Mechanical instabilities and dynamics of living matter. From single-cell motility to collective cell migration

[cat] Aquesta tesis s'emmarca dins del camp de la biofísica, en particular en l'estudi des de un punt de vista físic de processos biològics a l’escala cel·lular i multicel·lular que involucren fenòmens col·lectius d'auto-organització. Per tant, hem estudiat tres problemes qualitativament diferents: la locomoció sostinguda en fragments cel·lulars, l'expansió lliure d'una mono-capa de cèl·lules epitelials i l'evolució dinàmica de la forma de l'ala de la mosca Drosophila melanogaster. En el primer cas, mostrem com un fragment cel·lular es capaç de desplaçar-se de forma sostinguda, solament amb les forces de polimerització a la membrana cel·lular, si inicialment s'indueixi un trencament espontani de la simetria rotacional. Entre d’altres resultats, derivem una expressió exacte i fem palés que la velocitat de migració s'origina a través d'un mecanisme no-adiabatic. En el segon cas, estudiem la migració col·lectiva en un teixit cohesiu de cèl·lules epitelials que s'expandeix sobre d'un substrat elàstic. Per ajudar a entendre les propietats físiques i biofísiques d’aquest tipus de teixits, comparem directament observables físics amb els predits segons la nostre descripció continua del medi. D’aquesta forma, podem derivar l'evolució temporal de la força de tracció activa per cèl·lula, la correlació nemàtica del medi i la seva viscositat efectiva. Per altra banda, generalitzem el model anterior, incorporant nous efectes com: els esforços contràctils generats per l'activitat en la xarxa d'actomyosina. Hem observat que els materials actius permeten sostenir ones elàstiques, fins i tot si les propietats reològiques passives del medi són de tipus viscos. En el tercer cas, estudiem i classifiquem l'evolució temporal de les morfologies d'un teixit totalment polaritzat, que està sotmès a un creixement anisòtrop però espaialment homogeni. Estenem estudis teòrics previs, incorporant els efectes generats per la interacció entre els esforços actius produïts per la divisió cel·lular i tres tipus de forces passives: de tipus viscos, fricció amb el medi extern i capil·laritat. Demostrem que en general l' excentricitat d'un teixit allongat evoluciona de forma no-monòtona amb el temps, amb un màxim a temps finit, del qual hem derivat les seves lleis d'escala amb les paràmetres físics del model.[eng] The thesis belongs to the field of biophysicis, in particular we evaluate from a physicial perspective biological processes that occur at the celular and multicelular scales involving collective phenomena of self-organization. Our modelling approach is based on the formalism of the active gels theory. Similarly as living systems, an ideal active gel is intrinsically out of equilibrium, due to its capacity to consume chemical energy. Within a certain range of validity the cells, the cytoskeleton, the tissues or even schools of fishes are expected to satisfy the same material properties as an active gel. This approach, coarse grain the systems by assuming that the large-scale and long-time limits are well described by a limited number of continuum fields, like the density of cells or the velocity of actin monomers. We apply this formalism to three main topics: self-locomotion of lamellar fragments, free-expansion of an epithelial monolayers, and the morphodynamics of the wing disk of the Drosophila melanogaster. In the first topic, we show that actin lamellar fragments driven solely by polymerisation forces at the bounding membrane are generically motile when the circular symmetry is spontaneously broken, with no need of molecular motors or global polarisation. We base our study on a nonlinear analysis of a recently introduced minimal model for an actin lamellar fragment. We prove the nonlinear instability of the center of mass and find an exact and simple relation between shape and center-of-mass velocity. A complex subcritical bifurcation scenario into traveling solutions is unfolded, where finite velocities appear through a nonadiabatic mechanism. In the second topic, we study the collective cell migration occurring in expanding cohesive epithelial cell sheets. This process involves the coordination of single cell traction forces, which are mechanically transmitted to adjacent neighbours via cell-cell junctions. The maps of reactive intracellular forces display a complex and heterogeneous spatio-temporal distribution, and are directly compared with the analytical stress and velocity profiles, so that we are able to track the temporal variations of the active celular traction force, the nematic correlation length and the effective viscosity at ultra-slow time scales. Furthermore, we generalise the previous biophysical model by incorporating a more realistic description of the material properties of an active gel. In particular, we include active stresses originated in part from the interaction between myosin motors and the intertwined actin meshwork within epithelial cells. We unveil a transition into an oscillatory periodic pattern. Interestingly, the complex material properties of an active gel allows to sustain elastic waves, even if the passive rheology is viscous-like. We classify in a phase-diagram the nonlinear assymptotic steady profiles, showing a rich variety of phenomenology. In the third topic, we study and classify the time-dependent morphologies of polarised tissues subjected to anisotropic but spatially homogeneous growth. Extending previous studies, we model the tissue as a fluid, and discuss the interplay of the active stresses generated by the anisotropic cell division and three types of passive mechanical forces: viscous stresses, friction with the environment and tension at the tissue boundary. The morphology dynamics is formulated as a free-boundary problem, and conformal mapping techniques are used to solve the evolution numerically. We elucidate how the different passive forces compete with the active stresses to shape the tissue in different temporal regimes and derive the corresponding scaling laws. We show that in general the aspect ratio of elongated tissues is non-monotonic in time, eventually recovering isotropic shapes in the presence of friction forces, which are asymptotically dominant

Spontaneous motility of actin lamellar fragments

We show that actin lamellar fragments driven solely by polymerization forces at the bounding membrane are generically motile when the circular symmetry is spontaneously broken, with no need of molecular motors or global polarization. We base our study on a nonlinear analysis of a recently introduced minimal model [Callan-Jones et al Phys. Rev. Lett. 100, 258106 (2008)]. We prove the nonlinear instability of the center of mass and find an exact and simple relation between shape and center-of-mass velocity. A complex subcritical bifurcation scenario into traveling solutions is unfolded, where finite velocities appear through a nonadiabatic mechanism. Examples of traveling solutions and their stability are studied numericall

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.Comment: 5 pages, 4 figure

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 time scales 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.Comment: 41 pages, 11 figure

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

Density-polarity coupling in confined active polar films: asters, spirals, and biphasic orientational phases

Topological defects in active polar fluids can organise spontaneous flows and influence macroscopic density patterns. Both of them play, for example, 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 discs, we study the coupling between density and polar order for a compressible active polar fluid in 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 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

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 2D epithelial monolayers and 3D 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

Spontaneous migration of cellular aggregates from giant keratocytes to running spheroids

Despite extensive knowledge on the mechanisms that drive singlecell 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 narrowrange 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 collectivemigration by quantifying the flows and forces that drive them, andwe unveil the fundamental physical principles that govern these behaviors, which underscore the biological predisposition of living material to migrate, independent of length scale

Epithelial cells adapt to curvature induction via transient active osmotic swelling

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