Membrane sculpting by F-BAR domains studied by molecular dynamics simulations

Exploring the Properties of Curved Lipid Membranes: Comparative Analysis of Atomistic and Coarse-Grained Force Fields

Curvature emerges as a fundamental membrane characteristic crucial for diverse biological processes, including vesicle formation, cell signaling, and membrane trafficking. Increasingly valuable insights into atomistic details governing curvature-dependent membrane properties are provided by computer simulations. Nevertheless, the underlying force field models are conventionally calibrated and tested in relation to experimentally derived parameters of planar bilayers, thereby leaving uncertainties concerning their consistency in reproducing curved lipid systems. In this study we compare the depiction of buckled phosphatidylcholine (POPC) and POPC-cholesterol membranes by four popular force field models. Aside from agreement with respect to general trends in curvature dependence of a number of parameters, we observe a few qualitative differences. Among the most prominent ones is the difference between atomistic and coarse grained force fields in their representation of relative compressibility of the polar headgroup region and hydrophobic lipid core. Through a number of downstream effects, this discrepancy can influence the way in which curvature modulates the behavior of membrane bound proteins depending on the adopted simulation model.

Performance efficient macromolecular mechanics via sub-nanometer shape based coarse graining

Dimensionality reduction via coarse grain modeling is a valuable tool in biomolecular research. For large assemblies, ultra coarse models are often knowledge-based, relying on a priori information to parameterize models thus hindering general predictive capability. Here, we present substantial advances to the shape based coarse graining (SBCG) method, which we refer to as SBCG2. SBCG2 utilizes a revitalized formulation of the topology representing network which makes high-granularity modeling possible, preserving atomistic details that maintain assembly characteristics. Further, we present a method of granularity selection based on charge density Fourier Shell Correlation and have additionally developed a refinement method to optimize, adjust and validate high-granularity models. We demonstrate our approach with the conical HIV-1 capsid and heteromultimeric cofilin-2 bound actin filaments. Our approach is available in the Visual Molecular Dynamics (VMD) software suite, and employs a CHARMM-compatible Hamiltonian that enables high-performance simulation in the GPU-resident NAMD3 molecular dynamics engine.

Molecular mechanism of GTP binding- and dimerization-induced enhancement of Sar1-mediated membrane remodeling

The Sar1 GTPase initiates coat protein II (COPII)-mediated protein transport by generating membrane curvature at subdomains on the endoplasmic reticulum, where it is activated by the guanine nucleotide exchange factor (GEF) Sec12. Crystal structures of GDP- and GTP-bound forms of Sar1 suggest that it undergoes a conformational switch in which GTP binding enhances the exposure of an amino-terminal amphipathic helix necessary for efficient membrane penetration. However, key residues in the amino terminus were not resolved in crystal structures, and experimental studies have suggested that the amino terminus of Sar1 is solvent-exposed in the absence of a membrane, even in the GDP-bound state. Therefore, the molecular mechanism by which GTP binding activates the membrane-remodeling activity of Sar1 remains unclear. Using atomistic molecular dynamics simulations, we compare the membrane-binding and curvature generation activities of Sar1 in its GDP- and GTP-bound states. We show that in the GTP-bound state, Sar1 inserts into the membrane with its complete (residues 1 to 23) amphipathic amino-terminal helix, while Sar1-GDP binds to the membrane only through its first 12 residues. Such differential membrane-binding modes translate into significant differences in the protein volume inserted into the membrane. As a result, Sar1-GTP generates positive membrane curvature 10 to 20 times higher than Sar1-GDP. Dimerization of the GTP-bound form of Sar1 further amplifies curvature generation. Taken together, our results present a detailed molecular mechanism for how the nucleotide-bound state of Sar1 regulates its membrane-binding and remodeling activities in a concentration-dependent manner, paving the way toward a better understanding COPII-mediated membrane transport.

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.

A mechanical-thermodynamic model for understanding endocytosis of COVID-19 virus SARS-CoV-2

We analyze the endocytosis process of COVID-19 (coronavirus disease 2019) virus SARS-CoV-2 (severe acute respiratory syndrome coronavirus 2) using a mechanical-thermodynamic model. The virus particle is designed to interface with the cell membrane as a hard sphere. The role of cytoplasmic BAR (Bin/Amphiphysin/RVs) proteins is considered in the endocytosis. Interestingly, the Endophilin N-BAR cytoplasmic proteins show resistance in participating endocytosis, whereas F-BAR, Arfaptin BAR, Amphiphysin N-BAR, and PX-BAR proteins participate in endocytosis. The increase in membrane tension, concentrated force between the cell membrane receptor, and spike glycoprotein present on the surface of virus particle promote the endocytosis. Also, the increase in the bending modulus of membrane leads to the two-phase solution of BAR protein concentration on the interior of cell membrane surface. We observe an unstable region of protein concentration, which may help one to retard the endocytosis process and thus the viral infection. Though the present study is focused on SARS-CoV-2, it can be extended to understand any other viral infections, involving endocytosis process.

Data driven and biophysical insights into the regulation of trafficking vesicles by extracellular matrix stiffness

Biomechanical signals from remodeled extracellular matrix (ECM) promote tumor progression. Here, we show that cell-matrix and cell-cell communication may be inherently linked and tuned through mechanisms of mechanosensitive biogenesis of trafficking vesicles. Pan-cancer analysis of cancer cells' mechanical properties (focusing primarily on cell stiffness) on substrates of varied stiffness and composition elucidated a heterogeneous cellular response to mechanical stimuli. Through machine learning, we identified a fingerprint of cytoskeleton-related proteins that accurately characterize cell stiffness in different ECM conditions. Expression of their respective genes correlates with patient prognosis across different tumor types. The levels of selected cytoskeleton proteins indicated that cortical tension mirrors the increase (or decrease) in cell stiffness with a change in ECM stiffness. A mechanistic biophysical model shows that the tendency for curvature generation by curvature-inducing proteins has an ultrasensitive dependence on cortical tension. This study thus highlights the effect of ECM stiffness, mediated by cortical tension, in modulating vesicle biogenesis.

Molecular Dynamics Simulations of Curved Lipid Membranes

Eukaryotic cells contain membranes with various curvatures, from the near-plane plasma membrane to the highly curved membranes of organelles, vesicles, and membrane protrusions. These curvatures are generated and sustained by curvature-inducing proteins, peptides, and lipids, and describing these mechanisms is an important scientific challenge. In addition to that, some molecules can sense membrane curvature and thereby be trafficked to specific locations. The description of curvature sensing is another fundamental challenge. Curved lipid membranes and their interplay with membrane-associated proteins can be investigated with molecular dynamics (MD) simulations. Various methods for simulating curved membranes with MD are discussed here, including tools for setting up simulation of vesicles and methods for sustaining membrane curvature. The latter are divided into methods that exploit scaffolding virtual beads, methods that use curvature-inducing molecules, and methods applying virtual forces. The variety of simulation tools allow researcher to closely match the conditions of experimental studies of membrane curvatures.

Modes of adhesion of two Janus nanoparticles on the outer or inner side of lipid vesicles

Using molecular dynamics simulations of a coarse-grained model, in conjunction with the weighted histogram analysis method, the adhesion modes of two spherical Janus nanoparticles (NPs) on the outer or inner side of lipid vesicles are explored. In particular, the effects of the area fraction, J, of the NPs that interact attractively with lipid head groups, the adhesion strength and the size of the NPs on their adhesion modes are investigated. The NPs are found to exhibit two main modes of adhesion when adhered to the outer side of the vesicle. In the first mode, which occurs at relatively low values of J, the NPs are apart from each other. In the second mode, which occurs at higher values of J, the NPs form an in-plane dimer. Janus NPs, which adhere to the inner side of the vesicle, are always found to be apart from each other, regardless of the value of J and their diameter.

Binding of anisotropic curvature-inducing proteins onto membrane tubes

Bin/Amphiphysin/Rvs superfamily proteins and other curvature-inducing proteins have anisotropic shapes and anisotropically bend biomembranes. Here, we report how the anisotropic proteins bind the membrane tube and are orientationally ordered using mean-field theory including an orientation-dependent excluded volume. The proteins exhibit a second-order or first-order nematic transition with increasing protein density depending on the radius of the membrane tube. The tube curvatures for the maximum protein binding and orientational order are different and varied by the protein density and rigidity. As the external force along the tube axis increases, a first-order transition from a large tube radius with low protein density to a small radius with high density occurs once, and subsequently, the protein orientation tilts to the tube-axis direction. When an isotropic bending energy is used for the proteins with an elliptic shape, the force-dependence curves become symmetric and the first-order transition occurs twice. This theory quantitatively reproduces the results of meshless membrane simulation for short proteins, whereas deviations are seen for long proteins owing to the formation of protein clusters.

Specific interactions of peripheral membrane proteins with lipids: what can molecular simulations show us?

Peripheral membrane proteins (PMPs) can reversibly and specifically bind to biological membranes to carry out functions such as cell signalling, enzymatic activity, or membrane remodelling. Structures of these proteins and of their lipid-binding domains are typically solved in a soluble form, sometimes with a lipid or lipid headgroup at the binding site. To provide a detailed molecular view of PMP interactions with the membrane, computational methods such as molecular dynamics (MD) simulations can be applied. Here, we outline recent attempts to characterise these binding interactions, focusing on both intracellular proteins, such as phosphatidylinositol phosphate (PIP)-binding domains, and extracellular proteins such as glycolipid-binding bacterial exotoxins. We compare methods used to identify and analyse lipid-binding sites from simulation data and highlight recent work characterising the energetics of these interactions using free energy calculations. We describe how improvements in methodologies and computing power will help MD simulations to continue to contribute to this field in the future.

Insights into Membrane Curvature Sensing and Membrane Remodeling by Intrinsically Disordered Proteins and Protein Regions

Cellular membranes are highly dynamic in shape. They can rapidly and precisely regulate their shape to perform various cellular functions. The protein’s ability to sense membrane curvature is essential in various biological events such as cell signaling and membrane trafficking. As they are bound, these curvature-sensing proteins may also change the local membrane shape by one or more curvature driving mechanisms. Established curvature-sensing/driving mechanisms rely on proteins with specific structural features such as amphipathic helices and intrinsically curved shapes. However, the recent discovery and characterization of many proteins have shattered the protein structure–function paradigm, believing that the protein functions require a unique structural feature. Typically, such structure-independent functions are carried either entirely by intrinsically disordered proteins or hybrid proteins containing disordered regions and structured domains. It is becoming more apparent that disordered proteins and regions can be potent sensors/inducers of membrane curvatures. In this article, we outline the basic features of disordered proteins and regions, the motifs in such proteins that encode the function, membrane remodeling by disordered proteins and regions, and assays that may be employed to investigate curvature sensing and generation by ordered/disordered proteins.

Membrane-mediated interactions between hinge-like particles

Adsorption of nanoparticles on a membrane can give rise to interactions between particles, mediated by membrane deformations, that play an important role in self-assembly and membrane remodeling. Previous theoretical and experimental research has focused on nanoparticles with fixed shapes, such as spherical, rod-like, and curved nanoparticles. Recently, hinge-like DNA origami nanostructures have been designed with tunable mechanical properties. Inspired by this, we investigate the equilibrium properties of hinge-like particles adsorbed on an elastic membrane using Monte Carlo and umbrella sampling simulations. The configurations of an isolated particle are influenced by competition between bending energies of the membrane and the particle, which can be controlled by changing adsorption strength and hinge stiffness. When two adsorbed particles interact, they effectively repel one another when the strength of adhesion to the membrane is weak. However, a strong adhesive interaction induces an effective attraction between the particles, which drives their aggregation. The configurations of the aggregate can be tuned by adjusting the hinge stiffness: tip-to-tip aggregation occurs for flexible hinges, whereas tip-to-middle aggregation also occurs for stiffer hinges. Our results highlight the potential for using the mechanical features of deformable nanoparticles to influence their self-assembly when the particles and membrane mutually influence one another.

Endocytic proteins with prion-like domains form viscoelastic condensates that enable membrane remodeling

Membrane invagination and vesicle formation are key steps in endocytosis and cellular trafficking. Here, we show that endocytic coat proteins with prion-like domains (PLDs) form hemispherical puncta in the budding yeast, Saccharomyces cerevisiae These puncta have the hallmarks of biomolecular condensates and organize proteins at the membrane for actin-dependent endocytosis. They also enable membrane remodeling to drive actin-independent endocytosis. The puncta, which we refer to as endocytic condensates, form and dissolve reversibly in response to changes in temperature and solution conditions. We find that endocytic condensates are organized around dynamic protein-protein interaction networks, which involve interactions among PLDs with high glutamine contents. The endocytic coat protein Sla1 is at the hub of the protein-protein interaction network. Using active rheology, we inferred the material properties of endocytic condensates. These experiments show that endocytic condensates are akin to viscoelastic materials. We use these characterizations to estimate the interfacial tension between endocytic condensates and their surroundings. We then adapt the physics of contact mechanics, specifically modifications of Hertz theory, to develop a quantitative framework for describing how interfacial tensions among condensates, the membrane, and the cytosol can deform the plasma membrane to enable actin-independent endocytosis.

Binding of thermalized and active membrane curvature-inducing proteins

The phase behavior of a membrane induced by the binding of curvature-inducing proteins is studied by a combination of analytical and numerical approaches. In thermal equilibrium under the detailed balance between binding and unbinding, the membrane exhibits three phases: an unbound uniform flat phase (U), a bound uniform flat phase (B), and a separated/corrugated phase (SC). In the SC phase, the bound proteins form hexagonally-ordered bowl-shaped domains. The transitions between the U and SC phases and between the B and SC phases are second order and first order, respectively. At a small spontaneous curvature of the protein or high surface tension, the transition between B and SC phases becomes continuous. Moreover, a first-order transition between the U and B phases is found at zero spontaneous curvature driven by the Casimir-like interactions between rigid proteins. Furthermore, nonequilibrium dynamics is investigated by the addition of active binding and unbinding at a constant rate. The active binding and unbinding processes alter the stability of the SC phase.

Thermodynamics and Free Energy Landscape of BAR-Domain Dimerization from Molecular Simulations

Proteins with BAR domains function to bind to and remodel biological membranes, where the dimerization of BAR domains is a key step in this function. These domains can dimerize in solution or after localizing to the membrane surface. Here, we characterize the binding thermodynamics of homodimerization between the LSP1 BAR domain proteins in solution, using molecular dynamics (MD) simulations. By combining the MARTINI coarse-grained protein models with enhanced sampling through metadynamics, we construct a two-dimensional free energy surface quantifying the bound versus unbound ensembles as a function of two distance variables. With this methodology, our simulations can simultaneously characterize the structures and relative stabilities of a range of sampled dimers, portraying a heterogeneous and extraordinarily stable bound ensemble, where the proper crystal structure dimer is the most stable in a 100 mM NaCl solution. Nonspecific dimers that are sampled involve contacts that are consistent with experimental structures of higher-order oligomers formed by the LSP1 BAR domain. Because the BAR dimers and oligomers can assemble on membranes, we characterize the relative alignment of the known membrane binding patches, finding that only the specific dimer is aligned to form strong interactions with the membrane. Hence, we would predict a strong selection of the specific dimer in binding to or assembling when on the membrane. Establishing the pairwise stabilities of homodimer contacts is difficult experimentally when the proteins form stable oligomers, but through the method used here, we can isolate these contacts, providing a foundation to study the same interactions on the membrane.

A theory of ordering of elongated and curved proteins on membranes driven by density and curvature

Cell membranes interact with a myriad of curvature-active proteins that control membrane morphology and are responsible for mechanosensation and mechanotransduction. Some of these proteins, such as those containing BAR domains, are curved and elongated, and hence may adopt different states of orientational order, from isotropic to maximize entropy to nematic as a result of crowding or to adapt to the curvature of the underlying membrane. Here, extending the classical work of Onsager for ordering in hard particle systems and that of [E. S. Nascimento et al., Phys. Rev. E, 2017, 96, 022704], we develop a mean-field density functional theory to predict the orientational order and evaluate the free energy of ensembles of elongated and curved objects on curved membranes. This theory depends on the microscopic properties of the particles and explains how a density-dependent isotropic-to-nematic transition is modified by anisotropic curvature. We also examine the coexistence of isotropic and nematic phases. This theory predicts how ordering depends on geometry but we assume here that the geometry is fixed. It also lays the ground to understand the interplay between membrane reshaping by BAR proteins and molecular order, examined by [Le Roux et al., submitted, 2020].

Structural insights into membrane remodeling by SNX1

The sorting nexin (SNX) family of proteins deform the membrane to generate transport carriers in endosomal pathways. Here, we elucidate how a prototypic member, SNX1, acts in this process. Performing cryoelectron microscopy, we find that SNX1 assembles into a protein lattice that consists of helical rows of SNX1 dimers wrapped around tubular membranes in a crosslinked fashion. We also visualize the details of this structure, which provides a molecular understanding of how various parts of SNX1 contribute to its ability to deform the membrane. Moreover, we have compared the SNX1 structure with a previously elucidated structure of an endosomal coat complex formed by retromer coupled to a SNX, which reveals how the molecular organization of the SNX in this coat complex is affected by retromer. The comparison also suggests insight into intermediary stages of assembly that results in the formation of the retromer-SNX coat complex on the membrane.

Binding, unbinding and aggregation of crescent-shaped nanoparticles on nanoscale tubular membranes

Using molecular dynamics simulations of a coarse-grained implicit solvent model, we investigate the binding of crescent-shaped nanoparticles (NPs) on tubular lipid membranes. The NPs adhere to the membrane through their concave side. We found that the binding/unbinding transition is first-order, with the threshold binding energy being higher than the unbinding threshold, and the energy barrier between the bound and unbound states at the transition that increases with increasing the NP's arclength L_np or curvature mismatch μ = R_c/R_np, where R_c and R_np are the radii of curvature of the tubular membrane and the NP, respectively. Furthermore, we found that the threshold binding energy increases with increasing either L_np or μ. NPs with curvature larger than that of the tubule (μ > 1) lie perpendicularly to the tubule's axis. However, for μ smaller than a specific arclength-dependent mismatch μ*, the NPs are tilted with respect to the tubule's axis, with the tilt angle that increases with decreasing μ. We also investigated the self-assembly of the NPs on the tubule at relatively weak adhesion strength and found that for μ > 1 and high values of L_np, the NPs self-assemble into linear chains, and lie side-by-side. For μ < μ* and high L_np, the NPs also self-assemble into chains, while being tilted with respect to the tubule's axis.

Divalent cations bind to phosphoinositides to induce ion and isomer specific propensities for nano-cluster initiation in bilayer membranes

We report all-atom molecular dynamics simulations of asymmetric bilayers containing phosphoinositides in the presence of monovalent and divalent cations. We have characterized the molecular mechanism by which these divalent cations interact with phosphoinositides. Ca²⁺ desolvates more readily, consistent with single-molecule calculations, and forms a network of ionic-like bonds that serve as a 'molecular glue' that allows a single ion to coordinate with up to three phosphatidylinositol-(4,5)-bisphosphate (PI(4, 5)P₂) lipids. The phosphatidylinositol-(3,5)-bisphosphate isomer shows no such effect and neither does PI(4, 5)P₂ in the presence of Mg²⁺. The resulting network of Ca²⁺-mediated lipid-lipid bonds grows to span the entire simulation space and therefore has implications for the lateral distribution of phosophoinositides in the bilayer. We observe context-specific differences in lipid diffusion rates, lipid surface densities and bilayer structure. The molecular-scale delineation of ion-lipid arrangements reported here provides insight into similar nanocluster formation induced by peripheral proteins to regulate the formation of functional signalling complexes on the membrane.

Mechanisms of negative membrane curvature sensing and generation by ESCRT III subunit Snf7

Certain proteins have the propensity to bind to negatively curved membranes and generate negative membrane curvature. The mechanism of action of these proteins is much less studied and understood than those that sense and generate positive curvature. In this work, we use implicit membrane modeling to explore the mechanism of an important negative curvature sensing and generating protein: the main ESCRT III subunit Snf7. We find that Snf7 monomers alone can sense negative curvature and that curvature sensitivity increases for dimers and trimers. We have observed spontaneous bending of Snf7 oligomers into circular structures with preferred radius of ~20 nm. The preferred curvature of Snf7 filaments is further confirmed by the simulations of preformed spirals on a cylindrical membrane surface. Snf7 filaments cannot bind with the same interface to flat and curved membranes. We find that even when a filament has the preferred radius, it is always less stable on the flat membrane surface than on the interior cylindrical membrane surface. This provides an additional energy for membrane bending which has not been considered in the spiral spring model. Furthermore, the rings on the cylindrical spirals are bridged together by helix 4 and hence are extra stabilized compared to the spirals on the flat membrane surface.

Computational Modeling of Claudin Structure and Function

Tight junctions form a barrier to control passive transport of ions and small molecules across epithelia and endothelia. In addition to forming a barrier, some of claudins control transport properties of tight junctions by forming charge- and size-selective ion channels. It has been suggested claudin monomers can form or incorporate into tight junction strands to form channels. Resolving the crystallographic structure of several claudins in recent years has provided an opportunity to examine structural basis of claudins in tight junctions. Computational and theoretical modeling relying on atomic description of the pore have contributed significantly to our understanding of claudin pores and paracellular transport. In this paper, we review recent computational and mathematical modeling of claudin barrier function. We focus on dynamic modeling of global epithelial barrier function as a function of claudin pores and molecular dynamics studies of claudins leading to a functional model of claudin channels.

Curvature induction and sensing of the F-BAR protein Pacsin1 on lipid membranes via molecular dynamics simulations

F-Bin/Amphiphysin/Rvs (F-BAR) domain proteins play essential roles in biological processes that involve membrane remodelling, such as endocytosis and exocytosis. It has been shown that such proteins transform the lipid membrane into tubes. Notably, Pacsin1 from the Pacsin/Syndapin subfamily has the ability to transform the membrane into various morphologies: striated tubes, featureless wide and thin tubes, and pearling vesicles. The molecular mechanism of this interesting ability remains elusive. In this study, we performed all-atom (AA) and coarse-grained (CG) molecular dynamics simulations to investigate the curvature induction and sensing mechanisms of Pacsin1 on a membrane. From AA simulations, we show that Pacsin1 has internal structural flexibility. In CG simulations with parameters tuned from the AA simulations, spontaneous assembly of two Pacsin1 dimers through lateral interaction is observed. Based on the complex structure, we show that the regularly assembled Pacsin1 dimers bend a tensionless membrane. We also show that a single Pacsin1 dimer senses the membrane curvature, binding to a buckled membrane with a preferred curvature. These results provide molecular insights into polymorphic membrane remodelling.

The plasma membrane as a mechanochemical transducer

Cells are constantly submitted to external mechanical stresses, which they must withstand and respond to. By forming a physical boundary between cells and their environment that is also a biochemical platform, the plasma membrane (PM) is a key interface mediating both cellular response to mechanical stimuli, and subsequent biochemical responses. Here, we review the role of the PM as a mechanosensing structure. We first analyse how the PM responds to mechanical stresses, and then discuss how this mechanical response triggers downstream biochemical responses. The molecular players involved in PM mechanochemical transduction include sensors of membrane unfolding, membrane tension, membrane curvature or membrane domain rearrangement. These sensors trigger signalling cascades fundamental both in healthy scenarios and in diseases such as cancer, which cells harness to maintain integrity, keep or restore homeostasis and adapt to their external environment. This article is part of a discussion meeting issue 'Forces in cancer: interdisciplinary approaches in tumour mechanobiology'.

Shape transition from elliptical to cylindrical membrane tubes induced by chiral crescent-shaped protein rods

Proteins often form chiral assembly structures on a biomembrane. However, the role of the chirality in the interaction with an achiral membrane is poorly understood. Here, we report how chirality of crescent-shaped protein rods changes their assembly and tubulation using meshless membrane simulations. The achiral rods deformed the membrane tube into an elliptical shape by stabilizing the edges of the ellipse. In contrast, the chiral rods formed a helical assembly that generated a cylindrical membrane tube with a constant radius in addition to the elliptical tube. This helical assembly could be further stabilized by the direct side-to-side attraction between the protein rods. The chirality also promotes the tubulation from a flat membrane. These results agree with experimental findings of the constant radius of membrane tubules induced by the Bin/Amphiphysin/Rvs (BAR) superfamily proteins.

PIP2 Reshapes Membranes through Asymmetric Desorption

Phosphatidylinositol-4,5-bisphosphate (PIP2) is an important signaling lipid in eukaryotic cell plasma membranes, playing an essential role in diverse cellular processes. The headgroup of PIP2 is highly negatively charged, and this lipid displays a high critical micellar concentration compared to housekeeping phospholipid analogs. Given the crucial role of PIP2, it is imperative to study its localization, interaction with proteins, and membrane-shaping properties. Biomimetic membranes have served extensively to elucidate structural and functional aspects of cell membranes including protein-lipid and lipid-lipid interactions, as well as membrane mechanics. Incorporation of PIP2 into biomimetic membranes, however, has at times resulted in discrepant findings described in the literature. With the goal to elucidate the mechanical consequences of PIP2 incorporation, we studied the desorption of PIP2 from biomimetic giant unilamellar vesicles by means of a fluorescent marker. A decrease in fluorescence intensity with the age of the vesicles suggested that PIP2 lipids were being desorbed from the outer leaflet of the membrane. To evaluate whether this desorption was asymmetric, the vesicles were systematically diluted. This resulted in an increase in the number of internally tubulated vesicles within minutes after dilution, suggesting that the desorption was asymmetric and also generated membrane curvature. By means of a saturated chain homolog of PIP2, we showed that the fast desorption of PIP2 is facilitated by presence of an arachidonic lipid tail and is possibly due to its oxidation. Through measurements of the pulling force of membrane tethers, we quantified the effect of this asymmetric desorption on the spontaneous membrane curvature. Furthermore, we found that the spontaneous curvature could be modulated by externally increasing the concentration of PIP2 micelles. Given that the local concentration of PIP2 in biological membranes is variable, spontaneous curvature generated by PIP2 may affect the formation of highly curved structures that can serve as initiators for signaling events.

ACAP1 assembles into an unusual protein lattice for membrane deformation through multiple stages

Studies on the Bin-Amphiphysin-Rvs (BAR) domain have advanced a fundamental understanding of how proteins deform membrane. We previously showed that a BAR domain in tandem with a Pleckstrin Homology (PH domain) underlies the assembly of ACAP1 (Arfgap with Coil-coil, Ankryin repeat, and PH domain I) into an unusual lattice structure that also uncovers a new paradigm for how a BAR protein deforms membrane. Here, we initially pursued computation-based refinement of the ACAP1 lattice to identify its critical protein contacts. Simulation studies then revealed how ACAP1, which dimerizes into a symmetrical structure in solution, is recruited asymmetrically to the membrane through dynamic behavior. We also pursued electron microscopy (EM)-based structural studies, which shed further insight into the dynamic nature of the ACAP1 lattice assembly. As ACAP1 is an unconventional BAR protein, our findings broaden the understanding of the mechanistic spectrum by which proteins assemble into higher-ordered structures to achieve membrane deformation.

Curvature- and Phase-Induced Protein Sorting Quantified in Transfected Cell-Derived Giant Vesicles

Eukaryotic cells possess a dynamic network of membranes that vary in lipid composition. To perform numerous biological functions, cells modulate their shape and the lateral organization of proteins associated with membranes. The modulation is generally facilitated by physical cues that recruit proteins to specific regions of the membrane. Analyzing these cues is difficult due to the complexity of the membrane conformations that exist in cells. Here, we examine how different types of membrane proteins respond to changes in curvature and to lipid phases found in the plasma membrane. By using giant plasma membrane vesicles derived from transfected cells, the proteins were positioned in the correct orientation and the analysis was performed in plasma membranes with a biological composition. Nanoscale membrane curvatures were generated by extracting nanotubes from these vesicles with an optical trap. The viral membrane protein neuraminidase was not sensitive to curvature, but it did exhibit strong partitioning (coefficient of K = 0.16) disordered membrane regions. In contrast, the membrane repair protein annexin 5 showed a preference for nanotubes with a density up to 10-15 times higher than that on the more flat vesicle membrane. The investigation of nanoscale effects in isolated plasma membranes provides a quantitative platform for studying peripheral and integral membrane proteins in their natural environment.

Computational Modeling of Realistic Cell Membranes

Cell membranes contain a large variety of lipid types and are crowded with proteins, endowing them with the plasticity needed to fulfill their key roles in cell functioning. The compositional complexity of cellular membranes gives rise to a heterogeneous lateral organization, which is still poorly understood. Computational models, in particular molecular dynamics simulations and related techniques, have provided important insight into the organizational principles of cell membranes over the past decades. Now, we are witnessing a transition from simulations of simpler membrane models to multicomponent systems, culminating in realistic models of an increasing variety of cell types and organelles. Here, we review the state of the art in the field of realistic membrane simulations and discuss the current limitations and challenges ahead.

Multiscale Simulations of Biological Membranes: The Challenge To Understand Biological Phenomena in a Living Substance

Biological membranes are tricky to investigate. They are complex in terms of molecular composition and structure, functional over a wide range of time scales, and characterized by nonequilibrium conditions. Because of all of these features, simulations are a great technique to study biomembrane behavior. A significant part of the functional processes in biological membranes takes place at the molecular level; thus computer simulations are the method of choice to explore how their properties emerge from specific molecular features and how the interplay among the numerous molecules gives rise to function over spatial and time scales larger than the molecular ones. In this review, we focus on this broad theme. We discuss the current state-of-the-art of biomembrane simulations that, until now, have largely focused on a rather narrow picture of the complexity of the membranes. Given this, we also discuss the challenges that we should unravel in the foreseeable future. Numerous features such as the actin-cytoskeleton network, the glycocalyx network, and nonequilibrium transport under ATP-driven conditions have so far received very little attention; however, the potential of simulations to solve them would be exceptionally high. A major milestone for this research would be that one day we could say that computer simulations genuinely research biological membranes, not just lipid bilayers.

Characterization of Lipid-Protein Interactions and Lipid-Mediated Modulation of Membrane Protein Function through Molecular Simulation

The cellular membrane constitutes one of the most fundamental compartments of a living cell, where key processes such as selective transport of material and exchange of information between the cell and its environment are mediated by proteins that are closely associated with the membrane. The heterogeneity of lipid composition of biological membranes and the effect of lipid molecules on the structure, dynamics, and function of membrane proteins are now widely recognized. Characterization of these functionally important lipid-protein interactions with experimental techniques is however still prohibitively challenging. Molecular dynamics (MD) simulations offer a powerful complementary approach with sufficient temporal and spatial resolutions to gain atomic-level structural information and energetics on lipid-protein interactions. In this review, we aim to provide a broad survey of MD simulations focusing on exploring lipid-protein interactions and characterizing lipid-modulated protein structure and dynamics that have been successful in providing novel insight into the mechanism of membrane protein function.

Flexible lipid nanomaterials studied by NMR spectroscopy

Advances in solid-state nuclear magnetic resonance spectroscopy inform the emergence of material properties from atomistic-level interactions in membrane lipid nanostructures.

Interplay between Membrane Curvature and Cholesterol: Role of Palmitoylated Caveolin-1

Caveolin-1 (cav-1) is an important player in cell signaling and endocytosis that has been shown to colocalize with cholesterol-rich membrane domains. Experimental studies with varying cav-1 constructs have suggested that it can induce both cholesterol clustering and membrane curvature. Here, we probe the molecular origin of membrane curvature and cholesterol clustering by cav-1 by using coarse-grain molecular dynamics simulations. We have performed a series of simulations of a functionally important cav-1 construct, comprising the membrane-interacting domains and a C-terminal palmitoyl tail. Our results suggest that cav-1 is able to induce cholesterol clustering in the membrane leaflet to which it is bound as well as the opposing leaflet. A positive membrane curvature is observed upon cav-1 binding in cholesterol-containing bilayers. Interestingly, we observe an interplay between cholesterol clustering and membrane curvature such that cav-1 is able to induce higher membrane curvature in cholesterol-rich membranes. The role of the cav-1 palmitoyl tail is less clear and appears to increase the membrane contacts. Further, we address the importance of the secondary structure of cav-1 domains and show that it could play an important role in membrane curvature and cholesterol clustering. Our work is an important step toward a molecular picture of caveolae and vesicular endocytosis.

Molecular Dynamics Simulations of Membrane Proteins: An Overview

Simulations of membrane proteins have been rising in popularity in the past decade. Advancements in technology and force fields made it possible to simulate behavior of membrane proteins. Membrane protein simulations can now be used as supporting evidence for experimental findings, for elucidating protein mechanisms, and validating protein crystal structures. Unrelated to experimental data, these simulations can also serve to investigate larger scale processes like protein sorting, protein-membrane interactions, and more. In this review, the history as well as the state-of-the-art methodologies in membrane protein simulations will be summarized. An emphasis will be put on how to set up the system and on the current models for the different components of the simulation system. An overview of the available tools for membrane protein simulation will be given, and current limitations and prospects will also be discussed.

Organizing membrane-curving proteins: the emerging dynamical picture

Lipid membranes play key roles in cells, such as in trafficking, division, infection, remodeling of organelles, among others. The key step in all these processes is creating membrane curvature, typically under the control of many anchored, adhered or included proteins. However, it has become clear that the membrane itself can mediate the interactions among proteins to produce highly ordered assemblies. Computer simulations are ideally suited to investigate protein organization and the dynamics of membrane remodeling at near-micron scales, something that is extremely challenging to tackle experimentally. We review recent computational efforts in modeling protein-caused membrane deformation mechanisms, specifically focusing on coarse-grained simulations. We highlight work that exposed the membrane-mediated ordering of proteins into lines, meshwork, spirals and other assemblies, in what seems to be a very generic mechanism driven by a combination of short and long-ranged forces. Modulating the mechanical properties of membranes is an underexplored signaling mechanism in various processes deserving of more attention in the near future.

Biophysics of membrane curvature remodeling at molecular and mesoscopic lengthscales

At the micron scale, where cell organelles display an amazing complexity in their shape and organization, the physical properties of a biological membrane can be better-understood using continuum models subject to thermal (stochastic) undulations. Yet, the chief orchestrators of these complex and intriguing shapes are a specialized class of membrane associating often peripheral proteins called curvature remodeling proteins (CRPs) that operate at the molecular level through specific protein-lipid interactions. We review multiscale methodologies to model these systems at the molecular as well as at the mesoscopic and cellular scales, and also present a free energy perspective of membrane remodeling through the organization and assembly of CRPs. We discuss the morphological space of nearly planar to highly curved membranes, methods to include thermal fluctuations, and review studies that model such proteins as curvature fields to describe the emergent curved morphologies. We also discuss several mesoscale models applied to a variety of cellular processes, where the phenomenological parameters (such as curvature field strength) are often mapped to models of real systems based on molecular simulations. Much insight can be gained from the calculation of free energies of membranes states with protein fields, which enable accurate mapping of the state and parameter values at which the membrane undergoes morphological transformations such as vesiculation or tubulation. By tuning the strength, anisotropy, and spatial organization of the curvature-field, one can generate a rich array of membrane morphologies that are highly relevant to shapes of several cellular organelles. We review applications of these models to budding of vesicles commonly seen in cellular signaling and trafficking processes such as clathrin mediated endocytosis, sorting by the ESCRT protein complexes, and cellular exocytosis regulated by the exocyst complex. We discuss future prospects where such models can be combined with other models for cytoskeletal assembly, and discuss their role in understanding the effects of cell membrane tension and the mechanics of the extracellular microenvironment on cellular processes.

Perturbations of Native Membrane Protein Structure in Alkyl Phosphocholine Detergents: A Critical Assessment of NMR and Biophysical Studies

Membrane proteins perform a host of vital cellular functions. Deciphering the molecular mechanisms whereby they fulfill these functions requires detailed biophysical and structural investigations. Detergents have proven pivotal to extract the protein from its native surroundings. Yet, they provide a milieu that departs significantly from that of the biological membrane, to the extent that the structure, the dynamics, and the interactions of membrane proteins in detergents may considerably vary, as compared to the native environment. Understanding the impact of detergents on membrane proteins is, therefore, crucial to assess the biological relevance of results obtained in detergents. Here, we review the strengths and weaknesses of alkyl phosphocholines (or foscholines), the most widely used detergent in solution-NMR studies of membrane proteins. While this class of detergents is often successful for membrane protein solubilization, a growing list of examples points to destabilizing and denaturing properties, in particular for α-helical membrane proteins. Our comprehensive analysis stresses the importance of stringent controls when working with this class of detergents and when analyzing the structure and dynamics of membrane proteins in alkyl phosphocholine detergents.

Membrane shape-mediated wave propagation of cortical protein dynamics

Immune cells exhibit stimulation-dependent traveling waves in the cortex, much faster than typical cortical actin waves. These waves reflect rhythmic assembly of both actin machinery and peripheral membrane proteins such as F-BAR domain-containing proteins. Combining theory and experiments, we develop a mechanochemical feedback model involving membrane shape changes and F-BAR proteins that render the cortex an interesting dynamical system. We show that such cortical dynamics manifests itself as ultrafast traveling waves of cortical proteins, in which the curvature sensitivity-driven feedback always constrains protein lateral diffusion in wave propagation. The resulting protein wave propagation mainly reflects the spatial gradient in the timing of local protein recruitment from cytoplasm. We provide evidence that membrane undulations accompany these protein waves and potentiate their propagation. Therefore, membrane shape change and protein curvature sensitivity may have underappreciated roles in setting high-speed cortical signal transduction rhythms.

Traveling waves in the cell cortex can propagate much faster than actin waves, and the mechanism is unknown. Here the authors propose a mechanochemical feedback model for traveling waves that incorporates membrane shape changes and recruitment of F-BAR proteins that enables fast wave propagation.

Long-Range Organization of Membrane-Curving Proteins

Biological membranes have a central role in mediating the organization of membrane-curving proteins, a dynamic process that has proven to be challenging to probe experimentally. Using atomic force microscopy, we capture the hierarchically organized assemblies of Bin/amphiphysin/Rvs (BAR) proteins on supported lipid membranes. Their structure reveals distinct long linear aggregates of proteins, regularly spaced by up to 300 nm. Employing accurate free-energy calculations from large-scale coarse-grained computer simulations, we found that the membrane mediates the interaction among protein filaments as a combination of short- and long-ranged interactions. The long-ranged component acts at strikingly long distances, giving rise to a variety of micron-sized ordered patterns. This mechanism may contribute to the long-ranged spatiotemporal control of membrane remodeling by proteins in the cell.

Acceleration and suppression of banana-shaped-protein-induced tubulation by addition of small membrane inclusions of isotropic spontaneous curvatures

Membrane tubulation induced by banana-shaped protein rods is investigated by using coarse-grained meshless membrane simulations. It is found that tubulation is promoted by laterally isotropic membrane inclusions that generate the same sign of spontaneous curvature as the adsorbed protein rods. The inclusions are concentrated in the tubules and reduce the bending energy of the tip of the tubules. On the other hand, inclusions with an opposite curvature suppress tubulation by percolated-network formation at a high protein-rod density while they induce the formation of a spherical membrane bud at a low rod density. When equal amounts of the two types of inclusions (with positive and negative curvatures) are added, their effects cancel each other for the first short period but later the tubulation is slowly accelerated. Positive surface tension suppresses tubulation. Our results suggest that the cooperation of scaffolding of BAR (Bin/Amphiphysin/Rvs) domains and isotropic membrane inclusions is important for tubulation.

Multiple interactions between an Arf/GEF complex and charged lipids determine activation kinetics on the membrane

Lipidated small GTPases and their regulators need to bind to membranes to propagate actions in the cell, but an integrated understanding of how the lipid bilayer exerts its effect has remained elusive. Here we focused on ADP ribosylation factor (Arf) GTPases, which orchestrate a variety of regulatory functions in lipid and membrane trafficking, and their activation by the guanine-nucleotide exchange factor (GEF) Brag2, which controls integrin endocytosis and cell adhesion and is impaired in cancer and developmental diseases. Biochemical and structural data are available that showed the exceptional efficiency of Arf activation by Brag2 on membranes. We determined the high-resolution crystal structure of unbound Brag2 containing the GEF (Sec7) and membrane-binding (pleckstrin homology) domains, revealing that it has a constitutively active conformation. We used this structure to analyze the interaction of uncomplexed Brag2 and of the myristoylated Arf1/Brag2 complex with a phosphatidylinositol bisphosphate (PIP₂) -containing lipid bilayer, using coarse-grained molecular dynamics. These simulations revealed that the system forms a close-packed, oriented interaction with the membrane, in which multiple PIP₂ lipids bind the canonical lipid-binding site and unique peripheral sites of the PH domain, the Arf GTPase and, unexpectedly, the Sec7 domain. We cross-validated these predictions by reconstituting the binding and kinetics of Arf and Brag2 in artificial membranes. Our coarse-grained structural model thus suggests that the high efficiency of Brag2 requires interaction with multiple lipids and a well-defined orientation on the membrane, resulting in a local PIP₂ enrichment, which has the potential to signal toward the Arf pathway.

Salt Bridge Formation between the I-BAR Domain and Lipids Increases Lipid Density and Membrane Curvature

The BAR domain superfamily proteins sense or induce curvature in membranes. The inverse-BAR domain (I-BAR) is a BAR domain that forms a straight “zeppelin-shaped” dimer. The mechanisms by which IRSp53 I-BAR binds to and deforms a lipid membrane are investigated here by all-atom molecular dynamics simulation (MD), binding energy analysis, and the effects of mutation experiments on filopodia on HeLa cells. I-BAR adopts a curved structure when crystallized, but adopts a flatter shape in MD. The binding of I-BAR to membrane was stabilized by ~30 salt bridges, consistent with experiments showing that point mutations of the interface residues have little effect on the binding affinity whereas multiple mutations have considerable effect. Salt bridge formation increases the local density of lipids and deforms the membrane into a concave shape. In addition, the point mutations that break key intra-molecular salt bridges within I-BAR reduce the binding affinity; this was confirmed by expressing these mutants in HeLa cells and observing their effects. The results indicate that the stiffness of I-BAR is important for membrane deformation, although I-BAR does not act as a completely rigid template.

Lipid-mediated PX-BAR domain recruitment couples local membrane constriction to endocytic vesicle fission

Clathrin-mediated endocytosis (CME) involves membrane-associated scaffolds of the bin-amphiphysin-rvs (BAR) domain protein family as well as the GTPase dynamin, and is accompanied and perhaps triggered by changes in local lipid composition. How protein recruitment, scaffold assembly and membrane deformation is spatiotemporally controlled and coupled to fission is poorly understood. We show by computational modelling and super-resolution imaging that phosphatidylinositol 3,4-bisphosphate [PI(3,4)P₂] synthesis within the clathrin-coated area of endocytic intermediates triggers selective recruitment of the PX-BAR domain protein SNX9, as a result of complex interactions of endocytic proteins competing for phospholipids. The specific architecture induces positioning of SNX9 at the invagination neck where its self-assembly regulates membrane constriction, thereby providing a template for dynamin fission. These data explain how lipid conversion at endocytic pits couples local membrane constriction to fission. Our work demonstrates how computational modelling and super-resolution imaging can be combined to unravel function and mechanisms of complex cellular processes.

The spatiotemporal regulation of membrane scaffolds recruitment and coupling between membrane deformation and fission in endocytosis are unclear. Here the authors show that lipid conversion at endocytic pits recruits SNX9, which couples local membrane constriction to fission in endocytosis.

Membrane structure formation induced by two types of banana-shaped proteins

The assembly of banana-shaped rodlike proteins on membranes and the associated membrane shape transformations are investigated by analytical theory and coarse-grained simulations. The membrane-mediated interactions between two banana-shaped inclusions are derived theoretically using a point-like formalism based on fixed anisotropic curvatures, both for zero surface tension and for finite surface tension. On a larger scale, the interactions between the assemblies of such rodlike inclusions are determined analytically. Meshless membrane simulations are performed in the presence of a large number of inclusions of two types, corresponding to the curved rods of opposite curvatures, both for flat membranes and vesicles. Rods of the same type aggregate into linear assemblies perpendicular to the rod axis, leading to membrane tubulation. However, rods of the other type, those of opposite curvature, are attracted to the lateral sides of these assemblies, and stabilize a straight bump structure that prevents tubulation. When the two types of rods have almost opposite curvatures, the bumps attract one another, forming a striped structure. Positive surface tension is found to stabilize stripe formation. The simulation results agree well with the theoretical predictions provided the point-like curvatures of the model are scaled-down to account for the effective flexibility of the simulated rods.