Cells respond to mechanical stress by rapid disassembly of caveolae.

The functions of caveolae, the characteristic plasma membrane invaginations, remain debated. Their abundance in cells experiencing mechanical stress led us to investigate their role in membrane-mediated mechanical response. Acute mechanical stress induced by osmotic swelling or by uniaxial stretching results in a rapid disappearance of caveolae, in a reduced caveolin/Cavin1 interaction, and in an increase of free caveolins at the plasma membrane. Tether-pulling force measurements in cells and in plasma membrane spheres demonstrate that caveola flattening and disassembly is the primary actin- and ATP-independent cell response that buffers membrane tension surges during mechanical stress. Conversely, stress release leads to complete caveola reassembly in an actin- and ATP-dependent process. The absence of a functional caveola reservoir in myotubes from muscular dystrophic patients enhanced membrane fragility under mechanical stress. Our findings support a new role for caveolae as a physiological membrane reservoir that quickly accommodates sudden and acute mechanical stresses.

Quantitative comparison of cell-cell detachment force in different experimental setups.

We compare three different setups for measuring cell-cell adhesion. We show that the measured strength depends on the type of setup that is used. For identical cells different assays measure different detachment forces. This can be understood from the fact that cell-cell detachment is a global property of the system. We also analyse the role of external force and line tension on contact angle and cell-cell detachment. Comparison with the experiments suggest that viscous forces play an important role in the process. We dedicate this article to Fyl Pincus who for many of us is an example to be followed not only for outstanding science but also for a marvelous human behavior.

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.

Stick-slip model for actin-driven cell protrusions, cell polarization, and crawling.

Cell crawling requires the generation of intracellular forces by the cytoskeleton and their transmission to an extracellular substrate through specific adhesion molecules. Crawling cells show many features of excitable systems, such as spontaneous symmetry breaking and crawling in the absence of external cues, and periodic and propagating waves of activity. Mechanical instabilities in the active cytoskeleton network and feedback loops in the biochemical network of activators and repressors of cytoskeleton dynamics have been invoked to explain these dynamical features. Here, I show that the interplay between the dynamics of cell-substrate adhesion and linear cellular mechanics is sufficient to reproduce many nonlinear dynamical patterns observed in spreading and crawling cells. Using an analytical formalism of the molecular clutch model of cell adhesion, regulated by local mechanical forces, I show that cellular traction forces exhibit stick-slip dynamics resulting in periodic waves of protrusion/retraction and propagating waves along the cell edge. This can explain spontaneous symmetry breaking and polarization of spreading cells, leading to steady crawling or bipedal motion, and bistability, where persistent cell motion requires a sufficiently strong transient external stimulus. The model also highlights the role of membrane tension in providing the long-range mechanical communication across the cell required for symmetry breaking.

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.

Shear-Driven Instabilities of Membrane Tubes and Dynamin-Induced Scission.

Motivated by the mechanics of dynamin-mediated membrane tube fission, we analyze the stability of fluid membrane tubes subjected to shear flow in azimuthal direction. We find a novel helical instability driven by the membrane shear flow which results in a nonequilibrium steady state for the tube fluctuations. This instability has its onset at shear rates that may be physiologically accessible under the action of dynamin and could also be probed using in vitro experiments on membrane nanotubes, e.g., using magnetic tweezers. We discuss how such an instability may play a role in the mechanism for dynamin-mediated membrane tube fission.

Dynamics of passive and active membrane tubes.

Utilising Onsager's variational formulation, we derive dynamical equations for the relaxation of a fluid membrane tube in the limit of small deformation, allowing for a contrast of solvent viscosity across the membrane and variations in surface tension due to membrane incompressibility. We compute the relaxation rates, recovering known results in the case of purely axis-symmetric perturbations and making new predictions for higher order (azimuthal) m-modes. We analyse the long and short wavelength limits of these modes by making use of various asymptotic arguments. We incorporate stochastic terms to our dynamical equations suitable to describe both passive thermal forces and non-equilibrium active forces. We derive expressions for the fluctuation amplitudes, an effective temperature associated with active fluctuations, and the power spectral density for both the thermal and active fluctuations. We discuss an experimental assay that might enable measurement of these fluctuations to infer the properties of the active noise. Finally we discuss our results in the context of active membranes more generally and give an overview of some open questions in the field.

Cellular Blebs and Membrane Invaginations Are Coupled through Membrane Tension Buffering.

Bleb-type cellular protrusions play key roles in a range of biological processes. It was recently found that bleb growth is facilitated by a local supply of membrane from tubular invaginations, but the interplay between the expanding bleb and the membrane tubes remains poorly understood. On the one hand, the membrane area stored in tubes may serve as a reservoir for bleb expansion. On the other hand, the sequestering of excess membrane in stabilized invaginations may effectively increase the cell membrane tension, which suppresses spontaneous protrusions. Here, we investigate this duality through physical modeling and in vivo experiments. In agreement with observations, our model describes the transition into a tube-flattening mode of bleb expansion while also predicting that the blebbing rate is impaired by elevating the concentration of the curved membrane proteins that form the tubes. We show both theoretically and experimentally that the stabilizing effect of tubes could be counterbalanced by the cortical myosin contractility. Our results largely suggest that proteins able to induce membrane tubulation, such as those containing N-BAR domains, can buffer the effective membrane tension-a master regulator of all cell deformations.

Wrapping of a nanowire by a supported lipid membrane.

Internalization of particles by cells plays a crucial role for adsorbing nutrients and fighting infection. Endocytosis is one of the most important mechanisms of particle uptake, which encompasses multiple pathways. Although endocytosis is a complex mechanism involving biochemical signaling and active force generation, the energetic cost associated with the large deformations of the cell membrane wrapping around a foreign particle is an important factor controlling this process, which can be studied using quantitative physical models. Of particular interest is the competition between membrane-cytoskeleton and membrane-target adhesion. This competitive adhesion mechanism can be reproduced to some extent by studying particle wrapping by a membrane adhered to a substrate. We propose a theoretical analysis of this process. Here, we explore the wrapping of a lipid membrane around a long cylindrical object in the presence of a substrate mimicking the cytoskeleton. Using discretization of the Helfrich elastic energy, which accounts for the membrane bending rigidity and surface tension, we obtain a wrapping phase diagram as a function of the membrane-cytoskeleton and the membrane-target adhesion energy, which includes unwrapped, partially wrapped and fully wrapped states. We provide an analytical expression for the boundary between the different regimes. While the transition to partial wrapping is independent of the membrane tension, the transition to full wrapping is very much influenced by the membrane tension. We also show that target wrapping may proceed in an asymmetric fashion in the full wrapping regime.

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.

Stochastic Model of Maturation and Vesicular Exchange in Cellular Organelles.

The dynamical organization of membrane-bound organelles along intracellular transport pathways relies on vesicular exchange between organelles and on the maturation of the organelle's composition by enzymatic reactions or exchange with the cytoplasm. The relative importance of each mechanism in controlling organelle dynamics remains controversial, in particular for transport through the Golgi apparatus. Using a stochastic model, we identify two classes of dynamical behavior that can lead to full maturation of membrane-bound compartments. In the first class, maturation corresponds to the stochastic escape from a steady state in which export is dominated by vesicular exchange, and is very unlikely for large compartments. In the second class, it occurs in a quasi-deterministic fashion and is almost size independent. Whether a system belongs to the first or second class is largely controlled by homotypic fusion.

Stochastic Model of Vesicular Sorting in Cellular Organelles.

The proper sorting of membrane components by regulated exchange between cellular organelles is crucial to intracellular organization. This process relies on the budding and fusion of transport vesicles, and should be strongly influenced by stochastic fluctuations, considering the relatively small size of many organelles. We identify the perfect sorting of two membrane components initially mixed in a single compartment as a first passage process, and we show that the mean sorting time exhibits two distinct regimes as a function of the ratio of vesicle fusion to budding rates. Low ratio values lead to fast sorting but result in a broad size distribution of sorted compartments dominated by small entities. High ratio values result in two well-defined sorted compartments but sorting is exponentially slow. Our results suggest an optimal balance between vesicle budding and fusion for the rapid and efficient sorting of membrane components and highlight the importance of stochastic effects for the steady-state organization of intracellular compartments.

Hydro-osmotic Instabilities in Active Membrane Tubes.

We study a membrane tube with unidirectional ion pumps driving an osmotic pressure difference. A pressure-driven peristaltic instability is identified, qualitatively distinct from similar tension-driven Rayleigh-type instabilities on membrane tubes. We discuss how this instability could be related to the function and biogenesis of membrane bound organelles, in particular, the contractile vacuole complex. The unusually long natural wavelength of this instability is in agreement with that observed in cells.

Quantitative analysis of intra-Golgi transport shows intercisternal exchange for all cargo.

The mechanisms controlling the transport of proteins through the Golgi stack of mammalian and plant cells is the subject of intense debate, with two models, cisternal progression and intercisternal exchange, emerging as major contenders. A variety of transport experiments have claimed support for each of these models. We reevaluate these experiments using a single quantitative coarse-grained framework of intra-Golgi transport that accounts for both transport models and their many variants. Our analysis makes a definitive case for the existence of intercisternal exchange both for small membrane proteins and large protein complexes--this implies that membrane structures larger than the typical protein-coated vesicles must be involved in transport. Notwithstanding, we find that current observations on protein transport cannot rule out cisternal progression as contributing significantly to the transport process. To discriminate between the different models of intra-Golgi transport, we suggest experiments and an analysis based on our extended theoretical framework that compare the dynamics of transiting and resident proteins.

Model for probing membrane-cortex adhesion by micropipette aspiration and fluctuation spectroscopy.

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 acto-myosin 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.

Biophysical approaches to protein-induced membrane deformations in trafficking.

Membrane traffic requires membrane deformation to generate vesicles and tubules. Strong evidence suggests that assembly of curvature-active proteins can drive such membrane shape changes. Well-documented pathways often involve protein scaffolds, in particular coats (clathrin or COP). However, membrane curvature should, in principle, be influenced by any protein binding asymmetrically on a membrane; large membrane morphological changes could result from their aggregation. In the case of Shiga toxin or viral matrix proteins, tubules and buds appear to result from the cargo-driven formation of protein-lipid nanodomains, showing that collective protein behaviour is crucial in the process. We argue here that a combination of in vitro experiments on giant unilamellar vesicles and theoretical modelling based on statistical physics is ideally suited to tackle these collective effects.

Emerging roles for lipids in shaping membrane-protein function.

Studies of membrane proteins have revealed a direct link between the lipid environment and the structure and function of some of these proteins. Although some of these effects involve specific chemical interactions between lipids and protein residues, many can be understood in terms of protein-induced perturbations to the membrane shape. The free-energy cost of such perturbations can be estimated quantitatively, and measurements of channel gating in model systems of membrane proteins with their lipid partners are now confirming predictions of simple models.

Membrane tension regulates motility by controlling lamellipodium organization.

Many cell movements proceed via a crawling mechanism, where polymerization of the cytoskeletal protein actin pushes out the leading edge membrane. In this model, membrane tension has been seen as an impediment to filament growth and cell motility. Here we use a simple model of cell motility, the Caenorhabditis elegans sperm cell, to test how membrane tension affects movement and cytoskeleton dynamics. To enable these analyses, we create transgenic worm strains carrying sperm with a fluorescently labeled cytoskeleton. Via osmotic shock and deoxycholate treatments, we relax or tense the cell membrane and quantify apparent membrane tension changes by the membrane tether technique. Surprisingly, we find that membrane tension reduction is correlated with a decrease in cell displacement speed, whereas an increase in membrane tension enhances motility. We further demonstrate that apparent polymerization rates follow the same trends. We observe that membrane tension reduction leads to an unorganized, rough lamellipodium, composed of short filaments angled away from the direction of movement. On the other hand, an increase in tension reduces lateral membrane protrusions in the lamellipodium, and filaments are longer and more oriented toward the direction of movement. Overall we propose that membrane tension optimizes motility by streamlining polymerization in the direction of movement, thus adding a layer of complexity to our current understanding of how membrane tension enters into the motility equation.

A cell fate decision map reveals abundant direct neurogenesis bypassing intermediate progenitors in the human developing neocortex.

The human neocortex has undergone strong evolutionary expansion, largely due to an increased progenitor population, the basal radial glial cells. These cells are responsible for the production of a diversity of cell types, but the successive cell fate decisions taken by individual progenitors remain unknown. Here we developed a semi-automated live/fixed correlative imaging method to map basal radial glial cell division modes in early fetal tissue and cerebral organoids. Through the live analysis of hundreds of dividing progenitors, we show that basal radial glial cells undergo abundant symmetric amplifying divisions, and frequent self-consuming direct neurogenic divisions, bypassing intermediate progenitors. These direct neurogenic divisions are more abundant in the upper part of the subventricular zone. We furthermore demonstrate asymmetric Notch activation in the self-renewing daughter cells, independently of basal fibre inheritance. Our results reveal a remarkable conservation of fate decisions in cerebral organoids, supporting their value as models of early human neurogenesis.

Unexpected membrane dynamics unveiled by membrane nanotube extrusion.

In cell mechanics, distinguishing the respective roles of the plasma membrane and of the cytoskeleton is a challenge. The difference in the behavior of cellular and pure lipid membranes is usually attributed to the presence of the cytoskeleton as explored by membrane nanotube extrusion. Here we revisit this prevalent picture by unveiling unexpected force responses of plasma membrane spheres devoid of cytoskeleton and synthetic liposomes. We show that a tiny variation in the content of synthetic membranes does not affect their static mechanical properties, but is enough to reproduce the dynamic behavior of their cellular counterparts. This effect is attributed to an amplified intramembrane friction. Reconstituted actin cortices inside liposomes induce an additional, but not dominant, contribution to the effective membrane friction. Our work underlines the necessity of a careful consideration of the role of membrane proteins on cell membrane rheology in addition to the role of the cytoskeleton.