Bending resistance and chemically induced moments in membrane bilayers

OrganL: Dynamic triangulation of biomembranes using curved elements

We describe a method for simulating biomembranes of arbitrary shape. In contrast to other dynamically triangulated surface (DTS) algorithms, our method provides a rich, quasi-tangent-continuous, yet local description of the surface. We use curved Nagata triangles, which we generalize to cubic order to achieve the requisite flexibility. The resulting interpolation can be constructed locally without iterations, at the cost of having only approximate tangent continuity away from the vertices. This allows us to provide a parallelized and fine-tuned Monte Carlo implementation. As a first example of the potential benefits of the enhanced description, our method supports inhomogeneous lipid distributions as well as lipid mixing. It also supports restraints and constraints of various types and is constructed to be as easily extensible as possible. We validate the approach by testing its numerical accuracy, followed by reproducing the known Helfrich solutions for shapes with rotational symmetry. Finally, we present some example applications, including curvature-driven demixing and stylized effects of proteins. Input files for these examples, as well as the implementation itself, are freely available for researchers under the name OrganL (https://zenodo.org/doi/10.5281/zenodo.11204709).

Controlled node growth on the surface of polymersomes

Incorporating nucleobases into synthetic polymers has proven to be a versatile method for controlling self-assembly. The formation of strong directional hydrogen bonds between complementary nucleobases provides a driving force that permits access to complex particle morphologies. Here, nucleobase pairing was used to direct the formation and lengthening of nodes on the outer surface of vesicles formed from polymers (polymersomes) functionalised with adenine in their membrane-forming domains. Insertion of a self-assembling short diblock copolymer containing thymine into the polymersome membranes caused an increase in steric crowding at the hydrophilic/hydrophobic interface, which was relieved by initial node formation and subsequent growth. Nano-objects were imaged by (cryo-)TEM, which permitted quantification of node coverage and length. The ability to control node growth on the surface of polymersomes provides a new platform to develop higher-order nanomaterials with tailorable properties.

Stationary shapes of axisymmetric vesicles beyond lowest-energy configurations

We conduct a systematic exploration of the energy landscape of vesicle morphologies within the framework of the Helfrich model. Vesicle shapes are determined by minimizing the elastic energy subject to constraints of constant area and volume. The results show that pressurized vesicles can adopt higher-energy spindle-like configurations that require the action of point forces at the poles. If the internal pressure is lower than the external one, multilobed shapes are predicted. We utilize our results to rationalize experimentally observed spindle shapes of giant vesicles in a uniform AC electric field.

Bottom-up approach to explore alpha-amylase assisted membrane remodelling

Soluble alpha-amylases play an important role in the catabolism of polysaccharides. In this work, we show that the malt α -amylase can interact with the lipid membrane and further alter its mechanical properties. Vesicle fluctuation spectroscopy is used for quantitative measurement of the membrane bending rigidity of phosphatidylcholines lipid vesicles from the shape fluctuation based on the whole contour of Giant Unilamellar Vesicles (GUVs). The bending rigidity of the 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine lipid vesicles in water increases significantly with the presence of 0.14 micromolar alpha-amylase (AA) in the exterior solution. It appears that the enzyme present in the external solution interacts with the outer layer of the bilayer membrane, leading to an asymmetry of the solution on either side of the bilayer membrane and altering its elasticity. At AA concentration of 1.5 micromolars and above, changes in the morphology of the GUV membrane are observed. The interaction between AA in the external solution and the external leaflet causes the bilayer membrane to curve spontaneously, leading to the formation of outbuds, giving a positive spontaneous curvature of C0 ≤ 0.05 μm-1 at ≈ 1 mg / ml of the AA concentration. We validate and characterize its concentration-dependent role in stabilizing the membrane curvature. Our findings indicate that the involvement of the enzyme, depending on the concentration, can have a considerable effect on the mechanical characteristics of the membrane.

Stationary shapes of axisymmetric vesicles beyond lowest-energy configurations

We conduct a systematic exploration of the energy landscape of vesicle morphologies within the framework of the Helfrich model. Vesicle shapes are determined by minimizing the elastic energy subject to constraints of constant area and volume. The results show that pressurized vesicles can adopt higher-energy spindle-like configurations that require the action of point forces at the poles. If the internal pressure is lower than the external one, multilobed shapes are predicted. We utilize our results to rationalize the experimentally observed spindle shapes of giant vesicles in a uniform AC field.

Mitochondrial membrane model: Lipids, elastic properties, and the changing curvature of cardiolipin

Mammalian and Drosophila melanogaster model mitochondrial membrane compositions are constructed from experimental data. Simplified compositions for inner and outer mitochondrial membranes are provided, including an asymmetric inner mitochondrial membrane. We performed atomistic molecular dynamics simulations of these membranes and computed their material properties. When comparing these properties to those obtained by extrapolation from their constituting lipids, we find good overall agreement. Finally, we analyzed the curvature effect of cardiolipin, considering ion concentration effects, oxidation, and pH. We draw the conclusion that cardiolipin-negative curvature is most likely due to counterion effects, such as cation adsorption, in particular of H3O+. This oft-neglected effect might account for the puzzling behavior of this lipid.

Photomanipulation of Minimal Synthetic Cells: Area Increase, Softening, and Interleaflet Coupling of Membrane Models Doped with Azobenzene-Lipid Photoswitches

Light can effectively interrogate biological systems in a reversible and physiologically compatible manner with high spatiotemporal precision. Understanding the biophysics of photo-induced processes in bio-systems is crucial for achieving relevant clinical applications. Employing membranes doped with the photolipid azobenzene-phosphatidylcholine (azo-PC), a holistic picture of light-triggered changes in membrane kinetics, morphology, and material properties obtained from correlative studies on cell-sized vesicles, Langmuir monolayers, supported lipid bilayers, and molecular dynamics simulations is provided. Light-induced membrane area increases as high as ≈25% and a ten-fold decrease in the membrane bending rigidity is observed upon trans-to-cis azo-PC isomerization associated with membrane leaflet coupling and molecular curvature changes. Vesicle electrodeformation measurements and atomic force microscopy reveal that trans azo-PC bilayers are thicker than palmitoyl-oleoyl phosphatidylcholine (POPC) bilayers but have higher specific membrane capacitance and dielectric constant suggesting an increased ability to store electric charges across the membrane. Lastly, incubating POPC vesicles with azo-PC solutions results in the insertion of azo-PC in the membrane enabling them to become photoresponsive. All these results demonstrate that light can be used to finely manipulate the shape, mechanical and electric properties of photolipid-doped minimal cell models, and liposomal drug carriers, thus, presenting a promising therapeutic alternative for the repair of cellular disorders.

The ins and outs of membrane bending by intrinsically disordered proteins

Membrane curvature is essential to diverse cellular functions. While classically attributed to structured domains, recent work illustrates that intrinsically disordered proteins are also potent drivers of membrane bending. Specifically, repulsive interactions among disordered domains drive convex bending, while attractive interactions drive concave bending, creating membrane-bound, liquid-like condensates. How might disordered domains that contain both repulsive and attractive domains affect curvature? Here, we examined chimeras that combined attractive and repulsive interactions. When the attractive domain was closer to the membrane, its condensation amplified steric pressure among repulsive domains, leading to convex curvature. In contrast, when the repulsive domain was closer to the membrane, attractive interactions dominated, resulting in concave curvature. Further, a transition from convex to concave curvature occurred with increasing ionic strength, which reduced repulsion while enhancing condensation. In agreement with a simple mechanical model, these results illustrate a set of design rules for membrane bending by disordered proteins.

Dynamics of fluid bilayer vesicles: Soft meshes and robust curvature energy discretization

Continuum models like the Helfrich Hamiltonian are widely used to describe fluid bilayer vesicles. Here we study the molecular dynamics compatible dynamics of the vertices of two-dimensional meshes representing the bilayer, whose in-plane motion is only weakly constrained. We show (i) that Jülicher's discretization of the curvature energy offers vastly superior robustness for soft meshes compared to the commonly employed expression by Gommper and Kroll and (ii) that for sufficiently soft meshes, the typical behavior of fluid bilayer vesicles can emerge even if the mesh connectivity remains fixed throughout the simulations. In particular, soft meshes can accommodate large shape transformations, and the model can generate the typical ℓ^{-4} signal for the amplitude of surface undulation modes of nearly spherical vesicles all the way up to the longest wavelength modes. Furthermore, we compare results for Newtonian, Langevin, and Brownian dynamics simulations of the mesh vertices to demonstrate that the internal friction of the membrane model is negligible, making it suitable for studying the internal dynamics of vesicles via coupling to hydrodynamic solvers or particle-based solvent models.

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

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

Extracellular vesicle-matrix interactions

The extracellular matrix in microenvironments harbors a variety of signals to control cellular functions and the materiality of tissues. Most efforts to synthetically reconstitute the matrix by biomaterial design have focused on decoupling cell-secreted and polymer-based cues. Cells package molecules into nanoscale lipid membrane-bound extracellular vesicles and secrete them. Thus, extracellular vesicles inherently interact with the meshwork of the extracellular matrix. In this Review, we discuss various aspects of extracellular vesicle-matrix interactions. Cells receive feedback from the extracellular matrix and leverage intracellular processes to control the biogenesis of extracellular vesicles. Once secreted, various biomolecular and biophysical factors determine whether extracellular vesicles are locally incorporated into the matrix or transported out of the matrix to be taken up by other cells or deposited into tissues at a distal location. These insights can be utilized to develop engineered biomaterials where EV release and retention can be precisely controlled in host tissue to elicit various biological and therapeutic outcomes.

Stability of Branched Tubular Membrane Structures

We study the energetics and stability of branched tubular membrane structures by computer simulations of a triangulated network model. We find that triple (Y) junctions can be created and stabilized by applying mechanical forces, if the angle between branches is 120°. The same holds for tetrahedral junctions with tetraeder angles. If the wrong angles are enforced, the branches coalesce to a linear structure, a pure tube. After releasing the mechanical force, Y-branched structures remain metastable if one constrains the enclosed volume and the average curvature (the area difference) to a fixed value; tetrahedral junctions however split up into two Y junctions. Somewhat counterintuitively, the energy cost of adding a Y branch is negative in structures with fixed surface area and tube diameter, even if one accounts for the positive contribution of the additional branch end. For fixed average curvature, however, adding a branch also enforces a thinning of tubes, therefore the overall curvature energy cost is positive. Possible implications for the stability of branched networks structures in cells are discussed.

Dependence of protein-induced lipid bilayer deformations on protein shape

Membrane proteins typically deform the surrounding lipid bilayer membrane, which can play an important role in the function, regulation, and organization of membrane proteins. Membrane elasticity theory provides a beautiful description of protein-induced lipid bilayer deformations, in which all physical parameters can be directly determined from experiments. While analytic solutions of protein-induced elastic bilayer deformations are most easily developed for proteins with approximately circular cross sections, structural biology has shown that membrane proteins come in a variety of distinct shapes, with often considerable deviations from a circular cross section. We develop here a boundary value method (BVM) that permits the construction of analytic solutions of protein-induced elastic bilayer deformations for protein shapes with arbitrarily large deviations from a circular cross section, for constant as well as variable boundary conditions along the bilayer-protein interface. We apply this BVM to protein-induced lipid bilayer thickness deformations. Our BVM reproduces available analytic solutions for proteins with circular cross section and yields, for proteins with noncircular cross section, excellent agreement with numerical, finite element solutions. On this basis, we formulate a simple analytic approximation of the bilayer thickness deformation energy associated with general protein shapes and show that, for modest deviations from rotational symmetry, this analytic approximation is in good agreement with BVM solutions. Using the BVM, we survey the dependence of protein-induced elastic bilayer thickness deformations on protein shape, and thus explore how the coupling of protein shape and bilayer thickness deformations affects protein oligomerization and transitions in protein conformational state.

Capturing Lipid Nanodisc Shape and Properties Using a Continuum Elastic Theory

Lipid nanodiscs are nanometric bilayer patches enveloped by confining structures, commonly composed of membrane scaffolding proteins (MSPs). To resolve the interplay between MSP geometry, lipid confinement, and membrane material properties on the nanodisc shape, we apply a continuum elastic theory accounting for lipid bending, tilting, and area deformations. The equilibrium nanodisc shape is then determined by minimizing the elastic free energy functional. Analytic expressions derived under simplifying assumptions demonstrate that the nanodisc shape is sensitive to its size, lipid density, and the lipid tilt and thickness imposed at the contact with the MSP. Under matching physical parameters, these expressions quantitatively reproduce the shape of nanodiscs seen in molecular dynamics simulations, but only if lipid tilt is explicitly considered. We further demonstrate how the bending rigidity can be extracted from the membrane shape profile by fitting the numerically minimized full elastic functional to the membrane shape found in simulations. This fitting procedure faithfully informs on the bending rigidity of nanodiscs larger than ca. 5 nm in radius. The fitted profiles accurately reproduce the increase in bending modulus found using real-space fluctuation analysis of simulated nanodiscs and, for large nanodiscs, also accurately resolve its spatial variations. Our study shows how deformations in lipid patches confined in nanodiscs can be well described by a continuum elastic theory and how this fit can be used to determine local material properties from shape analysis of nanodiscs in simulations. This methodology could potentially allow direct determination of lipid properties from experiments, for example cryo-electron microscopy images of lipid nanodiscs, thereby allowing to guide the development of future nanodisc formulations with desired properties.

Mem3DG: Modeling membrane mechanochemical dynamics in 3D using discrete differential geometry

Biomembranes adopt varying morphologies that are vital to cellular functions. Many studies use computational modeling to understand how various mechanochemical factors contribute to membrane shape transformations. Compared with approximation-based methods (e.g., finite element method [FEM]), the class of discrete mesh models offers greater flexibility to simulate complex physics and shapes in three dimensions; its formulation produces an efficient algorithm while maintaining coordinate-free geometric descriptions. However, ambiguities in geometric definitions in the discrete context have led to a lack of consensus on which discrete mesh model is theoretically and numerically optimal; a bijective relationship between the terms contributing to both the energy and forces from the discrete and smooth geometric theories remains to be established. We address this and present an extensible framework, Mem3DG, for modeling 3D mechanochemical dynamics of membranes based on discrete differential geometry (DDG) on triangulated meshes. The formalism of DDG resolves the inconsistency and provides a unifying perspective on how to relate the smooth and discrete energy and forces. To demonstrate, Mem3DG is used to model a sequence of examples with increasing mechanochemical complexity: recovering classical shape transformations such as 1) biconcave disk, dumbbell, and unduloid; and 2) spherical bud on spherical, flat-patch membrane; investigating how the coupling of membrane mechanics with protein mobility jointly affects phase and shape transformation. As high-resolution 3D imaging of membrane ultrastructure becomes more readily available, we envision Mem3DG to be applied as an end-to-end tool to simulate realistic cell geometry under user-specified mechanochemical conditions.

Membrane stiffening in Chitosan mediated multilamellar vesicles of alkyl ether carboxylates

HYPOTHESIS

Membrane undulations are known to strongly affect the stability of uni- and multilamellar vesicles formed by surfactants or phospholipids. Herein, based on the same arguments, we hypothesise that the properties of polyelectrolyte mediated surfactant multilamellar vesicles, in particular the multiplicity - i.e. the number of layers forming the vesicle - depend on the dynamics of the membrane.

EXPERIMENTS

Small-angle neutron scattering (SANS) and neutron spin-echo (NSE) were used to probe the structure and the dynamics of the multilayered vesicles formed in mixtures of the biopolymer chitosan and oppositely charged alkyl ether carboxylates. The neutron scattering data are complemented by static and dynamic light scattering experiments. Experiments were performed in polyelectrolyte excess conditions, and at a pH close to the pKa of the surfactant.

FINDINGS

The structural investigation shows very clearly that multilayered surfactant/polyelectrolyte vesicles are formed in the investigated mixtures. Only 3 to 5 layers form, on average, one vesicle, as similarly found in mixtures of chitosan and phospholipid vesicles. NSE shows that the surfactant membrane becomes stiffer upon complexation with chitosan, and that the fluctuation of the layers is strongly coupled in time and space. Such strong coupling and the increase in overall stiffness is associated with a high entropic cost. Accordingly, the combined SANS and NSE study points out that the low multiplicity found in multilayered vesicles involving the rigid polysaccharide chitosan arises from the strongly coupled dynamics of the membrane layers.

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.

Multispherical shapes of vesicles highlight the curvature elasticity of biomembranes

Giant lipid vesicles form unusual multispherical or "multi-balloon" shapes consisting of several spheres that are connected by membrane necks. Such multispherical shapes have been recently observed when the two sides of the membranes were exposed to different sugar solutions. This sugar asymmetry induced a spontaneous curvature, the sign of which could be reversed by swapping the interior with the exterior solution. Here, previous studies of multispherical shapes are reviewed and extended to develop a comprehensive theory for these shapes. Each multisphere consists of large and small spheres, characterized by two radii, the large-sphere radius, R_l, and the small-sphere radius, R_s. For positive spontaneous curvature, the multisphere can be built up from variable numbers N_l and N_s of large and small spheres. In addition, multispheres consisting of N_*=N_l+N_s equally sized spheres are also possible and provide examples for constant-mean-curvature surfaces. For negative spontaneous curvature, all multispheres consist of one large sphere that encloses a variable number N_s of small spheres. These general features of multispheres arise from two basic properties of curvature elasticity: the local shape equation for spherical membrane segments and the stability conditions for closed membrane necks. In addition, the (N_l+N_s)-multispheres can form several (N_l+N_s)-patterns that differ in the way, in which the spheres are mutually connected. These patterns may involve multispherical junctions consisting of individual spheres that are connected to more than two neighboring spheres. The geometry of the multispheres is governed by two polynomial equations which imply that (N_l+N_s)-multispheres can only be formed within a certain restricted range of vesicle volumes. Each (N_l+N_s)-pattern can be characterized by a certain stability regime that depends both on the stability of the closed necks and on the multispherical geometry. Interesting and challenging topics for future studies include the response of multispheres to locally applied external forces, membrane fusion between spheres to create multispherical shapes of higher-genus topology, and the enlarged morphological complexity of multispheres arising from lipid phase separation and intramembrane domains.

Observed steric crowding at modest coverage requires a particular membrane-binding scheme or a complementary mechanism

Membrane shape transitions, including fusion and fission, play an important role in many biological processes. It is therefore essential to understand mechanisms of "curvature generation," the mathematical quantification of membrane shape. Among the different mechanisms is the effect of steric pressure between proteins crowded on a surface. At a higher curvature, there is more space for the crowders and less steric pressure. Currently, the physical model of curvature induction by crowding views the proteins as being bound to the surface as a whole rather than to the underlying lipids. Here, we split the previously understood model into two pieces: first, the reduction in steric pressure due to reduced collisions between proteins, and second, the increased area available to the protein that is independent of other crowders. The cases are distinguished by how the crowder is attached to the membrane. When a protein is attached to a specific lipid, as is the case in a typical crowding experiment, one should not model its lateral entropy; this has already been accounted for by the underlying lipid. The Carnahan-Starling pressure includes this lateral entropy. The revised theory predicts that a purely entropic crowding mechanism is inconsistent with observations of reshaping at the lower range of surface coverage, suggesting that an additional mechanism is at play.

Molecular self-assembly under nanoconfinement: indigo carmine scroll structures entrapped within polymeric capsules

Molecular self-assembly forms structures of well-defined organization that allow control over material properties, affording many advanced technological applications. Although the self-assembly of molecules is seemingly spontaneous, the structure into which they assemble can be altered by carefully modulating the driving forces. Here we study the self-assembly within the constraints of nanoconfined closed spherical volumes of polymeric nanocapsules, whereby a mixture of polyester-polyether block copolymer and methacrylic acid methyl methacrylate copolymer forms the entrapping capsule shell of nanometric dimensions. We follow the organization of the organic dye indigo carmine that serves as a model building unit due to its tendency to self-assemble into flat lamellar molecular sheets. Analysis of the structures formed inside the nanoconfined space using cryogenic-transmission electron microscopy (cryo-TEM) and cryogenic-electron tomography (cryo-ET) reveal that confinement drives the self-assembly to produce tubular scroll-like structures of the dye. Combined continuum theory and molecular modeling allow us to estimate the material properties of the confined nanosheets, including their elasticity and brittleness. Finally, we comment on the formation mechanism and forces that govern self-assembly under nanoconfinement.

Investigation of Shape Transformations of Vesicles, Induced by Their Adhesion to Flat Substrates Characterized by Different Adhesion Strength

The adhesion of lipid vesicles to a rigid flat surface is investigated. We examine the influence of the membrane spontaneous curvature, adhesion strength, and the reduced volume on the stability and shape transformations of adhered vesicles. The minimal strength of the adhesion necessary to stabilize the shapes of adhered vesicles belonging to different shape classes is determined. It is shown that the budding of an adhered vesicle may be induced by the change of the adhesion strength. The importance of the free vesicle shape for its susceptibility to adhesion is discussed.

Self-assembly of polyhedral bilayer vesicles from Piezo ion channels

Piezo ion channels underlie many forms of mechanosensation in vertebrates and have been found to bend the membrane into strongly curved dome shapes. We develop a methodology describing the self-assembly of lipids and Piezo proteins into polyhedral bilayer vesicles. We validate this methodology for bilayer vesicles formed from bacterial mechanosensitive channels of small conductance, for which experiments found a polyhedral arrangement of proteins with snub cube symmetry and a well-defined characteristic vesicle size. On this basis, we calculate the self-assembly diagram for polyhedral bilayer vesicles formed from Piezo proteins. We find that the radius of curvature of the Piezo dome provides a critical control parameter for the self-assembly of Piezo vesicles, with high abundances of Piezo vesicles with octahedral, icosahedral, and snub cube symmetry with increasing Piezo dome radius of curvature.

Mechanics of cup-shaped caveolae

Caveolae are cell membrane invaginations of defined lipid and protein composition that flatten with increasing membrane tension. Super-resolution light microscopy and electron microscopy have revealed that caveolae can take a variety of cuplike shapes. We show here that, for the range in membrane tension relevant for cell membranes, the competition between membrane tension and membrane bending yields caveolae with cuplike shapes similar to those observed experimentally. We find that the caveola shape and its sensitivity to changes in membrane tension can depend strongly on the caveola spontaneous curvature and on the size of caveola domains. Our results suggest that heterogeneity in caveola shape produces a staggered response of caveolae to mechanical perturbations of the cell membrane, which may facilitate regulation of membrane tension over the wide range of scales thought to be relevant for cell membranes.

A plasmon-based nanoruler to probe the mechanical properties of synthetic and biogenic nanosized lipid vesicles

Nanosized lipid vesicles are ubiquitous in living systems (e.g. cellular compartments or extracellular vesicles, EVs) and in formulations for nanomedicine (e.g. liposomes for RNA vaccine formulations). The mechanical properties of such vesicles are crucial in several physicochemical and biological processes, ranging from cellular uptake to stability in aerosols. However, their accurate determination remains challenging and requires sophisticated instruments and data analysis. Here we report the first evidence that the surface plasmon resonance (SPR) of citrated gold nanoparticles (AuNPs) adsorbed on synthetic vesicles is finely sensitive to the vesicles' mechanical properties. We then leverage this finding to show that the SPR tracking provides quantitative access to the stiffness of vesicles of synthetic and natural origin, such as EVs. The demonstration of this plasmon-based "stiffness nanoruler" paves the way for developing a facile, cost-effective and high-throughput method to assay the mechanical properties of dispersions of vesicles of nanometric size and unknown composition at a collective level.

Identifying systematic errors in a power spectral analysis of simulated lipid membranes

The elastic properties of lipid membranes can be measured by monitoring their thermal fluctuations. For instance, comparing the power spectra of membrane shape or lipid director fluctuations with predictions based on suitable continuum theories gives access to bending-, tilt-, and twist-moduli. However, to do so in a computer simulation, we must first define a continuum surface shape and lipid director field from the discrete configurations of lipid molecules in a typically fairly small box. Here, we show that the required mapping choices, as well as the details of the subsequent data analysis, can shift the measured values of these moduli by far more than their statistical uncertainties. We investigate the resulting systematic errors on the basis of atomistic simulation trajectories for 13 different lipids, previously published by Venable et al. [Chem. Phys. Lipids 192, 60-74 (2015)]. Specifically, we examine mapping choices for surface- and tilt-field definitions, normalizing and averaging lipid directors, accounting for wave vector dependent time autocorrelations, error propagation, and finding the right fitting range. We propose a set of criteria that may help to decide upon a particular combination of choices underlying the fluctuation analysis, and we make several recommendations based on these. While systematic shifts in observables that are extracted from large-wavelength limits vanish, in principle, for sufficiently large system size, no such exact limit exists for intrinsically local parameters, such as the twist modulus or the splay-tilt coupling, and so not all potential choices can be trivially verified.

Spatial extent of a single lipid's influence on bilayer mechanics

To what spatial extent does a single lipid affect the mechanical properties of the membrane that surrounds it? The lipid composition of a membrane determines its mechanical properties. The shapes available to the membrane depend on its compositional material properties, and therefore, the lipid environment. Because each individual lipid species' chemistry is different, it is important to know its range of influence on membrane mechanical properties. This is defined herein as the lipid's mechanical extent. Here, a lipid's mechanical extent is determined by quantifying lipid redistribution and the average curvature that lipid species experience on fluctuating membrane surfaces. A surprising finding is that, unlike unsaturated lipids, saturated lipids have a complicated, nonlocal effect on the surrounding surface, with the interaction strength maximal at a finite length-scale. The methodology provides the means to substantially enrich curvature-energy models of membrane structures, quantifying what was previously only conjecture.

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

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

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

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

Unraveling topology-induced shape transformations in dendrimersomes

The vital functions of cell membranes require their ability to quickly change shape to perform complex tasks such as motion, division, endocytosis, and apoptosis. Membrane curvature in cells is modulated by very complex processes such as changes in lipid composition, the oligomerization of curvature-scaffolding proteins, and the reversible insertion of protein regions that act like wedges in the membrane. But, could much simpler mechanisms support membrane shape transformation? In this work, we demonstrate how the change of amphiphile topology in the bilayer can drive shape transformations of cell membrane models. To tackle this, we have designed and synthesized new types of amphiphiles-Janus dendrimers-that self-assemble into uni-, multilamellar, or smectic-ordered vesicles, named dendrimersomes. We synthesized Janus dendrimers containing a photo-labile bond that upon UV-Vis irradiation cleavage lose a part of the hydrophilic dendron. This leads to a change from a cylindrically to a wedge-shaped amphiphile. The high mobility of these dendrimers allows for the concentration of the wedge-shaped amphiphiles and the generation of transmembrane asymmetries. The concentration of the wedges and their rate of segregation allowed control of the budding and generation of structures such as tubules and high genus vesicles.

Effect of quercetin on lipid membrane rigidity: assessment by atomic force microscopy and molecular dynamics simulations

Quercetin (3,3',4',5,7-pentahydroxyl-flavone) is a natural flavonoid with many valuable biological effects, but its solubility in water is low, posing major limitations in applications. Quercetin encapsulation in liposomes increases its bioavailability; the drug effect on liposome elastic properties is required for formulation development. Here, we quantify the effect of quercetin molecules on the rigidity of lipoid E80 liposomes using atomic force microscopy (AFM) and molecular dynamics (MD) simulations. AFM images show no effect of quercetin molecules on liposomes morphology and structure. However, AFM force curves suggest that quercetin softens lipid membranes; the Young modulus measured for liposomes encapsulating quercetin is smaller than that determined for blank liposomes. We then used MD simulations to interpret the effect of quercetin on membrane rigidity in terms of molecular interactions. The decrease in membrane rigidity was confirmed by the simulations, which also revealed that quercetin affects structural and dynamic properties: membrane thickness is decreased, acyl chains disorder is increased, and diffusion coefficients of lipid molecules are also increased. Such changes appear to be related to the preferential localization of quercetin within the membrane, near the interface between the hydrophobic core and polar head groups of the lipids.

Minimizing isotropic and deviatoric membrane energy - An unifying formation mechanism of different cellular membrane nanovesicle types

Tiny membrane-enclosed cellular fragments that can mediate interactions between cells and organisms have recently become a subject of increasing attention. In this work the mechanism of formation of cell membrane nanovesicles (CNVs) was studied experimentally and theoretically. CNVs were isolated by centrifugation and washing of blood cells and observed by optical microscopy and scanning electron microscopy. The shape of the biological membrane in the budding process, as observed in phospholipid vesicles, in erythrocytes and in CNVs, was described by an unifying model. Taking the mean curvature h and the curvature deviator d of the membrane surface as the relevant parameters, the shape and the distribution of membrane constituents were determined theoretically by minimization of membrane free energy. Considering these results and previous results on vesiculation of red blood cells it was interpreted that the budding processes may lead to formation of different types of CNVs as regards the compartment (exo/endovesicles), shape (spherical/tubular/torocytic) and composition (enriched/depleted in particular kinds of molecules). It was concluded that the specificity of pinched off nanovesicles derives from the shape of the membrane constituents and not primarily from their chemical identity, which explains evidences on great heterogeneity of isolated extracellular vesicles with respect to composition.

One of the amazing properties of a biological membrane is the ability to undergo dramatic changes of its shape. It may exhibit very high curvature and thereby enclose nano-sized compartments that pinch off from the mother membrane and become freely moving cellular nanovesicles (CNVs). CNVs externalize the pieces of the cell and make them available to other cells within the same organism or other organisms. Therefore they have been acknowledged as mediators of communication between microorganisms, plants, animals and human. Furthernore, they dwell on the border between living and non-living things. Recent findings report on heterogeneity of the size and composition of CNVs found in isolates from different biological samples. As communication between cells is involved in many physiological and patophysiological processes, it is of importance to understand the mechanisms of CNVs formation and recognize the natural laws that mainly govern them. We point to an unifying mechanism that explains stability of differently shaped and composed CNVs by taking into account that the biological membrane tends to attain the minimum of its relevant energy. Conveniently, the procedure can be described by a mathematical model which allows for transparent comparison between experimentally induced shapes of membrane-enclosed vesicular structures and numerical calculations.

A Computational Model of Protein Induced Membrane Morphology with Geodesic Curvature Driven Protein-Membrane Interface

Continuum or hybrid modeling of bilayer membrane morphological dynamics induced by embedded proteins necessitates the identification of protein-membrane interfaces and coupling of deformations of two surfaces. In this article we developed (i) a minimal total geodesic curvature model to describe these interfaces, and (ii) a numerical one-one mapping between two surface through a conformal mapping of each surface to the common middle annulus. Our work provides the first computational tractable approach for determining the interfaces between bilayer and embedded proteins. The one-one mapping allows a convenient coupling of the morphology of two surfaces. We integrated these two new developments into the energetic model of protein-membrane interactions, and developed the full set of numerical methods for the coupled system. Numerical examples are presented to demonstrate (1) the efficiency and robustness of our methods in locating the curves with minimal total geodesic curvature on highly complicated protein surfaces, (2) the usefulness of these interfaces as interior boundaries for membrane deformation, and (3) the rich morphology of bilayer surfaces for different protein-membrane interfaces.

Effect of protein steric constraints on the symmetry of membrane protein polyhedra

Experiments have shown that, in an aqueous environment, lipids and membrane proteins can self-assemble into membrane protein polyhedral nanoparticles (MPPNs). MPPNs are closed, spherical vesicles composed of a lipid bilayer membrane and membrane proteins, with a polyhedral arrangement of membrane proteins. The observed symmetry and size of MPPNs can be understood from the interplay of protein-induced lipid bilayer deformations in MPPNs, topological defects in protein packing necessitated by the spherical shape of MPPNs, and thermal fluctuations in MPPN self-assembly. We explore here the effect of protein steric constraints on MPPN shape. The protein steric constraints considered here may arise from a well-defined shape of protein domains outside the membrane, entropic repulsion between membrane proteins with flexible domains outside the membrane, or binding of other molecules to membrane proteins. Calculating MPPN self-assembly diagrams under protein steric constraints we find that protein steric constraints can strongly affect MPPN self-assembly. Depending on the specific scenario considered, protein steric constraints can leave large portions of the MPPN self-assembly diagrams with no clearly defined MPPN symmetry or substantially expand the regions of MPPN self-assembly diagrams dominated by highly symmetric MPPN states, such as MPPNs with icosahedral or snub cube symmetry. Our results suggest that modification of protein steric constraints may allow the directed self-assembly of MPPNs with specified symmetry, size, and protein composition and may thus facilitate the further utilization of MPPNs for membrane protein structural analysis or targeted drug delivery.

Elastic moduli of lipid membranes: Reproducibility of AFM measures

Membrane elastic properties play a major role in membrane remodeling events, such as vesicle fusion and fission. They are also crucial in drug delivery by liposomes. Different experimental techniques are available to measure elastic properties. Among them, atomic force microscopy (AFM) presents the unique advantage of being directly applicable to nano-sized liposomes. Unfortunately, different AFM measures reported in the literature show little agreement among each other and are difficult to compare with measures of bending modulus obtained by other experimental techniques or by molecular simulations. In this work we determine the bending rigidity of Egg PC liposomes in terms of Young modulus via AFM measurements, using two different tip shapes and different cantilever force constants. We interpret the measures using the Hertz and Shell models, and observe a clear dependency of the Young modulus values on the tip properties and on the interpretative theory. The effect of the AFM tip shape is less important than the effect of the cantilever force constant, and the mathematical model has a major effect on the interpretation of the data. The Shell theory provides the closest agreement between AFM data and other experimental data for the membrane bending modulus. Finally, we compare the results to calculations of bending modulus from molecular dynamics simulations of membrane buckles. Simulations provide values of bending modulus consistent with literature data, but the agreement with AFM experiments is reasonable only for some specific experimental conditions.

Nonaxisymmetric Shapes of Biological Membranes from Locally Induced Curvature

In various biological processes such as endocytosis and caveolae formation, the cell membrane is locally deformed into curved morphologies. Previous models to study membrane morphologies resulting from locally induced curvature often only consider the possibility of axisymmetric shapes-an indeed unphysical constraint. Past studies predict that the cell membrane buds at low resting tensions and stalls at a flat pit at high resting tensions. In this work, we lift the restriction to axisymmetry to study all possible membrane morphologies. Only if the resting tension of the membrane is low, we reproduce axisymmetric membrane morphologies. When the resting tension is moderate to high, we show that 1) axisymmetric membrane pits are unstable and 2) nonaxisymmetric ridge-shaped structures are energetically favorable. Furthermore, we find the interplay between intramembrane viscous flow and the rate of induced curvature affects the membrane's ability to transition into nonaxisymmetric ridges and axisymmetric buds. In particular, we show that axisymmetric buds are favored when the induced curvature is rapidly increased, whereas nonaxisymmetric ridges are favored when the curvature is slowly increased. Our results hold relevant implications for biological processes such as endocytosis and physical phenomena like phase separation in lipid bilayers.

Confinement in Nanodiscs Anisotropically Modifies Lipid Bilayer Elastic Properties

Lipid nanodiscs are small synthetic lipid bilayer structures that are stabilized in solution by special circumscribing (or scaffolding) proteins or polymers. Because they create native-like environments for transmembrane proteins, lipid nanodiscs have become a powerful tool for structural determination of this class of systems when combined with cryo-electron microscopy or nuclear magnetic resonance. The elastic properties of lipid bilayers determine how the lipid environment responds to membrane protein perturbations, and how the lipid in turn modifies the conformational state of the embedded protein. However, despite the abundant use of nanodiscs in determining membrane protein structure, the elastic material properties of even pure lipid nanodiscs (i.e., without embedded proteins) have not yet been quantitatively investigated. A major hurdle is due to the inherently nonlocal treatment of the elastic properties of lipid systems implemented by most existing methods, both experimental and computational. In addition, these methods are best suited for very large “infinite” size lipidic assemblies, or ones that contain periodicity, in the case of simulations. We have previously described a computational analysis of molecular dynamics simulations designed to overcome these limitations, so it allows quantification of the bending rigidity (K_C) and tilt modulus (κ_t) on a local scale even for finite, nonperiodic systems, such as lipid nanodiscs. Here we use this computational approach to extract values of K_C and κ_t for a set of lipid nanodisc systems that vary in size and lipid composition. We find that the material properties of lipid nanodiscs are different from those of infinite bilayers of corresponding lipid composition, highlighting the effect of nanodisc confinement. Nanodiscs tend to show higher stiffness than their corresponding macroscopic bilayers, and moreover, their material properties vary spatially within them. For small-size MSP1 nanodiscs, the stiffness decreases radially, from a value that is larger in their center than the moduli of the corresponding bilayers by a factor of ∼2–3. The larger nanodiscs (MSP1E3D1 and MSP2N2) show milder spatial changes of moduli that are composition dependent and can be maximal in the center or at some distance from it. These trends in moduli correlate with spatially varying structural properties, including the area per lipid and the nanodisc thickness. Finally, as has previously been reported, nanodiscs tend to show deformations from perfectly flat circular geometries to varying degrees, depending on size and lipid composition. The modulations of lipid elastic properties that we find should be carefully considered when making structural and functional inferences concerning embedded proteins.

Shape Transformations of Vesicles Induced by Their Adhesion to Flat Surfaces

The shape transformations of lipid vesicles induced by the adhesion to a flat surface is investigated. We perform the calculations within the framework of the Helfrich spontaneous curvature model. The calculations were performed for a few values of the reduced volume and the spontaneous curvature. The range of stability for different shapes (oblate, prolate, and stomatocyte) of adhered vesicles is determined. New physical phenomena such as budding induced by the adhesion of vesicles are reported.

Geometry and dynamics of lipid membranes: The Scriven-Love number

The equations governing lipid membrane dynamics in planar, spherical, and cylindrical geometries are presented here. Unperturbed and first-order perturbed equations are determined and nondimensionalized. In membrane systems with a nonzero base flow, perturbed in-plane and out-of-plane quantities are found to vary over different length scales. A new dimensionless number, named the Scriven-Love number, and the well-known Föppl-von Kármán number result from a scaling analysis. The Scriven-Love number compares out-of-plane forces arising from the in-plane, intramembrane viscous stresses to the familiar elastic bending forces, while the Föppl-von Kármán number compares tension to bending forces. Both numbers are calculated in past experimental works, and span a wide range of values in various biological processes across different geometries. In situations with large Scriven-Love and Föppl-von Kármán numbers, the dynamical response of a perturbed membrane is dominated by out-of-plane viscous and surface tension forces-with bending forces playing a negligible role. Calculations of non-negligible Scriven-Love numbers in various biological processes and in vitro experiments show in-plane intramembrane viscous flows cannot generally be ignored when analyzing lipid membrane behavior.

Active Contact Forces Drive Nonequilibrium Fluctuations in Membrane Vesicles

We analyze the nonequilibrium shape fluctuations of giant unilamellar vesicles encapsulating motile bacteria. Owing to bacteria-membrane collisions, we experimentally observe a significant increase in the magnitude of membrane fluctuations at low wave numbers, compared to the well-known thermal fluctuation spectrum. We interrogate these results by numerically simulating membrane height fluctuations via a modified Langevin equation, which includes bacteria-membrane contact forces. Taking advantage of the lengthscale and timescale separation of these contact forces and thermal noise, we further corroborate our results with an approximate theoretical solution to the dynamical membrane equations. Our theory and simulations demonstrate excellent agreement with nonequilibrium fluctuations observed in experiments. Moreover, our theory reveals that the fluctuation-dissipation theorem is not broken by the bacteria; rather, membrane fluctuations can be decomposed into thermal and active components.

On the Origin of the Anomalous Behavior of Lipid Membrane Properties in the Vicinity of the Chain-Melting Phase Transition

Biomembranes are key objects of numerous studies in biology and biophysics of great importance to medicine. A few nanometers thin quasi two-dimensional liquid crystalline membranes with bending rigidity of a few kT exhibit unusual properties and they are the focus of theoretical and experimental physics. The first order chain-melting phase transition of lipid membranes is observed to be accompanied by a pseudocritical behavior of membrane physical-chemical properties. However, the investigation of the nature of the anomalous swelling of a stack of lipid membranes in the vicinity of the transition by different groups led to conflicting conclusions about the level of critical density fluctuations and their impact on the membrane softening. Correspondingly, conclusions about the contribution of Helfrich's undulations to the effect of swelling were different. In our work we present a comprehensive complementary neutron small-angle and spin-echo study directly showing the presence of significant critical fluctuations in the vicinity of the transition which induce membrane softening. However, contrary to the existing paradigm, we demonstrate that the increased undulation forces cannot explain the anomalous swelling. We suggest that the observed effect is instead determined by the dominating increase of short-range entropic repulsion.

Vesicle formation mechanisms: an overview

Vesicle structures primarily embody spherical capsules composed of a single or multiple bilayers, entrapping a pool of aqueous solution in their interior. The bilayers can be synthesised by phospholipids or other amphiphiles (surfactants, block copolymers, etc.). Vesicles with broad-spectrum applications in numerous scientific disciplines, including biochemistry, biophysics, biology, and various pharmaceutical industries, have attracted widespread attention. Consequently, a multitude of protocols have been devised and proposed for their fabrication. In this review, with a motivation to derive the basic conditions for the formation of vesicles, the associated thermodynamic and kinetic aspects are comprehensively appraised. Contextually, an all-purpose overview of the underlying thermodynamics of bilayer/membrane generation and deformation, including the chemical potential of aggregates, geometric packing and the concept of elastic properties, is presented. Additionally, the current review highlights the probable, inherent mechanisms of vesicle formation under distinct modes of manufacturing. We lay focus on vesicle formation from pre-existing bilayers, as well as from bilayers, which form when lipids from an organic solvent are transferred into an aqueous medium. Furthermore, we outline the kinetic effects on vesicle formation from the lamellar phase, with and without the presence of shearing force. Wherever required, the experimental and/or theoretical outcomes, the driving forces for vesicle size selection, and various scaling laws are also reviewed, all of which facilitate an overall improved understanding of the vesicle formation mechanisms.

Physical properties of phospholipids and integral proteins and their biofunctional roles in pulmonary surfactant from molecular dynamics simulation

This work deals with a quantitative investigation of the physical properties of pulmonary surfactant near melting temperature. To this end, we make use of molecular dynamics simulations, using the MARTINI coarse-grained model, for determining the physical properties of the system, such as the potential energy, the specific heat, the microstructure, the diffusion laws, and the elastic properties of the surfactant. The microstructure is studied by computation of the radial-distribution-function upon varying the distance between constituents (lipid molecules or proteins). The diffusion phenomenon is investigated by determination of the mean-squared-displacement and the time dependent velocity-autocorrelation-function for various values of temperature. We show that the dynamics of lipids and proteins exhibit a subdiffusion regime (slow movement) due to the cage effect within pulmonary surfactant. From the obtained mean-squared-displacement, we get the values of the self-diffusion-coefficients and the anomalous exponents at different temperatures close to the melting temperature. For the mathematical description of the cage effect, we make use of the scale relations in terms of the waiting time probability distribution. The last study is concerned with determination of the dependence of the lateral stress upon the strain of pulmonary surfactant, which is found to be linear, and from which we deduce the lateral-elastic-modulus.

This work deals with a quantitative investigation of the physical properties of pulmonary surfactant near melting temperature.

Magnifying the Structural Components of Biomembranes: A Prototype for the Study of the Self-Assembly of Giant Lipids

How biomembranes are self-organized to perform their functions remains a pivotal issue in biological and chemical science. Understanding the self-assembly principles of lipid-like molecules hence becomes crucial. Herein, we report the mesostructural evolution of amphiphilic sphere-rod conjugates (giant lipids), and study the roles of geometric parameters (head-tail ratio and cross-sectional area) during this course. As a prototype system, giant lipids resemble natural lipidic molecules by capturing their essential features. The self-assembly behavior of two categories of giant lipids (I-shape and T-shape, a total of 8 molecules) is demonstrated. A rich variety of mesostructures is constructed in solution state and their molecular packing models are rationally understood. Giant lipids recast the phase behavior of natural lipids to a certain degree and the abundant self-assembled morphologies reveal distinct physiochemical behaviors when geometric parameters deviate from natural analogues.

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

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

Spontaneous Curvature, Differential Stress, and Bending Modulus of Asymmetric Lipid Membranes

Lipid bilayers can exhibit asymmetric states, in which the physical characteristics of one leaflet differ from those of the other. This most visibly manifests in a different lipid composition, but it can also involve opposing lateral stresses in each leaflet that combine to an overall vanishing membrane tension. Here, we use theoretical modeling and coarse-grained simulation to explore the interplay between a compositional asymmetry and a nonvanishing differential stress. Minimizing the total elastic energy leads to a preferred spontaneous curvature that balances torques due to both bending moments and differential stress, with sometimes unexpected consequences. For instance, asymmetric flat bilayers, whose specific areas in each leaflet are matched to those of corresponding tensionless symmetric flat membranes, still exhibit a residual differential stress because the conditions of vanishing area strain and vanishing bending moment differ. We also measure the curvature rigidity of asymmetric bilayers and find that a sufficiently strong differential stress, but not compositional asymmetry alone, can increase the bending modulus. The likely cause is a stiffening of the compressed leaflet, which appears to be related to its gel transition but not identical with it. We finally show that the impact of cholesterol on differential stress depends on the relative strength of elastic and thermodynamic driving forces: if cholesterol solvates equally well in both leaflets, it will redistribute to cancel both leaflet tensions almost completely, but if its partitioning free energy prefers one leaflet over the other, the resulting distribution bias may even create differential stress. Because cells keep most of their lipid bilayers in an asymmetric nonequilibrium steady state, our findings suggest that biomembranes are elastically more complex than previously thought: besides a spontaneous curvature, they might also exhibit significant differential stress, which could strongly affect their curvature energetics.

ssDNA-amphiphile architecture used to control dimensions of DNA nanotubes

Controlling the dimensions of DNA nanotubes is of great interest as they can be used in different applications ranging from functional elements in nanodevices to carriers for drug delivery. ssDNA-amphiphiles composed of a ssDNA headgroup, a hydrophobic dialkyl tail and a polycarbon spacer between the tail and the headgroup, self-assemble into hollow DNA nanotubes by forming bilayer nanotapes that transition from twisted nanotapes, to helical nanotapes, to nanotubes. The presence of the DNA nanotubes is verified via cryo-TEM and SAXS. We further explore the effect of the ssDNA secondary structure and tail length on the assembly of the ssDNA-amphiphiles. We demonstrate that the presence of intermolecular G-quadruplexes in the ssDNA sequence dictates the nanotube length. The nanotube diameter is controlled by the hydrophobic tail length, and coarse-grained molecular dynamics simulations are employed to elucidate the tail design impact on assembly.

A consistent quadratic curvature-tilt theory for fluid lipid membranes

The tilt of a lipid molecule describes the deviation of its orientation away from the local normal of its embedding membrane. Tilt is the subleading degree of freedom after a membrane's geometry, and it becomes relevant at scales comparable to lipid bilayer thickness. Building on earlier work by Hamm and Kozlov [Eur. Phys. J. E 3, 323 (2000)], who envisioned lipid membranes as thin prestressed fluid elastic films, and Terzi and Deserno [J. Chem. Phys. 147, 084702 (2017)], who discovered a new coupling term between splay and tilt divergence, we construct a theory of membrane elasticity that is quadratic in geometry and tilt and complete at order 1/length². We show that a general and consistent treatment of both lateral and transverse depth-dependent shear stresses creates several contributions to the elastic energy density, of which only a subset had previously been identified. Apart from the well-known penalty of lipid twist (the curl of tilt), these terms generate no qualitatively new phenomenology, but they quantitatively revise the connections between the moduli of a tilt-curvature theory and its underlying microscopic foundation. In particular, we argue that the monolayer Gaussian curvature modulus κ¯_m, widely believed to be equal to the second moment of the transmonolayer stress profile, acquires a second contribution from lipid twist, which is always negative. This could resolve the long-standing conundrum that many measured values of κ¯_m appeared to have a sign that violates basic stability considerations. We also show that the previously discovered novel coupling between splay and tilt divergence is not simply proportional to κ¯_m but acquires its own splay-tilt coupling modulus, κ_st,m. We explore the predictions of our theory for various elastic moduli and their mutual interrelations and use an extensive set of existing atomistic molecular dynamics simulations for 12 different lipid types to collectively reason about such predictions. We find that bending rigidities are captured fairly well by existing theories, while reliable predictions for local moduli, especially the splay-tilt coupling modulus, remain challenging.

Melting transitions in biomembranes

We investigated melting transitions in native biological membranes containing their membrane proteins. The membranes originated from E. coli, B. subtilis, lung surfactant and nerve tissue from the spinal cord of several mammals. For some preparations, we studied the pressure, pH and ionic strength dependence of the transition. For porcine spine, we compared the transition of the native membrane to that of the extracted lipids. All preparations displayed melting transitions of 10-20° below physiological or growth temperature, independent of the organism of origin and the respective cell type. We found that the position of the transitions in E. coli membranes depends on the growth temperature. We discuss these findings in the context of the thermodynamic theory of membrane fluctuations close to transition that predicts largely altered elastic constants, an increase in fluctuation lifetime and in membrane permeability. We also discuss how to distinguish lipid melting from protein unfolding transitions. Since the feature of a transition slightly below physiological temperature is conserved even when growth conditions change, we conclude that the transitions are likely to be of major biological importance for the survival and the function of the cell.