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.

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.

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.

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.

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.

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.

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.

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.

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.

Capturing Membrane Phase Separation by Dual Resolution Molecular Dynamics Simulations.

Understanding the lateral organization in plasma membranes remains an open problem and is of great interest to many researchers. Model membranes consisting of coexisting domains are commonly used as simplified models of plasma membranes. The coarse-grained (CG) Martini force field has successfully captured spontaneous separation of ternary membranes into a liquid-disordered and a liquid-ordered domain. With all-atom (AA) models, however, phase separation is much harder to achieve due to the slow underlying dynamics. To remedy this problem, here, we apply the virtual site (VS) hybrid method on a ternary membrane composed of saturated lipids, unsaturated lipids, and cholesterol to investigate the phase separation. The VS scheme couples the two membrane leaflets at CG and AA resolution. We found that the rapid phase separation reached by the CG leaflet can accelerate and guide this process in the AA leaflet.

Ceramide structure dictates glycosphingolipid nanodomain assembly and function.

Gangliosides in the outer leaflet of the plasma membrane of eukaryotic cells are essential for many cellular functions and pathogenic interactions. How gangliosides are dynamically organized and how they respond to ligand binding is poorly understood. Using fluorescence anisotropy imaging of synthetic, fluorescently labeled GM1 gangliosides incorporated into the plasma membrane of living cells, we found that GM1 with a fully saturated C16:0 acyl chain, but not with unsaturated C16:1 acyl chain, is actively clustered into nanodomains, which depends on membrane cholesterol, phosphatidylserine and actin. The binding of cholera toxin B-subunit (CTxB) leads to enlarged membrane domains for both C16:0 and C16:1, owing to binding of multiple GM1 under a toxin, and clustering of CTxB. The structure of the ceramide acyl chain still affects these domains, as co-clustering with the glycosylphosphatidylinositol (GPI)-anchored protein CD59 occurs only when GM1 contains the fully saturated C16:0 acyl chain, and not C16:1. Thus, different ceramide species of GM1 gangliosides dictate their assembly into nanodomains and affect nanodomain structure and function, which likely underlies many endogenous cellular processes.

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.

Long chain sphingomyelin depletes cholesterol from the cytoplasmic leaflet in asymmetric lipid membranes.

The transbilayer distribution of cholesterol (CHL) in complex asymmetric lipid membranes remains controversial, with contrasting investigations suggesting that there is more CHL either in the exoplasmic, outer leaflet (OL) or the cytoplasmic, inner leaflet (IL) depending on cell type or model, membrane composition, and method of investigation. Here, we launch systematic coarse-grained molecular dynamics simulations to investigate the impact of the sphingomyelin (SM) acyl chain length upon CHL distribution in asymmetric lipid membrane mixtures which account for the variation of the most abundant headgroups and acyl chain unsaturation in the two membrane leaflets. We find that there is always more CHL in the OL, but longer chain SM depletes more CHL from the IL than short chain SM in simple membrane mixtures containing SM and 16 : 0, 18 : 1 phospholipids. The difference between longer and shorter chain SM is neutralised in a more complex asymmetric membrane, where there are more saturated tails in the outer leaflet. We propose that interdigitation of long-chain SM into the opposing IL pushes cytoplasmic CHL towards the OL, but higher chain saturation of the outer leaflet compensates for the effect of SM chain length.

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.

Coupling Coarse-Grained to Fine-Grained Models via Hamiltonian Replica Exchange.

The energy landscape of biomolecular systems contains many local minima that are separated by high energy barriers. Sampling this landscape in molecular dynamics simulations is a challenging task and often requires the use of enhanced sampling techniques. Here, we increase the sampling efficiency by coupling the fine-grained (FG) GROMOS force field to the coarse-grained (CG) Martini force field via the Hamiltonian replica exchange method (HREM). We tested the efficiency of this procedure using a lutein/octane system. In traditional simulations, cis-trans transitions of lutein are barely observed due to the high energy barrier separating these states. However, many of these transitions are sampled with our HREM scheme. The proposed method offers new possibilities for enhanced sampling of biomolecular conformations, making use of CG models without compromising the accuracy of the FG model.

Backmapping triangulated surfaces to coarse-grained membrane models.

Many biological processes involve large-scale changes in membrane shape. Computer simulations of these processes are challenging since they occur across a wide range of spatiotemporal scales that cannot be investigated in full by any single current simulation technique. A potential solution is to combine different levels of resolution through a multiscale scheme. Here, we present a multiscale algorithm that backmaps a continuum membrane model represented as a dynamically triangulated surface (DTS) to its corresponding molecular model based on the coarse-grained (CG) Martini force field. Thus, we can use DTS simulations to equilibrate slow large-scale membrane conformational changes and then explore the local properties at CG resolution. We demonstrate the power of our method by backmapping a vesicular bud induced by binding of Shiga toxin and by transforming the membranes of an entire mitochondrion to near-atomic resolution. Our approach opens the way to whole cell simulations at molecular detail.

Dual Resolution Membrane Simulations Using Virtual Sites.

All-atomistic (AA) and coarse-grain (CG) simulations have been successfully applied to investigate a broad range of biomolecular processes. However, the accessible time and length scales of AA simulation are limited and the specific molecular details of CG simulation are simplified. Here, we propose a virtual site (VS) based hybrid scheme that can concurrently couple AA and CG resolutions in a single membrane simulation, mitigating the shortcomings of either representation. With some adjustments to make the AA and CG force fields compatible, we demonstrate that lipid bilayer properties are well kept in our hybrid approach. Our VS hybrid method was also applied to simulate a small lipid vesicle, with the inner leaflet and interior solvent represented in AA, and the outer leaflet together with exterior solvent at the CG level. Our multiscale method opens the way to investigate biomembrane properties at increased computational efficiency, in particular applications involving large solvent filled regions.

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.