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.

Active superelasticity in three-dimensional epithelia of controlled shape.

Fundamental biological processes are carried out by curved epithelial sheets that enclose a pressurized lumen. How these sheets develop and withstand three-dimensional deformations has remained unclear. Here we combine measurements of epithelial tension and shape with theoretical modelling to show that epithelial sheets are active superelastic materials. We produce arrays of epithelial domes with controlled geometry. Quantification of luminal pressure and epithelial tension reveals a tensional plateau over several-fold areal strains. These extreme strains in the tissue are accommodated by highly heterogeneous strains at a cellular level, in seeming contradiction to the measured tensional uniformity. This phenomenon is reminiscent of superelasticity, a behaviour that is generally attributed to microscopic material instabilities in metal alloys. We show that in epithelial cells this instability is triggered by a stretch-induced dilution of the actin cortex, and is rescued by the intermediate filament network. Our study reveals a type of mechanical behaviour-which we term active superelasticity-that enables epithelial sheets to sustain extreme stretching under constant tension.

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.

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.

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].

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.

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.

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.

Shape Transformations of Lipid Bilayers Following Rapid Cholesterol Uptake.

High cholesterol levels in the blood increase the risk of atherosclerosis. A common explanation is that the cholesterol increase in the plasma membrane perturbs the shape and functions of cells by disrupting the cell signaling pathways and the formation of membrane rafts. In this work, we show that after enhanced transient uptake of cholesterol, mono-component lipid bilayers change their shape similarly to cell membranes in vivo. The bilayers either expel lipid protrusions or spread laterally as a result of the ensuing changes in their lipid density, the mechanical constraints imposed on them, and the properties of cyclodextrin used as a cholesterol donor. In light of the increasingly recognized link between membrane tension and cell behavior, we propose that the physical adaptation of the plasma membrane to cholesterol uptake may play a substantial role in the biological response.

Hydraulic fracture during epithelial stretching.

The origin of fracture in epithelial cell sheets subject to stretch is commonly attributed to excess tension in the cells' cytoskeleton, in the plasma membrane, or in cell-cell contacts. Here, we demonstrate that for a variety of synthetic and physiological hydrogel substrates the formation of epithelial cracks is caused by tissue stretching independently of epithelial tension. We show that the origin of the cracks is hydraulic; they result from a transient pressure build-up in the substrate during stretch and compression manoeuvres. After pressure equilibration, cracks heal readily through actomyosin-dependent mechanisms. The observed phenomenology is captured by the theory of poroelasticity, which predicts the size and healing dynamics of epithelial cracks as a function of the stiffness, geometry and composition of the hydrogel substrate. Our findings demonstrate that epithelial integrity is determined in a tension-independent manner by the coupling between tissue stretching and matrix hydraulics.

Charting molecular free-energy landscapes with an atlas of collective variables.

Collective variables (CVs) are a fundamental tool to understand molecular flexibility, to compute free energy landscapes, and to enhance sampling in molecular dynamics simulations. However, identifying suitable CVs is challenging, and is increasingly addressed with systematic data-driven manifold learning techniques. Here, we provide a flexible framework to model molecular systems in terms of a collection of locally valid and partially overlapping CVs: an atlas of CVs. The specific motivation for such a framework is to enhance the applicability and robustness of CVs based on manifold learning methods, which fail in the presence of periodicities in the underlying conformational manifold. More generally, using an atlas of CVs rather than a single chart may help us better describe different regions of conformational space. We develop the statistical mechanics foundation for our multi-chart description and propose an algorithmic implementation. The resulting atlas of data-based CVs are then used to enhance sampling and compute free energy surfaces in two model systems, alanine dipeptide and ß-D-glucopyranose, whose conformational manifolds have toroidal and spherical topologies.

Hydraulic Fracture and Toughening of a Brittle Layer Bonded to a Hydrogel.

Brittle materials propagate opening cracks under tension. When stress increases beyond a critical magnitude, then quasistatic crack propagation becomes unstable. In the presence of several precracks, a brittle material always propagates only the weakest crack, leading to catastrophic failure. Here, we show that all these features of brittle fracture are fundamentally modified when the material susceptible to cracking is bonded to a hydrogel, a common situation in biological tissues. In the presence of the hydrogel, the brittle material can fracture in compression and can hydraulically resist cracking in tension. Furthermore, the poroelastic coupling regularizes the crack dynamics and enhances material toughness by promoting multiple cracking.

Examining the Mechanical Equilibrium of Microscopic Stresses in Molecular Simulations.

The microscopic stress field provides a unique connection between atomistic simulations and mechanics at the nanoscale. However, its definition remains ambiguous. Rather than a mere theoretical preoccupation, we show that this fact acutely manifests itself in local stress calculations of defective graphene, lipid bilayers, and fibrous proteins. We find that popular definitions of the microscopic stress violate the continuum statements of mechanical equilibrium, and we propose an unambiguous and physically sound definition.

Topological obstructions in the way of data-driven collective variables.

Nonlinear dimensionality reduction (NLDR) techniques are increasingly used to visualize molecular trajectories and to create data-driven collective variables for enhanced sampling simulations. The success of these methods relies on their ability to identify the essential degrees of freedom characterizing conformational changes. Here, we show that NLDR methods face serious obstacles when the underlying collective variables present periodicities, e.g., arising from proper dihedral angles. As a result, NLDR methods collapse very distant configurations, thus leading to misinterpretations and inefficiencies in enhanced sampling. Here, we identify this largely overlooked problem and discuss possible approaches to overcome it. We also characterize the geometry and topology of conformational changes of alanine dipeptide, a benchmark system for testing new methods to identify collective variables.

Reverse engineering the euglenoid movement.

Euglenids exhibit an unconventional motility strategy amongst unicellular eukaryotes, consisting of large-amplitude highly concerted deformations of the entire body (euglenoid movement or metaboly). A plastic cell envelope called pellicle mediates these deformations. Unlike ciliary or flagellar motility, the biophysics of this mode is not well understood, including its efficiency and molecular machinery. We quantitatively examine video recordings of four euglenids executing such motions with statistical learning methods. This analysis reveals strokes of high uniformity in shape and pace. We then interpret the observations in the light of a theory for the pellicle kinematics, providing a precise understanding of the link between local actuation by pellicle shear and shape control. We systematically understand common observations, such as the helical conformations of the pellicle, and identify previously unnoticed features of metaboly. While two of our euglenids execute their stroke at constant body volume, the other two exhibit deviations of about 20% from their average volume, challenging current models of low Reynolds number locomotion. We find that the active pellicle shear deformations causing shape changes can reach 340%, and estimate the velocity of the molecular motors. Moreover, we find that metaboly accomplishes locomotion at hydrodynamic efficiencies comparable to those of ciliates and flagellates. Our results suggest new quantitative experiments, provide insight into the evolutionary history of euglenids, and suggest that the pellicle may serve as a model for engineered active surfaces with applications in microfluidics.

Interplay of packing and flip-flop in local bilayer deformation. How phosphatidylglycerol could rescue mitochondrial function in a cardiolipin-deficient yeast mutant.

In a previous work, we have shown that a spatially localized transmembrane pH gradient, produced by acid micro-injection near the external side of cardiolipin-containing giant unilamellar vesicles, leads to the formation of tubules that retract after the dissipation of this gradient. These tubules have morphologies similar to mitochondrial cristae. The tubulation effect is attributable to direct phospholipid packing modification in the outer leaflet, that is promoted by protonation of cardiolipin headgroups. In this study, we compare the case of cardiolipin-containing giant unilamellar vesicles with that of giant unilamellar vesicles that contain phosphatidylglycerol (PG). Local acidification also promotes formation of tubules in the latter. However, compared with cardiolipin-containing giant unilamellar vesicles the tubules are longer, exhibit a visible pearling, and have a much longer lifetime after acid micro-injection is stopped. We attribute these differences to an additional mechanism that increases monolayer surface imbalance, namely inward PG flip-flop promoted by the local transmembrane pH gradient. Simulations using a fully nonlinear membrane model as well as geometrical calculations are in agreement with this hypothesis. Interestingly, among yeast mutants deficient in cardiolipin biosynthesis, only the crd1-null mutant, which accumulates phosphatidylglycerol, displays significant mitochondrial activity. Our work provides a possible explanation of such a property and further emphasizes the salient role of specific lipids in mitochondrial function.

Confined bilayers passively regulate shape and stress.

Lipid membranes are commonly confined to adjacent subcellular structures or to artificial substrates and particles. We develop an experimental and theoretical framework to investigate the mechanics of confined membranes, including the influence of adhesion, strain, and osmotic pressure. We find that supported lipid bilayers respond to stress by nucleating and evolving spherical and tubular protrusions. In cells, such transformations are generally attributed to proteins. Our results offer insights into the mechanics of cell membranes and can further extend the applications of supported bilayers.

Modeling and enhanced sampling of molecular systems with smooth and nonlinear data-driven collective variables.

Collective variables (CVs) are low-dimensional representations of the state of a complex system, which help us rationalize molecular conformations and sample free energy landscapes with molecular dynamics simulations. Given their importance, there is need for systematic methods that effectively identify CVs for complex systems. In recent years, nonlinear manifold learning has shown its ability to automatically characterize molecular collective behavior. Unfortunately, these methods fail to provide a differentiable function mapping high-dimensional configurations to their low-dimensional representation, as required in enhanced sampling methods. We introduce a methodology that, starting from an ensemble representative of molecular flexibility, builds smooth and nonlinear data-driven collective variables (SandCV) from the output of nonlinear manifold learning algorithms. We demonstrate the method with a standard benchmark molecule, alanine dipeptide, and show how it can be non-intrusively combined with off-the-shelf enhanced sampling methods, here the adaptive biasing force method. We illustrate how enhanced sampling simulations with SandCV can explore regions that were poorly sampled in the original molecular ensemble. We further explore the transferability of SandCV from a simpler system, alanine dipeptide in vacuum, to a more complex system, alanine dipeptide in explicit water.