. By analyzing a large population of vortices, we show that their area follows an exponential law with a constant mean value and their rotational frequency is size independent, both being characteristic features of the chaotic dynamics of active nematic suspensions. Indeed, we find that HBECs self-organize in nematic domains of several cell lengths. Nematic defects are found at the interface between domains with a total number that remains constant due to the dynamical balance of nucleation and annihilation events. The mean velocity fields in the vicinity of defects are well described by a hydrodynamic theory of extensile active nematics.

Emergence of collective modes and tri-dimensional structures from epithelial confinement.

Many in vivo processes, including morphogenesis or tumour maturation, involve small populations of cells within a spatially restricted region. However, the basic mechanisms underlying the dynamics of confined cell assemblies remain largely to be deciphered and would greatly benefit from well-controlled in vitro experiments. Here we show that confluent epithelial cells cultured on finite population-sized domains, exhibit collective low-frequency radial displacement modes as well as stochastic global rotation reversals. A simple mathematical model, in which cells are described as persistent random walkers that adapt their motion to that of their neighbours, captures the essential characteristics of these breathing oscillations. As these epithelia mature, a tri-dimensional peripheral cell cord develops at the domain edge by differential extrusion, as a result of the additional degrees of freedom of the border cells. These results demonstrate that epithelial confinement alone can induce morphogenesis-like processes including spontaneous collective pulsations and transition from 2D to 3D.

Perfect nematic order in confined monolayers of spindle-shaped cells.

Elongated, weakly interacting, apolar, fibroblast cells (mouse fibroblasts NIH-3T3) cultured at confluence align together, forming large domains (correlation length ∼ 500 µm) where they are perfectly ordered. We study the emergence of this mesoscopic nematic order by quantifying the ordering dynamics in a two-dimensional tissue. Cells are initially very motile and the monolayer is characterized by anomalous density fluctuations, a signature of far-from-equilibrium systems. As the cell density increases because of proliferation, the cells align with each other forming these large oriented domains while, at the same time, the cellular movements and the density fluctuations freeze. Topological defects that are characteristic of nematic phases remain trapped at long times thereby preventing the development of infinite domains. When confined within adhesive stripes of given widths (from 30 µm to 1.5 mm) cells spontaneously align with the domain edges. This orientation then propagates toward the pattern center. For widths smaller than the orientation correlation length, cells perfectly align in the direction of the stripe. Experiments performed in cross-shaped patterns show that in the situation of two competing populations, both the number of cells and the degree of alignment impact the final orientation.

Interplay of RhoA and mechanical forces in collective cell migration driven by leader cells.

The leading front of a collectively migrating epithelium often destabilizes into multicellular migration fingers where a cell initially similar to the others becomes a leader cell while its neighbours do not alter. The determinants of these leader cells include mechanical and biochemical cues, often under the control of small GTPases. However, an accurate dynamic cartography of both mechanical and biochemical activities remains to be established. Here, by mapping the mechanical traction forces exerted on the surface by MDCK migration fingers, we show that these structures are mechanical global entities with the leader cells exerting a large traction force. Moreover, the spatial distribution of RhoA differential activity at the basal plane strikingly mirrors this force cartography. We propose that RhoA controls the development of these fingers through mechanical cues: the leader cell drags the structure and the peripheral pluricellular acto-myosin cable prevents the initiation of new leader cells.

Directional persistence of chemotactic bacteria in a traveling concentration wave.

Chemotactic bacteria are known to collectively migrate towards sources of attractants. In confined convectionless geometries, concentration "waves" of swimming Escherichia coli can form and propagate through a self-organized process involving hundreds of thousands of these microorganisms. These waves are observed in particular in microcapillaries or microchannels; they result from the interaction between individual chemotactic bacteria and the macroscopic chemical gradients dynamically generated by the migrating population. By studying individual trajectories within the propagating wave, we show that, not only the mean run length is longer in the direction of propagation, but also that the directional persistence is larger compared to the opposite direction. This modulation of the reorientations significantly improves the efficiency of the collective migration. Moreover, these two quantities are spatially modulated along the concentration profile. We recover quantitatively these microscopic and macroscopic observations with a dedicated kinetic model.

Orientation and polarity in collectively migrating cell structures: statics and dynamics.

Collective cell migration is often characterized by the spontaneous onset of multicellular protrusions (known as fingers) led by a single leader cell. Working with epithelial Madin-Darby canine kidney monolayers we show that cells within the fingers, as compared with the epithelium, are well oriented and polarized along the main finger direction, which suggests that these cells actively migrate. The cell orientation and polarity decrease continuously from the tip toward the epithelium over a penetration distance of typically two finger lengths. Furthermore, laser photoablation experiments at various locations along these fingers demonstrate that the cells in the fingers are submitted to a tensile stress whose value is larger close to the tip. From a dynamical point of view, cells entering a finger gradually polarize on timescales that depend upon their particular initial position. Selective laser nanosurgery of the leader lamellipodium shows not only that these structures need a leader to progress, but that this leader itself is the consequence of a prior self-organization of the cells forming the finger. These results highlight the complex interplay between the collective orientation within the fingers and the mechanical action of the leader.

Velocity fields in a collectively migrating epithelium.

We report quantitative measurements of the velocity field of collectively migrating cells in a motile epithelium. The migration is triggered by presenting free surface to an initially confluent monolayer by using a microstencil technique that does not damage the cells. To avoid the technical difficulties inherent in the tracking of single cells, the field is mapped using the technique of particle image velocimetry. The main relevant parameters, such as the velocity module, the order parameter, and the velocity correlation function, are then extracted from this cartography. These quantities are dynamically measured on two types of cells (collectively migrating Madin-Darby canine kidney (MDCK) cells and fibroblastlike normal rat kidney (NRK) cells), first as they approach confluence, and then when the geometrical constraints are released. In particular, for MDCK cells filling up the patterns, we observe a sharp decrease in the average velocity after the point of confluence, whereas the densification of the monolayer is much more regular. After the peeling off of the stencil, a velocity correlation length of approximately 200 microm is measured for MDCK cells versus only approximately 40 microm for the more independent NRK cells. Our conclusions are supported by parallel single-cell tracking experiments. By using the biorthogonal decomposition of the velocity field, we conclude that the velocity field of MDCK cells is very coherent in contrast with the NRK cells. The displacements in the fingers arising from the border of MDCK epithelia are very oriented along their main direction. They influence the velocity field in the epithelium over a distance of approximately 200 microm.

Traction forces exerted by epithelial cell sheets.

Whereas the adhesion and migration of individual cells have been well described in terms of physical forces, the mechanics of multicellular assemblies is still poorly understood. Here, we study the behavior of epithelial cells cultured on microfabricated substrates designed to measure cell-to-substrate interactions. These substrates are covered by a dense array of flexible micropillars whose deflection enables us to measure traction forces. They are obtained by lithography and soft replica molding. The pillar deflection is measured by video microscopy and images are analyzed with home-made multiple particle tracking software. First, we have characterized the temporal and spatial distributions of traction forces of cellular assemblies of various sizes. The mechanical force balance within epithelial cell sheets shows that the forces exerted by neighboring cells strongly depend on their relative position in the monolayer: the largest deformations are always localized at the edge of the islands of cells in the active areas of cell protrusions. The average traction stress rapidly decreases from its maximum value at the edge but remains much larger than the inherent noise due to the force resolution of our pillar tracking software, indicating an important mechanical activity inside epithelial cell islands. Moreover, these traction forces vary linearly with the rigidity of the substrate over about two decades, suggesting that cells exert a given amount of deformation rather than a force. Finally, we engineer micropatterned substrates supporting pillars with anisotropic stiffness. On such substrates cellular growth is aligned with respect to the stiffest direction in correlation with the magnitude of the applied traction forces.

Collective migration of an epithelial monolayer in response to a model wound.

Using an original microfabrication-based technique, we experimentally study situations in which a virgin surface is presented to a confluent epithelium with no damage made to the cells. Although inspired by wound-healing experiments, the situation is markedly different from classical scratch wounding because it focuses on the influence of the free surface and uncouples it from the other possible contributions such as cell damage and/or permeabilization. Dealing with Madin-Darby canine kidney cells on various surfaces, we found that a sudden release of the available surface is sufficient to trigger collective motility. This migration is independent of the proliferation of the cells that mainly takes place on the fraction of the surface initially covered. We find that this motility is characterized by a duality between collective and individual behaviors. On the one hand, the velocity fields within the monolayer are very long range and involve many cells in a coordinated way. On the other hand, we have identified very active "leader cells" that precede a small cohort and destabilize the border by a fingering instability. The sides of the fingers reveal a pluricellular actin "belt" that may be at the origin of a mechanical signaling between the leader and the followers. Experiments performed with autocrine cells constitutively expressing hepatocyte growth factor (HGF) or in the presence of exogenous HGF show a higher average velocity of the border and no leader.

Adhesion enhancement through micropatterning at polydimethylsiloxane-acrylic adhesive interfaces.

Adhesion at polydimethylsiloxane (PDMS)-acrylic adhesive interfaces is shown to be enhanced through micropatterning of the PDMS substrate. By varying the geometry of the patterns (groves and hexagonal arrays of pillars of micrometer sizes, obtained through soft lithography techniques) and comparing rigid and deformable substrates, the respective roles of the geometry and the size and flexibility of the pattern features on the level of adhesion have been analyzed. For cylindrical pillars, two regimes are clearly identified: for a relatively low aspect ratio (h/r < 3, with h and r, respectively, the height and the radius of the pillars), soft patterned substrates are more efficient than rigid ones at increasing adhesion, pointing out the role of the elastic energy associated with the deformation of the pattern that is lost when the adhesive detaches from the substrate. Using scaling laws, the predominant contribution to that elastic energy can be further identified: deformation of the substrate underlying the pillars for h/r < 1.6 or bending of the pillars for h/r > 1.6.; for a high aspect ratio (h/r > 3), only rigid patterned substrates enhance adhesion, then the only possible contribution to energy dissipation comes from the enhanced viscoelastic losses associated with the pattern that induce modifications of the strain field within the adhesive layer. Soft, high aspect ratio patterns lose their efficiency even if still bent under the effect of the peel forces. This is because when bent, some of the pillars touch each other and remain stuck together, lying flat on the surface after the passage of the peel front. The bending elastic energy of the pillars (which is still lost) is then balanced by the corresponding gain in surface energy of the substrate in the peeled region. These systematic experiments demonstrate that the ability of the patterned surface to be deformed plays a crucial role in enhancing adhesion and allow us to propose a way to fine tune the level of adhesion at PDMS-acrylic adhesive interfaces, independently of the chemistry of the adhesive.

Homophilic interactions between cadherin fragments at the single molecule level: an AFM study.

We report measurements of the adhesion forces between single E-cadherin fragments anchored on solid surfaces. These fragments consist of the two outermost extracellular domains of the protein. The specificity of the measured rupture forces was demonstrated by Ca2+ exchange experiments. Two series of experiments were performed using two linkers of different rigidity and length. We find that the pull-off force is distributed with a maximum value independent of the linker and logarithmically dependent on the velocity of separation of the two surfaces. Our dynamical results are compatible with previous flow chamber experiments performed with the same fragments and can be compared from a different perspective with previously reported AFM experiments on the full-length extracellular domain of the VE-cadherin. Interestingly, using a rigid linker, we have been able for the first time to evidence the deformation of the cadherin molecule under mechanical stress, a piece of information not accessible with more classical grafting strategies.

Rectified motion of colloids in asymmetrically structured channels.

We set micron size particles into macroscopic motion by submitting them to a low frequency electric field (of zero mean value) in a microfabricated channel exhibiting a topological ratchet-like local polarity. Rectification is induced by the coupling between electrophoresis, electroosmosis, and dielectrophoresis. The macroscopic velocities of the particles are functions of the electric field and of the geometry of the channel; they strongly depend on their size which opens the way to potential separations.

Moving droplets on asymmetrically structured surfaces.

It is shown theoretically and experimentally that a liquid droplet can move on a surface structured with a locally asymmetric pattern when a breathing of the drop is induced by external means. Two different situations can be envisioned: a drop whose volume is modulated and a drop whose equilibrium contact angle is switched between two extreme values. This last case was experimentally investigated using electric fields acting on water droplets in castor oil. The main trends of the theory are verified although a quantitative analysis would necessitate either a simpler experimental geometry or a more elaborate model. The results are discussed with a miniaturization of the setup in mind which would have important potential applications in the field of integrated analysis systems.

Dielectrophoretic ratchets.

We have experimentally applied some concepts of "force-free" motion to micron size particles (latex beads). The coupling of dissipation and local spatial asymmetry of the potential experienced by the beads can put them into motion. The potentials used in these experiments are of dielectrophoretic nature. To that end, electrodes of particular shapes were used in order to submit the considered suspensions to inhomogeneous ac electric fields. Two regimes were explored: i-the Brownian ratchet case in which a Brownian particle is successively trapped in a factory roof-like potential and left free to diffuse. ii-the shifted ratchets case in which two potentials exhibiting similar characteristics are applied successively, one of them being shifted by a fraction of their common period relatively to the other. In both cases, a good agreement with the theoretical predictions was observed. In particular, particles of different sizes were characterized by different macroscopic velocities leading to the prospect of promising separation techniques. (c) 1998 American Institute of Physics.