Bending lipid membranes: experiments after W. Helfrich's model

Neutron spin echo shows pHLIP is capable of retarding membrane thickness fluctuations

Cell membranes are responsible for a range of biological processes that require interactions between lipids and proteins. While the effects of lipids on proteins are becoming better understood, our knowledge of how protein conformational changes influence membrane dynamics remains rudimentary. Here, we performed experiments and computer simulations to study the dynamic response of a lipid membrane to changes in the conformational state of pH-low insertion peptide (pHLIP), which transitions from a surface-associated (SA) state at neutral or basic pH to a transmembrane (TM) α-helix under acidic conditions. Our results show that TM-pHLIP significantly slows down membrane thickness fluctuations due to an increase in effective membrane viscosity. Our findings suggest a possible membrane regulatory mechanism, where the TM helix affects lipid chain conformations, and subsequently alters membrane fluctuations and viscosity.

Unveiling the Mechanism of Spontaneous Nanoscroll Formation from Janus Transition Metal Dichalcogenide Nanoribbons

Due to the atomic asymmetry, Janus transition metal dichalcogenide monolayers possess spontaneous curling and can even form one-dimensional nanoscrolls. Unveiling this spontaneous formation mechanism of nanoscrolls is of great importance for precise structural control. In this paper, we successfully simulate the process of Janus MoSSe nanoscroll formation from flat nanoribbons, based on molecular dynamics (MD) simulations with hybrid potentials. The spontaneous scrolling is purely driven by the relaxation of intrinsic strain in Janus MoSSe. The final structure of nanoscroll is strongly affected by the length of nanoribbon with a nonmonotonous relation. To further understand the mechanism, we establish a thermodynamic model to determine the inner radius of MoSSe nanoscrolls, which is shown to be related to spontaneous curvature, bending stiffness, interlayer van der Waals interaction, interlayer distance, and length of initial nanoribbon. The results correspond well with MD simulations of nanoscrolls from flat nanoribbons and the molecular static simulations of directly built nanoscrolls. Moreover, the inner radii of MoSeTe and MoSTe nanoscrolls are predicted based on the model. Our results provide insights into the Janus TMD nanoscroll formation and a pathway for controllable fabrication of nanoscrolls.

Parallel on-chip micropipettes enabling quantitative multiplexed characterization of vesicle mechanics and cell aggregates rheology

Micropipette aspiration (MPA) is one of the gold standards for quantifying biological samples' mechanical properties, which are crucial from the cell membrane scale to the multicellular tissue. However, relying on the manipulation of individual home-made glass pipettes, MPA suffers from low throughput and no automation. Here, we introduce the sliding insert micropipette aspiration method, which permits parallelization and automation, thanks to the insertion of tubular pipettes, obtained by photolithography, within microfluidic channels. We show its application both at the lipid bilayer level, by probing vesicles to measure membrane bending and stretching moduli, and at the tissue level by quantifying the viscoelasticity of 3D cell aggregates. This approach opens the way to high-throughput, quantitative mechanical testing of many types of biological samples, from vesicles and individual cells to cell aggregates and explants, under dynamic physico-chemical stimuli.

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.

A review on the measurement of the bending rigidity of lipid membranes

This review provides an overview of the latest developments in both experimental and simulation techniques used to assess the bending rigidity of lipid membranes. It places special emphasis on experimental methods that utilize model vesicles to manipulate lipid compositions and other experimental parameters to determine the bending rigidity of the membrane. It also describes two commonly used simulation methods for estimating bending rigidity. The impact of various factors on membrane bending rigidity is summarized, including cholesterol, lipids, salt concentration, surface charge, membrane phase state, peptides, proteins, and polyethylene glycol. These factors are shown to influence the bending rigidity, contributing to a better understanding of the biophysical properties of membranes and their role in biological processes. Furthermore, the review discusses future directions and potential advancements in this research field, highlighting areas where further investigation is required.

Effect of cholesterol on the ion-membrane interaction: Zeta potential and dynamic light scattering study

Cholesterol in a bio-membrane plays a significant role in many cellular event and is known to regulate the functional activity of protein and ion channel. In this study we report a significant effect of cholesterol on the ion-membrane interaction. We prepare large unilamellar vesicles, composed of zwitterionic lipid DOPC and anionic lipid DOPG with different cholesterol concentration. Electrostatics of anionic membranes containing cholesterol in the presence of NaCl has systematically been explored using dynamic light scattering and zeta potential. Negative zeta potential of the membrane decreases its negative value with increasing ion concentration for all cholesterol concentrations. However, zeta potential itself decreases with increasing cholesterol content even in the absence of monovalent ions. Electrostatic behaviour of the membrane is determined from well-known Gouy Chapmann model. Negative surface charge density of the membrane decreases with increasing cholesterol content. Binding constant, estimated from the electrostatic double layer theory, is found to increase significantly in the presence of cholesterol. Comparison of electrostatic parameters of the membrane in the presence and absence of cholesterol suggests that cholesterol significantly alter the electrostatic behaviour of the membrane.

Active morphogenesis of patterned epithelial shells

Shape transformations of epithelial tissues in three dimensions, which are crucial for embryonic development or in vitro organoid growth, can result from active forces generated within the cytoskeleton of the epithelial cells. How the interplay of local differential tensions with tissue geometry and with external forces results in tissue-scale morphogenesis remains an open question. Here, we describe epithelial sheets as active viscoelastic surfaces and study their deformation under patterned internal tensions and bending moments. In addition to isotropic effects, we take into account nematic alignment in the plane of the tissue, which gives rise to shape-dependent, anisotropic active tensions and bending moments. We present phase diagrams of the mechanical equilibrium shapes of pre-patterned closed shells and explore their dynamical deformations. Our results show that a combination of nematic alignment and gradients in internal tensions and bending moments is sufficient to reproduce basic building blocks of epithelial morphogenesis, including fold formation, budding, neck formation, flattening, and tubulation.

Biophysics of Membrane Stiffening by Cholesterol and Phosphatidylinositol 4,5-bisphosphate (PIP2)

Cell membranes regulate a wide range of phenomena that are implicated in key cellular functions. Cholesterol, a critical component of eukaryotic cell membranes, is responsible for cellular organization, membrane elasticity, and other critical physicochemical parameters. Besides cholesterol, other lipid components such as phosphatidylinositol 4,5-bisphosphate (PIP2) are found in minor concentrations in cell membranes yet can also play a major regulatory role in various cell functions. In this chapter, we describe how solid-state deuterium nuclear magnetic resonance (²H NMR) spectroscopy together with neutron spin-echo (NSE) spectroscopy can inform synergetic changes to lipid molecular packing due to cholesterol and PIP2 that modulate the bending rigidity of lipid membranes. Fundamental structure-property relations of molecular self-assembly are illuminated and point toward a length and time-scale dependence of cell membrane mechanics, with significant implications for biological activity and membrane lipid-protein interactions.

Cholesterol Stiffening of Lipid Membranes

Biomembrane order, dynamics, and other essential physicochemical parameters are controlled by cholesterol, a major component of mammalian cell membranes. Although cholesterol is well known to exhibit a condensing effect on fluid lipid membranes, the extent of stiffening that occurs with different degrees of lipid acyl chain unsaturation remains an enigma. In this review, we show that cholesterol locally increases the bending rigidity of both unsaturated and saturated lipid membranes, suggesting there may be a length-scale dependence of the bending modulus. We review our published data that address the origin of the mechanical effects of cholesterol on unsaturated and polyunsaturated lipid membranes and their role in biomembrane functions. Through a combination of solid-state deuterium NMR spectroscopy and neutron spin-echo spectroscopy, we show that changes in molecular packing cause the universal effects of cholesterol on the membrane bending rigidity. Our findings have broad implications for the role of cholesterol in lipid–protein interactions as well as raft-like mixtures, drug delivery applications, and the effects of antimicrobial peptides on lipid membranes.

Bending Rigidity, Capacitance, and Shear Viscosity of Giant Vesicle Membranes Prepared by Spontaneous Swelling, Electroformation, Gel-Assisted, and Phase Transfer Methods: A Comparative Study

Closed lipid bilayers in the form of giant unilamellar vesicles (GUVs) are commonly used membrane models. Various methods have been developed to prepare GUVs, however it is unknown if all approaches yield membranes with the same elastic, electric, and rheological properties. Here, we combine flickering spectroscopy and electrodefomation of GUVs to measure, at identical conditions, membrane capacitance, bending rigidity and shear surface viscosity of palmitoyloleoylphosphatidylcholine (POPC) membranes formed by several commonly used preparation methods: thin film hydration (spontaneous swelling), electroformation, gel-assisted swelling using poly(vinyl alcohol) (PVA) or agarose, and phase-transfer. We find relatively similar bending rigidity value across all the methods except for the agarose hydration method. In addition, the capacitance values are similar except for vesicles prepared via PVA gel hydration. Intriguingly, membranes prepared by the gel-assisted and phase-transfer methods exhibit much higher shear viscosity compared to electroformation and spontaneous swelling, likely due to remnants of polymers (PVA and agarose) and oils (hexadecane and mineral) in the lipid bilayer structure.

Investigating the entropic nature of membrane-mediated interactions driving the aggregation of peripheral proteins

Peripheral membrane-associated proteins are known to accumulate on the surface of biomembranes as a result of membrane-mediated interactions. For a pair of rotationally-symmetric curvature-inducing proteins, membrane mechanics at the low-temperature limit predicts pure repulsion. On the other hand, temperature-dependent entropic forces arise between pairs of stiff-binding proteins suppressing membrane fluctuations. These Casimir-like interactions have thus been suggested as candidates for attractive forces leading to aggregation. With dense assemblies of peripheral proteins on the membrane, both these abstractions encounter short-range and multi-body complications. Here, we make use of a particle-based membrane model augmented with flexible peripheral proteins to quantify purely membrane-mediated interactions and investigate their underlying nature. We introduce a continuous reaction coordinate corresponding to the progression of protein aggregation. We obtain free energy and entropy landscapes for different surface concentrations along this reaction coordinate. In parallel, we investigate time-dependent estimates of membrane entropy corresponding to membrane undulations and coarse-grained director field and how they change dynamically with protein aggregation. Congruent outcomes of the two approaches point to the conclusion that for low surface concentrations, interactions with an entropic nature may drive the aggregation. But at high concentrations, enthalpic contributions due to concerted membrane deformation by protein clusters are dominant.

Bending Modulus of Lipid Membranes from Density Correlation Functions

The bending modulus κ quantifies the elasticity of biological membranes in terms of the free energy cost of increasing the membrane corrugation. Molecular dynamics (MD) simulations provide a powerful approach to quantify κ by analyzing the thermal fluctuations of the lipid bilayer. However, existing methods require the identification and filtering of non-mesoscopic fluctuation modes. State of the art methods rely on identifying a smooth surface to describe the membrane shape. These methods introduce uncertainties in calculating κ since they rely on different criteria to select the relevant fluctuation modes. Here, we present a method to compute κ using molecular simulations. Our approach circumvents the need to define a mesoscopic surface or an orientation field for the lipid tails explicitly. The bending and tilt moduli can be extracted from the analysis of the density correlation function (DCF). The method introduced here builds on the Bedeaux and Weeks (BW) theory for the DCF of fluctuating interfaces and on the coupled undulatory (CU) mode introduced by us in previous work. We test the BW-DCF method by computing the elastic properties of lipid membranes with different system sizes (from 500 to 6000 lipid molecules) and using coarse-grained (for POPC and DPPC lipids) and fully atomistic models (for DPPC). Further, we quantify the impact of cholesterol on the bending modulus of DPPC bilayers. We compare our results with bending moduli obtained with X-ray diffraction data and different computer simulation methods.

Layer-by-layer assembly of multi-layered droplet interface bilayers (multi-DIBs)

Droplet interface bilayers (DIBs) have tremendous promise as platforms for fundamental biomembrane studies and in biotechnology. Being composed of a single bilayer however limits their biomimetic potential, as many cell membrane motifs are composed of multiple aligned bilayers. We describe a technology to manufacture cell-sized multi-layered DIBs (multi-DIBs) by coating giant unilamellar vesicles with a further monolayer, and allowing such structures to make contact with themselves or a monolayer coated droplet. This easily customisable strategy will pave the way for an expanded repertoire of DIB functionality, for example by facilitating the incorporation of multiple-bilayer spanning protein complexes.

Quantitative Nanomechanical Analysis of Small Extracellular Vesicles for Tumor Malignancy Indication

The nanomechanical properties of tumor-derived small extracellular vesicles (sEVs) are essential to cancer progression. Here, nanoindentation is utilized on atomic force microscopy (AFM) to quantitatively investigate the nanomechanical properties of human breast cancer cell-derived sEVs at single vesicle level and explore their relationship with tumor malignancy and vesicle size. It is demonstrated that the stiffness of the sEVs results from the combined contribution of the bending modulus and osmotic pressure of the sEVs. The stiffness and osmotic pressure increase with increasing malignancy of the sEVs and decrease with increasing size of the sEVs. The bending modulus decreases with increasing malignancy of the sEVs and is lower in smaller sEVs. This study builds relationship between the nanomechanical signature of the sEV and tumor malignancy, adding information for better understanding cancer mechanobiology.

Cholesterol plays a decisive role in tetraspanin assemblies during bilayer deformations

The tetraspanin family plays key roles in many physiological processes, such as, tumour invasion, cell motility, virus infection, cell attachment and entry. Tetraspanins function as molecular scaffolds organized in microdomains with interesting downstream cellular consequences. However, despite their relevance in human physiology, the precise mechanisms of their various functions remain elusive. In particular, the full-length CD81 tetraspanin has interesting cholesterol-related properties that modulate its activity in cells. In this work, we study the opening transition of CD81 under different conditions. We propose that such conformational change is a collaborative process enhanced by simultaneous interactions between multiple identical CD81 tetraspanins. With molecular dynamics simulations we describe the crucial role of a ternary lipid bilayer with cholesterol in CD81 conformational dynamics, observing two emergent properties: first, clusters of CD81 collectively segregate one tetraspanin while favouring one opening transition, second, cumulative cholesterol sequestering by CD81 tetraspanins inhibits large membrane deformations due to local density variations.

FtsZ induces membrane deformations via torsional stress upon GTP hydrolysis

FtsZ is a key component in bacterial cell division, being the primary protein of the presumably contractile Z ring. In vivo and in vitro, it shows two distinctive features that could so far, however, not be mechanistically linked: self-organization into directionally treadmilling vortices on solid supported membranes, and shape deformation of flexible liposomes. In cells, circumferential treadmilling of FtsZ was shown to recruit septum-building enzymes, but an active force production remains elusive. To gain mechanistic understanding of FtsZ dependent membrane deformations and constriction, we design an in vitro assay based on soft lipid tubes pulled from FtsZ decorated giant lipid vesicles (GUVs) by optical tweezers. FtsZ filaments actively transform these tubes into spring-like structures, where GTPase activity promotes spring compression. Operating the optical tweezers in lateral vibration mode and assigning spring constants to FtsZ coated tubes, the directional forces that FtsZ-YFP-mts rings exert upon GTP hydrolysis can be estimated to be in the pN range. They are sufficient to induce membrane budding with constricting necks on both, giant vesicles and E.coli cells devoid of their cell walls. We hypothesize that these forces result from torsional stress in a GTPase activity dependent manner.

More than just a barrier: using physical models to couple membrane shape to cell function

The correct execution of many cellular processes, such as division and motility, requires the cell to adopt a specific shape. Physically, these shapes are determined by the interplay of the plasma membrane and internal cellular driving factors. While the plasma membrane defines the boundary of the cell, processes inside the cell can result in the generation of forces that deform the membrane. These processes include protein binding, the assembly of protein superstructures, and the growth and contraction of cytoskeletal networks. Due to the complexity of the cell, relating observed membrane deformations back to internal processes is a challenging problem. Here, we review cell shape changes in endocytosis, cell adhesion, cell migration and cell division and discuss how by modeling membrane deformations we can investigate the inner working principles of the cell.

Domain formation in bicomponent vesicles induced by composition-curvature coupling

Lipid vesicles composed of a mixture of two types of lipids are studied by intensive Monte Carlo numerical simulations. The coupling between the local composition and the membrane shape is induced by two different spontaneous curvatures of the components. We explore the various morphologies of these biphasic vesicles coupled to the observed patterns such as nano-domains or labyrinthine mesophases. The effect of the difference in curvatures, the surface tension, and the interaction parameter between components is thoroughly explored. Our numerical results quantitatively agree with the previous analytical results obtained by Gueguen et al. [Eur. Phys. J. E 37, 76 (2014)] in the disordered (high temperature) phase. Numerical simulations allow us to explore the full parameter space, especially close to and below the critical temperature, where analytical results are not accessible. Phase diagrams are constructed and domain morphologies are quantitatively studied by computing the structure factor and the domain size distribution. This mechanism likely explains the existence of nano-domains in cell membranes as observed by super-resolution fluorescence microscopy.

Floating and Diving Loops of ABA Triblock Copolymers in Lipid Bilayers and Stability Enhancement for Asymmetric Membranes

Hybrid membranes of lipids and A_xB_yA_z triblock copolymers can possess better biocompatibility and mechanical stability. In this work, triblock copolymer conformations and stability of asymmetric membranes are explored by dissipative particle dynamics. The triblock copolymers in the membranes exhibit either the bridge or loop conformation. As hydrophobic B-blocks interact attractively with lipid heads, bridge-shaped copolymers are significantly inhibited and loop-shaped copolymers prefer to stay at the interface between hydrophilic and hydrophobic layers. This floating loop has a flattened conformation, consistent with the experimental findings. In contrast, for repulsive interactions between B-blocks and lipid heads, bridge-shaped copolymers are abundant and loop-shaped copolymers tend to plunge into the hydrophobic layer. This diving loop displays a random coil conformation. The asymmetric membrane in which the fractions of loop-shaped copolymers in the upper and lower leaflets are different is thermodynamically unstable. Two approaches are proposed to acquire kinetically stable asymmetric membranes. First, membrane symmetrization is arrested by eliminating bridge-shaped copolymers, which is achieved by B-block/lipid head attraction and B-block/lipid tail repulsion. Second, asymmetric triblock copolymers (x ≠ z) are used to prevent the passage of the long A-block through the hydrophobic layer.

Active particles induce large shape deformations in giant lipid vesicles

Biological cells generate intricate structures by sculpting their membrane from within to actively sense and respond to external stimuli or to explore their environment^1-4. Several pathogenic bacteria also provide examples of how localized forces strongly deform cell membranes from inside, leading to the invasion of neighbouring healthy mammalian cells⁵. Giant unilamellar vesicles have been successfully used as a minimal model system with which to mimic biological cells^6-11, but the realization of a minimal system with localized active internal forces that can strongly deform lipid membranes from within and lead to dramatic shape changes remains challenging. Here we present a combined experimental and simulation study that demonstrates how self-propelled particles enclosed in giant unilamellar vesicles can induce a plethora of non-equilibrium shapes and active membrane fluctuations. Using confocal microscopy, in the experiments we explore the membrane response to local forces exerted by self-phoretic Janus microswimmers. To quantify dynamic membrane changes, we perform Langevin dynamics simulations of active Brownian particles enclosed in thin membrane shells modelled by dynamically triangulated surfaces. The most pronounced shape changes are observed at low and moderate particle loadings, with the formation of tether-like protrusions and highly branched, dendritic structures, whereas at high volume fractions globally deformed vesicle shapes are observed. The resulting state diagram predicts the conditions under which local internal forces generate various membrane shapes. A controlled realization of such distorted vesicle morphologies could improve the design of artificial systems such as small-scale soft robots and synthetic cells.

Fluctuation spectroscopy of giant unilamellar vesicles using confocal and phase contrast microscopy

A widely used method to measure the bending rigidity of bilayer membranes is fluctuation spectroscopy, which analyses the thermally-driven membrane undulations of giant unilamellar vesicles recorded with either phase-contrast or confocal microscopy. Here, we analyze the fluctuations of the same vesicle using both techniques and obtain consistent values for the bending modulus. We discuss the factors that may lead to discrepancies.

How cholesterol stiffens unsaturated lipid membranes

Cholesterol is an integral component of eukaryotic cell membranes and a key molecule in controlling membrane fluidity, organization, and other physicochemical parameters. It also plays a regulatory function in antibiotic drug resistance and the immune response of cells against viruses, by stabilizing the membrane against structural damage. While it is well understood that, structurally, cholesterol exhibits a densification effect on fluid lipid membranes, its effects on membrane bending rigidity are assumed to be nonuniversal; i.e., cholesterol stiffens saturated lipid membranes, but has no stiffening effect on membranes populated by unsaturated lipids, such as 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC). This observation presents a clear challenge to structure-property relationships and to our understanding of cholesterol-mediated biological functions. Here, using a comprehensive approach-combining neutron spin-echo (NSE) spectroscopy, solid-state deuterium NMR (²H NMR) spectroscopy, and molecular dynamics (MD) simulations-we report that cholesterol locally increases the bending rigidity of DOPC membranes, similar to saturated membranes, by increasing the bilayer's packing density. All three techniques, inherently sensitive to mesoscale bending fluctuations, show up to a threefold increase in effective bending rigidity with increasing cholesterol content approaching a mole fraction of 50%. Our observations are in good agreement with the known effects of cholesterol on the area-compressibility modulus and membrane structure, reaffirming membrane structure-property relationships. The current findings point to a scale-dependent manifestation of membrane properties, highlighting the need to reassess cholesterol's role in controlling membrane bending rigidity over mesoscopic length and time scales of important biological functions, such as viral budding and lipid-protein interactions.

Mechanical Characterization of Liposomes and Extracellular Vesicles, a Protocol

Both natural as well as artificial vesicles are of tremendous interest in biology and nanomedicine. Small vesicles (<200 nm) perform essential functions in cell biology and artificial vesicles (liposomes) are used as drug delivery vehicles. Atomic Force Microscopy (AFM) is a powerful technique to study the structural properties of these vesicles. AFM is a well-established technique for imaging at nanometer resolution and for mechanical measurements under physiological conditions. Here, we describe the procedure of AFM imaging and force spectroscopy on small vesicles. We discuss how to image vesicles with minimal structural disturbance, and how to analyze the data for accurate size and shape measurements. In addition, we describe the procedure for performing nanoindentations on vesicles and the subsequent data analysis including mechanical models used for data interpretation.

Constructing artificial respiratory chain in polymer compartments: Insights into the interplay between bo3 oxidase and the membrane

Cytochrome bo3 ubiquinol oxidase is a transmembrane protein, which oxidizes ubiquinone and reduces oxygen, while pumping protons. Apart from its combination with F1Fo-ATPase to assemble a minimal ATP regeneration module, the utility of the proton pump can be extended to other applications in the context of synthetic cells such as transport, signaling, and control of enzymatic reactions. In parallel, polymers have been speculated to be phospholipid mimics with respect to their ability to self-assemble in compartments with increased stability. However, their usability as interfaces for complex membrane proteins has remained questionable. In the present work, we optimized a fusion/electroformation approach to reconstitute bo3 oxidase in giant unilamellar vesicles made of PDMS-g-PEO and/or phosphatidylcholine (PC). This enabled optical access, while microfluidic trapping allowed for online analysis of individual vesicles. The tight polymer membranes and the inward oriented enzyme caused 1 pH unit difference in 30 min, with an initial rate of 0.35 pH·min-1 To understand the interplay in these composite systems, we studied the relevant mechanical and rheological membrane properties. Remarkably, the proton permeability of polymer/lipid hybrids decreased after protein insertion, while the latter also led to a 20% increase of the polymer diffusion coefficient in polymersomes. In addition, PDMS-g-PEO increased the activity lifetime and the resistance to free radicals. These advantageous properties may open diverse applications, ranging from cell-free biotechnology to biomedicine. Furthermore, the presented study serves as a comprehensive road map for studying the interactions between membrane proteins and synthetic membranes, which will be fundamental for the successful engineering of such hybrid systems.

The responsive behaviors of bilayer membrane under uniaxial mechanical probe

In experiments, atomic force microscopy technology was used to measure the modulus of the membrane. However, these studies mainly focus on the linear responsive behavior. In the present work, a theoretical study is performed to show the nonlinear responsive behavior, which includes the stretching induced structural transitions. It demonstrates that the structural transition of the bilayer membrane takes place during the stretching process of the mechanical probe. A vertical cylindrical micelle can be obtained by stretching the membrane under deep compression conditions, and the cylindrical micelle can grow continuously along the axial direction. Moreover, under shallow compression conditions, the probe pulls a spherical micelle from the membrane, and then, the membrane returns to flatness. A comprehensive study is performed to show the mechanism of the responsive behaviors of the structural transition during the compression and stretching processes. When the probe acts on the B-rich layer, it is more likely to pull out a regular micelle. However, when the probe acts on the bottom A-rich layer, complex vesicles are more likely to be pulled out from the bilayer membrane. This study provides a comprehensive diagram of the mechanical responsive behavior of the membrane, which would be a guide for an experiment of biomembranes and the design of new self-assembled structures.

Formation of Asymmetric and Symmetric Hybrid Membranes of Lipids and Triblock Copolymers

Hybrid membranes formed by co-assembly of A_xB_yA_x (hydrophilic-hydrophobic-hydrophilic) triblock copolymers into lipid bilayers are investigated by dissipative particle dynamics. Homogeneous hybrid membranes are developed as lipids and polymers are fully compatible. The polymer conformations can be simply classified into bridge- and loop-structures in the membranes. It is interesting to find that the long-time fraction of loop-conformation (fL) of copolymers in the membrane depends significantly on the hydrophilic block length (x). As x is small, an equilibrium fL* always results irrespective of the initial conformation distribution and its value depends on the hydrophobic block length (y). For large x, fL tends to be time-invariant because polymers are kinetically trapped in their initial structures. Our findings reveal that only symmetric hybrid membranes are formed for small x, while membranes with stable asymmetric leaflets can be constructed with large x. The effects of block lengths on the polymer conformations, such as transverse and lateral spans (d⊥ and d‖) of bridge- and loop-conformations, are discussed as well.

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.

Glycan-decorated protocells: novel features for rebuilding cellular processes

In synthetic biology approaches, lipid vesicles are widely used as protocell models. While many compounds have been encapsulated in vesicles (e.g. DNA, cytoskeleton and enzymes), the incorporation of glycocalyx components in the lipid bilayer has attracted much less attention so far. In recent years, glycoconjugates have been integrated in the membrane of giant unilamellar vesicles (GUVs). These minimal membrane systems have largely contributed to shed light on the molecular mechanisms of cellular processes. In this review, we first introduce several preparation and biophysical characterization methods of GUVs. Then, we highlight specific applications of protocells investigating glycolipid-mediated endocytosis of toxins, viruses and bacteria. In addition, we delineate how prototissues have been assembled from glycan-decorated protocells by using lectin-mediated cross-linking of opposed glycoreceptors (e.g. glycolipids and glycopeptides). In future applications, glycan-decorated protocells might be useful for investigating cell-cell interactions (e.g. adhesion and communication). We also speculate about the implication of lectin-glycoreceptor interactions in membrane fusion processes.

The role of traction in membrane curvature generation

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

Bridging molecular simulation models and elastic theories for amphiphilic membranes

The Single Chain Mean Field theory is used to link coarse-grained models of amphiphilic molecules with analytical models for membrane elasticity, where phenomenological parameters are deduced from explicit molecular models and force fields. We estimate the elastic constants based on the free energy of the amphiphilic bilayer in planar and cylindrical geometries on the example of four amphiphilic molecules that differ in length and stiffness. We study how these variations affect the equilibrium bilayer structure, the equilibrium free energy, and the elastic constants. Bending rigidities are obtained within the typical range of experimental values for phospholipid membranes in a liquid state.

Multilamellar nanovesicles show distinct mechanical properties depending on their degree of lamellarity

Small multilamellar vesicles may have benefits over unilamellar vesicles for drug delivery, such as an increased volume for hydrophobic drugs. In addition, their altered mechanical properties might be beneficial for cellular uptake. Here, we show how atomic force microscopy (AFM) can be used to detect and characterize multilamellar vesicles. We quantify the size of each break event occurring during AFM nanoindentations, which shows good agreement with the thickness of supported lipid bilayers. Analyzing the size and number of these events for individual vesicles allows us to distinguish between vesicles consisting of 1 up to 5 bilayers. We validate these results by comparison with correlative cryo-electron microscopy (cryo-EM) data at the vesicle population level. Finally, we quantify the vesicle geometry and mechanical properties, and show that with additional bilayers adherent vesicles are more spherical and stiffer. Surprisingly, at ∼20% stiffening for each additional bilayer, the vesicle stiffness scales only weakly with lamellarity. Our results show the potential of AFM for studying liposomal nanoparticles and suggest that small multilamellar vesicles may have beneficial mechanical properties for cellular uptake.

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.

Fluctuation tension and shape transition of vesicles: renormalisation calculations and Monte Carlo simulations

It has been known for long that the fluctuation surface tension of membranes r, computed from the height fluctuation spectrum, is not equal to the bare surface tension σ, which is introduced in the theory either as a Lagrange multiplier to conserve the total membrane area or as an external constraint. In this work we relate these two surface tensions both analytically and numerically. They are also compared to the Laplace tension γ, and the mechanical frame tension τ. Using the Helfrich model and one-loop renormalisation calculations, we obtain, in addition to the effective bending modulus κ_eff, a new expression for the effective surface tension σ_eff = σ - εk_BT/(2a_p) where k_BT is the thermal energy, a_p the projected cut-off area, and ε = 3 or 1 according to the allowed configurations that keep either the projected area or the total area constant. Moreover we show that the crumpling transition for an infinite planar membrane occurs for σ_eff = 0, and also that it coincides with vanishing Laplace and frame tensions. Using extensive Monte Carlo (MC) simulations, triangulated membranes of vesicles made of N = 100-2500 vertices are simulated within the Helfrich theory. As compared to alternative numerical models, no local constraint is applied and the shape is only controlled by the constant volume, the spontaneous curvature and σ. It is shown that the numerical fluctuation surface tension r is equal to σ_eff both with radial MC moves (ε = 3) and with corrected MC moves locally normal to the fluctuating membrane (ε = 1). For finite vesicles of typical size R, two different regimes are defined: a tension regime for [small sigma, Greek, circumflex]_eff = σ_effR²/κ_eff > 0 and a bending one for -1 < [small sigma, Greek, circumflex]_eff < 0. A shape transition from a quasi-spherical shape imposed by the large surface energy, to more deformed shapes only controlled by the bending energy, is observed numerically at [small sigma, Greek, circumflex]_eff ≃ 0. We propose that the buckling transition, observed for planar supported membranes in the literature, occurs for [small sigma, Greek, circumflex]_eff ≃ -1, the associated negative frame tension playing the role of a compressive force. Hence, a precise control of the value of σ_eff in simulations cannot but enhance our understanding of shape transitions of vesicles and cells.

Theory and algorithms to compute Helfrich bending forces: a review

Cell membranes are vital to shield a cell's interior from the environment. At the same time they determine to a large extent the cell's mechanical resistance to external forces. In recent years there has been considerable interest in the accurate computational modeling of such membranes, driven mainly by the amazing variety of shapes that red blood cells and model systems such as vesicles can assume in external flows. Given that the typical height of a membrane is only a few nanometers while the surface of the cell extends over many micrometers, physical modeling approaches mostly consider the interface as a two-dimensional elastic continuum. Here we review recent modeling efforts focusing on one of the computationally most intricate components, namely the membrane's bending resistance. We start with a short background on the most widely used bending model due to Helfrich. While the Helfrich bending energy by itself is an extremely simple model equation, the computation of the resulting forces is far from trivial. At the heart of these difficulties lies the fact that the forces involve second order derivatives of the local surface curvature which by itself is the second derivative of the membrane geometry. We systematically derive and compare the different routes to obtain bending forces from the Helfrich energy, namely the variational approach and the thin-shell theory. While both routes lead to mathematically identical expressions, so-called linear bending models are shown to reproduce only the leading order term while higher orders differ. The main part of the review contains a description of various computational strategies which we classify into three categories: the force, the strong and the weak formulation. We finally give some examples for the application of these strategies in actual simulations.

The role of optical projection in the analysis of membrane fluctuations

The spectral analysis of thermal fluctuations, or flickering, is a simple and non-invasive method widely used to determine the mechanical properties of artificial and biological lipid membranes. In its most common implementation, the position of the edge of a cell or vesicle is tracked from optical microscopy videos. However, a systematic disagreement with X-ray scattering and micromechanical manipulation data has brought into question the validity of the method. We present an improved analysis protocol that resolves these discrepancies by accounting for the finite vertical resolution of the optics used to image fluctuations.

Competition between Bending and Internal Pressure Governs the Mechanics of Fluid Nanovesicles

Nanovesicles (∼100 nm) are ubiquitous in cell biology and an important vector for drug delivery. Mechanical properties of vesicles are known to influence cellular uptake, but the mechanism by which deformation dynamics affect internalization is poorly understood. This is partly due to the fact that experimental studies of the mechanics of such vesicles remain challenging, particularly at the nanometer scale where appropriate theoretical models have also been lacking. Here, we probe the mechanical properties of nanoscale liposomes using atomic force microscopy (AFM) indentation. The mechanical response of the nanovesicles shows initial linear behavior and subsequent flattening corresponding to inward tether formation. We derive a quantitative model, including the competing effects of internal pressure and membrane bending, that corresponds well to these experimental observations. Our results are consistent with a bending modulus of the lipid bilayer of ∼14kbT. Surprisingly, we find that vesicle stiffness is pressure dominated for adherent vesicles under physiological conditions. Our experimental method and quantitative theory represents a robust approach to study the mechanics of nanoscale vesicles, which are abundant in biology, as well as being of interest for the rational design of liposomal vectors for drug delivery.

Is the European regulatory framework sufficient to assure the safety of citizens using health products containing nanomaterials?

The growing application of nanomaterials in healthcare products (i.e., cosmetics, medical devices, and medicinal products) has encouraged the upgrade of the regulatory framework within the European Community to better control their use and manage the risk of negative effects on human health and environment. Unfortunately, despite the efforts of European Authorities, the current legislation is still stratified and several criticisms remain because of the lack of well-established scientific knowledge on nanomaterials. Although the regulatory framework for cosmetic products is almost complete, the efficacy and/or safety assessment of nanomaterials in medicinal products and medical devices is still based on case-by-case evaluation because of the complexity of such systems.

Design principles for robust vesiculation in clathrin-mediated endocytosis

A critical step in cellular-trafficking pathways is the budding of membranes by protein coats, which recent experiments have demonstrated can be inhibited by elevated membrane tension. The robustness of processes like clathrin-mediated endocytosis (CME) across a diverse range of organisms and mechanical environments suggests that the protein machinery in this process has evolved to take advantage of some set of physical design principles to ensure robust vesiculation against opposing forces like membrane tension. Using a theoretical model for membrane mechanics and membrane protein interaction, we have systematically investigated the influence of membrane rigidity, curvature induced by the protein coat, area covered by the protein coat, membrane tension, and force from actin polymerization on bud formation. Under low tension, the membrane smoothly evolves from a flat to budded morphology as the coat area or spontaneous curvature increases, whereas the membrane remains essentially flat at high tensions. At intermediate, physiologically relevant, tensions, the membrane undergoes a "snap-through instability" in which small changes in the coat area, spontaneous curvature or membrane tension cause the membrane to "snap" from an open, U-shape to a closed bud. This instability can be smoothed out by increasing the bending rigidity of the coat, allowing for successful budding at higher membrane tensions. Additionally, applied force from actin polymerization can bypass the instability by inducing a smooth transition from an open to a closed bud. Finally, a combination of increased coat rigidity and force from actin polymerization enables robust vesiculation even at high membrane tensions.

Membrane stiffness is modified by integral membrane proteins

The ease with which a cell membrane can bend and deform is important for a wide range of biological functions. Peripheral proteins that induce curvature in membranes (e.g. BAR domains) have been studied for a number of years. Little is known, however, about the effect of integral membrane proteins on the stiffness of a membrane (characterised by the bending rigidity, Kc). We demonstrate by computer simulation that adding integral membrane proteins at physiological densities alters the stiffness of the membrane. First we establish that the coarse-grained MARTINI forcefield is able to accurately reproduce the bending rigidity of a small patch of 1500 phosphatidyl choline lipids by comparing the calculated value to both experiment and an atomistic simulation of the same system. This enables us to simulate the dynamics of large (ca. 50 000 lipids) patches of membrane using the MARTINI coarse-grained description. We find that altering the lipid composition changes the bending rigidity. Adding integral membrane proteins to lipid bilayers also changes the bending rigidity, whilst adding a simple peripheral membrane protein has no effect. Our results suggest that integral membrane proteins can have different effects, and in the case of the bacterial outer membrane protein, BtuB, the greater the density of protein, the larger the reduction in stiffness.

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'.

Millimeter-area, free standing, phospholipid bilayers

Minimal model biomembrane studies have the potential to unlock the fundamental mechanisms of cellular function that govern the processes upon which life relies. However, existing methods to fabricate free-standing model membranes currently have significant limitations. Bilayer sizes are often tens of micrometers, decoupling curvature or substrate effects, orthogonal control over tension, and solvent exchange combined with microscopy techniques is not possible, which restricts the studies that can be performed. Here, we describe a versatile platform to generate free standing, planar, phospholipid bilayers with millimeter scale areas. The technique relies on an adapted thin-film balance apparatus allowing for the dynamic control of the nucleation and growth of a planar black lipid membrane in the center of an orifice surrounded by microfluidic channels. Success is demonstrated using several different lipid types, including mixtures that show the same temperature dependent phase separation as existing protocols, moreover, membranes are highly stable. Two advantages unique to the proposed method are the dynamic control of the membrane tension and the possibility to make extremely large area membranes. We demonstrate this by showing how a block polymer, F68, used in drug delivery increases the membrane compliance. Together, the results demonstrate a new paradigm for studying the mechanics, structure, and function of model membranes.

Toward cell-inspired materials that feel: measurements and modeling of mechanotransduction in droplet-based, multi-membrane arrays

The droplet interface bilayer (DIB) was recently used to show that a 5 nm thick lipid membrane placed near a vibrating synthetic hair could transduce hair motion into electrical current. Herein, we study for the first time mechanoelectrical transduction of hair motion using multi-membrane DIB arrays formed with more than 2 droplets connected in series, and we introduce a transduction model to investigate how airflow across the hair generates current in a membrane-based hair cell. Measurements of sensing currents across every membrane in serial chains of up to 5 connected droplets demonstrate that perturbation of a single hair creates vibrations that propagate across several droplets, allowing for membranes that are not directly attached to the hair to still transduce its motion. Membranes positioned closest to the hair generate the largest currents, while those farther away produce less current due to energy loss from fluid damping. Inserting multiple hairs of different lengths into different droplets in the array yields sensing currents that exhibit multiple characteristic frequencies in addition to location specific current intensities, features that can be used to spatially localize mechanical perturbations. We also develop a transduction model that provides an order-of-magnitude approximation of the sensing current generated by a membrane in response to airflow across the hair. This model provides physical insights into how membrane-based materials can be used for sensing mechanical stimuli--just like nature does.

Membrane bending by protein crowding is affected by protein lateral confinement

Crowding of asymmetrically-distributed membrane proteins has been recently recognized as an important factor in remodeling of biological membranes, for example during transport vesicle formation. In this paper, we theoretically analyze the effect of protein crowding on membrane bending and examine its dependence on protein size, shape, transmembrane asymmetry and lateral confinement. We consider three scenarios of protein lateral organization, which are highly relevant for cellular membranes in general: freely diffusing membrane proteins without lateral confinement, the presence of a diffusion barrier and interactions with a vesicular coat. We show that protein crowding affects vesicle formation even if the proteins are distributed symmetrically across the membrane and that this effect depends significantly on lateral confinement. The largest crowding effect is predicted for the proteins that are confined to the forming vesicle by a diffusion barrier. We calculate the bending properties of a crowded membrane and find that its spontaneous curvature depends primarily on the degree of transmembrane asymmetry, and its effective bending modulus on the type of lateral confinement. Using the example of COPII vesicle formation from the endoplasmic reticulum, we analyze the energetic cost of vesicle formation. The results provide a novel insight into the effects of lateral and transmembrane organization of membrane proteins, and can guide data interpretation and future experimental approaches.