Patterning and dynamics of membrane adhesion under hydraulic stress.

Hydraulic fracturing plays a major role in cavity formation during embryonic development, when pressurized fluid opens microlumens at cell-cell contacts, which evolve to form a single large lumen. However, the fundamental physical mechanisms behind these processes remain masked by the complexity and specificity of biological systems. Here, we show that adhered lipid vesicles subjected to osmotic stress form hydraulic microlumens similar to those in cells. Combining vesicle experiments with theoretical modelling and numerical simulations, we provide a physical framework for the hydraulic reconfiguration of cell-cell adhesions. We map the conditions for microlumen formation from a pristine adhesion, the emerging dynamical patterns and their subsequent maturation. We demonstrate control of the fracturing process depending on the applied pressure gradients and the type and density of membrane bonds. Our experiments further reveal an unexpected, passive transition of microlumens to closed buds that suggests a physical route to adhesion remodeling by endocytosis.

A mechanosensing mechanism controls plasma membrane shape homeostasis at the nanoscale.

As cells migrate and experience forces from their surroundings, they constantly undergo mechanical deformations which reshape their plasma membrane (PM). To maintain homeostasis, cells need to detect and restore such changes, not only in terms of overall PM area and tension as previously described, but also in terms of local, nanoscale topography. Here, we describe a novel phenomenon, by which cells sense and restore mechanically induced PM nanoscale deformations. We show that cell stretch and subsequent compression reshape the PM in a way that generates local membrane evaginations in the 100 nm scale. These evaginations are recognized by I-BAR proteins, which triggers a burst of actin polymerization mediated by Rac1 and Arp2/3. The actin polymerization burst subsequently re-flattens the evagination, completing the mechanochemical feedback loop. Our results demonstrate a new mechanosensing mechanism for PM shape homeostasis, with potential applicability in different physiological scenarios.

The laminin-keratin link shields the nucleus from mechanical deformation and signalling.

The mechanical properties of the extracellular matrix dictate tissue behaviour. In epithelial tissues, laminin is a very abundant extracellular matrix component and a key supporting element. Here we show that laminin hinders the mechanoresponses of breast epithelial cells by shielding the nucleus from mechanical deformation. Coating substrates with laminin-111-unlike fibronectin or collagen I-impairs cell response to substrate rigidity and YAP nuclear localization. Blocking the laminin-specific integrin ß4 increases nuclear YAP ratios in a rigidity-dependent manner without affecting the cell forces or focal adhesions. By combining mechanical perturbations and mathematical modelling, we show that ß4 integrins establish a mechanical linkage between the substrate and keratin cytoskeleton, which stiffens the network and shields the nucleus from actomyosin-mediated mechanical deformation. In turn, this affects the nuclear YAP mechanoresponses, chromatin methylation and cell invasion in three dimensions. Our results demonstrate a mechanism by which tissues can regulate their sensitivity to mechanical signals.

Nonaffine Mechanics of Entangled Networks Inspired by Intermediate Filaments.

Inspired by massive intermediate filament (IF) reorganization in superstretched epithelia, we examine computationally the principles controlling the mechanics of a set of entangled filaments whose ends slide on the cell boundary. We identify an entanglement metric and threshold beyond which random loose networks respond nonaffinely and nonlinearly to stretch by self-organizing into structurally optimal star-shaped configurations. A simple model connecting cellular and filament strains links emergent mechanics to cell geometry, network topology, and filament mechanics. We identify a safety net mechanism in IF networks and provide a framework to harness entanglement in soft fibrous materials.

Estimation of anisotropic bending rigidities and spontaneous curvatures of crescent curvature-inducing proteins from tethered-vesicle experimental data.

The Bin/amphiphysin/Rvs (BAR) superfamily proteins have a crescent binding domain and bend biomembranes along the domain axis. However, their anisotropic bending rigidities and spontaneous curvatures have not been experimentally determined. Here, we estimated these values from the bound protein densities on tethered vesicles using a mean-field theory of anisotropic bending energy and orientation-dependent excluded volume. The dependence curves of the protein density on the membrane curvature are fitted to the experimental data for the I-BAR and N-BAR domains reported by C. Prévost et al. Nat. Commun., 2015, 6, 8529 and F.-C. Tsai et al. Soft Matter, 2021, 17, 4254-4265, respectively. For the I-BAR domain, all three density curves of different chemical potentials exhibit excellent fits with a single parameter set of anisotropic bending energy. When the classical isotropic bending energy is used instead, one of the curves can be fitted well, but the others exhibit large deviations. In contrast, for the N-BAR domain, two curves are not well fitted simultaneously the anisotropic model, although it is significantly improved compared to the isotropic model. This deviation likely suggests a cluster formation of the N-BAR domains.

Mapping mechanical stress in curved epithelia of designed size and shape.

The function of organs such as lungs, kidneys and mammary glands relies on the three-dimensional geometry of their epithelium. To adopt shapes such as spheres, tubes and ellipsoids, epithelia generate mechanical stresses that are generally unknown. Here we engineer curved epithelial monolayers of controlled size and shape and map their state of stress. We design pressurized epithelia with circular, rectangular and ellipsoidal footprints. We develop a computational method, called curved monolayer stress microscopy, to map the stress tensor in these epithelia. This method establishes a correspondence between epithelial shape and mechanical stress without assumptions of material properties. In epithelia with spherical geometry we show that stress weakly increases with areal strain in a size-independent manner. In epithelia with rectangular and ellipsoidal cross-section we find pronounced stress anisotropies that impact cell alignment. Our approach enables a systematic study of how geometry and stress influence epithelial fate and function in three-dimensions.

Caveolin-1 dolines form a distinct and rapid caveolae-independent mechanoadaptation system.

In response to different types and intensities of mechanical force, cells modulate their physical properties and adapt their plasma membrane (PM). Caveolae are PM nano-invaginations that contribute to mechanoadaptation, buffering tension changes. However, whether core caveolar proteins contribute to PM tension accommodation independently from the caveolar assembly is unknown. Here we provide experimental and computational evidence supporting that caveolin-1 confers deformability and mechanoprotection independently from caveolae, through modulation of PM curvature. Freeze-fracture electron microscopy reveals that caveolin-1 stabilizes non-caveolar invaginations-dolines-capable of responding to low-medium mechanical forces, impacting downstream mechanotransduction and conferring mechanoprotection to cells devoid of caveolae. Upon cavin-1/PTRF binding, doline size is restricted and membrane buffering is limited to relatively high forces, capable of flattening caveolae. Thus, caveolae and dolines constitute two distinct albeit complementary components of a buffering system that allows cells to adapt efficiently to a broad range of mechanical stimuli.

Peeling dynamics of fluid membranes bridged by molecular bonds: moving or breaking.

Biological adhesion is a critical mechanical function of complex organisms. At the scale of cell-cell contacts, adhesion is remarkably tunable to enable both cohesion and malleability during development, homeostasis and disease. It is physically supported by transient and laterally mobile molecular bonds embedded in fluid membranes. Thus, unlike specific adhesion at solid-solid or solid-fluid interfaces, peeling at fluid-fluid interfaces can proceed by breaking bonds, by moving bonds or by a combination of both. How the additional degree of freedom provided by bond mobility changes the mechanics of peeling is not understood. To address this, we develop a theoretical model coupling diffusion, reactions and mechanics. Mobility and reaction rates determine distinct peeling regimes. In a diffusion-dominated Stefan-like regime, bond motion establishes self-stabilizing dynamics that increase the effective fracture energy. In a reaction-dominated regime, peeling proceeds by travelling fronts where marginal diffusion and unbinding control peeling speed. In a mixed reaction-diffusion regime, strengthening by bond motion competes with weakening by bond breaking in a force-dependent manner, defining the strength of the adhesion patch. In turn, patch strength depends on molecular properties such as bond stiffness, force sensitivity or crowding. We thus establish the physical rules enabling tunable cohesion in cellular tissues and in engineered biomimetic systems.

Binding of anisotropic curvature-inducing proteins onto membrane tubes.

Bin/Amphiphysin/Rvs superfamily proteins and other curvature-inducing proteins have anisotropic shapes and anisotropically bend biomembranes. Here, we report how the anisotropic proteins bind the membrane tube and are orientationally ordered using mean-field theory including an orientation-dependent excluded volume. The proteins exhibit a second-order or first-order nematic transition with increasing protein density depending on the radius of the membrane tube. The tube curvatures for the maximum protein binding and orientational order are different and varied by the protein density and rigidity. As the external force along the tube axis increases, a first-order transition from a large tube radius with low protein density to a small radius with high density occurs once, and subsequently, the protein orientation tilts to the tube-axis direction. When an isotropic bending energy is used for the proteins with an elliptic shape, the force-dependence curves become symmetric and the first-order transition occurs twice. This theory quantitatively reproduces the results of meshless membrane simulation for short proteins, whereas deviations are seen for long proteins owing to the formation of protein clusters.

Dynamic mechanochemical feedback between curved membranes and BAR protein self-organization.

In many physiological situations, BAR proteins reshape membranes with pre-existing curvature (templates), contributing to essential cellular processes. However, the mechanism and the biological implications of this reshaping process remain unclear. Here we show, both experimentally and through modelling, that BAR proteins reshape low curvature membrane templates through a mechanochemical phase transition. This phenomenon depends on initial template shape and involves the co-existence and progressive transition between distinct local states in terms of molecular organization (protein arrangement and density) and membrane shape (template size and spherical versus cylindrical curvature). Further, we demonstrate in cells that this phenomenon enables a mechanotransduction mode, in which cellular stretch leads to the mechanical formation of membrane templates, which are then reshaped into tubules by BAR proteins. Our results demonstrate the interplay between membrane mechanics and BAR protein molecular organization, integrating curvature sensing and generation in a comprehensive framework with implications for cell mechanical responses.

Mechanical compartmentalization of the intestinal organoid enables crypt folding and collective cell migration.

Intestinal organoids capture essential features of the intestinal epithelium such as crypt folding, cellular compartmentalization and collective movements. Each of these processes and their coordination require patterned forces that are at present unknown. Here we map three-dimensional cellular forces in mouse intestinal organoids grown on soft hydrogels. We show that these organoids exhibit a non-monotonic stress distribution that defines mechanical and functional compartments. The stem cell compartment pushes the extracellular matrix and folds through apical constriction, whereas the transit amplifying zone pulls the extracellular matrix and elongates through basal constriction. The size of the stem cell compartment depends on the extracellular-matrix stiffness and endogenous cellular forces. Computational modelling reveals that crypt shape and force distribution rely on cell surface tensions following cortical actomyosin density. Finally, cells are pulled out of the crypt along a gradient of increasing tension. Our study unveils how patterned forces enable compartmentalization, folding and collective migration in the intestinal epithelium.

A theory of ordering of elongated and curved proteins on membranes driven by density and curvature.

Cell membranes interact with a myriad of curvature-active proteins that control membrane morphology and are responsible for mechanosensation and mechanotransduction. Some of these proteins, such as those containing BAR domains, are curved and elongated, and hence may adopt different states of orientational order, from isotropic to maximize entropy to nematic as a result of crowding or to adapt to the curvature of the underlying membrane. Here, extending the classical work of Onsager for ordering in hard particle systems and that of [E. S. Nascimento et al., Phys. Rev. E, 2017, 96, 022704], we develop a mean-field density functional theory to predict the orientational order and evaluate the free energy of ensembles of elongated and curved objects on curved membranes. This theory depends on the microscopic properties of the particles and explains how a density-dependent isotropic-to-nematic transition is modified by anisotropic curvature. We also examine the coexistence of isotropic and nematic phases. This theory predicts how ordering depends on geometry but we assume here that the geometry is fixed. It also lays the ground to understand the interplay between membrane reshaping by BAR proteins and molecular order, examined by [Le Roux et al., submitted, 2020].

A physical mechanism of TANGO1-mediated bulky cargo export.

The endoplasmic reticulum (ER)-resident protein TANGO1 assembles into a ring around ER exit sites (ERES), and links procollagens in the ER lumen to COPII machinery, tethers, and ER-Golgi intermediate compartment (ERGIC) in the cytoplasm (Raote et al., 2018). Here, we present a theoretical approach to investigate the physical mechanisms of TANGO1 ring assembly and how COPII polymerization, membrane tension, and force facilitate the formation of a transport intermediate for procollagen export. Our results indicate that a TANGO1 ring, by acting as a linactant, stabilizes the open neck of a nascent COPII bud. Elongation of such a bud into a transport intermediate commensurate with bulky procollagens is then facilitated by two complementary mechanisms: (i) by relieving membrane tension, possibly by TANGO1-mediated fusion of retrograde ERGIC membranes and (ii) by force application. Altogether, our theoretical approach identifies key biophysical events in TANGO1-driven procollagen export.

Self-Propulsion of Active Colloids via Ion Release: Theory and Experiments.

We study the self-propulsion of a charged colloidal particle that releases ionic species using theory and experiments. We relax the assumptions of thin Debye length and weak nonequilibrium effects assumed in classical phoretic models. This leads to a number of unexpected features that cannot be rationalized considering the classic phoretic framework: an active particle can reverse the direction of motion by increasing the rate of ion release and can propel even with zero surface charge. Our theory predicts that there are optimal conditions for self-propulsion and a novel regime in which the velocity is insensitive to the background electrolyte concentration. The theoretical results quantitatively capture the salt-dependent velocity measured in our experiments using active colloids that propel by decomposing urea via a surface enzymatic reaction.

The 2020 motile active matter roadmap.

Activity and autonomous motion are fundamental in living and engineering systems. This has stimulated the new field of 'active matter' in recent years, which focuses on the physical aspects of propulsion mechanisms, and on motility-induced emergent collective behavior of a larger number of identical agents. The scale of agents ranges from nanomotors and microswimmers, to cells, fish, birds, and people. Inspired by biological microswimmers, various designs of autonomous synthetic nano- and micromachines have been proposed. Such machines provide the basis for multifunctional, highly responsive, intelligent (artificial) active materials, which exhibit emergent behavior and the ability to perform tasks in response to external stimuli. A major challenge for understanding and designing active matter is their inherent nonequilibrium nature due to persistent energy consumption, which invalidates equilibrium concepts such as free energy, detailed balance, and time-reversal symmetry. Unraveling, predicting, and controlling the behavior of active matter is a truly interdisciplinary endeavor at the interface of biology, chemistry, ecology, engineering, mathematics, and physics. The vast complexity of phenomena and mechanisms involved in the self-organization and dynamics of motile active matter comprises a major challenge. Hence, to advance, and eventually reach a comprehensive understanding, this important research area requires a concerted, synergetic approach of the various disciplines. The 2020 motile active matter roadmap of Journal of Physics: Condensed Matter addresses the current state of the art of the field and provides guidance for both students as well as established scientists in their efforts to advance this fascinating area.

Surface Tension Controls the Hydraulic Fracture of Adhesive Interfaces Bridged by Molecular Bonds.

Biological function requires cell-cell adhesions to tune their cohesiveness; for instance, during the opening of new fluid-filled cavities under hydraulic pressure. To understand the physical mechanisms supporting this adaptability, we develop a stochastic model for the hydraulic fracture of adhesive interfaces bridged by molecular bonds. We find that surface tension strongly enhances the stability of these interfaces by controlling flaw sensitivity, lifetime, and optimal architecture in terms of bond clustering. We also show that bond mobility embrittles adhesions and changes the mechanism of decohesion. Our study provides a mechanistic background to understand the biological regulation of cell-cell cohesion and fracture.

The plasma membrane as a mechanochemical transducer.

Cells are constantly submitted to external mechanical stresses, which they must withstand and respond to. By forming a physical boundary between cells and their environment that is also a biochemical platform, the plasma membrane (PM) is a key interface mediating both cellular response to mechanical stimuli, and subsequent biochemical responses. Here, we review the role of the PM as a mechanosensing structure. We first analyse how the PM responds to mechanical stresses, and then discuss how this mechanical response triggers downstream biochemical responses. The molecular players involved in PM mechanochemical transduction include sensors of membrane unfolding, membrane tension, membrane curvature or membrane domain rearrangement. These sensors trigger signalling cascades fundamental both in healthy scenarios and in diseases such as cancer, which cells harness to maintain integrity, keep or restore homeostasis and adapt to their external environment. This article is part of a discussion meeting issue 'Forces in cancer: interdisciplinary approaches in tumour mechanobiology'.

Combined molecular/continuum modeling reveals the role of friction during fast unfolding of coiled-coil proteins.

Coiled-coils are filamentous proteins that form the basic building block of important force-bearing cellular elements, such as intermediate filaments and myosin motors. In addition to their biological importance, coiled-coil proteins are increasingly used in new biomaterials including fibers, nanotubes, or hydrogels. Coiled-coils undergo a structural transition from an α-helical coil to an unfolded state upon extension, which allows them to sustain large strains and is critical for their biological function. By performing equilibrium and out-of-equilibrium all-atom molecular dynamics (MD) simulations of coiled-coils in explicit solvent, we show that two-state models based on Kramers' or Bell's theories fail to predict the rate of unfolding at high pulling rates. We further show that an atomistically informed continuum rod model accounting for phase transformations and for the hydrodynamic interactions with the solvent can reconcile two-state models with our MD results. Our results show that frictional forces, usually neglected in theories of fibrous protein unfolding, reduce the thermodynamic force acting on the interface, and thus control the dynamics of unfolding at different pulling rates. Our results may help interpret MD simulations at high pulling rates, and could be pertinent to cytoskeletal networks or protein-based artificial materials subjected to shocks or blasts.