Bending of a lipid membrane edge by annexin A5 trimers.

Plasma membrane damage occurs in healthy cells and more frequently in cancer cells where high growth rates and metastasis result in frequent membrane damage. The annexin family of proteins plays a key role in membrane repair. Annexins are recruited at the membrane injury site by Ca+2 and repair the damaged membrane in concert with several other proteins. Annexin A4 (ANXA4) and ANXA5 form trimers at the bilayer surface, and previous simulations show that the trimers induce high local negative membrane curvature on a flat bilayer. The membrane-curvature-inducing property of ANXA5 is presumed to be vital to the membrane repair mechanism. A previously proposed descriptive model hypothesizes that ANXA5-mediated curvature force is utilized at the free edge of the membrane at a wound site to pull the wound edges together, resulting in the formation of a "neck"-shaped structure, which, when combined with a constriction force exerted by ANXA6, leads to membrane repair. The molecular details and mechanisms of repair remain unknown, in part because the membrane edge is a transient structure that is difficult to investigate both experimentally and computationally. For the first time, we investigate the impact of ANXA5 near a membrane edge, which is modeled by a bicelle under periodic boundary conditions. ANXA5 trimers induce local curvature on the membrane leading to global bending of the bicelle. The global curvature depends on the density of annexins on the bicelle, and the curvature increases with the ANXA5 concentration until it reaches a plateau. The simulations suggest that not only do annexins induce local membrane curvature, but they can change the overall shape of a free-standing membrane. We also demonstrate that ANXA5 trimers reduce the rate of phosphatidylserine lipid diffusion from the cytoplasmic to the exoplasmic leaflet along the edge of the bicelle. In this way, membrane-bound annexins can potentially delay the apoptotic signal triggered by the presence of phosphatidylserine lipids in the outer leaflet, thus biding time for repair of the membrane hole. Our findings provide new insights into the role of ANXA5 at the edges of the membrane (the injury site) and support the curvature-constriction model of membrane repair.

Shape of the membrane neck around a hole during plasma membrane repair.

Plasma membrane damage and rupture occurs frequently in cells, and holes must be sealed rapidly to ensure homeostasis and cell survival. The membrane repair machinery is known to involve recruitment of curvature-inducing annexin proteins, but the connection between membrane remodeling and hole closure is poorly described. The induction of curvature by repair proteins leads to the possible formation of a membrane neck around the hole as a key intermediate structure before sealing. We formulate a theoretical model of equilibrium neck shapes to examine the potential connection to a repair mechanism. Using variational calculus, the shape equations for the membrane near a hole are formulated and solved numerically. The system is described under a condition of fixed area, and a shooting approach is applied to fulfill the boundary conditions at the free membrane edge. A state diagram of neck shapes is produced describing the variation in neck morphology with respect to the membrane area. Two distinct types of necks are predicted, one with conformations curved beyond π existing at positive excess area, whereas flat neck conformations (curved below π) have negative excess area. The results indicate that in cells, the supply of additional membrane area and a change in edge tension is linked to the formation of narrow and curved necks. Such necks may be susceptible to passive or actively induced membrane fission as a possible mechanism for hole sealing during membrane repair in cells.

There and back again: bridging meso- and nano-scales to understand lipid vesicle patterning.

We describe a complete methodology to bridge the scales between nanoscale molecular dynamics and (micrometer) mesoscale Monte Carlo simulations in lipid membranes and vesicles undergoing phase separation, in which curving molecular species are furthermore embedded. To go from the molecular to the mesoscale, we notably appeal to physical renormalization arguments enabling us to rigorously infer the mesoscale interaction parameters from its molecular counterpart. We also explain how to deal with the physical timescales at stake at the mesoscale. Simulating the as-obtained mesoscale system enables us to equilibrate the long wavelengths of the vesicles of interest, up to the vesicle size. Conversely, we then backmap from the meso- to the nano-scale, which enables us to equilibrate in turn the short wavelengths down to the molecular length-scales. By applying our approach to the specific situation of patterning a vesicle membrane, we show that macroscopic membranes can thus be equilibrated at all length-scales in achievable computational time offering an original strategy to address the fundamental challenge of timescale in simulations of large bio-membrane systems.

Mesoscale simulations: An indispensable approach to understand biomembranes.

Computer simulation techniques form a versatile tool, a computational microscope, for exploring biological processes. This tool has been particularly effective in exploring different features of biological membranes. In recent years, thanks to elegant multiscale simulation schemes, some fundamental limitations of investigations by distinct simulation techniques have been resolved. As a result, we are now capable of exploring processes spanning multiple scales beyond the capacity of any single technique. In this perspective, we argue that mesoscale simulations require more attention and must be further developed to fill evident gaps in a quest toward simulating and modeling living cell membranes.

Strength in numbers: effect of protein crowding on the shape of cell membranes.

Continuous reshaping of the plasma membrane into pleomorphic shapes is critical for a plethora of cellular functions. How the cell carries out this enigmatic control of membrane remodeling has remained an active research field for decades and several molecular and biophysical mechanisms have shown to be involved in overcoming the energy barrier associated with membrane bending. The reported mechanisms behind membrane bending have been largely concerned with structural protein features, however, in the last decade, reports on the ability of densely packed proteins to bend membranes by protein-protein crowding, have challenged prevailing mechanistic views. Crowding has now been shown to generate spontaneous vesicle formation and tubular morphologies on cell- and model membranes, demonstrating crowding as a relevant player involved in the bending of membranes. Still, current research is largely based on unnatural overexpression of proteins in non-native domains, and together with efforts in modeling, this has led to questioning the in vivo impact of crowding. In this review, we examine this previously overlooked mechanism by summarizing recent advances in the understanding of protein-protein crowding and its prevalence in cellular membrane-shaping processes.

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

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

Fluctuations and conformational stability of a membrane patch with curvature inducing inclusions.

Membranes with curvature inducing inclusions display a range of cooperative phenomena, which can be linked to biomembrane function, e.g. membrane tubulation, vesiculation, softening and spontaneous tension. We investigate how these phenomena are related for a fluctuating, framed membrane through analysis of a descretized membrane model by Monte Carlo simulation techniques. The membrane model is based on a dynamically triangulated surface equipped with non-interacting, up-down symmetry breaking inclusions where only terms coupled linearly to mean-curvature are maintained. We show that the lateral configurational entropy plays a key role for the mechanical properties of the semi-flexible membrane, e.g. a pronounced softening at intermediate inclusion coverages of the membrane and generation of membrane tension. Tensionless framed membranes will remain quasi-flat up to some threshold coverage, where a shape instability occurs with formation of pearling or tubular membranes, which below full coverage is associated with segregation of inclusions between the curved and flat membrane geometries. For inclusions with preference for highly curved membranes the instability appears at dilute inclusion coverages and is accompanied by strong configurational fluctuations.

Lipid Configurations from Molecular Dynamics Simulations.

The extent to which current force fields faithfully reproduce conformational properties of lipids in bilayer membranes, and whether these reflect the structural principles established for phospholipids in bilayer crystals, are central to biomembrane simulations. We determine the distribution of dihedral angles in palmitoyl-oleoyl phosphatidylcholine from molecular dynamics simulations of hydrated fluid bilayer membranes. We compare results from the widely used lipid force field of Berger et al. with those from the most recent C36 release of the CHARMM force field for lipids. Only the CHARMM force field produces the chain inequivalence with sn-1 as leading chain that is characteristic of glycerolipid packing in fluid bilayers. The exposure and high partial charge of the backbone carbonyls in Berger lipids leads to artifactual binding of Na+ ions reported in the literature. Both force fields predict coupled, near-symmetrical distributions of headgroup dihedral angles, which is compatible with models of interconverting mirror-image conformations used originally to interpret NMR order parameters. The Berger force field produces rotamer populations that correspond to the headgroup conformation found in a phosphatidylcholine lipid bilayer crystal, whereas CHARMM36 rotamer populations are closer to the more relaxed crystal conformations of phosphatidylethanolamine and glycerophosphocholine. CHARMM36 alone predicts the correct relative signs of the time-average headgroup order parameters, and reasonably reproduces the full range of NMR data from the phosphate diester to the choline methyls. There is strong motivation to seek further experimental criteria for verifying predicted conformational distributions in the choline headgroup, including the 31P chemical shift anisotropy and 14N and CD3 NMR quadrupole splittings.

Membrane Tubulation in Lipid Vesicles Triggered by the Local Application of Calcium Ions.

Experimental and theoretical studies on ion-lipid interactions predict that binding of calcium ions to cell membranes leads to macroscopic mechanical effects and membrane remodeling. Herein, we provide experimental evidence that a point source of Ca2+ acting upon a negatively charged membrane generates spontaneous curvature and triggers the formation of tubular protrusions that point away from the ion source. This behavior is rationalized by strong binding of the divalent cations to the surface of the charged bilayer, which effectively neutralizes the surface charge density of outer leaflet of the bilayer. The mismatch in the surface charge density of the two leaflets leads to nonzero spontaneous curvature. We probe this mismatch through the use of molecular dynamics simulations and validate that calcium ion binding to a lipid membrane is sufficient to generate inward spontaneous curvature, bending the membrane. Additionally, we demonstrate that the formed tubular protrusions can be translated along the vesicle surface in a controlled manner by repositioning the site of localized Ca2+ exposure. The findings demonstrate lipid membrane remodeling in response to local chemical gradients and offer potential insights into the cell membrane behavior under conditions of varying calcium ion concentrations.

The effects of globotriaosylceramide tail saturation level on bilayer phases.

Globotriaosylceramide (Gb3) is a glycosphingolipid present in the plasma membrane that is the natural receptor of the bacterial Shiga toxin. The unsaturation level of Gb3 acyl chains has a drastic impact on lipid bilayer properties and phase behaviour, and on many Gb3-related cellular processes. For example: the Shiga toxin B subunit forms tubular invaginations in the presence of Gb3 with an unsaturated acyl chain (U-Gb3), while in the presence of Gb3 with a saturated acyl chain (S-Gb3) such invagination does not occur. We have used all-atom molecular dynamics simulations to investigate the effects of the Gb3 concentration and its acyl chain saturation on the phase behaviour of a mixed bilayer of dioleoylphosphatidylcholine and Gb3. The simulation results show that: (1) the Gb3 acyl chains (longer tails) from one leaflet interdigitate into the opposing leaflet and lead to significant bilayer rigidification and immobilisation of the lipid tails. S-Gb3 can form a highly ordered, relatively immobile phase which is resistant to bending while these changes for U-Gb3 are not significant. (2) At low concentrations of Gb3, U-Gb3 and S-Gb3 have a similar impact on the bilayer reminiscent of the effect of sphingomyelin lipids and (3) At higher Gb3 concentrations, U-Gb3 mixes better with dioleoylphosphatidylcholine than S-Gb3. Our simulations also provide the first molecular level structural model of Gb3 in membranes.

Mesoscale simulation of biomembranes with FreeDTS.

We present FreeDTS software for performing computational research on biomembranes at the mesoscale. In this software, a membrane is represented by a dynamically triangulated surface equipped with vertex-based inclusions to integrate the effects of integral and peripheral membrane proteins. Several algorithms are included in the software to simulate complex membranes at different conditions such as framed membranes with constant tension, vesicles and high-genus membranes with various fixed volumes or constant pressure differences and applying external forces to membrane regions. Furthermore, the software allows the user to turn off the shape evolution of the membrane and focus solely on the organization of proteins. As a result, we can take realistic membrane shapes obtained from, for example, cryo-electron tomography and backmap them into a finer simulation model. In addition to many biomembrane applications, this software brings us a step closer to simulating realistic biomembranes with molecular resolution. Here we provide several interesting showcases of the power of the software but leave a wide range of potential applications for interested users.

Close, but not too close: a mesoscopic description of (a)symmetry and membrane shaping mechanisms.

Biomembranes are fundamental to our understanding of the cell, the basic building block of all life. An intriguing aspect of membranes is their ability to assume a variety of shapes, which is crucial for cell function. Here, we review various membrane shaping mechanisms with special focus on the current understanding of how local curvature and local rigidity induced by membrane proteins leads to emerging forces and consequently large-scale membrane deformations. We also argue that describing the interaction of rigid proteins with membranes purely in terms of local membrane curvature is incomplete and that changes in the membrane rigidity moduli must also be considered.

Molecular architecture and dynamics of SARS-CoV-2 envelope by integrative modeling.

Despite tremendous efforts, the exact structure of SARS-CoV-2 and related betacoronaviruses remains elusive. SARS-CoV-2 envelope is a key structural component of the virion that encapsulates viral RNA. It is composed of three structural proteins, spike, membrane (M), and envelope, which interact with each other and with the lipids acquired from the host membranes. Here, we developed and applied an integrative multi-scale computational approach to model the envelope structure of SARS-CoV-2 with near atomistic detail, focusing on studying the dynamic nature and molecular interactions of its most abundant, but largely understudied, M protein. The molecular dynamics simulations allowed us to test the envelope stability under different configurations and revealed that the M dimers agglomerated into large, filament-like, macromolecular assemblies with distinct molecular patterns. These results are in good agreement with current experimental data, demonstrating a generic and versatile approach to model the structure of a virus de novo.

Inferring mechanical properties of the SARS-CoV-2 virus particle with nano-indentation tests and numerical simulations.

The pandemic caused by the SARS-CoV-2 virus has claimed more than 6.5 million lives worldwide. This global challenge has led to accelerated development of highly effective vaccines tied to their ability to elicit a sustained immune response. While numerous studies have focused primarily on the spike (S) protein, less is known about the interior of the virus. Here we propose a methodology that combines several experimental and simulation techniques to elucidate the internal structure and mechanical properties of the SARS-CoV-2 virus. The mechanical response of the virus was analyzed by nanoindentation tests using a novel flat indenter and evaluated in comparison to a conventional sharp tip indentation. The elastic properties of the viral membrane were estimated by analytical solutions, molecular dynamics (MD) simulations on a membrane patch and by a 3D Finite Element (FE)-beam model of the virion's spike protein and membrane molecular structure. The FE-based inverse engineering approach provided a reasonable reproduction of the mechanical response of the virus from the sharp tip indentation and was successfully verified against the flat tip indentation results. The elastic modulus of the viral membrane was estimated in the range of 7-20 MPa. MD simulations showed that the presence of proteins significantly reduces the fracture strength of the membrane patch. However, FE simulations revealed an overall high fracture strength of the virus, with a mechanical behavior similar to the highly ductile behavior of engineering metallic materials. The failure mechanics of the membrane during sharp tip indentation includes progressive damage combined with localized collapse of the membrane due to severe bending. Furthermore, the results support the hypothesis of a close association of the long membrane proteins (M) with membrane-bound hexagonally packed ribonucleoproteins (RNPs). Beyond improved understanding of coronavirus structure, the present findings offer a knowledge base for the development of novel prevention and treatment methods that are independent of the immune system.

Synthetic Membrane Shaper for Controlled Liposome Deformation.

Shape defines the structure and function of cellular membranes. In cell division, the cell membrane deforms into a "dumbbell" shape, while organelles such as the autophagosome exhibit "stomatocyte" shapes. Bottom-up in vitro reconstitution of protein machineries that stabilize or resolve the membrane necks in such deformed liposome structures is of considerable interest to characterize their function. Here we develop a DNA-nanotechnology-based approach that we call the synthetic membrane shaper (SMS), where cholesterol-linked DNA structures attach to the liposome membrane to reproducibly generate high yields of stomatocytes and dumbbells. In silico simulations confirm the shape-stabilizing role of the SMS. We show that the SMS is fully compatible with protein reconstitution by assembling bacterial divisome proteins (DynaminA, FtsZ:ZipA) at the catenoidal neck of these membrane structures. The SMS approach provides a general tool for studying protein binding to complex membrane geometries that will greatly benefit synthetic cell research.

Martini 3 Coarse-Grained Force Field for Carbohydrates.

The Martini 3 force field is a full reparametrization of the Martini coarse-grained model for biomolecular simulations. Due to the improved interaction balance, it allows for a more accurate description of condensed phase systems. In the present work, we develop a consistent strategy to parametrize carbohydrate molecules accurately within the framework of Martini 3. In particular, we develop a canonical mapping scheme which decomposes arbitrarily large carbohydrates into a limited number of fragments. Bead types for these fragments have been assigned by matching physicochemical properties of mono- and disaccharides. In addition, guidelines for assigning bonds, angles, and dihedrals were developed. These guidelines enable a more accurate description of carbohydrate conformations than in the Martini 2 force field. We show that models obtained with this approach are able to accurately reproduce osmotic pressures of carbohydrate water solutions. Furthermore, we provide evidence that the model differentiates correctly the solubility of the polyglucoses dextran (water-soluble) and cellulose (water insoluble but soluble in ionic liquids). Finally, we demonstrate that the new building blocks can be applied to glycolipids. We show they are able to reproduce membrane properties and induce binding of peripheral membrane proteins. These test cases demonstrate the validity and transferability of our approach.

Creasing of flexible membranes at vanishing tension.

The properties of freestanding tensionless interfaces and membranes at low bending rigidity κ are dominated by strong fluctuations and self-avoidance and are thus outside the range of standard perturbative analysis. We analyze this regime by a simple discretized, self-avoiding membrane model on a frame subject to periodic boundary conditions by use of Monte Carlo simulation and dynamically triangulated surface techniques. We find that at low bending rigidities, the membrane properties fall into three regimes: Below the collapse transition κ_{BP} it is subject to branched polymer instability where the framed surface is not defined, in a range below a threshold rigidity κ_{c} the conformational correlation function are characterized by power-law behavior with a continuously varying exponent α, 2<α≤4 and above κ_{c}, α=4 characteristic for linearized bending excitations. Response functions specific heat and area compressibility display pronounced peaks close to κ_{c}. The results may be important for the description of soft interface systems, such as microemulsions and membranes with in-plane cooperative phenomena.

Simulating realistic membrane shapes.

Biological membranes exhibit diversity in their shapes and complexity in chemical compositions that are linked to many cellular functions. These two central features of biomembranes have been the subject of numerous simulation studies, using a diverse range of computational techniques. Currently, the field is able to capture this complexity at increasing levels of realism and connect the microscopic view on protein-lipid interactions to cellular morphologies at the level of entire organelles. Here we highlight recent advances in this topic, identify current bottlenecks, and sketch possible ways ahead.

Computational Approaches to Explore Bacterial Toxin Entry into the Host Cell.

Many bacteria secrete toxic protein complexes that modify and disrupt essential processes in the infected cell that can lead to cell death. To conduct their action, these toxins often need to cross the cell membrane and reach a specific substrate inside the cell. The investigation of these protein complexes is essential not only for understanding their biological functions but also for the rational design of targeted drug delivery vehicles that must navigate across the cell membrane to deliver their therapeutic payload. Despite the immense advances in experimental techniques, the investigations of the toxin entry mechanism have remained challenging. Computer simulations are robust complementary tools that allow for the exploration of biological processes in exceptional detail. In this review, we first highlight the strength of computational methods, with a special focus on all-atom molecular dynamics, coarse-grained, and mesoscopic models, for exploring different stages of the toxin protein entry mechanism. We then summarize recent developments that are significantly advancing our understanding, notably of the glycolipid-lectin (GL-Lect) endocytosis of bacterial Shiga and cholera toxins. The methods discussed here are also applicable to the design of membrane-penetrating nanoparticles and the study of the phenomenon of protein phase separation at the surface of the membrane. Finally, we discuss other likely routes for future development.