Steric interactions and out-of-equilibrium processes control the internal organization of bacteria.

Despite the absence of a membrane-enclosed nucleus, the bacterial DNA is typically condensed into a compact body-the nucleoid. This compaction influences the localization and dynamics of many cellular processes including transcription, translation, and cell division. Here, we develop a model that takes into account steric interactions among the components of the Escherichia coli transcriptional-translational machinery (TTM) and out-of-equilibrium effects of messenger RNA (mRNA) transcription, translation, and degradation, to explain many observed features of the nucleoid. We show that steric effects, due to the different molecular shapes of the TTM components, are sufficient to drive equilibrium phase separation of the DNA, explaining the formation and size of the nucleoid. In addition, we show that the observed positioning of the nucleoid at midcell is due to the out-of-equilibrium process of mRNA synthesis and degradation: mRNAs apply a pressure on both sides of the nucleoid, localizing it to midcell. We demonstrate that, as the cell grows, the production of these mRNAs is responsible for the nucleoid splitting into two lobes and for their well-known positioning to 1/4 and 3/4 positions on the long cell axis. Finally, our model quantitatively accounts for the observed expansion of the nucleoid when the pool of cytoplasmic mRNAs is depleted. Overall, our study suggests that steric interactions and out-of-equilibrium effects of the TTM are key drivers of the internal spatial organization of bacterial cells.

Volume regulation in adhered cells: Roles of surface tension and cell swelling.

The volume of adhered cells has been shown experimentally to decrease during spreading. This effect can be understood from the pump-leak model, which we have extended to include mechano-sensitive ion transporters. We identify a novel effect that has important consequences on cellular volume loss: cells that are swollen due to a modulation of ion transport rates are more susceptible to volume loss in response to a tension increase. This effect explains in a plausible manner the discrepancies between three recent, independent experiments on adhered cells, between which both the magnitude of the volume change and its dynamics varied substantially. We suggest that starved and synchronized cells in two of the experiments were in a swollen state and, consequently, exhibited a large volume loss at steady state. Nonswollen cells, for which there is a very small steady-state volume decrease, are still predicted to transiently lose volume during spreading due to a relaxing viscoelastic tension that is large compared with the steady-state tension. We elucidate the roles of cell swelling and surface tension in cellular volume regulation and discuss their possible microscopic origins.

Instabilities and Geometry of Growing Tissues.

We present a covariant continuum formulation of a generalized two-dimensional vertexlike model of epithelial tissues which describes tissues with different underlying geometries, and allows for an analytical macroscopic description. Using a geometrical approach and out-of-equilibrium statistical mechanics, we calculate both mechanical and dynamical instabilities of a tissue, and their dependences on various variables, including activity, and cell-shape heterogeneity (disorder). We show how both plastic cellular rearrangements and the tissue elastic response depend on the existence of mechanical residual stresses at the cellular level. Even freely growing tissues may exhibit a growth instability depending on the intrinsic proliferation rate. Our main result is an explicit calculation of the cell pressure in a homeostatic state of a confined growing tissue. We show that the homeostatic pressure can be negative and depends on the existence of mechanical residual stresses. This geometric model allows us to sort out elastic and plastic effects in a growing, flowing, tissue.

Spontaneous flow created by active topological defects.

Topological defects are at the root of the large-scale organization of liquid crystals. In two-dimensional active nematics, two classes of topological defects of charges [Formula: see text] are known to play a major role due to active stresses. Despite this importance, few analytical results have been obtained on the flow-field and active-stress patterns around active topological defects. Using the generic hydrodynamic theory of active systems, we investigate the flow and stress patterns around these topological defects in unbounded, two-dimensional active nematics. Under generic assumptions, we derive analytically the spontaneous velocity and stall force of self-advected defects in the presence of both shear and rotational viscosities. Applying our formalism to the dynamics of monolayers of elongated cells at confluence, we show that the non-conservation of cell number generically increases the self-advection velocity and could provide an explanation for their observed role in cellular extrusion and multilayering. We finally investigate numerically the influence of the Ericksen stress. Our work paves the way to a generic study of the role of topological defects in active nematics, and in particular in monolayers of elongated cells.

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.

Permeation Instabilities in Active Polar Gels.

We present a theory of active, permeating, polar gels, based on a two-fluid model. An active relative force between the gel components creates a steady-state current. We analyze its stability, while considering two polar coupling terms to the relative current: a permeation-deformation term, which describes network deformation by the solvent flow, and a permeation-alignment term, which describes the alignment of the polarization field by the network deformation and flow. Novel instability mechanisms emerge at finite wave vectors, suggesting the formation of periodic domains and mesophases. Our results can be used to determine the physical conditions required for various types of multicellular migration across tissues.

Impact of the Wetting Length on Flexible Blade Spreading.

We study the spreading of a Newtonian fluid by a deformable blade, a common industrial problem, characteristic of elastohydrodynamic situations. Here, we consider the case of a finite reservoir of liquid, emptying as the liquid is spread. We evidence the role of a central variable: the wetting length l_{w}, which sets a boundary between the wet and dry parts of the blade. We show that the deposited film thickness e depends quadratically with l_{w}. We study this problem experimentally and numerically by integration of the elastohydrodynamic equations, and finally propose a scaling law model to explain how l_{w} influences the spreading dynamics.

Stress Field inside the Bath Determines Dip Coating with Yield-Stress Fluids in Cylindrical Geometry.

We study experimentally and theoretically the thickness of the coating obtained by pulling out a rod from a reservoir of yield-stress fluid. Opposite to Newtonian fluids, the coating thickness for a fluid of large enough yield stress is determined solely by the flow inside the reservoir and not by the flow inside the meniscus. The stress field inside the reservoir determines the thickness of the coating layer. The thickness is observed to increase nonlinearly with the sizes of the rod and of the reservoir. We develop a theoretical framework that describes this behavior and allows us to precisely predict the coating thickness.

Actin shells control buckling and wrinkling of biomembranes.

Global changes of cell shape under mechanical or osmotic external stresses are mostly controlled by the mechanics of the cortical actin cytoskeleton underlying the cell membrane. Some aspects of this process can be recapitulated in vitro on reconstituted actin-and-membrane systems. In this paper, we investigate how the mechanical properties of a branched actin network shell, polymerized at the surface of a liposome, control membrane shape when the volume is reduced. We observe a variety of membrane shapes depending on the actin thickness. Thin shells undergo buckling, characterized by a cup-shape deformation of the membrane that coincides with the one of the actin network. Thick shells produce membrane wrinkles, but do not deform their outer layer. For intermediate micrometer-thick shells, wrinkling of the membrane is observed, and the actin layer is slightly deformed. Confronting our experimental results with a theoretical description, we determine the transition between buckling and wrinkling, which depends on the thickness of the actin shell and the size of the liposome. We thus unveil the generic mechanism by which biomembranes are able to accommodate their shape against mechanical compression, through thickness adaptation of their cortical cytoskeleton.

Cortical instability drives periodic supracellular actin pattern formation in epithelial tubes.

An essential question of morphogenesis is how patterns arise without preexisting positional information, as inspired by Turing. In the past few years, cytoskeletal flows in the cell cortex have been identified as a key mechanism of molecular patterning at the subcellular level. Theoretical and in vitro studies have suggested that biological polymers such as actomyosin gels have the property to self-organize, but the applicability of this concept in an in vivo setting remains unclear. Here, we report that the regular spacing pattern of supracellular actin rings in the Drosophila tracheal tubule is governed by a self-organizing principle. We propose a simple biophysical model where pattern formation arises from the interplay of myosin contractility and actin turnover. We validate the hypotheses of the model using photobleaching experiments and report that the formation of actin rings is contractility dependent. Moreover, genetic and pharmacological perturbations of the physical properties of the actomyosin gel modify the spacing of the pattern, as the model predicted. In addition, our model posited a role of cortical friction in stabilizing the spacing pattern of actin rings. Consistently, genetic depletion of apical extracellular matrix caused strikingly dynamic movements of actin rings, mirroring our model prediction of a transition from steady to chaotic actin patterns at low cortical friction. Our results therefore demonstrate quantitatively that a hydrodynamical instability of the actin cortex can trigger regular pattern formation and drive morphogenesis in an in vivo setting.

Physics of active jamming during collective cellular motion in a monolayer.

Although collective cell motion plays an important role, for example during wound healing, embryogenesis, or cancer progression, the fundamental rules governing this motion are still not well understood, in particular at high cell density. We study here the motion of human bronchial epithelial cells within a monolayer, over long times. We observe that, as the monolayer ages, the cells slow down monotonously, while the velocity correlation length first increases as the cells slow down but eventually decreases at the slowest motions. By comparing experiments, analytic model, and detailed particle-based simulations, we shed light on this biological amorphous solidification process, demonstrating that the observed dynamics can be explained as a consequence of the combined maturation and strengthening of cell-cell and cell-substrate adhesions. Surprisingly, the increase of cell surface density due to proliferation is only secondary in this process. This analysis is confirmed with two other cell types. The very general relations between the mean cell velocity and velocity correlation lengths, which apply for aggregates of self-propelled particles, as well as motile cells, can possibly be used to discriminate between various parameter changes in vivo, from noninvasive microscopy data.

Theory of epithelial sheet morphology in three dimensions.

Morphogenesis during embryo development requires the coordination of mechanical forces to generate the macroscopic shapes of organs. We propose a minimal theoretical model, based on cell adhesion and actomyosin contractility, which describes the various shapes of epithelial cells and the bending and buckling of epithelial sheets, as well as the relative stability of cellular tubes and spheres. We show that, to understand these processes, a full 3D description of the cells is needed, but that simple scaling laws can still be derived. The morphologies observed in vivo can be understood as stable points of mechanical equations and the transitions between them are either continuous or discontinuous. We then focus on epithelial sheet bending, a ubiquitous morphogenetic process. We calculate the curvature of an epithelium as a function of actin belt tension as well as of cell-cell and and cell-substrate tension. The model allows for a comparison of the relative stabilities of spherical or cylindrical cellular structures (acini or tubes). Finally, we propose a unique type of buckling instability of epithelia, driven by a flattening of individual cell shapes, and discuss experimental tests to verify our predictions.

Transduction channels' gating can control friction on vibrating hair-cell bundles in the ear.

Hearing starts when sound-evoked mechanical vibrations of the hair-cell bundle activate mechanosensitive ion channels, giving birth to an electrical signal. As for any mechanical system, friction impedes movements of the hair bundle and thus constrains the sensitivity and frequency selectivity of auditory transduction. Friction is generally thought to result mainly from viscous drag by the surrounding fluid. We demonstrate here that the opening and closing of the transduction channels produce internal frictional forces that can dominate viscous drag on the micrometer-sized hair bundle. We characterized friction by analyzing hysteresis in the force-displacement relation of single hair-cell bundles in response to periodic triangular stimuli. For bundle velocities high enough to outrun adaptation, we found that frictional forces were maximal within the narrow region of deflections that elicited significant channel gating, plummeted upon application of a channel blocker, and displayed a sublinear growth for increasing bundle velocity. At low velocity, the slope of the relation between the frictional force and velocity was nearly fivefold larger than the hydrodynamic friction coefficient that was measured when the transduction machinery was decoupled from bundle motion by severing tip links. A theoretical analysis reveals that channel friction arises from coupling the dynamics of the conformational change associated with channel gating to tip-link tension. Varying channel properties affects friction, with faster channels producing smaller friction. We propose that this intrinsic source of friction may contribute to the process that sets the hair cell's characteristic frequency of responsiveness.

Filopodial retraction force is generated by cortical actin dynamics and controlled by reversible tethering at the tip.

Filopodia are dynamic, finger-like plasma membrane protrusions that sense the mechanical and chemical surroundings of the cell. Here, we show in epithelial cells that the dynamics of filopodial extension and retraction are determined by the difference between the actin polymerization rate at the tip and the retrograde flow at the base of the filopodium. Adhesion of a bead to the filopodial tip locally reduces actin polymerization and leads to retraction via retrograde flow, reminiscent of a process used by pathogens to invade cells. Using optical tweezers, we show that filopodial retraction occurs at a constant speed against counteracting forces up to 50 pN. Our measurements point toward retrograde flow in the cortex together with frictional coupling between the filopodial and cortical actin networks as the main retraction-force generator for filopodia. The force exerted by filopodial retraction, however, is limited by the connection between filopodial actin filaments and the membrane at the tip. Upon mechanical rupture of the tip connection, filopodia exert a passive retraction force of 15 pN via their plasma membrane. Transient reconnection at the tip allows filopodia to continuously probe their surroundings in a load-and-fail manner within a well-defined force range.

Theoretical study of actin layers attachment and separation.

We use the theory of active gels to study theoretically the merging and separation of two actin dense layers akin to cortical layers of animal cells. The layers bind at a distance equal to twice the thickness of a free layer, thus forming a single dense layer, similar in this sense to a lamellipodium. When that unique layer is stretched apart, it is resilient to break apart up to a critical length larger than twice the thickness of a free layer. We show that this behavior can result from the high contractile properties of the actomyosin gel due to the activity of myosin molecular motors. Furthermore, we establish that the stability of the stretched single layer is highly dependent on the properties of the gel. Indeed, the nematic order of the actin filaments along the polymerizing membranes is a destabilizing factor.

Furrow constriction in animal cell cytokinesis.

Cytokinesis is the process of physical cleavage at the end of cell division; it proceeds by ingression of an acto-myosin furrow at the equator of the cell. Its failure leads to multinucleated cells and is a possible cause of tumorigenesis. Here, we calculate the full dynamics of furrow ingression and predict cytokinesis completion above a well-defined threshold of equatorial contractility. The cortical acto-myosin is identified as the main source of mechanical dissipation and active forces. Thereupon, we propose a viscous active nonlinear membrane theory of the cortex that explicitly includes actin turnover and where the active RhoA signal leads to an equatorial band of myosin overactivity. The resulting cortex deformation is calculated numerically, and reproduces well the features of cytokinesis such as cell shape and cortical flows toward the equator. Our theory gives a physical explanation of the independence of cytokinesis duration on cell size in embryos. It also predicts a critical role of turnover on the rate and success of furrow constriction. Scaling arguments allow for a simple interpretation of the numerical results and unveil the key mechanism that generates the threshold for cytokinesis completion: cytoplasmic incompressibility results in a competition between the furrow line tension and the cell poles' surface tension.

Compressive stress inhibits proliferation in tumor spheroids through a volume limitation.

In most instances, the growth of solid tumors occurs in constrained environments and requires a competition for space. A mechanical crosstalk can arise from this competition. In this article, we dissect the biomechanical sequence caused by a controlled compressive stress on multicellular spheroids (MCSs) used as a tumor model system. On timescales of minutes, we show that a compressive stress causes a reduction of the MCS volume, linked to a reduction of the cell volume in the core of the MCS. On timescales of hours, we observe a reversible induction of the proliferation inhibitor, p27Kip1, from the center to the periphery of the spheroid. On timescales of days, we observe that cells are blocked in the cell cycle at the late G1 checkpoint, the restriction point. We show that the effect of pressure on the proliferation can be antagonized by silencing p27Kip1. Finally, we quantify a clear correlation between the pressure-induced volume change and the growth rate of the spheroid. The compression-induced proliferation arrest that we studied is conserved for five cell lines, and is completely reversible. It demonstrates a generic crosstalk between mechanical stresses and the key players of cell cycle regulation. Our results suggest a role of volume change in the sensitivity to pressure, and that p27Kip1 is strongly influenced by this change.

Mechanical detection of a long-range actin network emanating from a biomimetic cortex.

Actin is ubiquitous globular protein that polymerizes into filaments and forms networks that participate in the force generation of eukaryotic cells. Such forces are used for cell motility, cytokinesis, and tissue remodeling. Among those actin networks, we focus on the actin cortex, a dense branched network beneath the plasma membrane that is of particular importance for the mechanical properties of the cell. Here we reproduce the cellular cortex by activating actin filament growth on a solid surface. We unveil the existence of a sparse actin network that emanates from the surface and extends over a distance that is at least 10 times larger than the cortex itself. We call this sparse actin network the "actin cloud" and characterize its mechanical properties with optical tweezers. We show, both experimentally and theoretically, that the actin cloud is mechanically relevant and that it should be taken into account because it can sustain forces as high as several picoNewtons (pN). In particular, it is known that in plant cells, actin networks similar to the actin cloud have a role in positioning the nucleus; in large oocytes, they play a role in driving chromosome movement. Recent evidence shows that such networks even prevent granule condensation in large cells.

Mechanical checkpoint for persistent cell polarization in adhesion-naive fibroblasts.

Cell polarization is a fundamental biological process implicated in nearly every aspect of multicellular development. The role of cell-extracellular matrix contacts in the establishment and the orientation of cell polarity have been extensively studied. However, the respective contributions of substrate mechanics and biochemistry remain unclear. Here we propose a believed novel single-cell approach to assess the minimal polarization trigger. Using nonadhered round fibroblast cells, we show that stiffness sensing through single localized integrin-mediated cues are necessary and sufficient to trigger and direct a shape polarization. In addition, the traction force developed by cells has to reach a minimal threshold of 56 ± 1.6 pN for persistent polarization. The polarization kinetics increases with the stiffness of the cue. The polarized state is characterized by cortical actomyosin redistribution together with cell shape change. We develop a physical model supporting the idea that a local and persistent inhibition of actin polymerization and/or myosin activity is sufficient to trigger and sustain the polarized state. Finally, the cortical polarity propagates to an intracellular polarity, evidenced by the reorientation of the centrosome. Our results define the minimal adhesive requirements and quantify the mechanical checkpoint for persistent cell shape and organelle polarization, which are critical regulators of tissue and cell development.

Mechanical control of cell flow in multicellular spheroids.

Collective cell motion is observed in a wide range of biological processes. In tumors, physiological gradients of nutrients, growth factors, or even oxygen give rise to gradients of proliferation. We show using fluorescently labeled particles that these gradients drive a velocity field resulting in a cellular flow in multicellular spheroids. Under mechanical stress, the cellular flow is drastically reduced. We describe the results with a hydrodynamic model that considers only convection of the particles by the cellular flow.