Friction forces determine cytoplasmic reorganization and shape changes of ascidian oocytes upon fertilization.

Contraction and flow of the actin cell cortex have emerged as a common principle by which cells reorganize their cytoplasm and take shape. However, how these cortical flows interact with adjacent cytoplasmic components, changing their form and localization, and how this affects cytoplasmic organization and cell shape remains unclear. Here we show that in ascidian oocytes, the cooperative activities of cortical actomyosin flows and deformation of the adjacent mitochondria-rich myoplasm drive oocyte cytoplasmic reorganization and shape changes following fertilization. We show that vegetal-directed cortical actomyosin flows, established upon oocyte fertilization, lead to both the accumulation of cortical actin at the vegetal pole of the zygote and compression and local buckling of the adjacent elastic solid-like myoplasm layer due to friction forces generated at their interface. Once cortical flows have ceased, the multiple myoplasm buckles resolve into one larger buckle, which again drives the formation of the contraction pole-a protuberance of the zygote's vegetal pole where maternal mRNAs accumulate. Thus, our findings reveal a mechanism where cortical actomyosin network flows determine cytoplasmic reorganization and cell shape by deforming adjacent cytoplasmic components through friction forces.

Self-organization in amoeboid motility.

Amoeboid motility has come to refer to a spectrum of cell migration modes enabling a cell to move in the absence of strong, specific adhesion. To do so, cells have evolved a range of motile surface movements whose physical principles are now coming into view. In response to external cues, many cells-and some single-celled-organisms-have the capacity to turn off their default migration mode. and switch to an amoeboid mode. This implies a restructuring of the migration machinery at the cell scale and suggests a close link between cell polarization and migration mediated by self-organizing mechanisms. Here, I review recent theoretical models with the aim of providing an integrative, physical picture of amoeboid migration.

Comparing physical mechanisms for membrane curvature-driven sorting of BAR-domain proteins.

Protein enrichment at specific membrane locations in cells is crucial for many cellular functions. It is well-recognized that the ability of some proteins to sense membrane curvature contributes partly to their enrichment in highly curved cellular membranes. In the past, different theoretical models have been developed to reveal the physical mechanisms underlying curvature-driven protein sorting. This review aims to provide a detailed discussion of the two continuous models that are based on the Helfrich elasticity energy, (1) the spontaneous curvature model and (2) the curvature mismatch model. These two models are commonly applied to describe experimental observations of protein sorting. We discuss how they can be used to explain the curvature-induced sorting data of two BAR proteins, amphiphysin and centaurin. We further discuss how membrane rigidity, and consequently the membrane curvature generated by BAR proteins, could influence protein organization on the curved membranes. Finally, we address future directions in extending these models to describe some cellular phenomena involving protein sorting.

Cooperative epithelial phagocytosis enables error correction in the early embryo.

Errors in early embryogenesis are a cause of sporadic cell death and developmental failure1,2. Phagocytic activity has a central role in scavenging apoptotic cells in differentiated tissues3-6. However, how apoptotic cells are cleared in the blastula embryo in the absence of specialized immune cells remains unknown. Here we show that the surface epithelium of zebrafish and mouse embryos, which is the first tissue formed during vertebrate development, performs efficient phagocytic clearance of apoptotic cells through phosphatidylserine-mediated target recognition. Quantitative four-dimensional in vivo imaging analyses reveal a collective epithelial clearance mechanism that is based on mechanical cooperation by two types of Rac1-dependent basal epithelial protrusions. The first type of protrusion, phagocytic cups, mediates apoptotic target uptake. The second, a previously undescribed type of fast and extended actin-based protrusion that we call 'epithelial arms', promotes the rapid dispersal of apoptotic targets through Arp2/3-dependent mechanical pushing. On the basis of experimental data and modelling, we show that mechanical load-sharing enables the long-range cooperative uptake of apoptotic cells by multiple epithelial cells. This optimizes the efficiency of tissue clearance by extending the limited spatial exploration range and local uptake capacity of non-motile epithelial cells. Our findings show that epithelial tissue clearance facilitates error correction that is relevant to the developmental robustness and survival of the embryo, revealing the presence of an innate immune function in the earliest stages of embryonic development.

Cellular locomotion using environmental topography.

Eukaryotic cells migrate by coupling the intracellular force of the actin cytoskeleton to the environment. While force coupling is usually mediated by transmembrane adhesion receptors, especially those of the integrin family, amoeboid cells such as leukocytes can migrate extremely fast despite very low adhesive forces1. Here we show that leukocytes cannot only migrate under low adhesion but can also transmit forces in the complete absence of transmembrane force coupling. When confined within three-dimensional environments, they use the topographical features of the substrate to propel themselves. Here the retrograde flow of the actin cytoskeleton follows the texture of the substrate, creating retrograde shear forces that are sufficient to drive the cell body forwards. Notably, adhesion-dependent and adhesion-independent migration are not mutually exclusive, but rather are variants of the same principle of coupling retrograde actin flow to the environment and thus can potentially operate interchangeably and simultaneously. As adhesion-free migration is independent of the chemical composition of the environment, it renders cells completely autonomous in their locomotive behaviour.

The axonal actin-spectrin lattice acts as a tension buffering shock absorber.

Axons span extreme distances and are subject to significant stretch deformations during limb movements or sudden head movements, especially during impacts. Yet, axon biomechanics, and its relation to the ultrastructure that allows axons to withstand mechanical stress, is poorly understood. Using a custom developed force apparatus, we demonstrate that chick dorsal root ganglion axons exhibit a tension buffering or strain-softening response, where its steady state elastic modulus decreases with increasing strain. We then explore the contributions from the various cytoskeletal components of the axon to show that the recently discovered membrane-associated actin-spectrin scaffold plays a prominent mechanical role. Finally, using a theoretical model, we argue that the actin-spectrin skeleton acts as an axonal tension buffer by reversibly unfolding repeat domains of the spectrin tetramers to release excess mechanical stress. Our results revise the current viewpoint that microtubules and their associated proteins are the only significant load-bearing elements in axons.

The Roles of Microtubules and Membrane Tension in Axonal Beading, Retraction, and Atrophy.

Axonal beading, or the formation of a series of swellings along the axon, and retraction are commonly observed shape transformations that precede axonal atrophy in Alzheimer's disease, Parkinson's disease, and other neurodegenerative conditions. The mechanisms driving these morphological transformations are poorly understood. Here, we report controlled experiments that can induce either beading or retraction and follow the time evolution of these responses. By making quantitative analysis of the shape modes under different conditions, measurement of membrane tension, and using theoretical considerations, we argue that membrane tension is the main driving force that pushes cytosol out of the axon when microtubules are degraded, causing axonal thinning. Under pharmacological perturbation, atrophy is always retrograde, and this is set by a gradient in the microtubule stability. The nature of microtubule depolymerization dictates the type of shape transformation, vis-à-vis beading or retraction. Elucidating the mechanisms of these shape transformations may facilitate development of strategies to prevent or arrest axonal atrophy due to neurodegenerative conditions.

Curving Cells Inside and Out: Roles of BAR Domain Proteins in Membrane Shaping and Its Cellular Implications.

Many cellular processes rely on precise and timely deformation of the cell membrane. While many proteins participate in membrane reshaping and scission, usually in highly specialized ways, Bin/amphiphysin/Rvs (BAR) domain proteins play a pervasive role, as they not only participate in many aspects of cell trafficking but also are highly versatile membrane remodelers. Subtle changes in the shape and size of the BAR domain can greatly impact the way in which BAR domain proteins interact with the membrane. Furthermore, the activity of BAR domain proteins can be tuned by external physical parameters, and so they behave differently depending on protein surface density, membrane tension, or membrane shape. These proteins can form 3D structures that mold the membrane and alter its liquid properties, even promoting scission under various circumstances.As such, BAR domain proteins have numerous roles within the cell. Endocytosis is among the most highly studied processes in which BAR domain proteins take on important roles. Over the years, a more complete picture has emerged in which BAR domain proteins are tied to almost all intracellular compartments; examples include endosomal sorting and tubular networks in the endoplasmic reticulum and T-tubules. These proteins also have a role in autophagy, and their activity has been linked with cancer. Here, we briefly review the history of BAR domain protein discovery, discuss the mechanisms by which BAR domain proteins induce curvature, and attempt to settle important controversies in the field. Finally, we review BAR domain proteins in the context of a cell, highlighting their emerging roles in cell signaling and organelle shaping.

Large-scale curvature sensing by directional actin flow drives cellular migration mode switching.

Cell migration over heterogeneous substrates during wound healing or morphogenetic processes leads to shape changes driven by different organizations of the actin cytoskeleton and by functional changes including lamellipodial protrusions and contractile actin cables. Cells distinguish between cell-sized positive and negative curvatures in their physical environment by forming protrusions at positive ones and actin cables at negative ones; however, the cellular mechanisms remain unclear. Here, we report that concave edges promote polarized actin structures with actin flow directed towards the cell edge, in contrast to well-documented retrograde flow at convex edges. Anterograde flow and contractility induce a tension anisotropy gradient. A polarized actin network is formed, accompanied by a local polymerization-depolymerization gradient, together with leading-edge contractile actin cables in the front. These cables extend onto non-adherent regions while still maintaining contact with the substrate through focal adhesions. The contraction and dynamic reorganization of this actin structure allows forward movements enabling cell migration over non-adherent regions on the substrate. These versatile functional structures may help cells sense and navigate their environment by adapting to external geometric and mechanical cues.

Cell shape and substrate stiffness drive actin-based cell polarity.

A general trait of living cells is their ability to exert contractile stresses on their surroundings and thus respond to substrate rigidity. At the cellular scale, this response affects cell shape, polarity, and ultimately migration. The regulation of cell shape together with rigidity sensing remains largely unknown. In this article we show that both substrate rigidity and cell shape contribute to drive actin organization and cell polarity. Increasing substrate rigidity affects bulk properties of the actin cytoskeleton by favoring long-lived actin stress fibers with increased nematic interactions, whereas cell shape imposes a local alignment of actin fibers at the cell periphery.

Friction Mediates Scission of Tubular Membranes Scaffolded by BAR Proteins.

Membrane scission is essential for intracellular trafficking. While BAR domain proteins such as endophilin have been reported in dynamin-independent scission of tubular membrane necks, the cutting mechanism has yet to be deciphered. Here, we combine a theoretical model, in vitro, and in vivo experiments revealing how protein scaffolds may cut tubular membranes. We demonstrate that the protein scaffold bound to the underlying tube creates a frictional barrier for lipid diffusion; tube elongation thus builds local membrane tension until the membrane undergoes scission through lysis. We call this mechanism friction-driven scission (FDS). In cells, motors pull tubes, particularly during endocytosis. Through reconstitution, we show that motors not only can pull out and extend protein-scaffolded tubes but also can cut them by FDS. FDS is generic, operating even in the absence of amphipathic helices in the BAR domain, and could in principle apply to any high-friction protein and membrane assembly.

Membrane curvature regulates ligand-specific membrane sorting of GPCRs in living cells.

The targeted spatial organization (sorting) of Gprotein-coupled receptors (GPCRs) is essential for their biological function and often takes place in highly curved membrane compartments such as filopodia, endocytic pits, trafficking vesicles or endosome tubules. However, the influence of geometrical membrane curvature on GPCR sorting remains unknown. Here we used fluorescence imaging to establish a quantitative correlation between membrane curvature and sorting of three prototypic class A GPCRs (the neuropeptide Y receptor Y2, the ß1 adrenergic receptor and the ß2 adrenergic receptor) in living cells. Fitting of a thermodynamic model to the data enabled us to quantify how sorting is mediated by an energetic drive to match receptor shape and membrane curvature. Curvature-dependent sorting was regulated by ligands in a specific manner. We anticipate that this curvature-dependent biomechanical coupling mechanism contributes to the sorting, trafficking and function of transmembrane proteins in general.

Physical basis of some membrane shaping mechanisms.

In vesicular transport pathways, membrane proteins and lipids are internalized, externalized or transported within cells, not by bulk diffusion of single molecules, but embedded in the membrane of small vesicles or thin tubules. The formation of these 'transport carriers' follows sequential events: membrane bending, fission from the donor compartment, transport and eventually fusion with the acceptor membrane. A similar sequence is involved during the internalization of drug or gene carriers inside cells. These membrane-shaping events are generally mediated by proteins binding to membranes. The mechanisms behind these biological processes are actively studied both in the context of cell biology and biophysics. Bin/amphiphysin/Rvs (BAR) domain proteins are ideally suited for illustrating how simple soft matter principles can account for membrane deformation by proteins. We review here some experimental methods and corresponding theoretical models to measure how these proteins affect the mechanics and the shape of membranes. In more detail, we show how an experimental method employing optical tweezers to pull a tube from a giant vesicle may give important quantitative insights into the mechanism by which proteins sense and generate membrane curvature and the mechanism of membrane scission.This article is part of the themed issue 'Soft interfacial materials: from fundamentals to formulation'.

Actin flows in cell migration: from locomotion and polarity to trajectories.

Eukaryotic cell movement is characterized by very diverse migration modes. Recent studies show that cells can adapt to environmental cues, such as adhesion and geometric confinement, thereby readily switching their mode of migration. Among this diversity of motile behavior, actin flows have emerged as a highly conserved feature of both mesenchymal and amoeboid migration, and have also been identified as key regulators of cell polarity. This suggests that the various observed migration modes are continuous variations of elementary locomotion mechanisms, based on a very robust physical property of the actin/myosin system - its ability to sustain flows at the cell scale. This central role of actin/myosin flows is shown to affect the large scale properties of cell trajectories.

Hydrodynamics of bilayer membranes with diffusing transmembrane proteins.

We consider the hydrodynamics of lipid bilayers containing transmembrane proteins of arbitrary shape. This biologically-motivated problem is relevant to the cell membrane, whose fluctuating dynamics play a key role in phenomena ranging from cell migration, intercellular transport, and cell communication. Using Onsager's variational principle, we derive the equations that govern the relaxation dynamics of the membrane shape, of the mass densities of the bilayer leaflets, and of the diffusing proteins' concentration. With our generic formalism, we obtain several results on membrane dynamics. We find that proteins that span the bilayer increase the intermonolayer friction coefficient. The renormalization, which can be significant, is in inverse proportion to the protein's mobility. Second, we find that asymmetric proteins couple to the membrane curvature and to the difference in monolayer densities. For practically all accessible membrane tensions (σ > 10(-8) N m(-1)) we show that the protein density is the slowest relaxing variable. Furthermore, its relaxation rate decreases at small wavelengths due to the coupling to curvature. We apply our formalism to the large-scale diffusion of a concentrated protein patch. We find that the diffusion profile is not self-similar, owing to the wavevector dependence of the effective diffusion coefficient.

When Physics Takes Over: BAR Proteins and Membrane Curvature.

Cell membranes become highly curved during membrane trafficking, cytokinesis, infection, immune response, or cell motion. Bin/amphiphysin/Rvs (BAR) domain proteins with their intrinsically curved and anisotropic shape are involved in many of these processes, but with a large spectrum of modes of action. In vitro experiments and multiscale computer simulations have contributed in identifying a minimal set of physical parameters, namely protein density on the membrane, membrane tension, and membrane shape, that control how bound BAR domain proteins behave on the membrane. In this review, we summarize the multifaceted coupling of BAR proteins to membrane mechanics and propose a simple phase diagram that recapitulates the effects of these parameters.

IRSp53 senses negative membrane curvature and phase separates along membrane tubules.

BAR domain proteins contribute to membrane deformation in diverse cellular processes. The inverted-BAR (I-BAR) protein IRSp53, for instance, is found on the inner leaflet of the tubular membrane of filopodia; however its role in the formation of these structures is incompletely understood. Here we develop an original assay in which proteins are encapsulated in giant unilamellar vesicles connected to membrane nanotubes. Our results demonstrate that I-BAR dimers sense negative membrane curvature. Experiment and theory reveal that the I-BAR displays a non-monotonic sorting with curvature, and expands the tube at high imposed tension while constricting it at low tension. Strikingly, at low protein density and tension, protein-rich domains appear along the tube. This peculiar behaviour is due to the shallow intrinsic curvature of I-BAR dimers. It allows constriction of weakly curved membranes coupled to local protein enrichment at biologically relevant conditions. This might explain how IRSp53 contributes in vivo to the initiation of filopodia.

Adaptive rheology and ordering of cell cytoskeleton govern matrix rigidity sensing.

Matrix rigidity sensing regulates a large variety of cellular processes and has important implications for tissue development and disease. However, how cells probe matrix rigidity, and hence respond to it, remains unclear. Here, we show that rigidity sensing and adaptation emerge naturally from actin cytoskeleton remodelling. Our in vitro experiments and theoretical modelling demonstrate a biphasic rheology of the actin cytoskeleton, which transitions from fluid on soft substrates to solid on stiffer ones. Furthermore, we find that increasing substrate stiffness correlates with the emergence of an orientational order in actin stress fibres, which exhibit an isotropic to nematic transition that we characterize quantitatively in the framework of active matter theory. These findings imply mechanisms mediated by a large-scale reinforcement of actin structures under stress, which could be the mechanical drivers of substrate stiffness-dependent cell shape changes and cell polarity.

Confinement and low adhesion induce fast amoeboid migration of slow mesenchymal cells.

The mesenchymal-amoeboid transition (MAT) was proposed as a mechanism for cancer cells to adapt their migration mode to their environment. While the molecular pathways involved in this transition are well documented, the role of the microenvironment in the MAT is still poorly understood. Here, we investigated how confinement and adhesion affect this transition. We report that, in the absence of focal adhesions and under conditions of confinement, mesenchymal cells can spontaneously switch to a fast amoeboid migration phenotype. We identified two main types of fast migration--one involving a local protrusion and a second involving a myosin-II-dependent mechanical instability of the cell cortex that leads to a global cortical flow. Interestingly, transformed cells are more prone to adopt this fast migration mode. Finally, we propose a generic model that explains migration transitions and predicts a phase diagram of migration phenotypes based on three main control parameters: confinement, adhesion, and contractility.

Cortical contractility triggers a stochastic switch to fast amoeboid cell motility.

3D amoeboid cell migration is central to many developmental and disease-related processes such as cancer metastasis. Here, we identify a unique prototypic amoeboid cell migration mode in early zebrafish embryos, termed stable-bleb migration. Stable-bleb cells display an invariant polarized balloon-like shape with exceptional migration speed and persistence. Progenitor cells can be reversibly transformed into stable-bleb cells irrespective of their primary fate and motile characteristics by increasing myosin II activity through biochemical or mechanical stimuli. Using a combination of theory and experiments, we show that, in stable-bleb cells, cortical contractility fluctuations trigger a stochastic switch into amoeboid motility, and a positive feedback between cortical flows and gradients in contractility maintains stable-bleb cell polarization. We further show that rearward cortical flows drive stable-bleb cell migration in various adhesive and non-adhesive environments, unraveling a highly versatile amoeboid migration phenotype.