Ricard Alert
The Physics of Living Matter
PUBLICATIONS
Nonlinear spontaneous flow instability in active nematics
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Ido Lavi, Ricard Alert, Jean-François Joanny, and Jaume Casademunt
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arXiv:2403.16841 (2024)
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Active nematics exhibit spontaneous flows through a well-known linear instability of the uniformly-aligned quiescent state. Here we show that even a linearly stable uniform state can experience a nonlinear instability, resulting in a discontinuous transition to spontaneous flows. In this case, quiescent and flowing states may coexist. Through a weakly nonlinear analysis and a numerical study, we trace the bifurcation diagram of striped patterns and show that the underlying pitchfork bifurcation switches from supercritical (continuous) to subcritical (discontinuous) by varying the flow-alignment parameter. We predict that the discontinuous spontaneous flow transition occurs for a wide range of parameters, including systems of contractile flow-aligning rods. Our predictions are relevant to active nematic turbulence and can potentially be tested in experiments on either cell layers or active cytoskeletal suspensions.
Flocking by turning away
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Suchismita Das, Matteo Ciarchi, Ziqi Zhou, Jing Yan, Jie Zhang, and Ricard Alert
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arXiv:2401.17153 (2024)
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Flocking, as paradigmatically exemplified by birds, is the coherent collective motion of active agents. As originally conceived, flocking emerges through alignment interactions between the agents. Here, we report that flocking can also emerge through interactions that turn agents away from each other. Combining simulations, kinetic theory, and experiments, we demonstrate this mechanism of flocking in self-propelled Janus colloids with stronger repulsion on the front than on the rear. The polar state is stable because particles achieve a compromise between turning away from left and right neighbors. Unlike for alignment interactions, the emergence of polar order from turn-away interactions requires particle repulsion. At high concentration, repulsion produces flocking Wigner crystals. Whereas repulsion often leads to motility-induced phase separation of active particles, here it combines with turn-away torques to produce flocking. Therefore, our findings bridge the classes of aligning and non-aligning active matter. Our results could help to reconcile the observations that cells can flock despite turning away from each other via contact inhibition of locomotion. Overall, our work shows that flocking is a very robust phenomenon that arises even when the orientational interactions would seem to prevent it.
Optogenetic generation of leader cells reveals a force-velocity relation for collective cell migration
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Leone Rossetti, Steffen Grosser, Juan Francisco Abenza, Léo Valon, Pere Roca-Cusachs, Ricard Alert, and Xavier Trepat
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bioRxiv:2024.01.23.576733 (2024)
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The front of migratory cellular clusters during development, wound healing and cancer invasion is typically populated with highly protrusive cells that are called leader cells. Leader cells are thought to physically pull and direct their cohort of followers, but how leaders and followers are mechanically organized to migrate collectively remains controversial. One possibility is that the autonomous local action of a leader cell is sufficient to drive migration of the group. Yet another possibility is that a global mechanical organization is required for the group to move cohesively. Here we show that the effectiveness of leader-follower organization is proportional to the asymmetry of traction and tension within the cellular cluster. By combining hydrogel micropatterning and optogenetic activation of Rac1, we locally generate highly protrusive leaders at the edge of minimal cell groups. We find that the induced leader can robustly drag one follower but is generally unable to direct larger groups. By measuring traction forces and tension propagation in groups of increasing size, we establish a quantitative relationship between group velocity and the asymmetry of the traction and tension profiles. We propose a model of the motile cluster as an active polar fluid that explains this force-velocity relationship in terms of asymmetries in the distribution of active tractions. Our results challenge the notion of autonomous leader cells by showing that collective cell migration requires a global mechanical organization within the cluster.
Local polar order controls mechanical stress and triggers layer formation in developing Myxococcus xanthus colonies
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Endao Han, Chenyi Fei, Ricard Alert, Katherine Copenhagen, Matthias D. Koch, Ned S. Wingreen, and Joshua W. Shaevitz
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arXiv:2308.00368 (2023)
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Colonies of the social bacterium Myxococcus xanthus go through a morphological transition from a thin colony of cells to three-dimensional droplet-like fruiting bodies as a strategy to survive starvation. The biological pathways that control the decision to form a fruiting body have been studied extensively. However, the mechanical events that trigger the creation of multiple cell layers and give rise to droplet formation remain poorly understood. By measuring cell orientation, velocity, polarity, and force with cell-scale resolution, we reveal a stochastic local polar order in addition to the more obvious nematic order. Average cell velocity and active force at topological defects agree with predictions from active nematic theory, but their fluctuations are anomalously large due to polar active forces generated by the self-propelled rod-shaped cells. We find that M. xanthus cells adjust their reversal frequency to tune the magnitude of this local polar order, which in turn controls the mechanical stresses and triggers layer formation in the colonies.
Frictiotaxis underlies adhesion-independent durotaxis
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Adam Shellard, Peter A.E. Hampshire, Namid R. Stillman, Christina Dix, Richard Thorogate, Albane Imbert, Guillaume Charras, Ricard Alert, and Roberto Mayor
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bioRxiv:2023.06.01.543217 (2023)
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Cells move directionally along gradients of substrate stiffness, a process called durotaxis. The current consensus is that durotaxis relies on cell-substrate focal adhesions to transmit forces that drive directed motion. Such a mechanism implies that focal adhesion-independent durotaxis is impossible, although this assumption has never been tested. Here, we show that confined cells can perform durotaxis despite lacking strong or specific adhesions. We show that the mechanism of this adhesion-independent durotaxis is that stiffer substrates offer higher friction. We develop a physical model that predicts that non-adherent cells polarize and migrate towards regions of higher friction, a process that we call frictiotaxis. We demonstrate frictiotaxis in experiments by showing that cells migrate up a friction gradient even when stiffness is uniform. Our results broaden the potential of durotaxis to guide any cell that contacts a substrate and reveal a new mode of directed migration based on friction, with implications for immune and cancer cells, which commonly move with non-specific interactions.
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PRESS COVERAGE
World View: How to bridge the gap between theory and experiments in biological physics
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Xavier Trepat and Ricard Alert
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Nat. Phys. 19, 1738 (2023)
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Creating a common culture and language for successful collaboration across disciplines benefits both researchers and scientific discovery.
Curvature induces active velocity waves in rotating spherical tissues
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Tom Brandstätter*, David B. Brückner*, Yu Long Han, Ricard Alert, Ming Guo, and Chase P. Broedersz
Nat. Commun. 14, 1643 (2023) *Equal contributions
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The multicellular organization of diverse systems, including embryos, intestines, and tumors relies on coordinated cell migration in curved environments. In these settings, cells establish supracellular patterns of motion, including collective rotation and invasion. While such collective modes have been studied extensively in flat systems, the consequences of geometrical and topological constraints on collective migration in curved systems are largely unknown. Here, we discover a collective mode of cell migration in rotating spherical tissues manifesting as a propagating single-wavelength velocity wave. This wave is accompanied by an apparently incompressible supracellular flow pattern featuring topological defects as dictated by the spherical topology. Using a minimal active particle model, we reveal that this collective mode arises from the effect of curvature on the active flocking behavior of a cell layer confined to a spherical surface. Our results thus identify curvature-induced velocity waves as a mode of collective cell migration, impacting the dynamical organization of 3D curved tissues.
Stiffness-dependent active wetting enables optimal collective cell durotaxis
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Macià-Esteve Pallarès*, Irina Pi-Jaumà*, Isabela Corina Fortunato, Valeria Grazu, Manuel Gómez-González, Pere Roca-Cusachs, Jesus M. de la Fuente, Ricard Alert, Raimon Sunyer, Jaume Casademunt, and Xavier Trepat
Nat. Phys. 19, 279 (2023) *Equal contributions
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The directed migration of cellular clusters enables morphogenesis, wound healing, and collective cancer invasion. Gradients of substrate stiffness are known to direct the migration of cellular clusters in a process called collective durotaxis, but underlying mechanisms remain unclear. Here, we unveil a connection between collective durotaxis and the wetting properties of cellular clusters. We show that clusters of cancer cells dewet soft substrates and wet stiff ones. At intermediate stiffness, at the crossover from low to high wettability, clusters on uniform-stiffness substrates become maximally motile, and clusters on stiffness gradients exhibit optimal durotaxis. Durotactic velocity increases with cluster size, stiffness gradient, and actomyosin activity. We demonstrate this behavior on substrates coated with the cell-cell adhesion protein E-cadherin and then establish its generality on substrates coated with extracellular matrix. We develop a physical model of three-dimensional active wetting that explains this mode of collective durotaxis in terms of a balance between in-plane active traction and tissue contractility, and out-of-plane surface tension. Finally, we show that the distribution of cluster displacements has a heavy tail, with infrequent but large cellular hops that contribute to durotactic migration. Our study demonstrates a physical mechanism of collective durotaxis, through both cell-cell and cell-substrate adhesion ligands, based on the wetting properties of active droplets.
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PRESS COVERAGE
Self-assembly of tessellated tissue sheets by expansion and collision
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Matthew A. Heinrich*, Ricard Alert*, Abraham E. Wolf*, Andrej Košmrlj, and Daniel J. Cohen
Nat. Commun. 13, 4026 (2022)
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Tissues do not exist in isolation—they interact with other tissues within and across organs. While cell-cell interactions have been intensely investigated, less is known about tissue-tissue interactions. Here, we studied collisions between monolayer tissues with different geometries, cell densities, and cell types. First, we determine rules for tissue shape changes during binary collisions and describe complex cell migration at tri-tissue boundaries. Next, we propose that genetically identical tissues displace each other based on pressure gradients, which are directly linked to gradients in cell density. We present a physical model of tissue interactions that allows us to estimate the bulk modulus of the tissues from collision dynamics. Finally, we introduce TissEllate, a design tool for self-assembling complex tessellations from arrays of many tissues, and we use cell sheet engineering techniques to transfer these composite tissues like cellular films. Overall, our work provides insight into the mechanics of tissue collisions, harnessing them to engineer tissue composites as designable living materials.
Fingering instability in active nematic droplets
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Ricard Alert
J. Phys. A: Math. Theor. 55, 234009 (2022) Special issue "Emerging Talents 2021"
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From the mitotic spindle up to tissues and biofilms, many biological systems behave as active droplets, which often break symmetry and change shape spontaneously. Here, I show that active nematic droplets can experience a fingering instability. I consider an active fluid that acquires nematic order through anchoring at the droplet interface, and I predict its morphological stability in terms of three dimensionless parameters: the anchoring angle, the penetration length of nematic order compared to droplet size, and an active capillary number. Droplets with extensile (contractile) stresses and planar (homeotropic) anchoring are unstable above a critical activity or droplet size. This instability is interfacial in nature: It arises through the coupling of active flows with interface motion, even when the bulk instability of active nematics cannot take place. In contrast to the dynamic states characteristic of active matter, the instability could produce static fingering patterns. The number of fingers increases with activity but varies non-monotonically with the nematic penetration length. Overall, these results pave the way towards understanding the self-organized shapes of biological systems, and towards designing patterns in active materials.
Cellular Sensing Governs the Stability of Chemotactic Fronts
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Ricard Alert, Alejandro Martínez-Calvo, and Sujit S. Datta
Phys. Rev. Lett. 128, 148101 (2022)
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In contexts ranging from embryonic development to bacterial ecology, cell populations migrate chemotactically along self-generated chemical gradients, often forming a propagating front. Here, we theoretically show that the stability of such chemotactic fronts to morphological perturbations is determined by limitations in the ability of individual cells to sense and thereby respond to the chemical gradient. Specifically, cells at bulging parts of a front are exposed to a smaller gradient, which slows them down and promotes stability, but they also respond more strongly to the gradient, which speeds them up and promotes instability. We predict that this competition leads to chemotactic fingering when sensing is limited at too low chemical concentrations. Guided by this finding and by experimental data on E. coli chemotaxis, we suggest that the cells' sensory machinery might have evolved to avoid these limitations and ensure stable front propagation. Finally, as sensing of any stimuli is necessarily limited in living and active matter in general, the principle of sensing-induced stability may operate in other types of directed migration such as durotaxis, electrotaxis, and phototaxis.
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PRESS COVERAGE
Active Turbulence
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Ricard Alert, Jaume Casademunt, and Jean-François Joanny
Annu. Rev. Condens. Matter Phys. 13, 143 (2022)
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Active fluids exhibit spontaneous flows with complex spatiotemporal structure, which have been observed in bacterial suspensions, sperm cells, cytoskeletal suspensions, self-propelled colloids, and cell tissues. Despite occurring in the absence of inertia, chaotic active flows are reminiscent of inertial turbulence, and hence they are known as active turbulence. Here, we survey the field, providing a unified perspective over different classes of active turbulence. To this end, we divide our review in sections for systems with either polar or nematic order, and with or without momentum conservation (wet/dry). Comparing to inertial turbulence, we highlight the emergence of power-law scaling with either universal or non-universal exponents. We also contrast scenarios for the transition from steady to chaotic flows, and we discuss the absence of energy cascades. We link this feature to both the existence of intrinsic length scales and the self-organized nature of energy injection in active turbulence, which are fundamental differences with inertial turbulence. We close by outlining the emerging picture, remaining challenges, and future directions.
Chemotactic smoothing of collective migration
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Tapomoy Bhattacharjee*, Daniel B. Amchin*, Ricard Alert*, Jenna A. Ott, and Sujit S. Datta
eLife 11, e71226 (2022) *Equal contributions
Collective migration—the directed, coordinated motion of many self-propelled agents—is a fascinating emergent behavior exhibited by active matter with functional implications for biological systems. However, how migration can persist when a population is confronted with perturbations is poorly understood. Here, we address this gap in knowledge through studies of bacteria that migrate via directed motion, or chemotaxis, in response to a self-generated nutrient gradient. We find that bacterial populations autonomously smooth out large-scale perturbations in their overall morphology, enabling the cells to continue to migrate together. This smoothing process arises from spatial variations in the ability of cells to sense and respond to the local nutrient gradient—revealing a population-scale consequence of the manner in which individual cells trans- duce external signals. Altogether, our work provides insights to predict, and potentially control, the collective migration and morphology of cellular populations and diverse other forms of active matter.
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PRESS COVERAGE
Collective durotaxis of cohesive cell clusters on a stiffness gradient
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Irina Pi-Jaumà, Ricard Alert, and Jaume Casademunt
Eur. Phys. J. E 45, 7 (2022) Special issue "Tissue Mechanics"
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Many types of motile cells perform durotaxis, namely, directed migration following gradients of substrate
stiffness. Recent experiments have revealed that cell monolayers can migrate toward stiffer regions even when individual cells do not — a phenomenon known as collective durotaxis. Here we address the spontaneous motion of finite cohesive cell monolayers on a stiffness gradient. We theoretically analyze a continuum active polar fluid model that has been tested in recent wetting assays of epithelial tissues, and includes two types of active forces (cell-substrate traction and cell-cell contractility). The competition between the two active forces determines whether a cell monolayer spreads or contracts. Here, we show that this model generically predicts collective durotaxis, and that it features a variety of dynamical regimes as a result of the interplay between the spreading state and the global propagation, including sequential contraction and spreading of the monolayer as it moves toward higher stiffness. We solve the model exactly in some relevant cases, which provides both physical insights into the mechanisms of tissue durotaxis and spreading as well as a variety of predictions that could guide the design of future experiments.
Scaling Regimes of Active Turbulence with External Dissipation
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Berta Martínez-Prat*, Ricard Alert*, Fanlong Meng, Jordi Ignés-Mullol, Jean-François Joanny, Jaume Casademunt, Ramin Golestanian, and Francesc Sagués
Phys. Rev. X 11, 031065 (2021) *Equal contributions
Active fluids exhibit complex turbulent-like flows at low Reynolds number. Recent work predicted that 2d active nematic turbulence follows universal scaling laws. However, experimentally testing these predictions is conditioned by the coupling to the 3d environment. Here, we measure the spectrum of the kinetic energy, E(q), in an active nematic film in contact with a passive oil layer. At small and intermediate scales, we find the scaling regimes E(q) ~ q^(-4) and E(q) ~ q^(-1), respectively, in agreement with the theoretical prediction for 2d active nematics. At large scales, however, we find a new scaling E(q) ~ q, which emerges when the dissipation is dominated by the 3d oil layer. In addition, we derive an explicit expression for the spectrum that spans all length scales, thus explaining and connecting the different scaling regimes. This allows us to fit the data and extract the length scale that controls the crossover to the new large-scale regime, which we tune by varying the oil viscosity. Overall, our work experimentally demonstrates the emergence of scaling laws with universal exponents in active turbulence, and it establishes how the spectrum is affected by external dissipation.
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PRESS COVERAGE
Morphogenesis and cell ordering in confined bacterial biofilms
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Qiuting Zhang, Jian Li, Japinder Nijjer, Haoran Lu, Mrityunjay Kothari, Ricard Alert, Tal Cohen, and Jing Yan
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Proc. Natl. Acad. Sci. USA 118, e2107107118 (2021)
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Biofilms are aggregates of bacterial cells surrounded by an extracellular matrix. Much progress has been made in studying biofilm growth on solid substrates; however, little is known about the biophysical mechanisms underlying biofilm development in three-dimensional confined environments in which the biofilm-dwelling cells must push against and even damage the surrounding environment to proliferate. Here, combining single-cell imaging, mutagenesis, and rheological measurement, we reveal the key morphogenesis steps of Vibrio cholerae biofilms embedded in hydrogels as they grow by four orders of magnitude from their initial size. We show that the morphodynamics and cell ordering in embedded biofilms are fundamentally different from those of biofilms on flat surfaces. Treating embedded biofilms as inclusions growing in an elastic medium, we quantitatively show that the stiffness contrast between the biofilm and its environment determines biofilm morphology and internal architecture, selecting between spherical biofilms with no cell ordering and oblate ellipsoidal biofilms with high cell ordering. When embedded in stiff gels, cells self-organize into a bipolar structure that resembles the molecular ordering in nematic liquid crystal droplets. In vitro biomechanical analysis shows that cell ordering arises from stress transmission across the biofilm–environment interface, mediated by specific matrix components. Our imaging technique and theoretical approach are generalizable to other biofilm-forming species and potentially to biofilms embedded in mucus or host tissues as during infection. Our results open an avenue to understand how confined cell communities grow by means of a compromise between their inherent developmental program and the mechanical constraints imposed by the environment.
Living cells on the move
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Ricard Alert and Xavier Trepat
Phys. Today 74(6), 30 (2021)
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Spectacular collective phenomena, such as jamming, turbulence, wetting, and waves, emerge when living cells migrate in groups.
Active phase separation by turning towards regions of higher density
Jie Zhang*, Ricard Alert*, Jing Yan, Ned S. Wingreen, and Steve Granick
Nat. Phys. 17, 961 (2021) *Equal contributions
Studies of active matter, from molecular assemblies to animal groups, have revealed two broad classes of behaviour: a tendency to align yields orientational order and collective motion, whereas particle repulsion leads to self-trapping and motility-induced phase separation. Here we report a third class of behaviour: orientational interactions that produce active phase separation. Combining theory and experiments on self-propelled Janus colloids, we show that stronger repulsion on the rear than on the front of these particles produces non-reciprocal torques that reorient particle motion towards high-density regions. Particles thus self-propel towards crowded areas, which leads to phase separation. Clusters remain fluid and exhibit fast particle turnover, in contrast to the jammed clusters that typically arise from self-trapping, and interfaces are sufficiently wide that they span entire clusters. Overall, our work identifies a torque-based mechanism for phase separation in active fluids, and our theory predicts that these orientational interactions yield coexisting phases that lack internal orientational order.
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PRESS COVERAGE
Topological defects promote layer formation in Myxococcus xanthus colonies
Katherine Copenhagen*, Ricard Alert*, Ned S. Wingreen, and Joshua W. Shaevitz
Nat. Phys. 17, 211 (2021) *Equal contributions
The soil bacterium Myxococcus xanthus lives in densely packed groups that form dynamic three-dimensional patterns in response to environmental changes, such as droplet-like fruiting bodies during starvation. The development of these multicellular structures begins with the sequential formation of cell layers in a process that is poorly understood. Here, using confocal three-dimensional imaging, we find that motile rod-shaped M. xanthus cells are densely packed and aligned in each layer, forming an active nematic liquid crystal. Cell alignment is nearly perfect throughout the population except at point defects that carry half-integer topological charge. We observe that new cell layers preferentially form at the position of +1/2 defects, whereas holes open at −1/2 defects. To explain these findings, we model the bacterial colony as an extensile active nematic fluid with anisotropic friction. In agreement with our experimental measurements, this model predicts an influx of cells toward +1/2 defects, and an outflux of cells from −1/2 defects. Our results suggest that cell motility and mechanical cell-cell interactions are sufficient to induce the formation of cell layers at topological defects, thereby seeding fruiting bodies in colonies of M. xanthus.
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PRESS COVERAGE
Size-dependent patterns of cell proliferation and migration in freely-expanding epithelia
Matthew A. Heinrich, Ricard Alert, Julienne M. LaChance, Tom J. Zajdel, Andrej Košmrlj, and Daniel J. Cohen
eLife 9, e58945 (2020)
The coordination of cell proliferation and migration in growing tissues is crucial in development and regeneration but remains poorly understood. Here, we find that, while expanding with an edge speed independent of initial conditions, millimeter-scale epithelial monolayers exhibit internal patterns of proliferation and migration that depend not on the current but on the initial tissue size, indicating memory effects. Specifically, the core of large tissues becomes very dense, almost quiescent, and ceases cell-cycle progression. In contrast, initially-smaller tissues develop a local minimum of cell density and a tissue-spanning vortex. To explain vortex formation, we propose an active polar fluid model with a feedback between cell polarization and tissue flow. Taken together, our findings suggest that expanding epithelia decouple their internal and edge regions, which enables robust expansion dynamics despite the presence of size- and history-dependent patterns in the tissue interior.
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PRESS COVERAGE
Nonuniform growth and surface friction determine bacterial biofilm morphology on soft substrates
Chenyi Fei, Sheng Mao, Jing Yan, Ricard Alert, Howard A. Stone, Bonnie L. Bassler, Ned S. Wingreen, and Andrej Košmrlj
Proc. Natl Acad. Sci. USA 117, 7622 (2020)
During development, organisms acquire three-dimensional shapes with important physiological consequences. While basic mechanisms underlying morphogenesis are known in eukaryotes, it is often difficult to manipulate them in vivo. To circumvent this issue, here we present a study of developing Vibrio cholerae biofilms grown on agar substrates in which the spatiotemporal morphological patterns were altered by varying the agar concentration. Expanding biofilms are initially flat but later undergo a mechanical instability and become wrinkled. To gain mechanistic insights into this dynamic pattern-formation process, we developed a model that considers diffusion of nutrients and their uptake by bacteria, bacterial growth/biofilm matrix production, mechanical deformation of both the biofilm and the substrate, and the friction between them. Our model shows quantitative agreement with experimental measurements of biofilm expansion dynamics, and it accurately predicts two distinct spatiotemporal patterns observed in the experiments—the wrinkles initially appear either in the peripheral region and propagate inward (soft substrate/low friction) or in the central region and propagate outward (stiff substrate/high friction). Our results, which establish that nonuniform growth and friction are fundamental determinants of stress anisotropy and hence biofilm morphology, are broadly applicable to bacterial biofilms with similar morphologies and also provide insight into how other bacterial biofilms form distinct wrinkle patterns. We discuss the implications of forming undulated biofilm morphologies, which may enhance the availability of nutrients and signaling molecules and serve as a "bet hedging" strategy.
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PRESS COVERAGE
Universal scaling of active nematic turbulence
Ricard Alert, Jean-François Joanny, and Jaume Casademunt
Nat. Phys. 16, 682 (2020)
A landmark of turbulence is the emergence of universal scaling laws, such as Kolmogorov's E(q) ~ q^(−5∕3) scaling of the kinetic energy spectrum of inertial turbulence with the wavevector q. In recent years, active fluids have been shown to exhibit turbulent-like flows at low Reynolds number. However, the existence of universal scaling properties in these flows has remained unclear. To address this issue, here we propose a minimal defect-free hydrodynamic theory for two-dimensional active nematic fluids at vanishing Reynolds number. By means of large-scale simulations and analytical arguments, we show that the kinetic energy spectrum exhibits a universal scaling E(q) ~ q^(−1) at long wavelengths. We find that the energy injection due to activity has a peak at a characteristic length scale, which is selected by a nonlinear mechanism. In contrast to inertial turbulence, energy is entirely dissipated at the scale where it is injected, thus precluding energy cascades. Nevertheless, the non-local character of the Stokes flow establishes long-range velocity correlations, which lead to the scaling behaviour. We conclude that active nematic fluids define a distinct universality class of turbulence at low Reynolds number.
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University of Barcelona Research News
SINC Agency (Servicio de Información y Noticias Científicas)
Physical Models of Collective Cell Migration
Ricard Alert and Xavier Trepat
Annu. Rev. Condens. Matter Phys. 11, 77 (2020)
Collective cell migration is a key driver of embryonic development, wound healing, and some types of cancer invasion. Here we provide a physical perspective of the mechanisms underlying collective cell migration. We begin with a catalog of the cell-cell and cell-substrate interactions that govern cell migration, which we classify into positional and orientational interactions. We then review the physical models that have been developed to explain how these interactions give rise to collective cellular movement. These models span the sub-cellular to the supracellular scales, and they include lattice models, phase-field models, active network models, particle models, and continuum models. For each type of model, we discuss its formulation, its limitations, and the main emergent phenomena that it has successfully explained. These phenomena include flocking and fluid-solid transitions, as well as wetting, fingering, and mechanical waves in spreading epithelial monolayers. We close by outlining remaining challenges and future directions in the physics of collective cell migration.
Active Fingering Instability in Tissue Spreading
Ricard Alert, Carles Blanch-Mercader, and Jaume Casademunt
Phys. Rev. Lett. 122, 088104 (2019)
During the spreading of epithelial tissues, the advancing tissue front often develops finger-like 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.
Role of Substrate Stiffness in Tissue Spreading: Wetting Transition and Tissue Durotaxis
Ricard Alert and Jaume Casademunt
Langmuir 35, 7571 (2019) Special issue "Interfaces and Biology"
Living tissues undergo wetting transitions: On a surface, they can either form a droplet-like cell aggregate or spread as a monolayer of migrating cells. Tissue wetting depends not only on the chemical but also on the mechanical properties of the substrate. Here, we study the role of substrate stiffness in tissue spreading, which we describe by means of an active polar fluid model. Taking into account that cells exert larger active traction forces on stiffer substrates, we predict a tissue wetting transition at a critical substrate stiffness that decreases with tissue size. On substrates with a stiffness gradient, we find that the tissue spreads faster on the stiffer side. Furthermore, we show that the tissue can wet the substrate on the stiffer side while dewetting from the softer side. We also show that, by means of viscous forces transmitted across the tissue, the stiffer-side interface can transiently drag the softer-side interface toward increasing stiffness, against its spreading tendency. These two effects result in directed tissue migration up the stiffness gradient. This phenomenon —tissue durotaxis— can thus emerge both from dewetting on the soft side and from hydrodynamic interactions between the tissue interfaces. Overall, our work unveils mechanisms whereby substrate stiffness impacts the collective migration and the active wetting properties of living tissues, which are relevant in development, regeneration, and cancer.
Active wetting of epithelial tissues
Carlos Pérez-González*, Ricard Alert*, Carles Blanch-Mercader, Manuel Gómez-González, Tomasz Kolodziej, Elsa Bazellieres, Jaume Casademunt, and Xavier Trepat
Nat. Phys. 15, 79 (2019) *Equal contributions
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 length scale 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.
PRESS COVERAGE
Mixed-order phase transition in a colloidal crystal
Ricard Alert, Pietro Tierno, and Jaume Casademunt
Proc. Natl Acad. Sci. USA 114, 12906 (2017)
Mixed-order phase transitions display a discontinuity in the order parameter like first-order transitions yet feature critical behavior like second-order transitions. Such transitions have been predicted for a broad range of equilibrium and nonequilibrium systems, but their experimental observation has remained elusive. Here, we analytically predict and experimentally realize a mixed-order equilibrium phase transition. Specifically, a discontinuous solid–solid transition in a 2D crystal of paramagnetic colloidal particles is induced by a magnetic field H. At the transition field Hs, the energy landscape of the system becomes completely flat, which causes diverging fluctuations and correlation length ξ∝|H2−Hs2|−1/2. Mean-field critical exponents are predicted, since the upper critical dimension of the transition is du=2. Our colloidal system provides an experimental test bed to probe the unconventional properties of mixed-order phase transitions.
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PRESS COVERAGE
Fluidization and Active Thinning by Molecular Kinetics in Active Gels
David Oriola*, Ricard Alert*, and Jaume Casademunt *Equal contributions
Phys. Rev. Lett. 118, 088002 (2017)
We derive the constitutive equations of an active polar gel from a model for the dynamics of elastic molecules that link polar elements. Molecular binding kinetics induces the fluidization of the material, giving rise to Maxwell viscoelasticity and, provided that detailed balance is broken, to the generation of active stresses. We give explicit expressions for the transport coefficients of active gels in terms of molecular properties, including nonlinear contributions on the departure from equilibrium. In particular, when activity favors linker unbinding, we predict a decrease of viscosity with activity—active thinning—of kinetic origin, which could explain some experimental results on the cell cortex. By bridging the molecular and hydrodynamic scales, our results could help understand the interplay between molecular perturbations and the mechanics of cells and tissues.
Emergent structures and dynamics of cell colonies by contact inhibition of locomotion
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Bart Smeets, Ricard Alert, Jiri Pešek, Ignacio Pagonabarraga, Herman Ramon, and Romaric Vincent
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Proc. Natl Acad. Sci. USA 113, 14621 (2016)
Cells in tissues can organize into a broad spectrum of structures according to their function. Drastic changes of organization, such as epithelial-mesenchymal transitions or the formation of spheroidal aggregates, are often associated either to tissue morphogenesis or to cancer progression. Here, we study the organization of cell colonies by means of simulations of self-propelled particles with generic cell-like interactions. The interplay between cell softness, cell-cell adhesion, and contact inhibition of locomotion (CIL) yields structures and collective dynamics observed in several existing tissue phenotypes. These include regular distributions of cells, dynamic cell clusters, gel-like networks, collectively migrating monolayers, and 3D aggregates. We give analytical predictions for transitions between noncohesive, cohesive, and 3D cell arrangements. We explicitly show how CIL yields an effective repulsion that promotes cell dispersal, thereby hindering the formation of cohesive tissues. Yet, in continuous monolayers, CIL leads to collective cell motion, ensures tensile intercellular stresses, and opposes cell extrusion. Thus, our work highlights the prominent role of CIL in determining the emergent structures and dynamics of cell colonies.
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University of Barcelona Research News
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Formation of metastable phases by spinodal decomposition
Ricard Alert, Pietro Tierno, and Jaume Casademunt
Nat. Commun. 7, 13067 (2016)
Metastable phases may be spontaneously formed from other metastable phases through nucleation. Here we demonstrate the spontaneous formation of a metastable phase from an unstable equilibrium by spinodal decomposition, which leads to a transient coexistence of stable and metastable phases. This phenomenon is generic within the recently introduced scenario of the landscape-inversion phase transitions, which we experimentally realize as a structural transition in a colloidal crystal. This transition exhibits a rich repertoire of new phase-ordering phenomena, including the coexistence of two equilibrium phases connected by two physically different interfaces. In addition, this scenario enables the control of sizes and lifetimes of metastable domains. Our findings open a new setting that broadens the fundamental understanding of phase-ordering kinetics, and yield new prospects of applications in materials science.
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Bleb Nucleation through Membrane Peeling
Ricard Alert and Jaume Casademunt
Phys. Rev. Lett. 116, 068101 (2016)
We study the nucleation of blebs, i.e., protrusions arising from a local detachment of the membrane from the cortex of a cell. Based on a simple model of elastic linkers with force-dependent kinetics, we show that bleb nucleation is governed by membrane peeling. By this mechanism, the growth or shrinkage of a detached membrane patch is completely determined by the linker kinetics, regardless of the energetic cost of the detachment. We predict the critical nucleation radius for membrane peeling and the corresponding effective energy barrier. These may be typically smaller than those predicted by classical nucleation theory, implying a much faster nucleation. We also perform simulations of a continuum stochastic model of membrane-cortex adhesion to obtain the statistics of bleb nucleation times as a function of the stress on the membrane. The determinant role of membrane peeling changes our understanding of bleb nucleation and opens new directions in the study of blebs.
Model for Probing Membrane-Cortex Adhesion by Micropipette Aspiration and Fluctuation Spectroscopy
Ricard Alert, Jaume Casademunt, Jan Brugués, and Pierre Sens
Biophys. J. 108, 1878 (2015)
We propose a model for membrane-cortex adhesion that couples membrane deformations, hydrodynamics, and kinetics of membrane-cortex ligands. In its simplest form, the model gives explicit predictions for the critical pressure for membrane detachment and for the value of adhesion energy. We show that these quantities exhibit a significant dependence on the active actomyosin stresses. The model provides a simple framework to access quantitative information on cortical activity by means of micropipette experiments. We also extend the model to incorporate fluctuations and show that detailed information on the stability of membrane-cortex coupling can be obtained by a combination of micropipette aspiration and fluctuation spectroscopy measurements.
Landscape-Inversion Phase Transition in Dipolar Colloids:
Tuning the Structure and Dynamics of 2d Crystals
Ricard Alert, Jaume Casademunt, and Pietro Tierno
Phys. Rev. Lett. 113, 198301 (2014) Editors' suggestion
We study the 2D crystalline phases of paramagnetic colloidal particles with dipolar interactions and constrained on a periodic substrate. Combining theory, simulation, and experiments we demonstrate a new scenario of first-order phase transitions that occurs via a complete inversion of the energy landscape, featuring non-conventional properties that allow for: (i) tuning of crystal symmetry; (ii) control of dynamical properties of different crystalline orders via tuning of their relative stability with an external magnetic field; (iii) an equivalent but independent control of the same dynamic properties via temporal modulations of that field; and (iv) non-standard phase-ordering kinetics involving spontaneous formation of transient metastable domains.
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Materials 360 Online by the Materials Research Society
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