Quantifying Membrane Curvature Generation of Drosophila Amphiphysin N-BAR Domains

Triacylglycerol-droplet-induced bilayer spontaneous curvature in giant unilamellar vesicles

This study investigated the incorporation of triacylglycerol droplets in the bilayers of giant unilamellar vesicles (GUVs) using four triacylglycerols and four phosphatidylcholines by confocal laser scanning microscopy. The triacylglycerol droplets were incorporated between the monolayer leaflets of the GUVs. Among the spherical droplets protruding on only one side of the bilayers, the droplets bound to the outer leaflets outnumbered those bound to the inner leaflets. The more frequent droplet binding to the outer leaflet caused transbilayer asymmetry in the droplet surface density. A vesicle consisting of a single-bilayer spherical segment and a double-bilayer spherical segment was also observed. The yield of these vesicles was comparable with or higher than that of the droplet-incorporating GUVs for many of the phosphatidylcholine-triacylglycerol combinations. In a vesicle consisting of single-bilayer and double-bilayer segments, most of the triacylglycerol droplets were localized on the outermost membrane surface along the segment boundary and in the double-bilayer segment. To rationalize the formation of these vesicle structures, we propose that the transbilayer asymmetry in the droplet surface density induces spontaneous curvature of the bilayer, with the bilayer spontaneously bending away from the droplets. Energy calculations performed assuming the existence of spontaneous curvature of the bilayer corroborated the experimentally determined membrane shapes for the vesicles consisting of unilamellar and bilamellar regions.

Actin-membrane linkers: Insights from synthetic reconstituted systems

At the cell surface, the actin cytoskeleton and the plasma membrane interact reciprocally in a variety of processes related to the remodeling of the cell surface. The actin cytoskeleton has been known to modulate membrane organization and reshape the membrane. To this end, actin-membrane linking molecules play a major role in regulating actin assembly and spatially direct the interaction between the actin cytoskeleton and the membrane. While studies in cells have provided a wealth of knowledge on the molecular composition and interactions of the actin-membrane interface, the complex molecular interactions make it challenging to elucidate the precise actions of the actin-membrane linkers at the interface. Synthetic reconstituted systems, consisting of model membranes and purified proteins, have been a powerful approach to elucidate how actin-membrane linkers direct actin assembly to drive membrane shape changes. In this review, we will focus only on several actin-membrane linkers that have been studied by using reconstitution systems. We will discuss the design principles of these reconstitution systems and how they have contributed to the understanding of the cellular functions of actin-membrane linkers. Finally, we will provide a perspective on future research directions in understanding the intricate actin-membrane interaction.

Forceful patterning: theoretical principles of mechanochemical pattern formation

Biological pattern formation is essential for generating and maintaining spatial structures from the scale of a single cell to tissues and even collections of organisms. Besides biochemical interactions, there is an important role for mechanical and geometrical features in the generation of patterns. We review the theoretical principles underlying different types of mechanochemical pattern formation across spatial scales and levels of biological organization.

Molecular Dynamics Simulations of Curved Lipid Membranes

Eukaryotic cells contain membranes with various curvatures, from the near-plane plasma membrane to the highly curved membranes of organelles, vesicles, and membrane protrusions. These curvatures are generated and sustained by curvature-inducing proteins, peptides, and lipids, and describing these mechanisms is an important scientific challenge. In addition to that, some molecules can sense membrane curvature and thereby be trafficked to specific locations. The description of curvature sensing is another fundamental challenge. Curved lipid membranes and their interplay with membrane-associated proteins can be investigated with molecular dynamics (MD) simulations. Various methods for simulating curved membranes with MD are discussed here, including tools for setting up simulation of vesicles and methods for sustaining membrane curvature. The latter are divided into methods that exploit scaffolding virtual beads, methods that use curvature-inducing molecules, and methods applying virtual forces. The variety of simulation tools allow researcher to closely match the conditions of experimental studies of membrane curvatures.

Molecular Shape Solution for Mesoscopic Remodeling of Cellular Membranes

Cellular membranes self-assemble from and interact with various molecular species. Each molecule locally shapes the lipid bilayer, the soft elastic core of cellular membranes. The dynamic architecture of intracellular membrane systems is based on elastic transformations and lateral redistribution of these elementary shapes, driven by chemical and curvature stress gradients. The minimization of the total elastic stress by such redistribution composes the most basic, primordial mechanism of membrane curvature-composition coupling (CCC). Although CCC is generally considered in the context of dynamic compositional heterogeneity of cellular membrane systems, in this article we discuss a broader involvement of CCC in controlling membrane deformations. We focus specifically on the mesoscale membrane transformations in open, reservoir-governed systems, such as membrane budding, tubulation, and the emergence of highly curved sites of membrane fusion and fission. We reveal that the reshuffling of molecular shapes constitutes an independent deformation mode with complex rheological properties.This mode controls effective elasticity of local deformations as well as stationary elastic stress, thus emerging as a major regulator of intracellular membrane remodeling.

Quantification of Curvature Sensing Behavior of Curvature-Inducing Proteins on Model Wavy Substrates

Curvature-inducing proteins are involved in a variety of membrane remodeling processes in the cell. Several in vitro experiments have quantified the curvature sensing behavior of these proteins in model lipid systems. One such system consists of a membrane bilayer laid atop a wavy substrate (Hsieh in Langmuir 28:12838-12843, 2012). In these experiments, the bilayer conforms to the wavy substrate, and curvature-inducing proteins show preferential segregation on the wavy membrane. Using a mesoscale computational membrane model based on the Helfrich Hamiltonian, here we present a study which analyzes the curvature sensing characteristics of this membrane-protein system, and elucidates key physical principles governing protein segregation on the wavy substrate and other in vitro systems. In this article we compute the local protein densities from the free energy landscape associated with membrane remodeling by curvature-inducing proteins. In specific, we use the Widom insertion technique to compute the free energy landscape for an inhomogeneous system with spatially varying density and the results obtained with this minimal model show excellent agreement with experimental studies that demonstrate the association between membrane curvature and local protein density. The free energy-based framework employed in this study can be used for different membrane morphologies and varied protein characteristics to gain mechanistic insights into protein sorting on membranes.

Quantifying Membrane Curvature Sensing of Peripheral Proteins by Simulated Buckling and Umbrella Sampling

Membrane curvature plays an essential role in the organization and trafficking of membrane associated proteins. Comparison or prediction of the experimentally resolved protein concentrations adopted at different membrane curvatures requires direct quantification of the relative partitioning free energy. Here, we present a highly efficient and simple to implement a free-energy calculation method which is able to directly resolve the relative partitioning free energy of proteins as a direct function of membrane curvature, i.e., a curvature sensing profile, within (coarse-grained) molecular dynamics simulations. We demonstrate its utility by resolving these profiles for two known curvature sensing peptides, namely ALPS and α-synuclein, for a membrane curvature ranging from -1/6.5 to +1/6.5 nm^-1. We illustrate that the difference in relative partitioning (binding) free energy between these two extrema is only about 13 k_BT for both peptides, illustrating that the driving force of curvature sensing is subtle. Furthermore, we illustrate that ALPS and α-synuclein sense curvature via a contrasting mechanism, which is differentially affected by membrane composition. In addition, we demonstrate that the intrinsic spontaneous curvature of both of these peptides lies beyond the range of membrane curvature accessible in micropipette aspiration experiments, being about 1/7 nm ^-1. Our approach offers an efficient and simple to implement in silico tool for exploring and screening the membrane curvature sensing mechanisms of proteins.

Recent developments in membrane curvature sensing and induction by proteins

BACKGROUND

Membrane-bound intracellular organelles have characteristic shapes attributed to different local membrane curvatures, and these attributes are conserved across species. Over the past decade, it has been confirmed that specific proteins control the large curvatures of the membrane, whereas many others due to their specific structural features can sense the curvatures and bind to the specific geometrical cues. Elucidating the interplay between sensing and induction is indispensable to understand the mechanisms behind various biological processes such as vesicular trafficking and budding.

SCOPE OF REVIEW

We provide an overview of major classes of membrane proteins and the mechanisms of curvature sensing and induction. We then discuss the importance of membrane elastic characteristics to induce the membrane shapes similar to intracellular organelles. Finally, we survey recently available assays developed for studying the curvature sensing and induction by many proteins.

MAJOR CONCLUSIONS

Recent theoretical/computational modeling along with experimental studies have uncovered fascinating connections between lipid membrane and protein interactions. However, the phenomena of protein localization and synchronization to generate spatiotemporal dynamics in membrane morphology are yet to be fully understood.

GENERAL SIGNIFICANCE

The understanding of protein-membrane interactions is essential to shed light on various biological processes. This further enables the technological applications of many natural proteins/peptides in therapeutic treatments. The studies of membrane dynamic shapes help to understand the fundamental functions of membranes, while the medicinal roles of various macromolecules (such as proteins, peptides, etc.) are being increasingly investigated.

The Mechanics and Thermodynamics of Tubule Formation in Biological Membranes

Membrane tubulation is a ubiquitous process that occurs both at the plasma membrane and on the membranes of intracellular organelles. These tubulation events are known to be mediated by forces applied on the membrane either due to motor proteins, by polymerization of the cytoskeleton, or due to the interactions between membrane proteins binding onto the membrane. The numerous experimental observations of tube formation have been amply supported by mathematical modeling of the associated membrane mechanics and have provided insights into the force-displacement relationships of membrane tubes. Recent advances in quantitative biophysical measurements of membrane-protein interactions and tubule formation have necessitated the need for advances in modeling that will account for the interplay of multiple aspects of physics that occur simultaneously. Here, we present a comprehensive review of experimental observations of tubule formation and provide context from the framework of continuum modeling. Finally, we explore the scope for future research in this area with an emphasis on iterative modeling and experimental measurements that will enable us to expand our mechanistic understanding of tubulation processes in cells.

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.

Annexin A4 trimers are recruited by high membrane curvatures in giant plasma membrane vesicles

The plasma membrane (PM) of eukaryotic cells consists of a crowded environment comprised of a high diversity of proteins in a complex lipid matrix. The lateral organization of membrane proteins in the PM is closely correlated with biological functions such as endocytosis, membrane budding and other processes which involve protein mediated shaping of the membrane into highly curved structures. Annexin A4 (ANXA4) is a prominent player in a number of biological functions including PM repair. Its binding to membranes is activated by Ca2+ influx and it is therefore rapidly recruited to the cell surface near rupture sites where Ca2+ influx takes place. However, the free edges near rupture sites can easily bend into complex curvatures and hence may accelerate recruitment of curvature sensing proteins to facilitate rapid membrane repair. To analyze the curvature sensing behavior of curvature inducing proteins in crowded membranes, we quantifify the affinity of ANXA4 monomers and trimers for high membrane curvatures by extracting membrane nanotubes from giant PM vesicles (GPMVs). ANXA4 is found to be a sensor of negative membrane curvatures. Multiscale simulations, in which we extract molecular information from atomistic scale simulations as input to our macroscopic scale simulations, furthermore predicted that ANXA4 trimers generate membrane curvature upon binding and have an affinity for highly curved membrane regions only within a well defined membrane curvature window. Our results indicate that curvature sensing and mobility of ANXA4 depend on the trimer structure of ANXA4 which could provide new biophysical insight into the role of ANXA4 in membrane repair and other biological processes.

Nanobar Array Assay Revealed Complementary Roles of BIN1 Splice Isoforms in Cardiac T-Tubule Morphogenesis

Bridging integrator-1 (BIN1) is a family of banana-shaped molecules implicated in cell membrane tubulation. To understand the curvature sensitivity and functional roles of BIN1 splicing isoforms, we engineered vertical nanobars on a cell culture substrate to create high and low curvatures. When expressed individually, BIN1 isoforms with phosphoinositide-binding motifs (pBIN1) appeared preferentially at high-curvature nanobar ends, agreeing well with their membrane tubulation in cardiomyocytes. In contrast, the ubiquitous BIN1 isoform without phosphoinositide-binding motif (uBIN1) exhibited no affinity to membranes around nanobars but accumulated along Z-lines in cardiomyocytes. Importantly, in pBIN1-uBIN1 coexpression, pBIN1 recruited uBIN1 to high-curvature membranes at nanobar ends, and uBIN1 attached the otherwise messy pBIN1 tubules to Z-lines. The complementary cooperation of BIN1 isoforms (comboBIN1) represents a novel mechanism of T-tubule formation along Z-lines in cardiomyocytes. Dysregulation of BIN1 splicing, e.g., during myocardial infarction, underlied T-tubule disorganization, and correction of uBIN1/pBIN1 stoichiometry rescued T-tubule morphology in heart disease.

Simple differences in the protein-membrane attachment mechanism have functional consequences for surface mechanics

This paper describes two methods for propagating coupled membrane and embedded particle dynamics with ensembles that are valid to second order in the deformation of the membrane. Proteins and functional lipids associate with cellular membranes, and their attachments influence membrane physical and dynamical properties. Therefore, it is necessary to accurately model the coupled dynamics of the membrane and any associated material of interest. We have developed two methods for coupling membrane and particle dynamics that differ in the binding mechanism of the particle to the surface. The "on-surface" mechanism should be used for particles that slide along the membrane; this description leads to an effective reduction in the membrane surface tension. The "in-surface" mechanism treats the particles as tightly bound to the lipidic binding sites; the method avoids double counting lateral entropy of implicitly modeled lipids. We emphasize the differences between these two mechanisms, when it is appropriate to use them, and how the methods differ from previously used dynamic methods.

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.

PIP2 Reshapes Membranes through Asymmetric Desorption

Phosphatidylinositol-4,5-bisphosphate (PIP2) is an important signaling lipid in eukaryotic cell plasma membranes, playing an essential role in diverse cellular processes. The headgroup of PIP2 is highly negatively charged, and this lipid displays a high critical micellar concentration compared to housekeeping phospholipid analogs. Given the crucial role of PIP2, it is imperative to study its localization, interaction with proteins, and membrane-shaping properties. Biomimetic membranes have served extensively to elucidate structural and functional aspects of cell membranes including protein-lipid and lipid-lipid interactions, as well as membrane mechanics. Incorporation of PIP2 into biomimetic membranes, however, has at times resulted in discrepant findings described in the literature. With the goal to elucidate the mechanical consequences of PIP2 incorporation, we studied the desorption of PIP2 from biomimetic giant unilamellar vesicles by means of a fluorescent marker. A decrease in fluorescence intensity with the age of the vesicles suggested that PIP2 lipids were being desorbed from the outer leaflet of the membrane. To evaluate whether this desorption was asymmetric, the vesicles were systematically diluted. This resulted in an increase in the number of internally tubulated vesicles within minutes after dilution, suggesting that the desorption was asymmetric and also generated membrane curvature. By means of a saturated chain homolog of PIP2, we showed that the fast desorption of PIP2 is facilitated by presence of an arachidonic lipid tail and is possibly due to its oxidation. Through measurements of the pulling force of membrane tethers, we quantified the effect of this asymmetric desorption on the spontaneous membrane curvature. Furthermore, we found that the spontaneous curvature could be modulated by externally increasing the concentration of PIP2 micelles. Given that the local concentration of PIP2 in biological membranes is variable, spontaneous curvature generated by PIP2 may affect the formation of highly curved structures that can serve as initiators for signaling events.

Electroformation of Giant Unilamellar Vesicles on Stainless Steel Electrodes

Giant unilamellar vesicles (GUVs) are well-established model systems for studying membrane structure and dynamics. Electroformation, also referred to as electroswelling, is one of the most prevalent methods for producing GUVs, as it enables modulation of the lipid hydration process to form relatively monodisperse, defect-free vesicles. Currently, however, it is expensive and time-consuming compared with other methods. In this study, we demonstrate that 1,2-dioleoyl-sn-glycero-3-phosphatidylcholine GUVs can be prepared readily at a fraction of the cost on stainless steel electrodes, such as commercially available syringe needles, without any evidence of lipid oxidation or hydrolysis.

Multipole analysis of the strain-mediated coupling between proteins adsorbed at tubular lipid membrane surface

The tubular lipid membranes (TLMs) pulled out from vesicles are often used in in vitro studies of the interactions between curvature-inducing proteins and highly curved membranes. The protein molecules adsorbed at the membrane surface deform the TLM and couple with each other due to the induced strain. Here we propose an approach which models the single curvature-inducing protein action on the lipid bilayer by the multipole, the superposition of the point forces applied to the membrane in the region of the protein adsorption. We show that to be localized in the area of the protein size at the TLM surface, the force multipoles satisfying the mechanical equilibrium conditions should be composed of three or more point forces. The protein coupling energy mediated by the membrane strain is studied in detail. In the region of the tubular membrane stability the maximal distance between two neighboring interacting protein-induced force multipoles is estimated to be of the order of the TLM cross section perimeter. In the vicinity of the TLM instability in the region of the vanishing stretching force applied to the TLM, the interaction radius increases drastically. The high affinity of the single curvature-inducing protein molecule to the regions in the vicinity of the TLM ends is explained and related to the boundary conditions in the experimental set-ups. The reasons for the aggregate formation on the membrane surface are also discussed.

Suppressing membrane height fluctuations leads to a membrane-mediated interaction among proteins

Membrane-induced interactions can play a significant role in the spatial distribution of membrane-bound proteins. We develop a model that combines a continuum description of lipid bilayers with a discrete particle model of proteins to probe the emerging structure of the combined membrane-protein system. Our model takes into account the membrane's elastic behavior, the steric repulsion between proteins, and the quenching of membrane shape fluctuations due to the presence of the proteins. We employ coupled Langevin equations to describe the dynamics of the system. We show that coupling to the membrane induces an attractive interaction among proteins, which may contribute to the clustering of proteins in biological membranes. We investigate the lateral protein diffusion and find that it is reduced due to transient fluctuations in membrane shape.

Curvature-driven assembly in soft matter

Control over the spatial arrangement of colloids in soft matter hosts implies control over a wide variety of properties, ranging from the system's rheology, optics, and catalytic activity. In directed assembly, colloids are typically manipulated using external fields to form well-defined structures at given locations. We have been developing alternative strategies based on fields that arise when a colloid is placed within soft matter to form an inclusion that generates a potential field. Such potential fields allow particles to interact with each other. If the soft matter host is deformed in some way, the potential allows the particles to interact with the global system distortion. One important example is capillary assembly of colloids on curved fluid interfaces. Upon attaching, the particle distorts that interface, with an associated energy field, given by the product of its interfacial area and the surface tension. The particle's capillary energy depends on the local interface curvature. We explore this coupling in experiment and theory. There are important analogies in liquid crystals. Colloids in liquid crystals elicit an elastic energy response. When director fields are moulded by confinement, the imposed elastic energy field can couple to that of the colloid to define particle paths and sites for assembly. By improving our understanding of these and related systems, we seek to develop new, parallelizable routes for particle assembly to form reconfigurable systems in soft matter that go far beyond the usual close-packed colloidal structures.This article is part of the themed issue 'Soft interfacial materials: from fundamentals to formulation'.

Membrane remodeling and mechanics: Experiments and simulations of α-Synuclein

We review experimental and simulation approaches that have been used to determine curvature generation and remodeling of lipid bilayers by membrane-bending proteins. Particular emphasis is placed on the complementary approaches used to study α-Synuclein (αSyn), a major protein involved in Parkinson's disease (PD). Recent cellular and biophysical experiments have shown that the protein 1) deforms the native structure of mitochondrial and model membranes; and 2) inhibits vesicular fusion. Today's advanced experimental and computational technology has made it possible to quantify these protein-induced changes in membrane shape and material properties. Collectively, experiments, theory and multi-scale simulation techniques have established the key physical determinants of membrane remodeling and rigidity: protein binding energy, protein partition depth, protein density, and membrane tension. Despite the exciting and significant progress made in recent years in these areas, challenges remain in connecting biophysical insights to the cellular processes that lead to disease. This article is part of a Special Issue entitled: Membrane Proteins edited by J.C. Gumbart and Sergei Noskov.

Osmotically-induced tension and the binding of N-BAR protein to lipid vesicles

The binding affinity of a curvature-sensing protein domain (N-BAR) is measured as a function of applied osmotic stress while the membrane curvature is nearly constant. Varying the osmotic stress allows us to control membrane tension, which provides a probe of the mechanism of binding. We study the N-BAR domain of the Drosophila amphiphysin and monitor its binding on 50 nm-radius vesicles composed of 90 mol% DOPC and 10 mol% PIP. We find that the bound fraction of N-BAR is enhanced by a factor of approximately 6.5 when the tension increases from zero to 2.6 mN m(-1). This tension-induced response can be explained by the hydrophobic insertion mechanism. From the data we extract a hydrophobic domain area that is consistent with known structure. These results indicate that membrane stress and strain could play a major role in the previously reported curvature-affinity of N-BAR.

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

Membrane deformations induced by attached BAR superfamily domains could trigger or facilitate the growth of plasma membrane protrusions. The BAR domain family consists of BAR, F-BAR and I-BAR domains, each enforcing a different local curvature when attached to the membrane surface. Our theoretical study mainly focuses on the role of I-BAR in the membrane tubular deformations generated or stabilised by actin filaments. The influence of the area density of membrane attached BAR domains and their intrinsic curvature on the closed membrane shapes (vesicles) was investigated numerically. We derived an analytical approximative expression for the critical relative area density of BARs at which the membrane tubular protrusions on vesicles are most prominent. We have shown that the BARs with a higher intrinsic curvature induce thinner and longer cylindrical protrusions. The average orientation of the membrane attached BARs is altered when the vesicle shape is subjected to external force of growing actin rod-like structure inside a vesicle. The average orientation angle of membrane attached BARs may indicate whether the actin filaments are just stabilising the protrusion or generating it by stretching the vesicle.

Mutations in BIN1 associated with centronuclear myopathy disrupt membrane remodeling by affecting protein density and oligomerization

The regulation of membrane shapes is central to many cellular phenomena. Bin/Amphiphysin/Rvs (BAR) domain-containing proteins are key players for membrane remodeling during endocytosis, cell migration, and endosomal sorting. BIN1, which contains an N-BAR domain, is assumed to be essential for biogenesis of plasma membrane invaginations (T-tubules) in muscle tissues. Three mutations, K35N, D151N and R154Q, have been discovered so far in the BAR domain of BIN1 in patients with centronuclear myopathy (CNM), where impaired organization of T-tubules has been reported. However, molecular mechanisms behind this malfunction have remained elusive. None of the BIN1 disease mutants displayed a significantly compromised curvature sensing ability. However, two mutants showed impaired membrane tubulation both in vivo and in vitro, and displayed characteristically different behaviors. R154Q generated smaller membrane curvature compared to WT N-BAR. Quantification of protein density on membranes revealed a lower membrane-bound density for R154Q compared to WT and the other mutants, which appeared to be the primary reason for the observation of impaired deformation capacity. The D151N mutant was unable to tubulate liposomes under certain experimental conditions. At medium protein concentrations we found 'budding' structures on liposomes that we hypothesized to be intermediates during the tubulation process except for the D151N mutant. Chemical crosslinking assays suggested that the D151N mutation impaired protein oligomerization upon membrane binding. Although we found an insignificant difference between WT and K35N N-BAR in in vitro assays, depolymerizing actin in live cells allowed tubulation of plasma membranes through the K35N mutant. Our results provide insights into the membrane-involved pathophysiological mechanisms leading to human disease.

FBAR syndapin 1 recognizes and stabilizes highly curved tubular membranes in a concentration dependent manner

Syndapin 1 FBAR, a member of the Bin-amphiphysin-Rvs (BAR) domain protein family, is known to induce membrane curvature and is an essential component in biological processes like endocytosis and formation and growth of neurites. We quantify the curvature sensing of FBAR on reconstituted porcine brain lipid vesicles and show that it senses membrane curvature at low density whereas it induces and reinforces tube stiffness at higher density. FBAR strongly up-concentrates on the high curvature tubes pulled out of Giant Unilamellar lipid Vesicles (GUVs), this sorting behavior is strongly amplified at low protein densities. Interestingly, FBAR from syndapin 1 has a large affinity for tubular membranes with curvatures larger than its own intrinsic concave curvature. Finally, we studied the effect of FBAR on membrane relaxation kinetics with high temporal resolution and found that the protein increases relaxation time of the tube holding force in a density-dependent fashion.

Separation of components in lipid membranes induced by shape transformation

Vesicles composed of a two component membrane with each component characterized by different spontaneous curvature are investigated by minimization of the free energy consisting of Helfrich elastic energy and entropy of mixing. The results show that mixing and demixing of membrane components can be induced by elongating a vesicle or changing its volume, if one of the components forms a complex with macromolecules on the outer monolayer. The influence of elastic coefficients on the separation of components is also examined.

Nonlinear sorting, curvature generation, and crowding of endophilin N-BAR on tubular membranes

The curvature of biological membranes is controlled by membrane-bound proteins. For example, during endocytosis, the sorting of membrane components, vesicle budding, and fission from the plasma membrane are mediated by adaptor and accessory proteins. Endophilin is a peripherally binding membrane protein that functions as an endocytic accessory protein. Endophilin's membrane tubulation capacity is well known. However, to understand the thermodynamic and mechanical aspects of endophilin function, experimental measurements need to be compared to quantitative theoretical models. We present measurements of curvature sorting and curvature generation of the endophilin A1 N-BAR domain on tubular membranes pulled from giant unilamellar vesicles. At low concentration, endophilin functions primarily as a membrane curvature sensor; at high concentrations, it also generates curvature. We determine the spontaneous curvature induced by endophilin and observe sigmoidal curvature/composition coupling isotherms that saturate at high membrane tensions and protein solution concentrations. The observation of saturation is supported by a strong dependence of lateral diffusion coefficients on protein density on the tether membrane. We develop a nonlinear curvature/composition coupling model that captures our experimental observations. Our model predicts a curvature-induced phase transition among two states with varying protein density and membrane curvature. This transition could act as a switch during endocytosis.

Curvature sorting of peripheral proteins on solid-supported wavy membranes

Cellular membrane deformation and the associated redistribution of membrane-bound proteins are important aspects of membrane function. Current model membrane approaches for studying curvature sensing are limited to positive curvatures and often require complex and delicate experimental setups. To overcome these challenges, we fabricated a wavy substrate by imposing a range of curvatures onto an adhering lipid bilayer membrane. We examined the curvature sorting of several peripheral proteins binding to the wavy membrane and observed them to partition into distinct regions of curvature. Furthermore, single-molecule imaging experiments suggested that the curvature sensing of proteins on low-curvature substrates requires cooperative interactions.

Nature of curvature coupling of amphiphysin with membranes depends on its bound density

Cells are populated by a vast array of membrane-binding proteins that execute critical functions. Functions, like signaling and intracellular transport, require the abilities to bind to highly curved membranes and to trigger membrane deformation. Among these proteins is amphiphysin 1, implicated in clathrin-mediated endocytosis. It contains a Bin-Amphiphysin-Rvs membrane-binding domain with an N-terminal amphipathic helix that senses and generates membrane curvature. However, an understanding of the parameters distinguishing these two functions is missing. By pulling a highly curved nanotube of controlled radius from a giant vesicle in a solution containing amphiphysin, we observed that the action of the protein depends directly on its density on the membrane. At low densities of protein on the nearly flat vesicle, the distribution of proteins and the mechanical effects induced are described by a model based on spontaneous curvature induction. The tube radius and force are modified by protein binding but still depend on membrane tension. In the dilute limit, when practically no proteins were present on the vesicle, no mechanical effects were detected, but strong protein enrichment proportional to curvature was seen on the tube. At high densities, the radius is independent of tension and vesicle protein density, resulting from the formation of a scaffold around the tube. As a consequence, the scaling of the force with tension is modified. For the entire density range, protein was enriched on the tube as compared to the vesicle. Our approach shows that the strength of curvature sensing and mechanical effects on the tube depends on the protein density.

On the role of membrane anisotropy and BAR proteins in the stability of tubular membrane structures

Recent studies have demonstrated that actin filaments are not crucial for the short-term stability of tubular membrane protrusions originating from the cell surface. It has also been demonstrated that prominin nanodomains and curvature inducing I-BAR proteins could account for the stability of the membrane protrusion. Here we constructed an axisymmetric model of a membrane protrusion that excludes actin filaments in order to investigate the contributions of prominin nanodomains (rafts) and I-BAR proteins to the membrane protrusion stability. It was demonstrated that prominin nanodomains and I-BAR proteins can stabilize the membrane protrusion only over a specific range of spontaneous curvature. On the other hand, high spontaneous curvature and/or high density of I-BAR proteins could lead to system instability and to non-uniform contraction in the radial direction of the membrane protrusion. In agreement with previous studies, it was also shown that the isotropic bending energy of lipids is not sufficient to explain the stability of the observed tubular membrane protrusion without actin filaments.

Shapes of discoid intracellular compartments with small relative volumes

A prominent feature of many intracellular compartments is a large membrane surface area relative to their luminal volume, i.e., the small relative volume. In this study we present a theoretical analysis of discoid membrane compartments with a small relative volume and then compare the theoretical results to quantitative morphological assessment of fusiform vesicles in urinary bladder umbrella cells. Specifically, we employ three established extensions of the standard approach to lipid membrane shape calculation and determine the shapes that could be expected according to three scenarios of membrane shaping: membrane adhesion in the central discoid part, curvature driven lateral segregation of membrane constituents, and existence of stiffer membrane regions, e.g., support by protein scaffolds. The main characteristics of each scenario are analyzed. The results indicate that even though all three scenarios can lead to similar shapes, there are values of model parameters that yield qualitatively distinctive shapes. Consequently, a distinctive shape of an intracellular compartment may reveal its membrane shaping mechanism and the membrane structure. The observed shapes of fusiform vesicles fall into two qualitatively different classes, yet they are all consistent with the theoretical results and the current understanding of their structure and function.

Thermodynamics and mechanics of membrane curvature generation and sensing by proteins and lipids

Research investigating lipid membrane curvature generation and sensing is a rapidly developing frontier in membrane physical chemistry and biophysics. The fast recent progress is based on the discovery of a plethora of proteins involved in coupling membrane shape to cellular membrane function, the design of new quantitative experimental techniques to study aspects of membrane curvature, and the development of analytical theories and simulation techniques that allow a mechanistic interpretation of quantitative measurements. The present review first provides an overview of important classes of membrane proteins for which function is coupled to membrane curvature. We then survey several mechanisms that are assumed to underlie membrane curvature sensing and generation. Finally, we discuss relatively simple thermodynamic/mechanical models that allow quantitative interpretation of experimental observations.