The gaussian curvature elastic modulus of N-monomethylated dioleoylphosphatidylethanolamine: relevance to membrane fusion and lipid phase behavior

The diffuse interface description of fluid lipid membranes captures key features of the hemifusion pathway and lateral stress profile

Topological transitions of lipid membranes are ubiquitous in key biological processes for cell life, like neurotransmission, fertilization, morphogenesis, and viral infections. Despite this, they are not well understood due to their multiscale nature, which limits the use of molecular models and calls for a mesoscopic approach such as the celebrated Canham-Helfrich one. Unfortunately, such a model cannot handle topological transitions, hiding the crucial involved forces and the appearance of the experimentally observed hemifused intermediates. In this work, we describe the membrane as a diffuse interface preserving the Canham-Helfrich elasticity. We show that pivotal features of the hemifusion pathway are captured by this mesoscopic approach, e.g. a (meta)stable hemifusion state and the fusogenic behavior of negative monolayer spontaneous curvatures. The membrane lateral stress profile is calculated as a function of the elastic rigidities, yielding a coarse-grained version of molecular models findings. Insights into the fusogenic mechanism are reported and discussed.

Synaptotagmin 7 C2 domains induce membrane curvature stress via electrostatic interactions and the wedge mechanism

Synaptotagmin 7 (Syt-7) is part of the synaptotagmin protein family that regulates exocytotic lipid membrane fusion. Among the family, Syt-7 stands out by its membrane binding strength and stabilization of long-lived membrane fusion pores. Given that Syt-7 vesicles form long-lived fusion pores, we hypothesize that its interactions with the membrane stabilize the specific curvatures, thicknesses, and lipid compositions that support a metastable fusion pore. Using all-atom molecular dynamics simulations and FRET-based assays of Syt-7's membrane-binding C2 domains (C2A and C2B), we found that Syt-7 C2 domains sequester anionic lipids, are sensitive to cholesterol, thin membranes, and generate lipid membrane curvature by two competing, but related mechanisms. First, Syt-7 forms strong electrostatic contacts with the membrane, generating negative curvature stress. Second, Syt-7's calcium binding loops embed in the membrane surface, acting as a wedge to thin the membrane and induce positive curvature stress. These curvature mechanisms are linked by the protein insertion depth as well as the resulting protein tilt. Simplified quantitative models of the curvature-generating mechanisms link simulation observables to their membrane-reshaping effectiveness.

Experimental determination and mathematical modeling of standard shapes of forming autophagosomes

The formation of autophagosomes involves dynamic morphological changes of a phagophore from a flat membrane cisterna into a cup-shaped intermediate and a spherical autophagosome. However, the physical mechanism behind these morphological changes remains elusive. Here, we determine the average shapes of phagophores by statistically investigating three-dimensional electron micrographs of more than 100 phagophores. The results show that the cup-shaped structures adopt a characteristic morphology; they are longitudinally elongated, and the rim is catenoidal with an outwardly recurved shape. To understand these characteristic shapes, we establish a theoretical model of the shape of entire phagophores. The model quantitatively reproduces the average morphology and reveals that the characteristic shape of phagophores is primarily determined by the relative size of the open rim to the total surface area. These results suggest that the seemingly complex morphological changes during autophagosome formation follow a stable path determined by elastic bending energy minimization.

Lipid nanoparticle topology regulates endosomal escape and delivery of RNA to the cytoplasm

RNA therapeutics have the potential to resolve a myriad of genetic diseases. Lipid nanoparticles (LNPs) are among the most successful RNA delivery systems. Expanding their use for the treatment of more genetic diseases hinges on our ability to continuously evolve the design of LNPs with high potency, cellular-specific targeting, and low side effects. Overcoming the difficulty of releasing cargo from endocytosed LNPs remains a significant hurdle. Here, we investigate the fundamental properties of nonviral RNA nanoparticles pertaining to the activation of topological transformations of endosomal membranes and RNA translocation into the cytosol. We show that, beyond composition, LNP fusogenicity can be prescribed by designing LNP nanostructures that lower the energetic cost of fusion and fusion-pore formation with a target membrane. The inclusion of structurally active lipids leads to enhanced LNP endosomal fusion, fast evasion of endosomal entrapment, and efficacious RNA delivery. For example, conserving the lipid make-up, RNA-LNPs having cuboplex nanostructures are significantly more efficacious at endosomal escape than traditional lipoplex constructs.

Simulated dynamic cholesterol redistribution favors membrane fusion pore constriction

Endo- and exocytosis proceed through a highly strained membrane fusion pore topology regardless of the aiding protein machinery. The membrane's lipid components bias fusion pores toward expansion or closure, modifying the necessary work done by proteins. Cholesterol, a key component of plasma membranes, promotes both inverted lipid phases with concave leaflets (i.e., negative total curvature, which thins the leaflet) and flat bilayer phases with thick, ordered hydrophobic interiors. We demonstrate by theory and simulation that both leaflets of nascent catenoidal fusion pores have negative total curvature. Furthermore, the hydrophobic core of bilayers with strong negative Gaussian curvature is thinned. Therefore, it is an open question whether cholesterol will be enriched in these regions because of the negative total curvature or depleted because of the membrane thinning. Here, we compare all-atom molecular dynamics simulations (built using a procedure to create specific fusion pore geometries) and theory to understand the underlying reasons for lipid redistribution on fusion pores. Our all-atom molecular dynamics simulations resolve this question by showing that cholesterol is strongly excluded from the thinned neck of fusion and fission pores, revealing that thickness (and/or lipid order) influences cholesterol distributions more than curvature. The results imply that cholesterol exclusion can drive fusion pore closure by creating a small, cholesterol-depleted zone in the neck. This model agrees with literature evidence that membrane reshaping is connected to cholesterol-dependent lateral phase separation.

High curvature promotes fusion of lipid membranes: Predictions from continuum elastic theory

The fusion of lipid membranes progresses through a series of hemifusion intermediates with two significant energy barriers related to the formation of stalk and fusion pore, respectively. These energy barriers determine the speed and success rate of many critical biological processes, including the fusion of highly curved membranes, for example synaptic vesicles and enveloped viruses. Here we use continuum elastic theory of lipid monolayers to determine the relationship between membrane shape and energy barriers to fusion. We find that the stalk formation energy decreases with curvature by up to 31 kBT in a 20-nm-radius vesicle compared with planar membranes and by up to 8 kBT in the fusion of highly curved, long, tubular membranes. In contrast, the fusion pore formation energy barrier shows a more complicated behavior. Immediately after stalk expansion to the hemifusion diaphragm, the fusion pore formation energy barrier is low (15-25 kBT) due to lipid stretching in the distal monolayers and increased tension in highly curved vesicles. Therefore, the opening of the fusion pore is faster. However, these stresses relax over time due to lipid flip-flop from the proximal monolayer, resulting in a larger hemifusion diaphragm and a higher fusion pore formation energy barrier, up to 35 kBT. Therefore, if the fusion pore fails to open before significant lipid flip-flop takes place, the reaction proceeds to an extended hemifusion diaphragm state, which is a dead-end configuration in the fusion process and can be used to prevent viral infections. In contrast, in the fusion of long tubular compartments, the surface tension does not accumulate due to the formation of the diaphragm, and the energy barrier for pore expansion increases with curvature by up to 11 kBT. This suggests that inhibition of polymorphic virus infection could particularly target this feature of the second barrier.

Vesicle formation induced by thermal fluctuations

The process of fission and vesicle formation depends on the geometry of the membrane that will split. For instance, a flat surface finds it difficult to form vesicles because of the lack of curved regions where to start the process. Here we show that vesicle formation can be promoted by temperature, by using a membrane phase field model with Gaussian curvature. We find a phase transition between fluctuating and vesiculation phases that depends on temperature, spontaneous curvature, and the ratio between bending and Gaussian moduli. We analysed the energy dynamical behaviour of these processes and found that the main driving ingredient is the Gaussian energy term, although the curvature energy term usually helps with the process as well. We also found that the chemical potential can be used to investigate the temperature of the system. Finally we address how temperature changes the condition for spontaneous vesiculation for all geometries, making it happen in a wider range of values of the Gaussian modulus.

Synthesising a minimal cell with artificial metabolic pathways

A "synthetic minimal cell" is considered here as a cell-like artificial vesicle reproduction system in which a chemical and physico-chemical transformation network is regulated by information polymers. Here we synthesise such a minimal cell consisting of three units: energy production, information polymer synthesis, and vesicle reproduction. Supplied ingredients are converted to energy currencies which trigger the synthesis of an information polymer, where the vesicle membrane plays the role of a template. The information polymer promotes membrane growth. By tuning the membrane composition and permeability to osmolytes, the growing vesicles show recursive reproduction over several generations. Our "synthetic minimal cell" greatly simplifies the scheme of contemporary living cells while keeping their essence. The chemical pathways and the vesicle reproduction pathways are well described by kinetic equations and by applying the membrane elasticity model, respectively. This study provides new insights to better understand the differences and similarities between non-living forms of matter and life.

Light-Responsive Supramolecular Nanotubes-Based Chiral Plasmonic Assemblies

We describe the fabrication of dual-responsive (thermo/light) chiral plasmonic films. The idea is based on using photoswitchable achiral liquid crystal (LCs) forming chiral nanotubes for templating helical assemblies of Au NPs. Circular dichroism spectroscopy (CD) confirms chiroptical properties coming from the arrangement of organic and inorganic components, with up to 0.2 dissymmetry factor (g-factor). Upon exposure to UV light, organic molecules isomerize, resulting in controlled melting of organic nanotubes and/or inorganic nanohelices. The process can be reversed using visible light and further modified by varying the temperature, offering a control of chiroptical response of the composite material. These properties can play a key role in the future development of chiral plasmonics, metamaterials, and optoelectronic devices.

Lipidic lyotropic liquid crystals: Insights on biomedical applications

Liquid crystals (LCs) possess unique physicochemical properties, translatable into a wide range of applications. To date, lipidic lyotropic LCs (LLCs) have been extensively explored in drug delivery and imaging owing to the capability to encapsulate and release payloads with different characteristics. The current landscape of lipidic LLCs in biomedical applications is provided in this review. Initially, the main properties, types, methods of fabrication and applications of LCs are showcased. Then, a comprehensive discussion of the main biomedical applications of lipidic LLCs accordingly to the application (drug and biomacromolecule delivery, tissue engineering and molecular imaging) and route of administration is examined. Further discussion of the main limitations and perspectives of lipidic LLCs in biomedical applications are also provided. STATEMENT OF SIGNIFICANCE: Liquid crystals (LCs) are those systems between a solid and liquid state that possess unique morphological and physicochemical properties, translatable into a wide range of biomedical applications. A short description of the properties of LCs, their types and manufacturing procedures is given to serve as a background to the topic. Then, the latest and most innovative research in the field of biomedicine is examined, specifically the areas of drug and biomacromolecule delivery, tissue engineering and molecular imaging. Finally, prospects of LCs in biomedicine are discussed to show future trends and perspectives that might be utilized. This article is an ampliation, improvement and actualization of our previous short forum article "Bringing lipidic lyotropic liquid crystal technology into biomedicine" published in TIPS.

Effect of monolayer spontaneous curvature on constant tension-induced pore formation in lipid bilayers

The methodology of constant tension-induced rupture of giant unilamellar vesicles (GUVs) has provided information on tension-induced pore formation. This method was used to investigate the effect of spontaneous curvature (H₀) for a lipid monolayer on the rate constant (k_r) for constant tension (σ)-induced rupture, which originates from pore formation in lipid bilayers. Lipids were incorporated with different H₀ values into GUV membranes to change the overall H₀ value for the GUV monolayer. The dioleoylphosphatidylglycerol (DOPG)/dioleoylphosphatidylethanolamine (DOPE) (4/6, molar ratio, here and elsewhere) monolayer has a negative H₀, whereas the DOPG/dioleoylphosphatidylcholine (DOPC) (4/6) monolayer has an essentially zero H₀. A higher tension was required to induce the rupture of DOPG/DOPE (4/6)-GUVs compared with DOPG/DOPC (4/6)-GUVs. The line tension (Γ) for a pre-pore in DOPG/DOPE (4/6)-GUVs, determined by the analysis of the tension dependence of k_r, was 1.5 times larger than that in DOPG/DOPC (4/6)-GUVs. The k_r values for GUVs comprising DOPG/DOPC/18:1 lysophosphatidylcholine (LPC) (40/55/10), which has a positive H₀, were larger than those for DOPG/DOPC (4/6)-GUVs under the same tension. The Γ value for DOPG/DOPC/LPC (40/55/10)-GUVs was almost half that for DOPG/DOPC (4/6)-GUVs. These results indicate that Γ decreases with increasing H₀, which results in an increase in k_r. Based on these results, the effect of H₀ on k_r and Γ is discussed.

Generation of nanoscopic membrane curvature for membrane trafficking

Curved membranes are key features of intracellular organelles, and their generation involves dynamic protein complexes. Here we describe the fundamental mechanisms such as the hydrophobic insertion, scaffolding and crowding mechanisms these proteins use to produce membrane curvatures and complex shapes required to form intracellular organelles and vesicular structures involved in endocytosis and secretion. For each mechanism, we discuss its cellular functions as well as the underlying physical principles and the specific membrane properties required for the mechanism to be feasible. We propose that the integration of individual mechanisms into a highly controlled, robust process of curvature generation often relies on the assembly of proteins into coats. How cells unify and organize the curvature-generating factors at the nanoscale is presented for three ubiquitous coats central for membrane trafficking in eukaryotes: clathrin-coated pits, caveolae, and COPI and COPII coats. The emerging theme is that these coats arrange and coordinate curvature-generating factors in time and space to dynamically shape membranes to accomplish membrane trafficking within cells.

The interaction of viral fusion peptides with lipid membranes

In this paper, we studied fusogenic peptides of class I-III fusion proteins, which are relevant to membrane fusion for certain enveloped viruses, in contact with model lipid membranes. We resolved the vertical structure and examined the adsorption or penetration behavior of the fusogenic peptides at phospholipid Langmuir monolayers with different initial surface pressures with x-ray reflectometry. We show that the fusion loops of tick-borne encephalitis virus (TBEV) glycoprotein E and vesicular stomatitis virus (VSV) G-protein are not able to insert deeply into model lipid membranes, as they adsorbed mainly underneath the headgroups with only limited penetration depths into the lipid films. In contrast, we observed that the hemagglutinin 2 fusion peptide (HA2-FP) and the VSV-transmembrane domain (VSV-TMD) can penetrate deeply into the membranes. However, in the case of VSV-TMD, the penetration was suppressed already at low surface pressures, whereas HA2-FP was able to insert even into highly compressed films. Membrane fusion is accompanied by drastic changes of the membrane curvature. To investigate how the peptides affect the curvature of model lipid membranes, we examined the effect of the fusogenic peptides on the equilibration of cubic monoolein structures after a phase transition from a lamellar state induced by an abrupt hydrostatic pressure reduction. We monitored this process in presence and absence of the peptides with small-angle x-ray scattering and found that HA2-FP and VSV-TMD drastically accelerate the equilibration, while the fusion loops of TBEV and VSV stabilize the swollen state of the lipid structures. In this work, we show that the class I fusion peptide of HA2 penetrates deeply into the hydrophobic region of membranes and is able to promote and accelerate the formation of negative curvature. In contrast, we found that the class II and III fusion loops of TBEV and VSV tend to counteract negative membrane curvature.

Controlling the shape and topology of two-component colloidal membranes

Changes in the geometry and topology of self-assembled membranes underlie diverse processes across cellular biology and engineering. Similar to lipid bilayers, monolayer colloidal membranes have in-plane fluid-like dynamics and out-of-plane bending elasticity. Their open edges and micrometer-length scale provide a tractable system to study the equilibrium energetics and dynamic pathways of membrane assembly and reconfiguration. Here, we find that doping colloidal membranes with short miscible rods transforms disk-shaped membranes into saddle-shaped surfaces with complex edge structures. The saddle-shaped membranes are well approximated by Enneper's minimal surfaces. Theoretical modeling demonstrates that their formation is driven by increasing the positive Gaussian modulus, which in turn, is controlled by the fraction of short rods. Further coalescence of saddle-shaped surfaces leads to diverse topologically distinct structures, including shapes similar to catenoids, trinoids, four-noids, and higher-order structures. At long timescales, we observe the formation of a system-spanning, sponge-like phase. The unique features of colloidal membranes reveal the topological transformations that accompany coalescence pathways in real time. We enhance the functionality of these membranes by making their shape responsive to external stimuli. Our results demonstrate a pathway toward control of thin elastic sheets' shape and topology-a pathway driven by the emergent elasticity induced by compositional heterogeneity.

From vesicles toward protocells and minimal cells

In contrast to ordinary condensed matter systems, "living systems" are unique. They are based on molecular compartments that reproduce themselves through (i) an uptake of ingredients and energy from the environment, and (ii) spatially and timely coordinated internal chemical transformations. These occur on the basis of instructions encoded in information molecules (DNAs). Life originated on Earth about 4 billion years ago as self-organised systems of inorganic compounds and organic molecules including macromolecules (e.g. nucleic acids and proteins) and low molar mass amphiphiles (lipids). Before the first living systems emerged from non-living forms of matter, functional molecules and dynamic molecular assemblies must have been formed as prebiotic soft matter systems. These hypothetical cell-like compartment systems often are called "protocells". Other systems that are considered as bridging units between non-living and living systems are called "minimal cells". They are synthetic, autonomous and sustainable reproducing compartment systems, but their constituents are not limited to prebiotic substances. In this review, we focus on both membrane-bounded (vesicular) protocells and minimal cells, and provide a membrane physics background which helps to understand how morphological transformations of vesicle systems might have happened and how vesicle reproduction might be coupled with metabolic reactions and information molecules. This research, which bridges matter and life, is a great challenge in which soft matter physics, systems chemistry, and synthetic biology must take joined efforts to better understand how the transformation of protocells into living systems might have occurred at the origin of life.

Bicontinuous inverted cubic phase stabilization as an index of antimicrobial and membrane fusion peptide activity

Some antimicrobial peptides (AMPs) and membrane fusion-catalyzing peptides (FPs) stabilize bicontinuous inverted cubic (QII) phases. Previous authors proposed a topological rationale: since AMP-induced pores, fusion intermediates, and QII phases all have negative Gaussian curvature (NGC), peptides which produce NGC in one structure also do it in another. This assumes that peptides change the curvature energy of the lipid membranes. Here I test this with a Helfrich curvature energy model. First, experimentally, I show that lipid systems often used to study peptide NGC have NGC without peptides at higher temperatures. To determine the net effect of an AMP on NGC, the equilibrium phase behavior of the host lipids must be determined. Second, the model shows that AMPs must make large changes in the curvature energy to stabilize AMP-induced pores. Peptide-induced changes in elastic constants affect pores and QII phase differently. Changes in spontaneous curvature affect them in opposite ways. The observed correlation between QII phase stabilization and AMP activity doesn't show that AMPs act by lowering pore curvature energy. A different rationale is proposed. In theory, AMPs could simultaneously stabilize QII phase and pores by drastically changing two particular elastic constants. This could be tested by measuring AMP effects on the individual constants. I propose experiments to do that. Unlike AMPs, FPs must make only small changes in the curvature energy to catalyze fusion. It they act in this way, their fusion activity should correlate with their ability to stabilize QII phases.

Vesicle deformation and division induced by flip-flops of lipid molecules

We investigated the deformation of small unilamellar vesicles (SUVs) induced by flip-flops of lipids using coarse-grained molecular dynamics simulations. In the case of single-component SUVs composed of zero spontaneous curvature lipids (ZLs), the flip-flop of ZLs deformed stomatocyte-shaped SUVs into an oblate shape, whereas pear-shaped SUVs were deformed into a prolate shape. These two equilibrium shapes comply with the local minima of elastic energy. In the case of binary vesicles composed of ZLs and negative spontaneous curvature lipids (NLs), the vesicle deformation pathway depended on the initial NL distribution in the bilayer. If the initial difference in the NL concentration between the outer and inner leaflets was small, the flip-flop of ZLs and NLs rapidly deformed pear-shaped SUVs into an equilibrium prolate shape. On the other hand, when NLs were localised in the inner leaflet, the flip-flop of ZLs and NLs deformed pear-shaped SUVs into a limiting shape and then induced vesicle division. Because the flip-flop rate of NLs is much faster than that of ZLs, the total free energy was first relaxed by the flip-flop of NLs and then by that of ZLs. This kinetic effect is responsible for the observed vesicle division induced by flip-flops.

Calcium Ions Promote Membrane Fusion by Forming Negative-Curvature Inducing Clusters on Specific Anionic Lipids

Vesicles enriched in certain negatively charged lipids, such as phosphatidylserine and PIP2, are known to undergo fusion in the presence of calcium ions without assistance from protein assemblies. Other lipids do not exhibit this propensity, even if they are negatively charged. Using our recently developed methodology, we extract elastic properties of a representative set of lipids. This allows us to trace the origin of lipid-calcium selectivity in membrane fusion to the formation of lipid clusters with long-range correlations that induce negative curvature on the membrane surface. Furthermore, the clusters generate lateral tension in the headgroup region at the membrane surface, concomitantly also stabilizing negative Gaussian curvature. Finally, calcium binding also reduces the orientational polarization of water around the membrane head groups, potentially reducing the hydration force acting between membranes. Binding calcium only weakly increases membrane bending rigidity and tilt moduli, in agreement with experiments. We show how the combined effects of calcium binding to membranes lower the barriers along the fusion pathway that lead to the formation of the fusion stalk as well as the fusion pore.

Self-consistent field modeling of mesomorphic phase changes of monoolein and phospholipids in response to additives

Mapping the topological phase behaviour of lipids in aqueous solution is time consuming and finding the ideal lipid system for a desired application is often a matter of trial and error. Modelling techniques that can accurately predict the mesomorphic phase behaviour of lipid systems are therefore of paramount importance. Here, the self-consistent field theory of Scheutjens and Fleer (SF-SCF) in which a lattice refinement has been implemented, is used to scrutinize how various additives modify the self-assembled phase behaviour of monoolein (MO) and 1,2-dioleoyl-phosphatidylcholine (DOPC) lipids in water. The mesomorphic behaviour is inferred from trends in the mechanical properties of equilibrium lipid bilayers with increasing additive content. More specifically, we focus on the Helfrich parameters, that is, the mean and Gaussian bending rigidities (κ and [small kappa, Greek, macron], respectively) supplemented with the spontaneous curvature of the monolayer (Jm0). We use previously established interaction parameters that position the unperturbed DOPC system in the lamellar Lα phase ([small kappa, Greek, macron] < 0, κ > 0 and Jm0 ≈ 0). Similar interaction parameters position the MO system firmly in a bicontinuous cubic phase ([small kappa, Greek, macron] > 0). In line with experimental data, a mixture of MO and DOPC tends to be in one of these two phases, depending on the mixing ratio. Moreover we find good correlations between predicted trends and experimental data concerning the phase changes of MO in response to a wide range of additives. These correlations give credibility to the use of SF-SCF modelling as a valuable tool to quickly explore the mesomorphic phase space of (phospho)lipid bilayer systems including additives.

Does membrane curvature elastic energy play a role in mediating oxidative stress in lipid membranes?

The effects of oxidative stress on cells are associated with a wide range of pathologies. Oxidative stress is predominantly initiated by the action of reactive oxygen species and/or lipoxygenases on polyunsaturated fatty acid containing lipids. The downstream products are oxidised phospholipids, bioactive aldehydes and a range of Schiff base by-products between aldehydes and lipids, or other biomacromolecules. In this review we assess the impact of oxidative stress on lipid membranes, focusing on the changes that occur to the curvature preference (lipid spontaneous curvature) and elastic properties of membranes, since these biophysical properties modulate phospholipid homeostasis. Studies show that the lipid products of oxidative stress reduce stored curvature elastic energy in membranes. Based upon this observation, we hypothesize that the effects of oxidative stress on lipid membranes will be reduced by compounds that increase stored curvature elastic energy. We find a strong correlation appears across literature studies that we have reviewed, such that many compounds like vitamin E, Curcumin, Coenzyme Q10 and vitamin A show behaviour consistent with this hypothesis. Finally, we consider whether age-related changes in lipid composition represent the homeostatic response of cells to compensate for the accumulation of in vivo lipid oxidation products.

Lipid monolayer spontaneous curvatures: A collection of published values

Lipid monolayer spontaneous curvatures (or lipid intrinsic curvatures) are one of several material properties of lipids that enable the stored curvature elastic energy in a lipid aggregate to be determined. Stored curvature elastic energy is important since it can modulate the function of membrane proteins and plays a role in the regulatory pathways of phospholipid homeostasis. Due to the large number of different lipid molecules that might theoretically exist in nature, very few lipid spontaneous curvatures have been determined. Herein the values of lipid spontaneous curvatures that exist in the literature are collected, alongside key experimental details. Where possible, trends in the data are discussed and finally, obvious gaps in the knowledge are signposted.

The effect of headgroup methylation on polymorphic phase behaviour in hydrated N-methylated phosphoethanolamine:palmitic acid membranes

Mixtures of fatty acids and phospholipids can form hexagonal (HII) and inverse bicontinuous cubic phases, the latter of which are implicated in various cellular processes and have wide-ranging biotechnological applications in protein crystallisation and drug delivery systems. Therefore, it is vitally important to understand the formation conditions of inverse bicontinuous cubic phases and how their properties can be tuned. We have used differential scanning calorimetry and synchrotron-based small angle and wide angle X-ray scattering (SAXS/WAXS) to investigate the polymorphic phase behaviour of palmitic acid/partially-methylated phospholipid mixtures, and how headgroup methylation impacts on inverse bicontinuous cubic phase formation. We find that upon partial methylation of the phospholipid headgroup (1 or 2 methyl substituents) inverse bicontinuous cubic phases are formed (of the Im3m spacegroup), which is not the case with 0 or 3 methyl substituents. This shows how important headgroup methylation is for controlling phase behaviour and how a change in headgroup methylation can be used to controllably tune various inverse bicontinuous phase features such as their lattice parameter and the temperature range of their stability.

On Gaussian curvature and membrane fission

We propose a three-dimensional mathematical model to describe dynamical processes of membrane fission. The model is based on a phase field equation that includes the Gaussian curvature contribution to the bending energy. With the addition of the Gaussian curvature energy term numerical simulations agree with the predictions that tubular shapes can break down into multiple vesicles. A dispersion relation obtained with linear analysis predicts the wavelength of the instability and the number of formed vesicles. Finally, a membrane shape diagram is obtained for the different Gaussian and bending modulus, showing different shape regimes.

Curvature Energetics Determined by Alchemical Simulation on Four Topologically Distinct Lipid Phases

The relative curvature energetics of two lipids are tested using thermodynamic integration (TI) on four topologically distinct lipid phases. Simulations use TI to switch between choline headgroup lipids (POPC; that prefers to be flat) and ethanolamine headgroup lipids (POPE; that prefer, for example, the inner monolayer of vesicles). The thermodynamical moving of the lipids between planar, inverse hexagonal (H_II), cubic (Q_II; Pn3m space group), and vesicle topologies reveals differences in material parameters that were previously challenging to access. The methodology allows for predictions of two important lipid material properties: the difference in POPC/POPE monolayer intrinsic curvature (ΔJ₀) and the difference in POPC/POPE monolayer Gaussian curvature modulus (Δκ̅_m), both of which are connected to the energetics of topological variation. Analysis of the TI data indicates that, consistent with previous experiment and simulation, the J₀ of POPE is more negative than POPC (ΔJ₀ = -0.018 ± 0.001 Å^-1). The theoretical framework extracts significant differences in κ̅_m of which POPE is less negative than POPC by 2.0 to 4.0 kcal/mol. The range of these values is determined by considering subsets of the simulations, and disagreement between these subsets suggests separate mechanical parameters at very high curvature. Finally, the fit of the TI data to the model indicates that the position of the pivotal plane of curvature is not constant across topologies at high curvature. Overall, the results offer insights into lipid material properties, the limits of a single HC model, and how to test them using simulation.

Membrane Curvature, Trans-Membrane Area Asymmetry, Budding, Fission and Organelle Geometry

In biology, the modern scientific fashion is to mostly study proteins. Much less attention is paid to lipids. However, lipids themselves are extremely important for the formation and functioning of cellular membrane organelles. Here, the role of the geometry of the lipid bilayer in regulation of organelle shape is analyzed. It is proposed that during rapid shape transition, the number of lipid heads and their size (i.e., due to the change in lipid head charge) inside lipid leaflets modulates the geometrical properties of organelles, in particular their membrane curvature. Insertion of proteins into a lipid bilayer and the shape of protein trans-membrane domains also affect the trans-membrane asymmetry between surface areas of luminal and cytosol leaflets of the membrane. In the cases where lipid molecules with a specific shape are not predominant, the shape of lipids (cylindrical, conical, or wedge-like) is less important for the regulation of membrane curvature, due to the flexibility of their acyl chains and their high ability to diffuse.

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.

Continuum Models of Membrane Fusion: Evolution of the Theory

Starting from fertilization, through tissue growth, hormone secretion, synaptic transmission, and sometimes morbid events of carcinogenesis and viral infections, membrane fusion regulates the whole life of high organisms. Despite that, a lot of fusion processes still lack well-established models and even a list of main actors. A merger of membranes requires their topological rearrangements controlled by elastic properties of a lipid bilayer. That is why continuum models based on theories of membrane elasticity are actively applied for the construction of physical models of membrane fusion. Started from the view on the membrane as a structureless film with postulated geometry of fusion intermediates, they developed along with experimental and computational techniques to a powerful tool for prediction of the whole process with molecular accuracy. In the present review, focusing on fusion processes occurring in eukaryotic cells, we scrutinize the history of these models, their evolution and complication, as well as open questions and remaining theoretical problems. We show that modern approaches in this field allow continuum models of membrane fusion to stand shoulder to shoulder with molecular dynamics simulations, and provide the deepest understanding of this process in multiple biological systems.

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.

Bicontinuous cubic phases in biological and artificial self-assembled systems

Nature has created innumerable life forms with miraculous hierarchical structures and morphologies that are optimized for different life events through evolution over billions of years. Bicontinuous cubic structures, which are often described by triply periodic minimal surfaces (TPMSs) and their constant mean curvature (CMC)/parallel surface companions, are of special interest to various research fields because of their complex form with unique physical functionalities. This has prompted the scientific community to fully understand the formation, structure, and properties of these materials. In this review, we summarize and discuss the formation mechanism and relationships of the relevant biological structures and the artificial self-assembly systems. These structures can be formed through biological processes with amazing regulation across a great length scales; nevertheless, artificial construction normally produces the structure corresponding to the molecular size and shape. Notably, the block copolymeric system is considered to be an applicable and attractive model system for the study of biological systems due to their versatile design and rich phase behavior. Some of the phenomena found in these two systems are compared and discussed, and this information may provide new ideas for a comprehensive understanding of the relationship between molecular shape and resulting interface curvature and the self-assembly process in living organisms. We argue that the co-polymeric system may serve as a model to understand these biological systems and could encourage additional studies of artificial self-assembly and the creation of new functional materials.

Molecular basis of force-from-lipids gating in the mechanosensitive channel MscS

Prokaryotic mechanosensitive (MS) channels open by sensing the physical state of the membrane. As such, lipid-protein interactions represent the defining molecular process underlying mechanotransduction. Here, we describe cryo-electron microscopy (cryo-EM) structures of the E. coli small-conductance mechanosensitive channel (MscS) in nanodiscs (ND). They reveal a novel membrane-anchoring fold that plays a significant role in channel activation and establish a new location for the lipid bilayer, shifted ~14 Å from previous consensus placements. Two types of lipid densities are explicitly observed. A phospholipid that ‘hooks’ the top of each TM2-TM3 hairpin and likely plays a role in force sensing, and a bundle of acyl chains occluding the permeation path above the L105 cuff. These observations reshape our understanding of force-from-lipids gating in MscS and highlight the key role of allosteric interactions between TM segments and phospholipids bound to key dynamic components of the channel.

Mechanical properties of lipid bilayers: a note on the Poisson ratio

We investigate the Poisson ratio ν of fluid lipid bilayers, i.e., the question how area strains compare to the changes in membrane thickness (or, equivalently, volume) that accompany them. We first examine existing experimental results on the area- and volume compressibility of lipid membranes. Analyzing them within the framework of linear elasticity theory for homogeneous thin fluid sheets leads us to conclude that lipid membrane deformations are to a very good approximation volume-preserving, with a Poisson ratio that is likely about 3% smaller than the common soft matter limit . These results are fully consistent with atomistic simulations of a DOPC membrane at varying amount of applied lateral stress, for which we instead deduce ν by directly comparing area- and volume strains. To assess the problematic assumption of transverse homogeneity, we also define a depth-resolved Poisson ratio ν(z) and determine it through a refined analysis of the same set of simulations. We find that throughout the membrane's thickness, ν(z) is close to the value derived assuming homogeneity, with only minor variations of borderline statistical significance.

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.

Geometric coupling of helicoidal ramps and curvature-inducing proteins in organelle membranes

Cellular membranes display an incredibly diverse range of shapes, both in the plasma membrane and at membrane bound organelles. These morphologies are intricately related to cellular functions, enabling and regulating fundamental membrane processes. However, the biophysical mechanisms at the origin of these complex geometries are not fully understood from the standpoint of membrane-protein coupling. In this study, we focused on a minimal model of helicoidal ramps representative of specialized endoplasmic reticulum compartments. Given a helicoidal membrane geometry, we asked what is the distribution of spontaneous curvature required to maintain this shape at mechanical equilibrium? Based on the Helfrich energy of elastic membranes with spontaneous curvature, we derived the shape equation for minimal surfaces, and applied it to helicoids. We showed the existence of switches in the sign of the spontaneous curvature associated with geometric variations of the membrane structures. Furthermore, for a prescribed gradient of spontaneous curvature along the exterior boundaries, we identified configurations of the helicoidal ramps that are confined between two infinitely large energy barriers. Overall our results suggest possible mechanisms for geometric control of helicoidal ramps in membrane organelles based on curvature-inducing proteins.

Mechanical model of Golgi apparatus

The Golgi apparatus has intrigued researchers since its discovery and despite the advances, there are still many open questions in regards to its shape and function. We propose a mechanical model of Golgi apparatus stack and explain its most elementary geometrical properties: the equilibrium number of cisternae, the stack size, and its general equilibrium shape. Combining both analytical and numerical methods we successfully reconstruct the stack morphology within the theory of bending elasticity. We demonstrate that energy-wise the stack prefers an overall bent shape and show strong evidence that the adhesion strength determines the equilibrium number of cisternae per stack. We explore the morphological role of fenestrations and discuss their impact on the overall stack structure. We also comment on the effects of the asymmetry in the composition of membrane leaflets on the shape of the cisternae and thus offer a broad steady-state study of the stack morphology and present a method that can be used also for other membrane-bound organelles.

Arginine-rich cell-penetrating peptides induce membrane multilamellarity and subsequently enter via formation of a fusion pore

Arginine-rich cell-penetrating peptides do not enter cells by directly passing through a lipid membrane; they instead passively enter vesicles and live cells by inducing membrane multilamellarity and fusion. The molecular picture of this penetration mode, which differs qualitatively from the previously proposed direct mechanism, is provided by molecular dynamics simulations. The kinetics of vesicle agglomeration and fusion by an iconic cell-penetrating peptide-nonaarginine-are documented via real-time fluorescence techniques, while the induction of multilamellar phases in vesicles and live cells is demonstrated by a combination of electron and fluorescence microscopies. This concert of experiments and simulations reveals that the identified passive cell penetration mechanism bears analogy to vesicle fusion induced by calcium ions, indicating that the two processes may share a common mechanistic origin.

Arginine-rich cell-penetrating peptides induce membrane multilamellarity and subsequently enter via formation of a fusion pore

Arginine-rich cell-penetrating peptides do not enter cells by directly passing through a lipid membrane; they instead passively enter vesicles and live cells by inducing membrane multilamellarity and fusion. The molecular picture of this penetration mode, which differs qualitatively from the previously proposed direct mechanism, is provided by molecular dynamics simulations. The kinetics of vesicle agglomeration and fusion by an iconic cell-penetrating peptide-nonaarginine-are documented via real-time fluorescence techniques, while the induction of multilamellar phases in vesicles and live cells is demonstrated by a combination of electron and fluorescence microscopies. This concert of experiments and simulations reveals that the identified passive cell penetration mechanism bears analogy to vesicle fusion induced by calcium ions, indicating that the two processes may share a common mechanistic origin.

Machine learning antimicrobial peptide sequences: Some surprising variations on the theme of amphiphilic assembly

Antimicrobial peptides (AMPs) collectively constitute a key component of the host innate immune system. They span a diverse space of sequences and can be α-helical, β-sheet, or unfolded in structure. Despite a wealth of knowledge about them from decades of experiments, it remains difficult to articulate general principles governing such peptides. How are they different from other molecules that are also cationic and amphiphilic? What other functions, in immunity and otherwise, are enabled by these simple sequences? In this short review, we present some recent work that engages these questions using methods not usually applied to AMP studies, such as machine learning. We find that not only do AMP-like sequences confer membrane remodeling activity to an unexpectedly broad range of protein classes, their cationic and amphiphilic signature also allows them to act as meta-antigens and self-assemble with immune ligands into nanocrystalline complexes for multivalent presentation to Toll-like receptors.

Interaction between Surface Charge-Modified Gold Nanoparticles and Phospholipid Membranes

This report clarifies the interaction of surface charge-modified gold nanoparticles (AuNPs) with phospholipid membranes, which is helpful to understand the antibacterial mechanism of positive charge-modified AuNPs to Gram-negative bacteria. Although the simulated bacterial cell membranes as a whole are negatively charged, the local electrostatic repulsive interaction between the positive charge-coated AuNPs and the small-sized flexible cationic head group of dioleyl phosphatidylethanolamine molecules induces the phase transformation of the simulated bacterial cell membranes from a lamellar to an inverted hexagonal phase. Transmembrane pores with a diameter of about 3.0 nm in the inverted hexagonal structure would result in the destruction of cell membrane function. Such an interaction of positive charge-modified AuNPs with the membrane mimics provides a promising route to develop new antibacterial agents by modifying positive charges on the surface of nanoparticles.

Grazing-Angle Neutron Diffraction Study of the Water Distribution in Membrane Hemifusion: From the Lamellar to Rhombohedral Phase

The water distribution between lipid bilayers is important in understanding the role of the hydration force at different steps of the membrane fusion pathway. In this study, we used grazing-angle neutron diffraction to map out the water distribution in lipid bilayers transiting from a lamellar structure to the hemifusion "stalk" structure in a rhombohedral phase. Under osmotic pressure exerted by different levels of relative humidity, the lipid membrane sample was maintained in equilibrium at different lattices suitable for neutron diffraction. The D₂O used to hydrate the lipid membrane sample stood out from the lipid in the reconstructed structure because of its much higher coherent neutron scattering length density. The density map indicates that water dissociated from the headgroup in the lamellar phase. In the rhombohedral phase, water was significantly reduced and was squeezed into pockets around the stalk. This study complements earlier structural studies by grazing-angle X-ray diffraction, which is sensitive to only the parts of the structure with high electron density (such as phosphors). The experiment also demonstrated that the recently developed time-of-flight small-angle neutron scattering beamline at the Spallation Neutron Source is suitable for grazing-angle neutron diffraction to provide the structures of large unit cells on the order of a few nanometers, such as biomembrane structures.

Molecular mechanism of vesicle division induced by coupling between lipid geometry and membrane curvatures

We investigated the effects of lipid geometry on vesicle division using coarse grained molecular dynamics simulations. When the vesicle is composed of zero and negative spontaneous curvature lipids (ZSLs and NSLs), the difference in their molecular spontaneous curvatures destabilizes the neck of the limiting shape vesicle. In the vesicle division pathway, the neck developed into the stalk intermediates. The stalk was broken when the NSLs were expelled from the stalk. Free energy analysis shows that the coupling between the lipid geometry and the Gaussian rigidity is responsible for the observed vesicle division.

Membrane-Mediated Cooperativity of Proteins

Besides direct protein-protein interactions, indirect interactions mediated by membranes play an important role for the assembly and cooperative function of proteins in membrane shaping and adhesion. The intricate shapes of biological membranes are generated by proteins that locally induce membrane curvature. Indirect curvature-mediated interactions between these proteins arise because the proteins jointly affect the bending energy of the membranes. These curvature-mediated interactions are attractive for crescent-shaped proteins and are a driving force in the assembly of the proteins during membrane tubulation. Membrane adhesion results from the binding of receptor and ligand proteins that are anchored in the apposing membranes. The binding of these proteins strongly depends on nanoscale shape fluctuations of the membranes, leading to a fluctuation-mediated binding cooperativity. A length mismatch between receptor-ligand complexes in membrane adhesion zones causes repulsive curvature-mediated interactions that are a driving force for the length-based segregation of proteins during membrane adhesion.

On the thermotropic and magnetotropic phase behavior of lipid liquid crystals containing magnetic nanoparticles

The inclusion of superparamagnetic iron oxide nanoparticles (SPIONs) in lipid mesophases is a promising strategy for drug-delivery applications, combining the innate biocompatibility of lipid architectures with SPIONs' response to external magnetic fields. Moreover, the organization of SPIONs within the lipid scaffold can lead to locally enhanced SPIONs concentration and improved magnetic response, which is key to overcome the current limitations of hyperthermic treatments. Here we present a Small-Angle X-ray Scattering (SAXS) structural investigation of the thermotropic and magnetotropic behavior of glyceryl monooleate (GMO)/water mesophases, loaded with hydrophobic SPIONs. We prove that even very low amounts of SPIONs deeply alter the phase behavior and thermotropic properties of the mesophases, promoting a cubic to hexagonal phase transition, which is similarly induced upon application of an Alternating Magnetic Field (AMF). Moreover, in the hexagonal phase SPIONs spontaneously self-assemble within the lipid scaffold into a linear supraparticle. This phase behavior is interpreted in the framework of the Helfrich's theory, which shows that SPIONs affect the mesophase both from a viscoelastic and from a structural standpoint. Finally, the dispersion of these cubic phases into stable magnetic colloidal particles, which retain their liquid crystalline internal structure, is addressed as a promising route towards magneto-responsive drug-delivery systems (DDS).

Filamentous phages as building blocks for reconfigurable and hierarchical self-assembly

Filamentous bacteriophages such as fd-like viruses are monodisperse rod-like colloids that have well defined properties of diameter, length, rigidity, charge and chirality. Engineering these viruses leads to a library of colloidal rods, which can be used as building blocks for reconfigurable and hierarchical self-assembly. Their condensation in an aqueous solution with additive polymers, which act as depletants to induce attraction between the rods, leads to a myriad of fluid-like micronic structures ranging from isotropic/nematic droplets, colloid membranes, achiral membrane seeds, twisted ribbons, π-wall, pores, colloidal skyrmions, Möbius anchors, scallop membranes to membrane rafts. These structures, and the way that they shape-shift, not only shed light on the role of entropy, chiral frustration and topology in soft matter, but also mimic many structures encountered in different fields of science. On the one hand, filamentous phages being an experimental realization of colloidal hard rods, their condensation mediated by depletion interactions constitutes a blueprint for the self-assembly of rod-like particles and provides a fundamental foundation for bio- or material-oriented applications. On the other hand, the chiral properties of the viruses restrict the generalities of some results but vastly broaden the self-assembly possibilities.

What can machine learning do for antimicrobial peptides, and what can antimicrobial peptides do for machine learning?

Antimicrobial peptides (AMPs) are a diverse class of well-studied membrane-permeating peptides with important functions in innate host defense. In this short review, we provide a historical overview of AMPs, summarize previous applications of machine learning to AMPs, and discuss the results of our studies in the context of the latest AMP literature. Much work has been recently done in leveraging computational tools to design new AMP candidates with high therapeutic efficacies for drug-resistant infections. We show that machine learning on AMPs can be used to identify essential physico-chemical determinants of AMP functionality, and identify and design peptide sequences to generate membrane curvature. In a broader scope, we discuss the implications of our findings for the discovery of membrane-active peptides in general, and uncovering membrane activity in new and existing peptide taxonomies.

Lipid Phase Control and Secondary Structure of Viral Fusion Peptides Anchored in Monoolein Membranes

The fusion of lipid membranes involves major changes of the membrane curvatures and is mediated by fusion proteins that bind to the lipid membranes. For a better understanding of the way fusion proteins steer this process, we have studied the interaction of two different viral fusion peptides, HA2-FP and TBEV-FP, with monoolein mesophases as a function of temperature and pressure at limited hydration. The fusion peptides are derived from the influenza virus hemagglutinin fusion protein (HA2-FP) and from the tick-borne encephalitis virus envelope glycoprotein E (TBEV-FP). By using synchrotron X-ray diffraction, the changes of the monoolein phase behavior upon binding the peptides have been determined and the concomitant secondary structures of the peptides have been analyzed by FTIR spectroscopy. As main results we have found that the fusion peptides interact differently with monoolein and change the pressure and temperature dependent lipid phase behavior to different extents. However, they both destabilize the fluid lamellar phase and favor phases with negative curvature, i.e. inverse bicontinuous cubic and inverse hexagonal phases. These peptide-induced phase changes can partially be reversed by the application of high pressure, demonstrating that the promotion of negative curvature is achieved by a less dense packing of the monoolein membranes by the fusion peptides. Pressure jumps across the cubic-lamellar phase transition reveal that HA2-FP has a negligible effect on the rates of the cubic and the lamellar phase formation. Interestingly, the secondary structures of the fusion peptides appear unaffected by monoolein fluid-fluid phase transitions, suggesting that the fusion peptides are the structure dominant species in the fusion process of lipid membranes.

Determining the Gaussian Modulus and Edge Properties of 2D Materials: From Graphene to Lipid Bilayers

The dominant deformation behavior of two-dimensional materials (bending) is primarily governed by just two parameters: bending rigidity and the Gaussian modulus. These properties also set the energy scale for various important physical and biological processes such as pore formation, cell fission and generally, any event accompanied by a topological change. Unlike the bending rigidity, the Gaussian modulus is, however, notoriously difficult to evaluate via either experiments or atomistic simulations. In this Letter, recognizing that the Gaussian modulus and edge tension play a nontrivial role in the fluctuations of a 2D material edge, we derive closed-form expressions for edge fluctuations. Combined with atomistic simulations, we use the developed approach to extract the Gaussian modulus and edge tension at finite temperatures for both graphene and various types of lipid bilayers. Our results possibly provide the first reliable estimate of this elusive property at finite temperatures and appear to suggest that earlier estimates must be revised. In particular, we show that, if previously estimated properties are employed, the graphene-free edge will exhibit unstable behavior at room temperature. Remarkably, in the case of graphene, we show that the Gaussian modulus and edge tension even change sign at finite temperatures.

Gramicidin A Channel Formation Induces Local Lipid Redistribution II: A 3D Continuum Elastic Model

To change conformation, a protein must deform the surrounding bilayer. In this work, a three-dimensional continuum elastic model for gramicidin A in a lipid bilayer is shown to describe the sensitivity to thickness, curvature stress, and the mechanical properties of the lipid bilayer. A method is demonstrated to extract the gramicidin-lipid boundary condition from all-atom simulations that can be used in the three-dimensional continuum model. The boundary condition affects the deformation dramatically, potentially much more than typical variations in the material stiffness do as lipid composition is changed. Moreover, it directly controls the sensitivity to curvature stress. The curvature stress and hydrophobic surfaces of the all-atom and continuum models are found to be in excellent agreement. The continuum model is applied to estimate the enrichment of hydrophobically matched lipids near the channel in a mixture, and the results agree with single-channel experiments and extended molecular dynamics simulations from the companion article by Beaven et al. in this issue of Biophysical Journal.

Chiral edge fluctuations of colloidal membranes

We study edge fluctuations of a flat colloidal membrane comprised of a monolayer of aligned filamentous viruses. Experiments reveal that a peak in the spectrum of the in-plane edge fluctuations arises for sufficiently strong virus chirality. Accounting for internal liquid crystalline degrees of freedom by the length, curvature, and geodesic torsion of the edge, we calculate the spectrum of the edge fluctuations. The theory quantitatively describes the experimental data, demonstrating that chirality couples in-plane and out-of-plane edge fluctuations to produce the peak.