Computing Curvature Sensitivity of Biomolecules in Membranes by Simulated Buckling

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.

Computing the influence of lipids and lipid complexes on membrane mechanics

Methodology for extracting the spontaneous curvature, bending modulus, and neutral surface of a lipid bilayer is described. The "SPEX" method is a robust technique for computing the bilayer bending modulus while allowing for resolution of the spontaneous curvature of specific interacting lipids and complexes, and the dependence of spontaneous curvature on wavelength. The method is described referring to the publicly available MembraneAnalysis.jl software package.

Interaction of Hoechst 33342 with POPC Membranes at Different pH Values

Hoechst 33342 (H33342) is a fluorescent probe that is commonly used to stain the DNA of living cells. To do so, it needs to interact with and permeate through cell membranes, despite its high overall charge at physiological pH values. In this work, we address the effect of pH in the association of H33342 with lipid bilayers using a combined experimental and computational approach. The partition of H33342 to 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) lipid membranes was experimentally quantified using fluorescence spectroscopy and isothermal titration calorimetry (ITC) measurements. Quantum chemical calculations were performed to select the most stable isomer of H33342 for the overall charges 0, +1, and +2, expected to predominate across the 5 < pH < 10 range. The interaction of these isomers with POPC bilayers was then studied by both unrestrained and umbrella sampling molecular dynamics (MD) simulations. Both experimental results and computational free energy profiles indicate that the partition coefficient of H33342 displays a small variation over a wide pH range, not exceeding one order of magnitude. The enthalpy variation upon partition to the membrane suggests efficient hydrogen bonding between the probe and the lipid, namely, for the protonated +2 form, which was confirmed in the MD simulation studies. The relatively high lipophilicity obtained for the charged species contrasts with the decrease in their general hydrophobicity as estimated from octanol/water partition. This highlights the distinction between lipophilicity and hydrophobicity, as well as the importance of considering the association with lipid bilayers when predicting the affinity for biomembranes.

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.

Curvature-based sorting of eight lipid types in asymmetric buckled plasma membrane models

Curvature is a fundamental property of biological membranes and has essential roles in cellular function. Bending of membranes can be induced by their lipid and protein compositions, as well as peripheral proteins, such as those that make up the cytoskeleton. An important aspect of membrane function is the grouping of lipid species into microdomains, or rafts, which serve as platforms for specific biochemical processes. The fluid mosaic model of membranes has evolved to recognize the importance of curvature and leaflet asymmetry, and there are efforts towards evaluating their functional roles. This work investigates the effect of curvature on the sorting of lipids in buckled asymmetric bilayers containing eight lipid types, approximating an average mammalian plasma membrane, through coarse-grained (CG) molecular dynamics (MD) simulations with the Martini force field. The simulations reveal that i) leaflet compositional asymmetry can induce curvature asymmetry, ii) lipids are sorted by curvature to different extents, and iii) curvature-based partitioning trends show moderate to strong correlations with lipid molecular volumes and head to tail bead ratios, respectively. The findings provide unique insights into the role of curvature in membrane organization, and the curvature-based sorting trends should be useful references for later investigations, and potentially interpreting the functional roles of specific lipids.

Structure and dynamics of the SARS-CoV-2 envelope protein monomer

Coronaviruses, especially severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), present an ongoing threat to human wellbeing. Consequently, elucidation of molecular determinants of their function and interaction with the host is an important task. Whereas some of the coronaviral proteins are extensively characterized, others remain understudied. Here, we use molecular dynamics simulations to analyze the structure and dynamics of the SARS-CoV-2 envelope (E) protein (a viroporin) in the monomeric form. The protein consists of the hydrophobic α-helical transmembrane domain (TMD) and amphiphilic α-helices H2 and H3, connected by flexible linkers. We show that TMD has a preferable orientation in the membrane, while H2 and H3 reside at the membrane surface. Orientation of H2 is strongly influenced by palmitoylation of cysteines Cys40, Cys43, and Cys44. Glycosylation of Asn66 affects the orientation of H3. We also observe that the monomeric E protein both generates and senses the membrane curvature, preferably localizing with the C-terminus at the convex regions of the membrane; the protein in the pentameric form displays these properties as well. Localization to curved regions may be favorable for assembly of the E protein oligomers, whereas induction of curvature may facilitate the budding of the viral particles. The presented results may be helpful for a better understanding of the function of the coronaviral E protein and viroporins in general, and for overcoming the ongoing SARS-CoV-2 pandemic.

Coarse-Grained Simulations Suggest Potential Competing Roles of Phosphoinositides and Amphipathic Helix Structures in Membrane Curvature Sensing of the AP180 N-Terminal Homology Domain

The generation and sensing of membrane curvature by proteins has become of increasing interest to researchers with multiple mechanisms, from hydrophobic insertion to protein crowding, being identified. However, the role of charged lipids in the membrane curvature-sensing process is still far from understood. Many proteins involved in endocytosis bind phosphatidylinositol 4,5-bisphosphate (PIP2) lipids, allowing these proteins to accumulate at regions of local curvature. Here, using coarse-grained molecular dynamics simulations, we study the curvature-sensing behavior of the ANTH domain, a protein crucial for endocytosis. We selected three ANTH crystal structures containing either an intact, split, or truncated terminal amphipathic helix. On neutral membranes, the ANTH domain has innate curvature-sensing ability. In the presence of PIP2, however, only the domain with an intact helix senses curvature. Our work sheds light on the role of PIP2 and its modulation of membrane curvature sensing by proteins.

Quantifying Membrane Curvature Sensing of Peripheral Proteins by Simulated Buckling and Umbrella Sampling

Membrane curvature plays an essential role in the organization and trafficking of membrane associated proteins. Comparison or prediction of the experimentally resolved protein concentrations adopted at different membrane curvatures requires direct quantification of the relative partitioning free energy. Here, we present a highly efficient and simple to implement a free-energy calculation method which is able to directly resolve the relative partitioning free energy of proteins as a direct function of membrane curvature, i.e., a curvature sensing profile, within (coarse-grained) molecular dynamics simulations. We demonstrate its utility by resolving these profiles for two known curvature sensing peptides, namely ALPS and α-synuclein, for a membrane curvature ranging from -1/6.5 to +1/6.5 nm^-1. We illustrate that the difference in relative partitioning (binding) free energy between these two extrema is only about 13 k_BT for both peptides, illustrating that the driving force of curvature sensing is subtle. Furthermore, we illustrate that ALPS and α-synuclein sense curvature via a contrasting mechanism, which is differentially affected by membrane composition. In addition, we demonstrate that the intrinsic spontaneous curvature of both of these peptides lies beyond the range of membrane curvature accessible in micropipette aspiration experiments, being about 1/7 nm ^-1. Our approach offers an efficient and simple to implement in silico tool for exploring and screening the membrane curvature sensing mechanisms of proteins.

Membrane Thinning Induces Sorting of Lipids and the Amphipathic Lipid Packing Sensor (ALPS) Protein Motif

Heterogeneities (e.g., membrane proteins and lipid domains) and deformations (e.g., highly curved membrane regions) in biological lipid membranes cause lipid packing defects that may trigger functional sorting of lipids and membrane-associated proteins. To study these phenomena in a controlled and efficient way within molecular simulations, we developed an external field protocol that artificially enhances packing defects in lipid membranes by enforcing local thinning of a flat membrane region. For varying lipid compositions, we observed strong thinning-induced depletion or enrichment, depending on the lipid's intrinsic shape and its effect on a membrane's elastic modulus. In particular, polyunsaturated and lysolipids are strongly attracted to regions high in packing defects, whereas phosphatidylethanolamine (PE) lipids and cholesterol are strongly repelled from it. Our results indicate that externally imposed changes in membrane thickness, area, and curvature are underpinned by shared membrane elastic principles. The observed sorting toward the thinner membrane region is in line with the sorting expected for a positively curved membrane region. Furthermore, we have demonstrated that the amphipathic lipid packing sensor (ALPS) protein motif, a known curvature and packing defect sensor, is effectively attracted to thinner membrane regions. By extracting the force that drives amphipathic molecules toward the thinner region, our thinning protocol can directly quantify and score the lipid packing sensing of different amphipathic molecules. In this way, our protocol paves the way toward high-throughput exploration of potential defect- and curvature-sensing motifs, making it a valuable addition to the molecular simulation toolbox.

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.

Curvature sensing by cardiolipin in simulated buckled membranes

Cardiolipin is a non-bilayer phospholipid with a unique dimeric structure. It localizes to negative curvature regions in bacteria and is believed to stabilize respiratory chain complexes in the highly curved mitochondrial membrane. Cardiolipin's localization mechanism remains unresolved, because important aspects such as the structural basis and strength for lipid curvature preferences are difficult to determine, partly due to the lack of efficient simulation methods. Here, we report a computational approach to study curvature preferences of cardiolipin by simulated membrane buckling and quantitative modeling. We combine coarse-grained molecular dynamics with simulated buckling to determine the curvature preferences in three-component bilayer membranes with varying concentrations of cardiolipin, and extract curvature-dependent concentrations and lipid acyl chain order parameter profiles. Cardiolipin shows a strong preference for negative curvatures, with a highly asymmetric chain order parameter profile. The concentration profiles are consistent with an elastic model for lipid curvature sensing that relates lipid segregation to local curvature via the material constants of the bilayers. These computations constitute new steps to unravel the molecular mechanism by which cardiolipin senses curvature in lipid membranes, and the method can be generalized to other lipids and membrane components as well.

BUMPy: A Model-Independent Tool for Constructing Lipid Bilayers of Varying Curvature and Composition

Molecular dynamics is a powerful tool to investigate atomistic and mesoscopic phenomena in lipid bilayer systems. These studies have progressed with the advent of increased computational power, and efforts are now increasingly being directed toward investigating the role of curvature and bilayer morphology, as these are critical features of biological processes. Computational studies of lipid bilayers benefit from tools that can create starting configurations for molecular dynamics simulations, but the majority of such tools are restricted to generating flat bilayers. Generating curved bilayer configurations comes with practical complications and potential ramifications on physical properties in the simulated system if the bilayer is initiated in a high-strain state. We present a new tool for creating curved lipid bilayers that combines flexibility of shape, force field, model resolution, and bilayer composition. A key aspect of our approach is the use of the monolayer pivotal plane location to accurately estimate interleaflet area differences in a curved bilayer. Our tool is named BUMPy (Building Unique Membranes in Python), is written in Python, is fast, and has a simple command line interface.