A Multi-Scale Approach to Membrane Remodeling Processes

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.

Modeling membranes in situ

Molecular dynamics simulations of cellular membranes have come a long way-from simple model lipid bilayers to multicomponent systems capturing the crowded and complex nature of real cell membranes. In this opinionated minireview, we discuss the current challenge to simulate the dynamics of membranes in their native environment, in situ, with the prospect of reaching the level of whole cells and cell organelles using an integrative modeling framework.

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.

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.

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.

A brief history of visualizing membrane systems in molecular dynamics simulations

Understanding lipid dynamics and function, from the level of single, isolated molecules to large assemblies, is more than ever an intensive area of research. The interactions of lipids with other molecules, particularly membrane proteins, are now extensively studied. With advances in the development of force fields for molecular dynamics simulations (MD) and increases in computational resources, the creation of realistic and complex membrane systems is now common. In this perspective, we will review four decades of the history of molecular dynamics simulations applied to membranes and lipids through the prism of molecular graphics.

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.

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

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

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.

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.

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.

Generation of interconnected vesicles in a liposomal cell model

We introduce an experimental method based upon a glass micropipette microinjection technique for generating a multitude of interconnected vesicles (IVs) in the interior of a single giant unilamellar phospholipid vesicle (GUV) serving as a cell model system. The GUV membrane, consisting of a mixture of soybean polar lipid extract and anionic phosphatidylserine, is adhered to a multilamellar lipid vesicle that functions as a lipid reservoir. Continuous IV formation was achieved by bringing a micropipette in direct contact with the outer GUV surface and subjecting it to a localized stream of a Ca²⁺ solution from the micropipette tip. IVs are rapidly and sequentially generated and inserted into the GUV interior and encapsulate portions of the micropipette fluid content. The IVs remain connected to the GUV membrane and are interlinked by short lipid nanotubes and resemble beads on a string. The vesicle chain-growth from the GUV membrane is maintained for as long as there is the supply of membrane material and Ca²⁺ solution, and the size of the individual IVs is controlled by the diameter of the micropipette tip. We also demonstrate that the IVs can be co-loaded with high concentrations of neurotransmitter and protein molecules and displaying a steep calcium ion concentration gradient across the membrane. These characteristics are analogous to native secretory vesicles and could, therefore, serve as a model system for studying secretory mechanisms in biological systems.

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.

Computer simulations of large-scale changes in membrane shape are challenging since they occur across a wide range of spatiotemporal scales. Here, authors present a multiscale algorithm that backmaps a continuum membrane model represented as a dynamically triangulated surface to its corresponding molecular model based on the coarse-grained Martini force field.

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.