Integer topological defects organize stresses driving tissue morphogenesis.

Tissues acquire function and shape via differentiation and morphogenesis. Both processes are driven by coordinating cellular forces and shapes at the tissue scale, but general principles governing this interplay remain to be discovered. Here we report that self-organization of myoblasts around integer topological defects, namely spirals and asters, suffices to establish complex multicellular architectures. In particular, these arrangements can trigger localized cell differentiation or, alternatively, when differentiation is inhibited, they can drive the growth of swirling protrusions. Both localized differentiation and growth of cellular vortices require specific stress patterns. By analysing the experimental velocity and orientational fields through active gel theory, we show that integer topological defects can generate force gradients that concentrate compressive stresses. We reveal these gradients by assessing spatial changes in nuclear volume and deformations of elastic pillars. We propose integer topological defects as mechanical organizing centres controlling differentiation and morphogenesis.

Density-Polarity Coupling in Confined Active Polar Films: Asters, Spirals, and Biphasic Orientational Phases.

Topological defects in active polar fluids can organize spontaneous flows and influence macroscopic density patterns. Both of them play an important role during animal development. Yet the influence of density on active flows is poorly understood. Motivated by experiments on cell monolayers confined to disks, we study the coupling between density and polar order for a compressible active polar fluid in the presence of a +1 topological defect. As in the experiments, we find a density-controlled spiral-to-aster transition. In addition, biphasic orientational phases emerge as a generic outcome of such coupling. Our results highlight the importance of density gradients as a potential mechanism for controlling flow and orientational patterns in biological systems.

Active cargo positioning in antiparallel transport networks.

Cytoskeletal filaments assemble into dense parallel, antiparallel, or disordered networks, providing a complex environment for active cargo transport and positioning by molecular motors. The interplay between the network architecture and intrinsic motor properties clearly affects transport properties but remains poorly understood. Here, by using surface micropatterns of actin polymerization, we investigate stochastic transport properties of colloidal beads in antiparallel networks of overlapping actin filaments. We found that 200-nm beads coated with myosin Va motors displayed directed movements toward positions where the net polarity of the actin network vanished, accumulating there. The bead distribution was dictated by the spatial profiles of local bead velocity and diffusion coefficient, indicating that a diffusion-drift process was at work. Remarkably, beads coated with heavy-mero-myosin II motors showed a similar behavior. However, although velocity gradients were steeper with myosin II, the much larger bead diffusion observed with this motor resulted in less precise positioning. Our observations are well described by a 3-state model, in which active beads locally sense the net polarity of the network by frequently detaching from and reattaching to the filaments. A stochastic sequence of processive runs and diffusive searches results in a biased random walk. The precision of bead positioning is set by the gradient of net actin polarity in the network and by the run length of the cargo in an attached state. Our results unveiled physical rules for cargo transport and positioning in networks of mixed polarity.

Quantifying Material Properties of Cell Monolayers by Analyzing Integer Topological Defects.

In developing organisms, internal cellular processes generate mechanical stresses at the tissue scale. The resulting deformations depend on the material properties of the tissue, which can exhibit long-ranged orientational order and topological defects. It remains a challenge to determine these properties on the time scales relevant for developmental processes. Here, we build on the physics of liquid crystals to determine material parameters of cell monolayers. Specifically, we use a hydrodynamic description to characterize the stationary states of compressible active polar fluids around defects. We illustrate our approach by analyzing monolayers of C2C12 cells in small circular confinements, where they form a single topological defect with integer charge. We find that such monolayers exert compressive stresses at the defect centers, where localized cell differentiation and formation of three-dimensional shapes is observed.

Spontaneous migration of cellular aggregates from giant keratocytes to running spheroids.

Despite extensive knowledge on the mechanisms that drive single-cell migration, those governing the migration of cell clusters, as occurring during embryonic development and cancer metastasis, remain poorly understood. Here, we investigate the collective migration of cell on adhesive gels with variable rigidity, using 3D cellular aggregates as a model system. After initial adhesion to the substrate, aggregates spread by expanding outward a cell monolayer, whose dynamics is optimal in a narrow range of rigidities. Fast expansion gives rise to the accumulation of mechanical tension that leads to the rupture of cell-cell contacts and the nucleation of holes within the monolayer, which becomes unstable and undergoes dewetting like a liquid film. This leads to a symmetry breaking and causes the entire aggregate to move as a single entity. Varying the substrate rigidity modulates the extent of dewetting and induces different modes of aggregate motion: "giant keratocytes," where the lamellipodium is a cell monolayer that expands at the front and retracts at the back; "penguins," characterized by bipedal locomotion; and "running spheroids," for nonspreading aggregates. We characterize these diverse modes of collective migration by quantifying the flows and forces that drive them, and we unveil the fundamental physical principles that govern these behaviors, which underscore the biological predisposition of living material to migrate, independent of length scale.

Active Fingering Instability in Tissue Spreading.

During the spreading of epithelial tissues, the advancing tissue front often develops fingerlike protrusions. Their resemblance to traditional viscous fingering patterns in driven fluids suggests that epithelial fingers could arise from an interfacial instability. However, the existence and physical mechanism of such a putative instability remain unclear. Here, based on an active polar fluid model for epithelial spreading, we analytically predict a generic instability of the tissue front. On the one hand, active cellular traction forces impose a velocity gradient that leads to an accelerated front, which is, thus, unstable to long-wavelength perturbations. On the other hand, contractile intercellular stresses typically dominate over surface tension in stabilizing short-wavelength perturbations. Finally, the finite range of hydrodynamic interactions in the tissue selects a wavelength for the fingering pattern, which is, thus, given by the smallest between the tissue size and the hydrodynamic screening length. Overall, we show that spreading epithelia experience an active fingering instability based on a simple kinematic mechanism. Moreover, our results underscore the crucial role of long-range hydrodynamic interactions in the dynamics of tissue morphology.

Collective stresses drive competition between monolayers of normal and Ras-transformed cells.

We study the competition for space between two cell lines that differ only in the expression of the Ras oncogene. The two cell populations are initially separated and set to migrate antagonistically towards an in-between stripe of free substrate. After contact, their interface moves towards the population of normal cells. We interpret the velocity and traction force data taken before and after contact thanks to a hydrodynamic description of collectively migrating cohesive cell sheets. The kinematics of cells, before and after contact, allows us to estimate the relative material parameters for both cell lines. As predicted by the model, the transformed cell population with larger collective stresses pushes the wild type cell population.

Crisscross multilayering of cell sheets.

Hydrostatic skeletons such as the Hydra's consist of two stacked layers of muscle cells perpendicularly oriented. In vivo, these bilayers first assemble, and then the muscle fibers of both layers develop and organize with this crisscross orientation. In the present work, we identify an alternative mechanism of crisscross bilayering of myoblasts in vitro, which results from the prior local organization of these active cells in the initial monolayer. The myoblast sheet can be described as a contractile active nematic in which, as expected, most of the +1/2 topological defects associated with this nematic order self-propel. However, as a result of the production of extracellular matrix (ECM) by the cells, a subpopulation of these comet-like defects does not show any self-propulsion. Perpendicular bilayering occurs at these stationary defects. Cells located at the head of these defects converge toward their core where they accumulate until they start migrating on top of the tail of the first layer, while the tail cells migrate in the opposite direction under the head. Since the cells keep their initial orientations, the two stacked layers end up perpendicularly oriented. This concerted process leading to a crisscross bilayering is mediated by the secretion of ECM.

Epithelial cells adapt to curvature induction via transient active osmotic swelling.

Generation of tissue curvature is essential to morphogenesis. However, how cells adapt to changing curvature is still unknown because tools to dynamically control curvature in vitro are lacking. Here, we developed self-rolling substrates to study how flat epithelial cell monolayers adapt to a rapid anisotropic change of curvature. We show that the primary response is an active and transient osmotic swelling of cells. This cell volume increase is not observed on inducible wrinkled substrates, where concave and convex regions alternate each other over short distances; and this finding identifies swelling as a collective response to changes of curvature with a persistent sign over large distances. It is triggered by a drop in membrane tension and actin depolymerization, which is perceived by cells as a hypertonic shock. Osmotic swelling restores tension while actin reorganizes, probably to comply with curvature. Thus, epithelia are unique materials that transiently and actively swell while adapting to large curvature induction.

Pressure and curvature control of the cell cycle in epithelia growing under spherical confinement.

Morphogenesis requires spatiotemporal regulation of proliferation, both by biochemical and mechanical cues. In epithelia, this regulation is called contact inhibition of proliferation, but disentangling biochemical from mechanical cues remains challenging. Here, we show that epithelia growing under confinement accumulate pressure that inhibits proliferation above a threshold value. During growth, epithelia spontaneously buckle, and cell proliferation is transiently reactivated within the fold. Reactivation of proliferation within folds correlated with the local reactivation of the mechano-sensing YAP/TAZ pathway. At late time points, when the pressure is highest, ß-catenin activity increases. The threshold pressure increases when ß-catenin is overactivated and decreases when ß-catenin is inhibited. Altogether, our results suggest that different mechanical cues resulting from pressure inhibition of proliferation are at play through different mechano-sensing pathways: the ß-catenin pathway sustains cell division under high pressure, and the YAP pathway senses local curvature.

The emergence of spontaneous coordinated epithelial rotation on cylindrical curved surfaces.

Three-dimensional collective epithelial rotation around a given axis represents a coordinated cellular movement driving tissue morphogenesis and transformation. Questions regarding these behaviors and their relationship with substrate curvatures are intimately linked to spontaneous active matter processes and to vital morphogenetic and embryonic processes. Here, using interdisciplinary approaches, we study the dynamics of epithelial layers lining different cylindrical surfaces. We observe large-scale, persistent, and circumferential rotation in both concavely and convexly curved cylindrical tissues. While epithelia of inverse curvature show an orthogonal switch in actomyosin network orientation and opposite apicobasal polarities, their rotational movements emerge and vary similarly within a common curvature window. We further reveal that this persisting rotation requires stable cell-cell adhesion and Rac-1-dependent cell polarity. Using an active polar gel model, we unveil the different relationships of collective cell polarity and actin alignment with curvatures, which lead to coordinated rotational behavior despite the inverted curvature and cytoskeleton order.

Integer topological defects of cell monolayers: Mechanics and flows.

Monolayers of anisotropic cells exhibit long-ranged orientational order and topological defects. During the development of organisms, orientational order often influences morphogenetic events. However, the linkage between the mechanics of cell monolayers and topological defects remains largely unexplored. This holds specifically at the timescales relevant for tissue morphogenesis. Here, we build on the physics of liquid crystals to determine material parameters of cell monolayers. In particular, we use a hydrodynamical description of an active polar fluid to study the steady-state mechanical patterns at integer topological defects. Our description includes three distinct sources of activity: traction forces accounting for cell-substrate interactions as well as anisotropic and isotropic active nematic stresses accounting for cell-cell interactions. We apply our approach to C2C12 cell monolayers in small circular confinements, which form isolated aster or spiral topological defects. By analyzing the velocity and orientational order fields in spirals as well as the forces and cell number density fields in asters, we determine mechanical parameters of C2C12 cell monolayers. Our work shows how topological defects can be used to fully characterize the mechanical properties of biological active matter.

Unraveling the hidden complexity of quasideterministic ratchets: Random walks, graphs, and circle maps.

Brownian ratchets are shown to feature a nontrivial vanishing-noise limit where the dynamics is reduced to a stochastic alternation between two deterministic circle maps (quasideterministic ratchets). Motivated by cooperative dynamics of molecular motors, here we solve exactly the problem of two interacting quasideterministic ratchets. We show that the dynamics can be described as a random walk on a graph that is specific to each set of parameters. We compute point by point the exact velocity-force V(f) function as a summation over all paths in the specific graph for each f, revealing a complex structure that features self-similarity and nontrivial continuity properties. From a general perspective, we unveil that the alternation of two simple piecewise linear circle maps unfolds a very rich variety of dynamical complexity, in particular the phenomenon of piecewise chaos, where chaos emerges from the combination of nonchaotic maps. We show convergence of the finite-noise case to our exact solution.

Buckling of an Epithelium Growing under Spherical Confinement.

Many organs are formed through folding of an epithelium. This change in shape is usually attributed to tissue heterogeneities, for example, local apical contraction. In contrast, compressive stresses have been proposed to fold a homogeneous epithelium by buckling. While buckling is an appealing mechanism, demonstrating that it underlies folding requires measurement of the stress field and the material properties of the tissue, which are currently inaccessible in vivo. Here, we show that monolayers of identical cells proliferating on the inner surface of elastic spherical shells can spontaneously fold. By measuring the elastic deformation of the shell, we infer the forces acting within the monolayer and its elastic modulus. Using analytical and numerical theories linking forces to shape, we find that buckling quantitatively accounts for the shape changes of our monolayers. Our study shows that forces arising from epithelial growth in three-dimensional confinement are sufficient to drive folding by buckling.

Active wetting of epithelial tissues.

Development, regeneration and cancer involve drastic transitions in tissue morphology. In analogy with the behavior of inert fluids, some of these transitions have been interpreted as wetting transitions. The validity and scope of this analogy are unclear, however, because the active cellular forces that drive tissue wetting have been neither measured nor theoretically accounted for. Here we show that the transition between two-dimensional epithelial monolayers and three-dimensional spheroidal aggregates can be understood as an active wetting transition whose physics differs fundamentally from that of passive wetting phenomena. By combining an active polar fluid model with measurements of physical forces as a function of tissue size, contractility, cell-cell and cell-substrate adhesion, and substrate stiffness, we show that the wetting transition results from the competition between traction forces and contractile intercellular stresses. This competition defines a new intrinsic lengthscale that gives rise to a critical size for the wetting transition in tissues, a striking feature that has no counterpart in classical wetting. Finally, we show that active shape fluctuations are dynamically amplified during tissue dewetting. Overall, we conclude that tissue spreading constitutes a prominent example of active wetting - a novel physical scenario that may explain morphological transitions during tissue morphogenesis and tumor progression.

Macropinocytosis Overcomes Directional Bias in Dendritic Cells Due to Hydraulic Resistance and Facilitates Space Exploration.

The migration of immune cells can be guided by physical cues imposed by the environment, such as geometry, rigidity, or hydraulic resistance (HR). Neutrophils preferentially follow paths of least HR in vitro, a phenomenon known as barotaxis. The mechanisms and physiological relevance of barotaxis remain unclear. We show that barotaxis results from the amplification of a small force imbalance by the actomyosin cytoskeleton, resulting in biased directional choices. In immature dendritic cells (DCs), actomyosin is recruited to the cell front to build macropinosomes. These cells are therefore insensitive to HR, as macropinocytosis allows fluid transport across these cells. This may enhance their space exploration capacity in vivo. Conversely, mature DCs down-regulate macropinocytosis and are thus barotactic. Modeling suggests that HR may help guide these cells to lymph nodes where they initiate immune responses. Hence, DCs can either overcome or capitalize on the physical obstacles they encounter, helping their immune-surveillance function.

Cooperativity of self-organized Brownian motors pulling on soft cargoes.

We study the cooperative dynamics of Brownian motors moving along a one-dimensional track when an external load is applied to the leading motor, mimicking molecular motors pulling on membrane-bound cargoes in intracellular traffic. Due to the asymmetric loading, self-organized motor clusters form spontaneously. We model the motors with a two-state noise-driven ratchet formulation and study analytically and numerically the collective velocity-force and efficiency-force curves resulting from mutual interactions, mostly hard-core repulsion and weak (nonbinding) attraction. We analyze different parameter regimes including the limits of weak noise, mean-field behavior, rigid coupling, and large numbers of motors, for the different interactions. We present a general framework to classify and quantify cooperativity. We show that asymmetric loading leads generically to enhanced cooperativity beyond the simple superposition of the effects of individual motors. For weakly attracting interactions, the cooperativity is mostly enhanced, including highly coordinated motion of motors and complex nonmonotonic velocity-force curves, leading to self-regulated clusters. The dynamical scenario is enriched by resonances associated to commensurability of different length scales. Large clusters exhibit synchronized dynamics and bidirectional motion. Biological implications are discussed.