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

Distinct Bin/Amphiphysin/Rvs (BAR) family proteins may assemble on the same tubule to regulate membrane organization in vivo

Intracellular membrane tubules play a crucial role in diverse cellular processes, and their regulation is facilitated by Bin-Amphiphysin-Rvs (BAR) domain-containing proteins. This study investigates the roles of Drosophila ICA69 (dICA69) (an N-BAR protein) and Drosophila CIP4 (dCIP4) (an F-BAR protein), focusing on their impact on in vivo membrane tubule organization. In contrast to the prevailing models of BAR-domain protein function, we observed colocalization of endogenous dICA69 with dCIP4-induced tubules, indicating their potential recruitment for tubule formation and maintenance. Moreover, actin-regulatory proteins such as Wasp, SCAR, and Arp2/3 were recruited at the site of CIP4-induced tubule formation. An earlier study indicated that F-BAR proteins spontaneously segregate from the N-BAR domain proteins during membrane tubule formation. In contrast, our observation supports a model in which different BAR-domain family members can associate with the same tubule and cooperate to fine-tune the tubule width, possibly by recruiting actin modulators during the generation of tubules. Our data suggests that cooperative activities of distinct BAR-domain family proteins may determine the length and width of the membrane tubule in vivo.

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.

Quantification of membrane geometry and protein sorting on cell membrane protrusions using fluorescence microscopy

Plasma membranes are flexible and can exhibit numerous shapes below the optical diffraction limit. The shape of cell periphery can either induce or be a product of local protein density changes, encoding numerous cellular functions. However, quantifying membrane curvature and the ensuing sorting of proteins in live cells remains technically demanding. Here, we demonstrate the use of simple widefield fluorescence microscopy to study the geometrical properties (i.e., radius, length, and number) of thin membrane protrusions. Importantly, the quantification of protrusion radius establishes a platform for studying the curvature preferences of membrane proteins.

Intercellular Receptor-ligand Binding: Effect of Protein-membrane Interaction

Gaining insights into the intercellular receptor-ligand binding is of great importance for understanding numerous physiological and pathological processes, and stimulating new strategies in drug design and discovery. In contrast to the in vitro protein interaction in solution, the anchored receptor and ligand molecules interact with membrane in situ, which affects the intercellular receptor-ligand binding. Here, we review theoretical, simulation and experimental works regarding the regulatory effects of protein-membrane interactions on intercellular receptor-ligand binding mainly from the following aspects: membrane fluctuations, membrane curvature, glycocalyx, and lipid raft. In addition, we discuss biomedical significances and possible research directions to advance the field and highlight the importance of understanding of coupling effects of these factors in pharmaceutical development.

Membrane curvature governs the distribution of Piezo1 in live cells

Piezo1 is a bona fide mechanosensitive ion channel ubiquitously expressed in mammalian cells. The distribution of Piezo1 within a cell is essential for various biological processes including cytokinesis, cell migration, and wound healing. However, the underlying principles that guide the subcellular distribution of Piezo1 remain largely unexplored. Here, we demonstrate that membrane curvature serves as a key regulator of the spatial distribution of Piezo1 in the plasma membrane of living cells. Piezo1 depletes from highly curved membrane protrusions such as filopodia and enriches to nanoscale membrane invaginations. Quantification of the curvature-dependent sorting of Piezo1 directly reveals the in situ nano-geometry of the Piezo1-membrane complex. Piezo1 density on filopodia increases upon activation, independent of calcium, suggesting flattening of the channel upon opening. Consequently, the expression of Piezo1 inhibits filopodia formation, an effect that diminishes with channel activation.

A mechanical-thermodynamic model for understanding endocytosis of COVID-19 virus SARS-CoV-2

We analyze the endocytosis process of COVID-19 (coronavirus disease 2019) virus SARS-CoV-2 (severe acute respiratory syndrome coronavirus 2) using a mechanical-thermodynamic model. The virus particle is designed to interface with the cell membrane as a hard sphere. The role of cytoplasmic BAR (Bin/Amphiphysin/RVs) proteins is considered in the endocytosis. Interestingly, the Endophilin N-BAR cytoplasmic proteins show resistance in participating endocytosis, whereas F-BAR, Arfaptin BAR, Amphiphysin N-BAR, and PX-BAR proteins participate in endocytosis. The increase in membrane tension, concentrated force between the cell membrane receptor, and spike glycoprotein present on the surface of virus particle promote the endocytosis. Also, the increase in the bending modulus of membrane leads to the two-phase solution of BAR protein concentration on the interior of cell membrane surface. We observe an unstable region of protein concentration, which may help one to retard the endocytosis process and thus the viral infection. Though the present study is focused on SARS-CoV-2, it can be extended to understand any other viral infections, involving endocytosis process.

Curvature dependence of BAR protein membrane association and dissociation kinetics

BAR (Bin/Amphiphysin/Rvs) domain containing proteins function as lipid bilayer benders and curvature sensors, and they contribute to membrane shaping involved in cell signaling and metabolism. The mechanism for their membrane shape sensing has been investigated by both equilibrium binding and kinetic studies. In prior research, stopped-flow spectroscopy has been used to deduce a positive dependence on membrane curvature for the binding rate constant, k_on, of a BAR protein called endophilin. However, the impact of bulk diffusion of endophilin, on the kinetic binding parameters has not been thoroughly considered. Employing similar methods, and using lipid vesicles of multiple sizes, we obtained a linear dependence of k_on on vesicle curvature. However, we found that the observed relation can be explained without considering the local curvature sensing ability of endophilin in the membrane association process. In contrast, the diffusion-independent unbinding rate constant (k_off) obtained from stopped-flow measurements shows a negative dependence on membrane curvature, which is controlled/mediated by endophilin-membrane interactions. This latter dependency, in addition to protein-protein interactions on the membrane, explains the selective binding of BAR proteins to highly curved membranes in equilibrium binding experiments.

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.

Binding of anisotropic curvature-inducing proteins onto membrane tubes

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

Insights into Membrane Curvature Sensing and Membrane Remodeling by Intrinsically Disordered Proteins and Protein Regions

Cellular membranes are highly dynamic in shape. They can rapidly and precisely regulate their shape to perform various cellular functions. The protein’s ability to sense membrane curvature is essential in various biological events such as cell signaling and membrane trafficking. As they are bound, these curvature-sensing proteins may also change the local membrane shape by one or more curvature driving mechanisms. Established curvature-sensing/driving mechanisms rely on proteins with specific structural features such as amphipathic helices and intrinsically curved shapes. However, the recent discovery and characterization of many proteins have shattered the protein structure–function paradigm, believing that the protein functions require a unique structural feature. Typically, such structure-independent functions are carried either entirely by intrinsically disordered proteins or hybrid proteins containing disordered regions and structured domains. It is becoming more apparent that disordered proteins and regions can be potent sensors/inducers of membrane curvatures. In this article, we outline the basic features of disordered proteins and regions, the motifs in such proteins that encode the function, membrane remodeling by disordered proteins and regions, and assays that may be employed to investigate curvature sensing and generation by ordered/disordered proteins.

Sorting of proteins with shape and curvature anisotropy on a lipid bilayer tube

Curvature induced sorting of lipid membrane bound proteins has been widely studied through experiments that induce curvature variation in a giant unilamellar lipid-bilayer vesicle with adsorbed proteins by pulling thin cylindrical tethers. In the theoretical space, this has been supplemented with models that capture curvature dependent interaction between membrane and idealized protein particles, through free energy contributions. Many membrane proteins such as the BAR domain proteins are known to have extremely anisotropic shapes and soft interacting potentials, whereas the idealizations of protein particles explored in models have only assumed them as hard disk-like particles with curvature anisotropy. Here, we present a model of sorting of the proteins while including the effects of softness in their interaction potentials, shape anisotropy in the protein structure, and curvature anisotropy in the interactions with the membrane. This is based on a clean separation of free energy contributions from non-ideal fluid behavior of soft anisotropic particles and curvature interactions between proteins and membranes. We probe the behavior of the sorting function under limiting conditions and show that it converges to the previously derived models. In addition to this, we present a comparison of the variation in sorting ratio due to the observed variation in the shape parameter values in known membrane proteins. Finally, using published experimental data for membrane proteins, we perform fitting and derive model parameters. We observe that shape anisotropy adversely affects the sorting of proteins to a high curvature region, whereas curvature anisotropy and softer interaction between proteins favor sorting.

Unfolding Mechanisms and Conformational Stability of the Dimeric Endophilin N-BAR Domain

Endophilin, which is a member of the Bin-amphiphysin-Rvs (BAR) domain protein superfamily, contains a homodimeric N-BAR domain of a characteristic crescent shape. The N-BAR domain comprises a six-helix bundle and is known to sense and generate membrane curvature. Here, we characterize aspects of the unfolding mechanism of the endophilin A1 N-BAR domain during thermal denaturation and examine factors that influence the thermal stability of this domain. Far-UV circular dichroism (CD) spectroscopy was applied to monitor changes in the secondary structure above room temperature. The protein's conformational changes were further characterized through Foerster resonance energy transfer and cross-linking experiments at varying temperatures. Our results indicate that thermal unfolding of the endophilin N-BAR is (minimally) a two-step process, with a dimeric intermediate that displays partial helicity loss. Furthermore, a thermal shift assay and temperature-dependent CD were applied to compare the unfolding processes of several truncated versions of endophilin. The melting temperature of the N-BAR domain decreased when we deleted either the N-terminal H0 helix or the unstructured linker of endophilin. This result suggests that these intrinsically disordered domains may play a role in structurally stabilizing the functional N-BAR domain in vivo. Finally, we show that single-site mutations can also compromise endophilin's thermal stability.

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.

FisB relies on homo-oligomerization and lipid binding to catalyze membrane fission in bacteria

Little is known about mechanisms of membrane fission in bacteria despite their requirement for cytokinesis. The only known dedicated membrane fission machinery in bacteria, fission protein B (FisB), is expressed during sporulation in Bacillus subtilis and is required to release the developing spore into the mother cell cytoplasm. Here, we characterized the requirements for FisB-mediated membrane fission. FisB forms mobile clusters of approximately 12 molecules that give way to an immobile cluster at the engulfment pole containing approximately 40 proteins at the time of membrane fission. Analysis of FisB mutants revealed that binding to acidic lipids and homo-oligomerization are both critical for targeting FisB to the engulfment pole and membrane fission. Experiments using artificial membranes and filamentous cells suggest that FisB does not have an intrinsic ability to sense or induce membrane curvature but can bridge membranes. Finally, modeling suggests that homo-oligomerization and trans-interactions with membranes are sufficient to explain FisB accumulation at the membrane neck that connects the engulfment membrane to the rest of the mother cell membrane during late stages of engulfment. Together, our results show that FisB is a robust and unusual membrane fission protein that relies on homo-oligomerization, lipid binding, and the unique membrane topology generated during engulfment for localization and membrane scission, but surprisingly, not on lipid microdomains, negative-curvature lipids, or curvature sensing.

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.

ER-to-Golgi protein delivery through an interwoven, tubular network extending from ER

Cellular versatility depends on accurate trafficking of diverse proteins to their organellar destinations. For the secretory pathway (followed by approximately 30% of all proteins), the physical nature of the vessel conducting the first portage (endoplasmic reticulum [ER] to Golgi apparatus) is unclear. We provide a dynamic 3D view of early secretory compartments in mammalian cells with isotropic resolution and precise protein localization using whole-cell, focused ion beam scanning electron microscopy with cryo-structured illumination microscopy and live-cell synchronized cargo release approaches. Rather than vesicles alone, the ER spawns an elaborate, interwoven tubular network of contiguous lipid bilayers (ER exit site) for protein export. This receptacle is capable of extending microns along microtubules while still connected to the ER by a thin neck. COPII localizes to this neck region and dynamically regulates cargo entry from the ER, while COPI acts more distally, escorting the detached, accelerating tubular entity on its way to joining the Golgi apparatus through microtubule-directed movement.

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

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

Endophilin recruitment drives membrane curvature generation through coincidence detection of GPCR loop interactions and negative lipid charge

Endophilin plays key roles during endocytosis of cellular receptors, including generating membrane curvature to drive internalization. Electrostatic interactions between endophilin's BIN/Amphiphysin/Rvs domain and anionic membrane lipids have been considered the major driving force in curvature generation. However, the SH3 domain of endophilin also interacts with the proline-rich third intracellular loop (TIL) of various G-protein-coupled receptors (GPCRs), and it is unclear whether this interaction has a direct role in generating membrane curvature during endocytosis. To examine this, we designed model membranes with a membrane density of 1400 receptors per μm2 represented by a covalently conjugated TIL region from the β1-adrenergic receptor. We observed that TIL recruits endophilin to membranes composed of 95 mol% of zwitterionic lipids via the SH3 domain. More importantly, endophilin recruited via TIL tubulates vesicles and gets sorted onto highly curved membrane tubules. These observations indicate that the cellular membrane bending and curvature sensing activities of endophilin can be facilitated through detection of the TIL of activated GPCRs in addition to binding to anionic lipids. Furthermore, we show that TIL electrostatically interacts with membranes composed of anionic lipids. Therefore, anionic lipids can modulate TIL/SH3 domain binding. Overall, our findings imply that an interplay between TIL, charged membrane lipids, BAR domain, and SH3 domain could exist in the biological system and that these components may act in coordination to regulate the internalization of cellular receptors.

A Förster Resonance Energy Transfer-Based Sensor of Steric Pressure on Membrane Surfaces

Cellular membranes are densely covered by proteins. Steric pressure generated by protein collisions plays a significant role in shaping and curving biological membranes. However, no method currently exists for measuring steric pressure at membrane surfaces. Here, we developed a sensor based on Förster resonance energy transfer (FRET), which uses the principles of polymer physics to precisely detect changes in steric pressure. The sensor consists of a polyethylene glycol chain tethered to the membrane surface. The polymer has a donor fluorophore at its free end, such that FRET with acceptor fluorophores in the membrane provides a real-time readout of polymer extension. As a demonstration of the sensor, we measured the steric pressure generated by a model protein involved in membrane bending, the N-terminal homology domain (ENTH) of Epsin1. As the membrane becomes crowded by ENTH proteins, the polymer chain extends, increasing the fluorescence lifetime of the donor. Drawing on polymer theory, we use this change in lifetime to calculate steric pressure as a function of membrane coverage by ENTH, validating theoretical equations of state. Further, we find that ENTH's ability to break up larger vesicles into smaller ones correlates with steric pressure rather than the chemistry used to attach ENTH to the membrane surface. This result addresses a long-standing question about the molecular mechanisms of membrane remodeling. More broadly, this sensor makes it possible to measure steric pressure in situ during diverse biochemical events that occur on membrane surfaces, such as membrane remodeling, ligand-receptor binding, assembly of protein complexes, and changes in membrane organization.

Microfluidic chip with pillar arrays for controlled production and observation of lipid membrane nanotubes

Lipid membrane nanotubes (NTs) are a widespread template for in vitro studies of cellular processes happening at high membrane curvature. Traditionally NTs are manufactured one by one, using sophisticated membrane micromanipulations, while simplified methods for controlled batch production of NTs are in growing demand. Here we propose a lab-on-a-chip (LOC) approach to the simultaneous formation of multiple NTs with length and radius controlled by the chip design. The NTs form upon rolling silica microbeads covered by lipid lamellas over the pillars of a polymer micropillar array. The array's design and surface chemistry set the geometry of the resulting free-standing NTs. The integration of the array inside a microfluidic chamber further enables fast and turbulence-free addition of components, such as proteins, to multiple preformed NTs. This LOC approach to NT production is compatible with the use of high power objectives of a fluorescence microscope, making real-time quantification of the different modes of the protein activity in a single experiment possible.

Reconstitution and real-time quantification of membrane remodeling by single proteins and protein complexes

Cellular membrane processes, from signal transduction to membrane fusion and fission, depend on acute membrane deformations produced by small and short-lived protein complexes working in conditions far from equilibrium. Real-time monitoring and quantitative assessment of such deformations are challenging; hence, mechanistic analyses of the protein action are commonly based on ensemble averaging, which masks important mechanistic details of the action. In this protocol, we describe how to reconstruct and quantify membrane remodeling by individual proteins and small protein complexes in vitro, using an ultra-short (80- to 400-nm) lipid nanotube (usNT) template. We use the luminal conductance of the usNT as the real-time reporter of the protein interaction(s) with the usNT. We explain how to make and calibrate the usNT template to achieve subnanometer precision in the geometrical assessment of the molecular footprints on the nanotube membrane. We next demonstrate how membrane deformations driven by purified proteins implicated in cellular membrane remodeling can be analyzed at a single-molecule level. The preparation of one usNT takes ~1 h, and the shortest procedure yielding the basic geometrical parameters of a small protein complex takes 10 h.

Quantitative investigation of negative membrane curvature sensing and generation by I-BARs in filopodia of living cells

Membrane curvature has recently been recognized as an active regulator of cellular function, with several protein families identified as sensors and generators of membrane curvature. Amongst them, the inverse Bin/Amphiphysin/Rvs (I-BAR) domain family has been implicated in the sensing and generation of membrane structures with negative membrane curvature e.g. filopodia or dendritic spines. However, to date, quantitative biophysical investigations of I-BAR domains have mostly taken place in reconstitution. Here, we use fluorescence microscopy to quantitatively investigate membrane curvature sensing and generation by I-BARs in filopodia of living cells. As a model system, we selected two prototypic members of the I-BAR family, the insulin receptor substrate p53 and missing-in-metastasis. Our data demonstrated how I-BARs sense negative membrane curvature in the complex environment of live cells by revealing a dependence on membrane curvature for both their binding affinity to membranes and their saturation density. The non-monotonic dependence of protein sorting with negative membrane curvature allowed us to apply previously developed thermodynamic models to provide estimates of the effective intrinsic curvature and bending rigidity of the two I-BARs bound at the plasma membrane. Our results agree with studies performed on the insulin receptor substrate p53 in reconstitution. To quantitate membrane curvature generation by I-BARs we measured how their overexpression reduces the peak and the width of the size distribution of filopodia, resulting in filopodia populations with smaller and more uniform diameters. Our findings provide a quantitative biophysical insight in the ability of I-BARs to sense and generate negative membrane curvature in the crowded environment of living cells.

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.

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.

Thermodynamic equilibrium of binary mixtures on curved surfaces

We study the global influence of curvature on the free energy landscape of two-dimensional binary mixtures confined on closed surfaces. Starting from a generic effective free energy, constructed on the basis of symmetry considerations and conservation laws, we identify several model-independent phenomena, such as a curvature-dependent line tension and local shifts in the binodal concentrations. To shed light on the origin of the phenomenological parameters appearing in the effective free energy, we further construct a lattice-gas model of binary mixtures on nontrivial substrates, based on the curved-space generalization of the two-dimensional Ising model. This allows us to decompose the interaction between the local concentration of the mixture and the substrate curvature into four distinct contributions, as a result of which the phase diagram splits into critical subdiagrams. The resulting free energy landscape can admit, as stable equilibria, strongly inhomogeneous mixed phases, which we refer to as "antimixed" states below the critical temperature. We corroborate our semianalytical findings with phase-field numerical simulations on realistic curved lattices. Despite this work being primarily motivated by recent experimental observations of multicomponent lipid vesicles supported by colloidal scaffolds, our results are applicable to any binary mixture confined on closed surfaces of arbitrary geometry.

The plasma membrane as a mechanochemical transducer

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

Curvature- and Phase-Induced Protein Sorting Quantified in Transfected Cell-Derived Giant Vesicles

Eukaryotic cells possess a dynamic network of membranes that vary in lipid composition. To perform numerous biological functions, cells modulate their shape and the lateral organization of proteins associated with membranes. The modulation is generally facilitated by physical cues that recruit proteins to specific regions of the membrane. Analyzing these cues is difficult due to the complexity of the membrane conformations that exist in cells. Here, we examine how different types of membrane proteins respond to changes in curvature and to lipid phases found in the plasma membrane. By using giant plasma membrane vesicles derived from transfected cells, the proteins were positioned in the correct orientation and the analysis was performed in plasma membranes with a biological composition. Nanoscale membrane curvatures were generated by extracting nanotubes from these vesicles with an optical trap. The viral membrane protein neuraminidase was not sensitive to curvature, but it did exhibit strong partitioning (coefficient of K = 0.16) disordered membrane regions. In contrast, the membrane repair protein annexin 5 showed a preference for nanotubes with a density up to 10-15 times higher than that on the more flat vesicle membrane. The investigation of nanoscale effects in isolated plasma membranes provides a quantitative platform for studying peripheral and integral membrane proteins in their natural environment.

Curvature sensing by cardiolipin in simulated buckled membranes

Cardiolipin is a non-bilayer phospholipid with a unique dimeric structure. It localizes to negative curvature regions in bacteria and is believed to stabilize respiratory chain complexes in the highly curved mitochondrial membrane. Cardiolipin's localization mechanism remains unresolved, because important aspects such as the structural basis and strength for lipid curvature preferences are difficult to determine, partly due to the lack of efficient simulation methods. Here, we report a computational approach to study curvature preferences of cardiolipin by simulated membrane buckling and quantitative modeling. We combine coarse-grained molecular dynamics with simulated buckling to determine the curvature preferences in three-component bilayer membranes with varying concentrations of cardiolipin, and extract curvature-dependent concentrations and lipid acyl chain order parameter profiles. Cardiolipin shows a strong preference for negative curvatures, with a highly asymmetric chain order parameter profile. The concentration profiles are consistent with an elastic model for lipid curvature sensing that relates lipid segregation to local curvature via the material constants of the bilayers. These computations constitute new steps to unravel the molecular mechanism by which cardiolipin senses curvature in lipid membranes, and the method can be generalized to other lipids and membrane components as well.

Directed Supramolecular Organization of N-BAR Proteins through Regulation of H0 Membrane Immersion Depth

Many membrane remodeling events rely on the ability of curvature-generating N-BAR membrane proteins to organize into distinctive supramolecular configurations. Experiments have revealed a conformational switch in N-BAR proteins resulting in vesicular or tubular membrane shapes, with shallow membrane immersion of the H0 amphipathic helices of N-BAR proteins on vesicles but deep H0 immersion on tubes. We develop here a minimal elastic model of the local thinning of the lipid bilayer resulting from H0 immersion. Our model predicts that the observed conformational switch in N-BAR proteins produces a corresponding switch in the bilayer-mediated N-BAR interactions due to the H0 helices. In agreement with experiments, we find that bilayer-mediated H0 interactions oppose N-BAR multimerization for the shallow H0 membrane immersion depths measured on vesicles, but promote self-assembly of supramolecular N-BAR chains for the increased H0 membrane immersion depths measured on tubes. Finally, we consider the possibility that bilayer-mediated H0 interactions might contribute to the concerted structural reorganization of N-BAR proteins suggested by experiments. Our results indicate that the membrane immersion depth of amphipathic protein helices may provide a general molecular control parameter for membrane organization.

Ezrin enrichment on curved membranes requires a specific conformation or interaction with a curvature-sensitive partner

One challenge in cell biology is to decipher the biophysical mechanisms governing protein enrichment on curved membranes and the resulting membrane deformation. The ERM protein ezrin is abundant and associated with cellular membranes that are flat, positively or negatively curved. Using in vitro and cell biology approaches, we assess mechanisms of ezrin’s enrichment on curved membranes. We evidence that wild-type ezrin (ezrinWT) and its phosphomimetic mutant T567D (ezrinTD) do not deform membranes but self-assemble anti-parallelly, zipping adjacent membranes. EzrinTD’s specific conformation reduces intermolecular interactions, allows binding to actin filaments, which reduces membrane tethering, and promotes ezrin binding to positively-curved membranes. While neither ezrinTD nor ezrinWT senses negative curvature alone, we demonstrate that interacting with curvature-sensing I-BAR-domain proteins facilitates ezrin enrichment in negatively-curved membrane protrusions. Overall, our work demonstrates that ezrin can tether membranes, or be targeted to curved membranes, depending on conformations and interactions with actin and curvature-sensing binding partners.

Single-lipid tracking on nanoscale membrane buds: The effects of curvature on lipid diffusion and sorting

Nanoscale membrane curvature in cells is critical for endocytosis/exocytosis and membrane trafficking. However, the biophysical ramifications of nanoscale membrane curvature on the behavior of lipids remain poorly understood. Here, we created an experimental model system of membrane curvature at a physiologically-relevant scale and obtained nanoscopic information on single-lipid distributions and dynamics. Supported lipid bilayers were created over 50 and 70 nm radius nanoparticles to create membrane buds. Single-molecule localization microscopy was performed with diverse mixtures of fluorescent and non-fluorescent lipids. Variations in lipid acyl tales length, saturation, head-group, and fluorescent labeling strategy were tested while maintaining a single fluid lipid phase throughout the membrane. Monte Carlo simulations were used to fit our experimental results and quantify the effects of curvature on the lipid diffusion and sorting. Whereas varying the composition of the non-fluorescent lipids yielded minimal changes to the curvature effects, the labeling strategy of the fluorescent lipids yielded highly varying effects of curvature. Most conditions yield single-population Brownian diffusion throughout the membrane; however, curvature-induced lipid sorting, slowing, and aggregation were observed in some conditions. Head-group labeled lipids such as DPPE-Texas Red and POPE-Rhodamine diffused >2.4× slower on the curved vs. the planar membranes; tail-labeled lipids such as NBD-PPC, TopFluor-PPC, and TopFluor-PIP2, as well as DiIC₁₂ and DiIC₁₈ displayed no significant changes in diffusion due to the membrane curvature. This article is part of a Special Issue entitled: Emergence of Complex Behavior in Biomembranes edited by Marjorie Longo.

Computing Curvature Sensitivity of Biomolecules in Membranes by Simulated Buckling

Membrane curvature sensing, where the binding free energies of membrane-associated molecules depend on the local membrane curvature, is a key factor to modulate and maintain the shape and organization of cell membranes. However, the microscopic mechanisms are not well understood, partly due to absence of efficient simulation methods. Here, we describe a method to compute the curvature dependence of the binding free energy of a membrane-associated probe molecule that interacts with a buckled membrane, which has been created by lateral compression of a flat bilayer patch. This buckling approach samples a wide range of curvatures in a single simulation, and anisotropic effects can be extracted from the orientation statistics. We develop an efficient and robust algorithm to extract the motion of the probe along the buckled membrane surface, and evaluate its numerical properties by extensive sampling of three coarse-grained model systems: local lipid density in a curved environment for single-component bilayers, curvature preferences of individual lipids in two-component membranes, and curvature sensing by a homotrimeric transmembrane protein. The method can be used to complement experimental data from curvature partition assays and provides additional insight into mesoscopic theories and molecular mechanisms for curvature sensing.

Opposing Kinesin and Myosin-I Motors Drive Membrane Deformation and Tubulation along Engineered Cytoskeletal Networks

Microtubule and actin filament molecular motors such as kinesin-1 and myosin-Ic (Myo1c) transport and remodel membrane-bound vesicles; however, it is unclear how they coordinate to accomplish these tasks. We introduced kinesin-1- and Myo1c-bound giant unilamellar vesicles (GUVs) into a micropatterned in vitro cytoskeletal matrix modeled after the subcellular architecture where vesicular sorting and membrane remodeling are observed. This array was composed of sparse microtubules intersecting regions dense with actin filaments, and revealed that Myo1c-dependent tethering of GUVs enabled kinesin-1-driven membrane deformation and tubulation. Membrane remodeling at actin/microtubule intersections was modulated by lipid composition and the addition of the Bin-Amphiphysin-Rvs-domain (BAR-domain) proteins endophilin or FCH-domain-only (FCHo). Myo1c not only tethered microtubule-transported cargo, but also transported, deformed, and tubulated GUVs along actin filaments in a lipid-composition- and BAR-protein-responsive manner. These results suggest a mechanism for actin-based involvement in vesicular transport and remodeling of intracellular membranes, and implicate lipid composition as a key factor in determining whether vesicles will undergo transport, deformation, or tubulation driven by opposing actin and microtubule motors and BAR-domain proteins.

Pulling Membrane Nanotubes from Giant Unilamellar Vesicles

The reshaping of the cell membrane is an integral part of many cellular phenomena, such as endocytosis, trafficking, the formation of filopodia, etc. Many different proteins associate with curved membranes because of their ability to sense or induce membrane curvature. Typically, these processes involve a multitude of proteins making them too complex to study quantitatively in the cell. We describe a protocol to reconstitute a curved membrane in vitro, mimicking a curved cellular structure, such as the endocytic neck. A giant unilamellar vesicle (GUV) is used as a model of a cell membrane, whose internal pressure and surface tension are controlled with micropipette aspiration. Applying a point pulling force on the GUV using optical tweezers creates a nanotube of high curvature connected to a flat membrane. This method has traditionally been used to measure the fundamental mechanical properties of lipid membranes, such as bending rigidity. In recent years, it has been expanded to study how proteins interact with membrane curvature and the way they affect the shape and the mechanics of membranes. A system combining micromanipulation, microinjection, optical tweezers, and confocal microscopy allows measurement of membrane curvature, membrane tension, and the surface density of proteins, concurrently. From these measurements, many important mechanical and morphological properties of the protein-membrane system can be inferred. In addition, we lay out a protocol of creating GUVs in the presence of physiological salt concentration, and a method of quantifying the surface density of proteins on the membrane from fluorescence intensities of labeled proteins and lipids.

Acceleration and suppression of banana-shaped-protein-induced tubulation by addition of small membrane inclusions of isotropic spontaneous curvatures

Membrane tubulation induced by banana-shaped protein rods is investigated by using coarse-grained meshless membrane simulations. It is found that tubulation is promoted by laterally isotropic membrane inclusions that generate the same sign of spontaneous curvature as the adsorbed protein rods. The inclusions are concentrated in the tubules and reduce the bending energy of the tip of the tubules. On the other hand, inclusions with an opposite curvature suppress tubulation by percolated-network formation at a high protein-rod density while they induce the formation of a spherical membrane bud at a low rod density. When equal amounts of the two types of inclusions (with positive and negative curvatures) are added, their effects cancel each other for the first short period but later the tubulation is slowly accelerated. Positive surface tension suppresses tubulation. Our results suggest that the cooperation of scaffolding of BAR (Bin/Amphiphysin/Rvs) domains and isotropic membrane inclusions is important for tubulation.

Revealing the Effects of Nanoscale Membrane Curvature on Lipid Mobility

Recent advances in nanoengineering and super-resolution microscopy have enabled new capabilities for creating and observing membrane curvature. However, the effects of curvature on single-lipid diffusion have yet to be revealed. The simulations presented here describe the capabilities of varying experimental methods for revealing the effects of nanoscale curvature on single-molecule mobility. Traditionally, lipid mobility is revealed through fluorescence recovery after photobleaching (FRAP), fluorescence correlation spectroscopy (FCS), and single particle tracking (SPT). However, these techniques vary greatly in their ability to detect the effects of nanoscale curvature on lipid behavior. Traditionally, FRAP and FCS depend on diffraction-limited illumination and detection. A simulation of FRAP shows minimal effects on lipids diffusion due to a 50 nm radius membrane bud. Throughout the stages of the budding process, FRAP detected minimal changes in lipid recovery time due to the curvature versus flat membrane. Simulated FCS demonstrated small effects due to a 50 nm radius membrane bud that was more apparent with curvature-dependent lipid mobility changes. However, SPT achieves a sub-diffraction-limited resolution of membrane budding and lipid mobility through the identification of the single-lipid positions with ≤15 nm spatial and ≤20 ms temporal resolution. By mapping the single-lipid step lengths to locations on the membrane, the effects of membrane topography and curvature could be correlated to the effective membrane viscosity. Single-fluorophore localization techniques, such SPT, can detect membrane curvature and its effects on lipid behavior. These simulations and discussion provide a guideline for optimizing the experimental procedures in revealing the effects of curvature on lipid mobility and effective local membrane viscosity.

Lipid rafts enhance the binding constant of membrane-anchored receptors and ligands

Gaining insights into the binding of membrane-anchored receptors and ligands that mediate cell adhesion and signal transduction is of great significance for understanding numerous physiological processes driven by intercellular communication. Lipid rafts, microdomains in cell membranes enriched in cholesterol and saturated lipids such as sphingomyelin, are believed to serve as the essential platforms to recruit protein molecules for biological functions. An important question remains how the lipid rafts affect the binding constant of membrane-anchored receptors and ligands. We have investigated the adhesion of multicomponent membranes by using Monte Carlo simulations of a mesoscopic model with biologically relevant parameters. We find that the preferential partitioning of membrane-anchored receptor and ligand proteins in the lipid rafts significantly increases the binding constant of those proteins, in cooperation with the shape fluctuations of the membranes caused by thermal excitations. The binding constant can even be greater than that of the same receptors and ligands anchored to two apposing supported, planar membranes without shape fluctuations. The membrane shape fluctuations facilitate the binding of the anchored receptors and ligands, in contrast to the case of homogeneous membranes. Our results suggest that cells might regulate the binding of membrane-anchored receptor and ligand proteins by modulating the properties of lipid rafts such as area fraction, size and the affinity of rafts to the proteins.

Membrane structure formation induced by two types of banana-shaped proteins

The assembly of banana-shaped rodlike proteins on membranes and the associated membrane shape transformations are investigated by analytical theory and coarse-grained simulations. The membrane-mediated interactions between two banana-shaped inclusions are derived theoretically using a point-like formalism based on fixed anisotropic curvatures, both for zero surface tension and for finite surface tension. On a larger scale, the interactions between the assemblies of such rodlike inclusions are determined analytically. Meshless membrane simulations are performed in the presence of a large number of inclusions of two types, corresponding to the curved rods of opposite curvatures, both for flat membranes and vesicles. Rods of the same type aggregate into linear assemblies perpendicular to the rod axis, leading to membrane tubulation. However, rods of the other type, those of opposite curvature, are attracted to the lateral sides of these assemblies, and stabilize a straight bump structure that prevents tubulation. When the two types of rods have almost opposite curvatures, the bumps attract one another, forming a striped structure. Positive surface tension is found to stabilize stripe formation. The simulation results agree well with the theoretical predictions provided the point-like curvatures of the model are scaled-down to account for the effective flexibility of the simulated rods.

Protein sorting by lipid phase-like domains supports emergent signaling function in B lymphocyte plasma membranes

Diverse cellular signaling events, including B cell receptor (BCR) activation, are hypothesized to be facilitated by domains enriched in specific plasma membrane lipids and proteins that resemble liquid-ordered phase-separated domains in model membranes. This concept remains controversial and lacks direct experimental support in intact cells. Here, we visualize ordered and disordered domains in mouse B lymphoma cell membranes using super-resolution fluorescence localization microscopy, demonstrate that clustered BCR resides within ordered phase-like domains capable of sorting key regulators of BCR activation, and present a minimal, predictive model where clustering receptors leads to their collective activation by stabilizing an extended ordered domain. These results provide evidence for the role of membrane domains in BCR signaling and a plausible mechanism of BCR activation via receptor clustering that could be generalized to other signaling pathways. Overall, these studies demonstrate that lipid mediated forces can bias biochemical networks in ways that broadly impact signal transduction.

DOI:http://dx.doi.org/10.7554/eLife.19891.001

Membranes made of molecules called lipids surround every living cell to protect the cell's contents. Cells also communicate with the outside environment via their membranes. Proteins in the membrane receive information from the environment and trigger signaling pathways inside the cell to relay this information to the center of cell. The way in which proteins are organized on the membrane has a major influence on their signaling activity.

Some areas of the membrane are more crowded with certain lipids and signaling proteins than others. Lipid and protein molecules of particular types can come together and form distinct areas called “ordered” and “disordered” domains. The lipids in ordered domains are more tightly packed than disordered domains and it is thought that this difference allows domains to selectively exclude or include certain proteins. Ordered domains are also known as "lipid rafts". Lipid rafts and disordered domains may help cells to control the activities of signaling pathways, however, technical limitations have made it difficult to study the roles of these domains.

The membranes surrounding immune cells called B cells contain a protein called the B cell receptor, which engages with proteins from microbes and other foreign invaders. When the B cell receptor binds to a foreign protein it forms clusters with other B cell receptors and becomes active, triggering a signaling pathway that leads to immune responses.

Stone, Shelby et al. examined lipid rafts and disordered domains in B cells from mice using a technique called super-resolution fluorescence microscopy. The results show that clusters of B cell receptors are present within lipid rafts. These clusters made the lipid rafts larger and more stable. A protein that is needed during the early stages of B cell receptor signaling was also found in the same lipid rafts. Another protein that terminates signaling was excluded because it prefers disordered domains. Together, this provides a local environment in certain areas of the membrane that favors receptor activity and supports the subsequent immune response.

Future work is needed to understand how cells control the make-up of lipids and proteins within their membranes, and how defects in this regulation can alter signaling activity and lead to disease.

DOI:http://dx.doi.org/10.7554/eLife.19891.002

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.

The N-Terminal Amphipathic Helix of Endophilin Does Not Contribute to Its Molecular Curvature Generation Capacity

N-BAR proteins such as endophilin are thought to bend lipid membranes via scaffolding (the molding of membranes through the crescent protein shape) and membrane insertion (also called wedging) of amphipathic helices. However, the contributions from these distinct mechanisms to membrane curvature generation and sensing have remained controversial. Here we quantitatively demonstrate that the amphipathic N-terminal H0 helix of endophilin is important for recruiting this protein to the membrane, but does not contribute significantly to its intrinsic membrane curvature generation capacity. These observations elevate the importance of the scaffolding mechanism, rather than H0 insertion, for the membrane curvature generation by N-BAR domains. Furthermore, consistent with the thermodynamically required coupling between curvature generation and sensing, we observed that the H0-truncated N-BAR domain is capable of sensing membrane curvature. Overall, our contribution clarifies an important mechanistic controversy in the function of N-BAR domain proteins.

Analysis of diffusion in curved surfaces and its application to tubular membranes

Diffusion of particles in curved surfaces is inherently complex compared with diffusion in a flat membrane, owing to the nonplanarity of the surface. The consequence of such nonplanar geometry on diffusion is poorly understood but is highly relevant in the case of cell membranes, which often adopt complex geometries. To address this question, we developed a new finite element approach to model diffusion on curved membrane surfaces based on solutions to Fick's law of diffusion and used this to study the effects of geometry on the entry of surface-bound particles into tubules by diffusion. We show that variations in tubule radius and length can distinctly alter diffusion gradients in tubules over biologically relevant timescales. In addition, we show that tubular structures tend to retain concentration gradients for a longer time compared with a comparable flat surface. These findings indicate that sorting of particles along the surfaces of tubules can arise simply as a geometric consequence of the curvature without any specific contribution from the membrane environment. Our studies provide a framework for modeling diffusion in curved surfaces and suggest that biological regulation can emerge purely from membrane geometry.

Anisotropic Membrane Curvature Sensing by Amphipathic Peptides

Many proteins and peptides have an intrinsic capacity to sense and induce membrane curvature, and play crucial roles for organizing and remodeling cell membranes. However, the molecular driving forces behind these processes are not well understood. Here, we describe an approach to study curvature sensing by simulating the interactions of single molecules with a buckled lipid bilayer. We analyze three amphipathic antimicrobial peptides, a class of membrane-associated molecules that specifically target and destabilize bacterial membranes, and find qualitatively different sensing characteristics that would be difficult to resolve with other methods. Our findings provide evidence for direction-dependent curvature sensing mechanisms in amphipathic peptides and challenge existing theories of hydrophobic insertion. The buckling approach is generally applicable to a wide range of curvature-sensing molecules, and our results provide strong motivation to develop new experimental methods to track position and orientation of membrane proteins.

The Role of BAR Domain Proteins in the Regulation of Membrane Dynamics

Many cellular processes are associated with membrane remodeling. The BAR domain protein family plays a key role in the formation and detection of local membrane curvatures and in attracting other proteins, including the regulators of actin dynamics. Based on their structural and phylogenetic properties, BAR domains are divided into several groups which affect membrane in various ways and perform different functions in cells. However, recent studies have uncovered evidence of functional differences even within the same group. This review discusses the principles underlying the interactions of different groups of BAR domains, and their individual representatives ,with membranes.

How curvature-generating proteins build scaffolds on membrane nanotubes

Bin/Amphiphysin/Rvs (BAR) domain proteins control the curvature of lipid membranes in endocytosis, trafficking, cell motility, the formation of complex subcellular structures, and many other cellular phenomena. They form 3D assemblies that act as molecular scaffolds to reshape the membrane and alter its mechanical properties. It is unknown, however, how a protein scaffold forms and how BAR domains interact in these assemblies at protein densities relevant for a cell. In this work, we use various experimental, theoretical, and simulation approaches to explore how BAR proteins organize to form a scaffold on a membrane nanotube. By combining quantitative microscopy with analytical modeling, we demonstrate that a highly curving BAR protein endophilin nucleates its scaffolds at the ends of a membrane tube, contrary to a weaker curving protein centaurin, which binds evenly along the tube's length. Our work implies that the nature of local protein-membrane interactions can affect the specific localization of proteins on membrane-remodeling sites. Furthermore, we show that amphipathic helices are dispensable in forming protein scaffolds. Finally, we explore a possible molecular structure of a BAR-domain scaffold using coarse-grained molecular dynamics simulations. Together with fluorescence microscopy, the simulations show that proteins need only to cover 30-40% of a tube's surface to form a rigid assembly. Our work provides mechanical and structural insights into the way BAR proteins may sculpt the membrane as a high-order cooperative assembly in important biological processes.

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'.