Closed membrane shapes with attached BAR domains subject to external force of actin filaments

Coupling of nematic in-plane orientational ordering and equilibrium shapes of closed flexible nematic shells

The impact of the intrinsic curvature of in-plane orientationally ordered curved flexible nematic molecules attached to closed 3D flexible shells was studied numerically. A Helfrich-Landau-de Gennes-type mesoscopic approach was adopted where the flexible shell's curvature field and in-plane nematic field are coupled and concomitantly determined in the process of free energy minimisation. We demonstrate that this coupling has the potential to generate a rich diversity of qualitatively new shapes of closed 3D nematic shells and the corresponding specific in-plane orientational ordering textures, which strongly depend on the shell's volume-to-surface area ratio, so far not predicted in mesoscopic-type numerical studies of 3D shapes of closed flexible nematic shells.

Formation of protein-mediated bilayer tubes is governed by a snapthrough transition

Plasma membrane tubes are ubiquitous in cellular membranes and in the membranes of intracellular organelles. They play crucial roles in trafficking, ion transport, and cellular motility. These tubes can be formed due to localized forces acting on the membrane or by the curvature induced by membrane-bound proteins. Here, we present a mathematical framework to model cylindrical tubular protrusions formed by proteins that induce anisotropic spontaneous curvature. Our analysis revealed that the tube radius depends on an effective tension that includes contributions from the bare membrane tension and the protein-induced curvature. We also found that the length of the tube undergoes an abrupt transition from a short, dome-shaped membrane to a long cylinder and this transition is characteristic of a snapthrough instability. Finally, we show that the snapthrough instability depends on the different parameters including coat area, bending modulus, and extent of protein-induced curvature. Our findings have implications for tube formation due to BAR-domain proteins in processes such as endocytosis, t-tubule formation in myocytes, and cristae formation in mitochondria.

Theoretical model of membrane protrusions driven by curved active proteins

Eukaryotic cells intrinsically change their shape, by changing the composition of their membrane and by restructuring their underlying cytoskeleton. We present here further studies and extensions of a minimal physical model, describing a closed vesicle with mobile curved membrane protein complexes. The cytoskeletal forces describe the protrusive force due to actin polymerization which is recruited to the membrane by the curved protein complexes. We characterize the phase diagrams of this model, as function of the magnitude of the active forces, nearest-neighbor protein interactions and the proteins' spontaneous curvature. It was previously shown that this model can explain the formation of lamellipodia-like flat protrusions, and here we explore the regimes where the model can also give rise to filopodia-like tubular protrusions. We extend the simulation with curved components of both convex and concave species, where we find the formation of complex ruffled clusters, as well as internalized invaginations that resemble the process of endocytosis and macropinocytosis. We alter the force model representing the cytoskeleton to simulate the effects of bundled instead of branched structure, resulting in shapes which resemble filopodia.

Ca2+ Regulates Dimerization of the BAR Domain Protein PICK1 and Consequent Membrane Curvature

Bin-Amphiphysin-Rvs (BAR) domain proteins are critical regulators of membrane geometry. They induce and stabilize membrane curvature for processes, such as clathrin-coated pit formation and endosomal membrane tubulation. BAR domains form their characteristic crescent-shaped structure in the dimeric form, indicating that the formation of the dimer is critical to their function of inducing membrane curvature and suggesting that a dynamic monomer–dimer equilibrium regulated by cellular signaling would be a powerful mechanism for controlling BAR domain protein function. However, to the best of our knowledge, cellular mechanisms for regulating BAR domain dimerization remain unexplored. PICK1 is a Ca²⁺-binding BAR domain protein involved in the endocytosis and endosomal recycling of neuronal AMPA receptors and other transmembrane proteins. In this study, we demonstrated that PICK1 dimerization is regulated by a direct effect of Ca²⁺ ions via acidic regions in the BAR domain and at the N-terminus. While the cellular membrane tubulating activity of PICK1 is absent under basal conditions, Ca²⁺ influx causes the generation of membrane tubules that originate from the cell surface. Furthermore, in neurons, PICK1 dimerization increases transiently following NMDA receptor stimulation. We believe that this novel mechanism for regulating BAR domain dimerization and function represents a significant conceptual advance in our knowledge about the regulation of cellular membrane curvature.

Renormalization group study of the dynamics of active membranes: Universality classes and scaling laws

Motivated by experimental observations of patterning at the leading edge of motile eukaryotic cells, we introduce a general model for the dynamics of nearly-flat fluid membranes driven from within by an ensemble of activators. We include, in particular, a kinematic coupling between activator density and membrane slope which generically arises whenever the membrane has a nonvanishing normal speed. We unveil the phase diagram of the model by means of a perturbative field-theoretical renormalization group analysis. Due to the aforementioned kinematic coupling the natural early-time dynamical scaling is acoustic, that is the dynamical critical exponent is 1. However, as soon as the the normal velocity of the membrane is tuned to zero, the system crosses over to diffusive dynamic scaling in mean field. Distinct critical points can be reached depending on how the limit of vanishing velocity is realized: in each of them corrections to scaling due to nonlinear coupling terms must be taken into account. The detailed analysis of these critical points reveals novel scaling regimes which can be accessed with perturbative methods, together with signs of strong coupling behavior, which establishes a promising ground for further nonperturbative calculations. Our results unify several previous studies on the dynamics of active membrane, while also identifying nontrivial scaling regimes which cannot be captured by passive theories of fluctuating interfaces and are relevant for the physics of living membranes.

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.

On the Role of Curved Membrane Nanodomains, and Passive and Active Skeleton Forces in the Determination of Cell Shape and Membrane Budding

Biological membranes are composed of isotropic and anisotropic curved nanodomains. Anisotropic membrane components, such as Bin/Amphiphysin/Rvs (BAR) superfamily protein domains, could trigger/facilitate the growth of membrane tubular protrusions, while isotropic curved nanodomains may induce undulated (necklace-like) membrane protrusions. We review the role of isotropic and anisotropic membrane nanodomains in stability of tubular and undulated membrane structures generated or stabilized by cyto- or membrane-skeleton. We also describe the theory of spontaneous self-assembly of isotropic curved membrane nanodomains and derive the critical concentration above which the spontaneous necklace-like membrane protrusion growth is favorable. We show that the actin cytoskeleton growth inside the vesicle or cell can change its equilibrium shape, induce higher degree of segregation of membrane nanodomains or even alter the average orientation angle of anisotropic nanodomains such as BAR domains. These effects may indicate whether the actin cytoskeleton role is only to stabilize membrane protrusions or to generate them by stretching the vesicle membrane. Furthermore, we demonstrate that by taking into account the in-plane orientational ordering of anisotropic membrane nanodomains, direct interactions between them and the extrinsic (deviatoric) curvature elasticity, it is possible to explain the experimentally observed stability of oblate (discocyte) shapes of red blood cells in a broad interval of cell reduced volume. Finally, we present results of numerical calculations and Monte-Carlo simulations which indicate that the active forces of membrane skeleton and cytoskeleton applied to plasma membrane may considerably influence cell shape and membrane budding.

Lipid-Composition-Mediated Forces Can Stabilize Tubular Assemblies of I-BAR Proteins

Collective action by inverse-Bin/Amphiphysin/Rvs (I-BAR) domains drive micron-scale membrane remodeling. The macroscopic curvature sensing and generation behavior of I-BAR domains is well characterized, and computational models have suggested various mechanisms on simplified membrane systems, but there remain missing connections between the complex environment of the cell and the models proposed thus far. Here, we show a connection between the role of protein curvature and lipid clustering in the relaxation of large membrane deformations. When we include phosphatidylinositol 4,5-bisphosphate-like lipids that preferentially interact with the charged ends of an I-BAR domain, we find clustering of phosphatidylinositol 4,5-bisphosphate-like lipids that induce a directional membrane-mediated interaction between membrane-bound I-BAR domains. Lipid clusters mediate I-BAR domain interactions and cause I-BAR domain aggregates that would not arise through membrane fluctuation-based or curvature-based interactions. Inside of membrane protrusions, lipid cluster-mediated interaction draws long side-by-side aggregates together, resulting in more cylindrical protrusions as opposed to bulbous, irregularly shaped protrusions.

The BAR domain of the Arf GTPase-activating protein ASAP1 directly binds actin filaments

The Arf GTPase-activating protein (Arf GAP) with SH3 domain, ankyrin repeat and PH domain 1 (ASAP1) establishes a connection between the cell membrane and the cortical actin cytoskeleton. The formation, maintenance, and turnover of actin filaments and bundles in the actin cortex are important for cell adhesion, invasion, and migration. Here, using actin cosedimentation, polymerization, and depolymerization assays, along with total internal reflection fluorescence (TIRF), confocal, and EM analyses, we show that the N-terminal N-BAR domain of ASAP1 directly binds to F-actin. We found that ASAP1 homodimerization aligns F-actin in predominantly unipolar bundles and stabilizes them against depolymerization. Furthermore, the ASAP1 N-BAR domain moderately reduced the spontaneous polymerization of G-actin. The overexpression of the ASAP1 BAR-PH tandem domain in fibroblasts induced the formation of actin-filled projections more effectively than did full-length ASAP1. An ASAP1 construct that lacked the N-BAR domain failed to induce cellular projections. Our results suggest that ASAP1 regulates the dynamics and the formation of higher-order actin structures, possibly through direct binding to F-actin via its N-BAR domain. We propose that ASAP1 is a hub protein for dynamic protein-protein interactions in mechanosensitive structures, such as focal adhesions, invadopodia, and podosomes, that are directly implicated in oncogenic events. The effect of ASAP1 on actin dynamics puts a spotlight on its function as a central signaling molecule that regulates the dynamics of the actin cytoskeleton by transmitting signals from the plasma membrane.

Modeling membrane nanotube morphology: the role of heterogeneity in composition and material properties

Membrane nanotubes are dynamic structures that may connect cells over long distances. Nanotubes are typically thin cylindrical tubes, but they may occasionally have a beaded architecture along the tube. In this paper, we study the role of membrane mechanics in governing the architecture of these tubes and show that the formation of bead-like structures along the nanotubes can result from local heterogeneities in the membrane either due to protein aggregation or due to membrane composition. We present numerical results that predict how membrane properties, protein density, and local tension compete to create a phase space that governs the morphology of a nanotube. We also find that there exists a discontinuity in the energy that impedes two beads from fusing. These results suggest that the membrane-protein interaction, membrane composition, and membrane tension closely govern the tube radius, number of beads, and the bead morphology.

Normal red blood cells' shape stabilized by membrane's in-plane ordering

Red blood cells (RBCs) are present in almost all vertebrates and their main function is to transport oxygen to the body tissues. RBCs' shape plays a significant role in their functionality. In almost all mammals in normal conditions, RBCs adopt a disk-like (discocyte) shape, which optimizes their flow properties in vessels and capillaries. Experimentally measured values of the reduced volume (v) of stable discocyte shapes range in a relatively broad window between v ~ 0.58 and 0.8. However, these observations are not supported by existing theoretical membrane-shape models, which predict that discocytic RBC shape is stable only in a very narrow interval of v values, ranging between v ~ 0.59 and 0.65. In this study, we demonstrate that this interval is broadened if a membrane's in-plane ordering is taken into account. We model RBC structures by using a hybrid Helfrich-Landau mesoscopic approach. We show that an extrinsic (deviatoric) curvature free energy term stabilizes the RBC discocyte shapes. In particular, we show on symmetry grounds that the role of extrinsic curvature is anomalously increased just below the nematic in-plane order-disorder phase transition temperature.

Protein Recruitment through Indirect Mechanochemical Interactions

Some of the key proteins essential for important cellular processes are capable of recruiting other proteins from the cytosol to phospholipid membranes. The physical basis for this cooperativity of binding is, surprisingly, still unclear. Here, we suggest a general feedback mechanism that explains cooperativity through mechanochemical coupling mediated by the mechanical properties of phospholipid membranes. Our theory predicts that protein recruitment, and therefore also protein pattern formation, involves membrane deformation and is strongly affected by membrane composition.

Cell confinement reveals a branched-actin independent circuit for neutrophil polarity

Migratory cells use distinct motility modes to navigate different microenvironments, but it is unclear whether these modes rely on the same core set of polarity components. To investigate this, we disrupted actin-related protein 2/3 (Arp2/3) and the WASP-family verprolin homologous protein (WAVE) complex, which assemble branched actin networks that are essential for neutrophil polarity and motility in standard adherent conditions. Surprisingly, confinement rescues polarity and movement of neutrophils lacking these components, revealing a processive bleb-based protrusion program that is mechanistically distinct from the branched actin-based protrusion program but shares some of the same core components and underlying molecular logic. We further find that the restriction of protrusion growth to one site does not always respond to membrane tension directly, as previously thought, but may rely on closely linked properties such as local membrane curvature. Our work reveals a hidden circuit for neutrophil polarity and indicates that cells have distinct molecular mechanisms for polarization that dominate in different microenvironments.

Cells display a high degree of plasticity in migration, but how polarity is organized in different microenvironments has remained unclear. This study uses mechanical perturbations to reveal that migration using actin-rich or bleb-based protrusions are both organized around Rac GTPase.

Theoretical study of vesicle shapes driven by coupling curved proteins and active cytoskeletal forces

Eukaryote cells have a flexible shape, which dynamically changes according to the function performed by the cell. One mechanism for deforming the cell membrane into the desired shape is through the expression of curved membrane proteins. Furthermore, these curved membrane proteins are often associated with the recruitment of the cytoskeleton, which then applies active forces that deform the membrane. This coupling between curvature and activity was previously explored theoretically in the linear limit of small deformations, and low dimensionality. Here we explore the unrestricted shapes of vesicles that contain active curved membrane proteins, in three-dimensions, using Monte-Carlo numerical simulations. The activity of the proteins is in the form of protrusive forces that push the membrane outwards, as may arise from the cytoskeleton of the cell due to actin or microtubule polymerization occurring near the membrane. For proteins that have an isotropic convex shape, the additional protrusive force enhances their tendency to aggregate and form membrane protrusions (buds). In addition, we find another transition from deformed spheres with necklace type aggregates, to flat pancake-shaped vesicles, where the curved proteins line the outer rim. This second transition is driven by the active forces, coupled to the spontaneous curvature, and the resulting configurations may shed light on the formation of sheet-like protrusions and lamellipodia of adhered and motile cells.

Unusual Organization of I-BAR Proteins on Tubular and Vesicular Membranes

Protein-mediated membrane remodeling is a ubiquitous and critical process for proper cellular function. Inverse Bin/Amphiphysin/Rvs (I-BAR) domains drive local membrane deformation as a precursor to large-scale membrane remodeling. We employ a multiscale approach to provide the molecular mechanism of unusual I-BAR domain-driven membrane remodeling at a low protein surface concentration with near-atomistic detail. We generate a bottom-up coarse-grained model that demonstrates similar membrane-bound I-BAR domain aggregation behavior as our recent Mesoscopic Membrane with Explicit Proteins model. Together, these models bridge several length scales and reveal an aggregation behavior of I-BAR domains. We find that at low surface coverage (i.e., low bound protein density), I-BAR domains form transient, tip-to-tip strings on periodic flat membrane sheets. Inside of lipid bilayer tubules, we find linear aggregates parallel to the axis of the tubule. Finally, we find that I-BAR domains form tip-to-tip aggregates around the edges of membrane domes. These results are supported by in vitro experiments showing low curvature bulges surrounded by I-BAR domains on giant unilamellar vesicles. Overall, our models reveal new I-BAR domain aggregation behavior in membrane tubules and on the surface of vesicles at low surface concentration that add insight into how I-BAR domain proteins may contribute to certain aspects of membrane remodeling in cells.

Inception Mechanisms of Tunneling Nanotubes

Tunneling nanotubes (TNTs) are thin membranous tubes that interconnect cells, representing a novel route of cell-to-cell communication and spreading of pathogens. TNTs form between many cell types, yet their inception mechanisms remain elusive. We review in this study general concepts related to the formation and stability of membranous tubular structures with a focus on a deviatoric elasticity model of membrane nanodomains. We review experimental evidence that tubular structures initiate from local membrane bending facilitated by laterally distributed proteins or anisotropic membrane nanodomains. We further discuss the numerical results of several theoretical and simulation models of nanodomain segregation suggesting the mechanisms of TNT inception and stability. We discuss the coupling of nanodomain segregation with the action of protruding cytoskeletal forces, which are mostly provided in eukaryotic cells by the polymerization of f-actin, and review recent inception mechanisms of TNTs in relation to motor proteins.

Sidewall contact regulating the nanorod packing inside vesicles with relative volumes

Intracellular packing of one-dimensional and rodlike materials plays an important role in many biological processes such as cell mimicking, microtubule protrusion, cell division, frustrated phagocytosis, and pathogenicity. To understand the mechanical interplay between cells/intracellular membranous organelles and encapsulated rodlike materials, we perform theoretical analyses to investigate how the morphologies and mechanical behaviors of lipid vesicles of given relative volumes are regulated by encapsulated rigid nanorods of finite diameters and selected geometries, including a cylindrical nanorod, a nanorod with one widened end, and a cone-shaped nanorod. The contact between the vesicle protrusion and the sidewall of the rod, neglected in most theoretical studies, is shown to play an important role in regulating vesicle tubulation, membrane tension, and axial contact force on the nanorod. As the nanorod length increases, the confining vesicle evolves from a prolate into different shapes, such as a lemon, a conga drum, a cherry, and a bowling pin, depending on the radical size of the nanorod and the relative vesicle volume. The corresponding morphological phase diagrams are determined. Moreover, phase diagrams of the buckling of the encapsulated nanorods are determined based on the classical Euler buckling theory. It is shown that there exists an optimal filament number at which the encapsulated weakly cross-linked filament bundle maintains the largest length in a mechanically stable state. Similarities and differences between the nanorod packing in vesicles at a given pressure difference and a relative volume are discussed. Our results provide valuable insight into the biophysics underlying cell interactions with one-dimensional and rodlike materials.

Guided by curvature: shaping cells by coupling curved membrane proteins and cytoskeletal forces

Eukaryote cells have flexible membranes that allow them to have a variety of dynamical shapes. The shapes of the cells serve important biological functions, both for cells within an intact tissue, and during embryogenesis and cellular motility. How cells control their shapes and the structures that they form on their surface has been a subject of intensive biological research, exposing the building blocks that cells use to deform their membranes. These processes have also drawn the interest of theoretical physicists, aiming to develop models based on physics, chemistry and nonlinear dynamics. Such models explore quantitatively different possible mechanisms that the cells can employ to initiate the spontaneous formation of shapes and patterns on their membranes. We review here theoretical work where one such class of mechanisms was investigated: the coupling between curved membrane proteins, and the cytoskeletal forces that they recruit. Theory indicates that this coupling gives rise to a rich variety of membrane shapes and dynamics, while experiments indicate that this mechanism appears to drive many cellular shape changes.This article is part of the theme issue 'Self-organization in cell biology'.

Tubulation pattern of membrane vesicles coated with biofilaments

Narrow membrane tubes are commonly pulled out from the surface of phospholipid vesicles using forces applied either through laser or magnetic tweezers or through the action of processive motor proteins. Recent examples have emerged in which an array of such tubes grows spontaneously from vesicles coated with bioactive cytoskeletal filaments (e.g., FtsZ, microtubule) in the presence GTP or ATP. We show how a soft vesicle deforms as a result of the interplay between its topology, local curvature, and the forces due to filament bundles. We present results from dynamically triangulated Monte Carlo simulations of a closed membrane vesicle coated with a nematic field (the filaments), and we show how the intrinsic curvature of the filaments and their bundling interactions drive membrane tubulation. We predict interesting patterns consisting of a large number of nematic defects that accompany tubulation. A common theme emerges: defect locations on vesicle surfaces are hot spots of membrane deformation activity, which could be useful for vesicle origami. Although our equilibrium model is not applicable to the nonequilibrium shape dynamics exhibited by active microtubule-coated vesicles, we show that some of the features, such as the size-dependent vesicle shape and the number of tubes, can still be understood from our equilibrium model.

The role of traction in membrane curvature generation

Curvature of biological membranes can be generated by a variety of molecular mechanisms including protein scaffolding, compositional heterogeneity, and cytoskeletal forces. These mechanisms have the net effect of generating tractions (force per unit length) on the bilayer that are translated into distinct shapes of the membrane. Here, we demonstrate how the local shape of the membrane can be used to infer the traction acting locally on the membrane. We show that buds and tubes, two common membrane deformations studied in trafficking processes, have different traction distributions along the membrane and that these tractions are specific to the molecular mechanism used to generate these shapes. Furthermore, we show that the magnitude of an axial force applied to the membrane as well as that of an effective line tension can be calculated from these tractions. Finally, we consider the sensitivity of these quantities with respect to uncertainties in material properties and follow with a discussion on sources of uncertainty in membrane shape.

Tissue Force Programs Cell Fate and Tumor Aggression

Biomechanical and biochemical cues within a tissue collaborate across length scales to direct cell fate during development and are critical for the maintenance of tissue homeostasis. Loss of tensional homeostasis in a tissue not only accompanies malignancy but may also contribute to oncogenic transformation. High mechanical stress in solid tumors can impede drug delivery and may additionally drive tumor progression and promote metastasis. Mechanistically, biomechanical forces can drive tumor aggression by inducing a mesenchymal-like switch in transformed cells so that they attain tumor-initiating or stem-like cell properties. Given that cancer stem cells have been linked to metastasis and treatment resistance, this raises the intriguing possibility that the elevated tissue mechanics in tumors could promote their aggression by programming their phenotype toward that exhibited by a stem-like cell.Significance: Recent findings argue that mechanical stress and elevated mechanosignaling foster malignant transformation and metastasis. Prolonged corruption of tissue tension may drive tumor aggression by altering cell fate specification. Thus, strategies that could reduce tumor mechanics might comprise effective approaches to prevent the emergence of treatment-resilient metastatic cancers. Cancer Discov; 7(11); 1224-37. ©2017 AACR.

On the role of external force of actin filaments in the formation of tubular protrusions of closed membrane shapes with anisotropic membrane components

Biological membranes are composed of different components and there is no a priori reason to assume that all components are isotropic. It was previously shown that the anisotropic properties of membrane components may explain the stability of membrane tubular protrusions even without the application of external force. Our theoretical study focuses on the role of anisotropic membrane components in the stability of membrane tubular structures generated or stabilized by actin filaments. We show that the growth of the actin cytoskeleton inside the vesicle can induce the partial lateral segregation of different membrane components. The entropy of mixing of membrane components hinders the total lateral segregation of the anisotropic and isotropic membrane components. Self-assembled aggregates formed by anisotropic membrane components facilitate the growth of long membrane tubular protrusions. Protrusive force generated by actin filaments favors strong segregation of membrane components by diminishing the opposing effect of mixing entropy.