Implementation of a methodology for determining elastic properties of lipid assemblies from molecular dynamics simulations

Mechanisms of SNARE proteins in membrane fusion

Soluble N-ethylmaleimide-sensitive factor attachment protein receptors (SNAREs) are a family of small conserved eukaryotic proteins that mediate membrane fusion between organelles and with the plasma membrane. SNAREs are directly or indirectly anchored to membranes. Prior to fusion, complementary SNAREs assemble between membranes with the aid of accessory proteins that provide a scaffold to initiate SNARE zippering, pulling the membranes together and mediating fusion. Recent advances have enabled the construction of detailed models describing bilayer transitions and energy barriers along the fusion pathway and have elucidated the structures of SNAREs complexed in various states with regulatory proteins. In this Review, we discuss how these advances are yielding an increasingly detailed picture of the SNARE-mediated fusion pathway, leading from first contact between the membranes via metastable non-bilayer intermediates towards the opening and expansion of a fusion pore. We describe how SNARE proteins assemble into complexes, how this assembly is regulated by accessory proteins and how SNARE complexes overcome the free energy barriers that prevent spontaneous membrane fusion.

Mitochondrial membrane model: Lipids, elastic properties, and the changing curvature of cardiolipin

Mammalian and Drosophila melanogaster model mitochondrial membrane compositions are constructed from experimental data. Simplified compositions for inner and outer mitochondrial membranes are provided, including an asymmetric inner mitochondrial membrane. We performed atomistic molecular dynamics simulations of these membranes and computed their material properties. When comparing these properties to those obtained by extrapolation from their constituting lipids, we find good overall agreement. Finally, we analyzed the curvature effect of cardiolipin, considering ion concentration effects, oxidation, and pH. We draw the conclusion that cardiolipin-negative curvature is most likely due to counterion effects, such as cation adsorption, in particular of H3O+. This oft-neglected effect might account for the puzzling behavior of this lipid.

Photomanipulation of Minimal Synthetic Cells: Area Increase, Softening, and Interleaflet Coupling of Membrane Models Doped with Azobenzene-Lipid Photoswitches

Light can effectively interrogate biological systems in a reversible and physiologically compatible manner with high spatiotemporal precision. Understanding the biophysics of photo-induced processes in bio-systems is crucial for achieving relevant clinical applications. Employing membranes doped with the photolipid azobenzene-phosphatidylcholine (azo-PC), a holistic picture of light-triggered changes in membrane kinetics, morphology, and material properties obtained from correlative studies on cell-sized vesicles, Langmuir monolayers, supported lipid bilayers, and molecular dynamics simulations is provided. Light-induced membrane area increases as high as ≈25% and a ten-fold decrease in the membrane bending rigidity is observed upon trans-to-cis azo-PC isomerization associated with membrane leaflet coupling and molecular curvature changes. Vesicle electrodeformation measurements and atomic force microscopy reveal that trans azo-PC bilayers are thicker than palmitoyl-oleoyl phosphatidylcholine (POPC) bilayers but have higher specific membrane capacitance and dielectric constant suggesting an increased ability to store electric charges across the membrane. Lastly, incubating POPC vesicles with azo-PC solutions results in the insertion of azo-PC in the membrane enabling them to become photoresponsive. All these results demonstrate that light can be used to finely manipulate the shape, mechanical and electric properties of photolipid-doped minimal cell models, and liposomal drug carriers, thus, presenting a promising therapeutic alternative for the repair of cellular disorders.

Molecular simulations and NMR reveal how lipid fluctuations affect membrane mechanics

Lipid bilayers form the main matrix of functional cell membranes, and their dynamics underlie a host of physical and biological processes. Here we show that elastic membrane properties and collective molecular dynamics (MD) are related by the mean-square amplitudes (order parameters) and relaxation rates (correlation times) of lipid acyl chain motions. We performed all-atom MD simulations of liquid-crystalline bilayers that allow direct comparison with carbon-hydrogen (CH) bond relaxations measured with NMR spectroscopy. Previous computational and theoretical approaches have assumed isotropic relaxation, which yields inaccurate description of lipid chain dynamics and incorrect data interpretation. Instead, the new framework includes a fixed bilayer normal (director axis) and restricted anisotropic motion of the CH bonds in accord with their segmental order parameters, enabling robust validation of lipid force fields. Simulated spectral densities of thermally excited CH bond fluctuations exhibited well-defined spin-lattice (Zeeman) relaxations analogous to those in NMR measurements. Their frequency signature could be fit to a simple power-law function, indicative of nematic-like collective dynamics. Moreover, calculated relaxation rates scaled as the squared order parameters yielding an apparent κC modulus for bilayer bending. Our results show a strong correlation with κC values obtained from solid-state NMR studies of bilayers without and with cholesterol as validated by neutron spin-echo measurements of membrane elasticity. The simulations uncover a critical role of interleaflet coupling in membrane mechanics and thus provide important insights into molecular sites of emerging elastic properties within lipid bilayers.

Capturing Lipid Nanodisc Shape and Properties Using a Continuum Elastic Theory

Lipid nanodiscs are nanometric bilayer patches enveloped by confining structures, commonly composed of membrane scaffolding proteins (MSPs). To resolve the interplay between MSP geometry, lipid confinement, and membrane material properties on the nanodisc shape, we apply a continuum elastic theory accounting for lipid bending, tilting, and area deformations. The equilibrium nanodisc shape is then determined by minimizing the elastic free energy functional. Analytic expressions derived under simplifying assumptions demonstrate that the nanodisc shape is sensitive to its size, lipid density, and the lipid tilt and thickness imposed at the contact with the MSP. Under matching physical parameters, these expressions quantitatively reproduce the shape of nanodiscs seen in molecular dynamics simulations, but only if lipid tilt is explicitly considered. We further demonstrate how the bending rigidity can be extracted from the membrane shape profile by fitting the numerically minimized full elastic functional to the membrane shape found in simulations. This fitting procedure faithfully informs on the bending rigidity of nanodiscs larger than ca. 5 nm in radius. The fitted profiles accurately reproduce the increase in bending modulus found using real-space fluctuation analysis of simulated nanodiscs and, for large nanodiscs, also accurately resolve its spatial variations. Our study shows how deformations in lipid patches confined in nanodiscs can be well described by a continuum elastic theory and how this fit can be used to determine local material properties from shape analysis of nanodiscs in simulations. This methodology could potentially allow direct determination of lipid properties from experiments, for example cryo-electron microscopy images of lipid nanodiscs, thereby allowing to guide the development of future nanodisc formulations with desired properties.

Biophysics of Membrane Stiffening by Cholesterol and Phosphatidylinositol 4,5-bisphosphate (PIP2)

Cell membranes regulate a wide range of phenomena that are implicated in key cellular functions. Cholesterol, a critical component of eukaryotic cell membranes, is responsible for cellular organization, membrane elasticity, and other critical physicochemical parameters. Besides cholesterol, other lipid components such as phosphatidylinositol 4,5-bisphosphate (PIP2) are found in minor concentrations in cell membranes yet can also play a major regulatory role in various cell functions. In this chapter, we describe how solid-state deuterium nuclear magnetic resonance (²H NMR) spectroscopy together with neutron spin-echo (NSE) spectroscopy can inform synergetic changes to lipid molecular packing due to cholesterol and PIP2 that modulate the bending rigidity of lipid membranes. Fundamental structure-property relations of molecular self-assembly are illuminated and point toward a length and time-scale dependence of cell membrane mechanics, with significant implications for biological activity and membrane lipid-protein interactions.

Multiscale compression-induced restructuring of stacked lipid bilayers: From buckling delamination to molecular packing

Lipid membranes in nature adapt and reconfigure to changes in composition, temperature, humidity, and mechanics. For instance, the oscillating mechanical forces on lung cells and alveoli influence membrane synthesis and structure during breathing. However, despite advances in the understanding of lipid membrane phase behavior and mechanics of tissue, there is a critical knowledge gap regarding the response of lipid membranes to micromechanical forces. Most studies of lipid membrane mechanics use supported lipid bilayer systems missing the structural complexity of pulmonary lipids in alveolar membranes comprising multi-bilayer interconnected stacks. Here, we elucidate the collective response of the major component of pulmonary lipids to strain in the form of multi-bilayer stacks supported on flexible elastomer substrates. We utilize X-ray diffraction, scanning probe microscopy, confocal microscopy, and molecular dynamics simulation to show that lipid multilayered films both in gel and fluid states evolve structurally and mechanically in response to compression at multiple length scales. Specifically, compression leads to increased disorder of lipid alkyl chains comparable to the effect of cholesterol on gel phases as a direct result of the formation of nanoscale undulations in the lipid multilayers, also inducing buckling delamination and enhancing multi-bilayer alignment. We propose this cooperative short- and long-range reconfiguration of lipid multilayered films under compression constitutes a mechanism to accommodate stress and substrate topography. Our work raises fundamental insights regarding the adaptability of complex lipid membranes to mechanical stimuli. This is critical to several technologies requiring mechanically reconfigurable surfaces such as the development of electronic devices interfacing biological materials.

Phospholipid Monolayer/Graphene Interfaces: Curvature Effect on Lipid Morphology and Dynamics

Phospholipids are an important class of lipids that are widely used as model platforms for the study of biological processes and interactions. These lipids can form stable interfaces with solid substrates, such as graphene, and these interfaces have potential applications in biosensing and targeted drug delivery. In this paper, we perform molecular dynamics simulations of graphene-supported lipid monolayers to characterize the lipid properties of such interfaces. We observed substantial differences between the supported monolayer and free-standing bilayer in terms of the lipid properties, such as the tail order parameters, density profiles, diffusion rates, and so on. Furthermore, we studied these interfaces on sinusoidally deformed graphene substrates to understand the effect of curvature on the supported lipids. Here, we observed that the nature of the substrate curvature, that is, concave or convex, can locally affect the lipid/substrate adhesion strength and induce structural and dynamic changes in the adsorbed lipid monolayer. Together, these results help characterize the properties of lipid/graphene interfaces and provide insights into the substrate curvature effect on these interfaces, which can enable the tuning of lipid properties for various sensor devices and drug delivery applications.

Probing the Link between Pancratistatin and Mitochondrial Apoptosis through Changes in the Membrane Dynamics on the Nanoscale

Pancratistatin (PST) is a natural antiviral alkaloid that has demonstrated specificity toward cancerous cells and explicitly targets the mitochondria. PST initiates apoptosis while leaving healthy, noncancerous cells unscathed. However, the manner by which PST induces apoptosis remains elusive and impedes the advancement of PST as a natural anticancer therapeutic agent. Herein, we use neutron spin-echo (NSE) spectroscopy, molecular dynamics (MD) simulations, and supporting small angle scattering techniques to study PST's effect on membrane dynamics using biologically representative model membranes. Our data suggests that PST stiffens the inner mitochondrial membrane (IMM) by being preferentially associated with cardiolipin, which would lead to the relocation and release of cytochrome c. Second, PST has an ordering effect on the lipids and disrupts their distribution within the IMM, which would interfere with the maintenance and functionality of the active forms of proteins in the electron transport chain. These previously unreported findings implicate PST's effect on mitochondrial apoptosis.

Bending Modulus of Lipid Membranes from Density Correlation Functions

The bending modulus κ quantifies the elasticity of biological membranes in terms of the free energy cost of increasing the membrane corrugation. Molecular dynamics (MD) simulations provide a powerful approach to quantify κ by analyzing the thermal fluctuations of the lipid bilayer. However, existing methods require the identification and filtering of non-mesoscopic fluctuation modes. State of the art methods rely on identifying a smooth surface to describe the membrane shape. These methods introduce uncertainties in calculating κ since they rely on different criteria to select the relevant fluctuation modes. Here, we present a method to compute κ using molecular simulations. Our approach circumvents the need to define a mesoscopic surface or an orientation field for the lipid tails explicitly. The bending and tilt moduli can be extracted from the analysis of the density correlation function (DCF). The method introduced here builds on the Bedeaux and Weeks (BW) theory for the DCF of fluctuating interfaces and on the coupled undulatory (CU) mode introduced by us in previous work. We test the BW-DCF method by computing the elastic properties of lipid membranes with different system sizes (from 500 to 6000 lipid molecules) and using coarse-grained (for POPC and DPPC lipids) and fully atomistic models (for DPPC). Further, we quantify the impact of cholesterol on the bending modulus of DPPC bilayers. We compare our results with bending moduli obtained with X-ray diffraction data and different computer simulation methods.

Mechanical properties of anionic asymmetric bilayers from atomistic simulations

Mechanotransduction, the biological response to mechanical stress, is often initiated by activation of mechanosensitive (MS) proteins upon mechanically induced deformations of the cell membrane. A current challenge in fully understanding this process is in predicting how lipid bilayers deform upon the application of mechanical stress. In this context, it is now well established that anionic lipids influence the function of many proteins. Here, we test the hypothesis that anionic lipids could indirectly modulate MS proteins by alteration of the lipid bilayer mechanical properties. Using all-atom molecular dynamics simulations, we computed the bilayer bending rigidity (K_C), the area compressibility (K_A), and the surface shear viscosity (η_m) of 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (PC) lipid bilayers with and without phosphatidylserine (PS) or phosphatidylinositol bisphosphate (PIP₂) at physiological concentrations in the lower leaflet. Tensionless leaflets were first checked for each asymmetric bilayer model, and a formula for embedding an asymmetric channel in an asymmetric bilayer is proposed. Results from two different sized bilayers show consistently that the addition of 20% surface charge in the lower leaflet of the PC bilayer with PIP₂ has minimal impact on its mechanical properties, while PS reduced the bilayer bending rigidity by 22%. As a comparison, supplementing the PIP₂-enriched PC membrane with 30% cholesterol, a known rigidifying steroid lipid, produces a significant increase in all three mechanical constants. Analysis of pairwise splay moduli suggests that the effect of anionic lipids on bilayer bending rigidity largely depends on the number of anionic lipid pairs formed during simulations. The potential implication of bilayer bending rigidity is discussed in the framework of MS piezo channels.

Making biological membrane resistant to the toxicity of misfolded protein oligomers: a lesson from trodusquemine

Trodusquemine is an aminosterol known to prevent the binding of misfolded protein oligomers to cell membranes and to reduce their toxicity in a wide range of neurodegenerative diseases. Its precise mechanism of action, however, remains unclear. To investigate this mechanism, we performed confocal microscopy, fluorescence resonance energy transfer (FRET) and nuclear magnetic resonance (NMR) measurements, which revealed a strong binding of trodusquemine to large unilamellar vesicles (LUVs) and neuroblastoma cell membranes. Then, by combining quartz crystal microbalance (QCM), fluorescence quenching and anisotropy, and molecular dynamics (MD) simulations, we found that trodusquemine localises within, and penetrates, the polar region of lipid bilayer. This binding behaviour causes a decrease of the negative charge of the bilayer, as observed through ζ potential measurements, an increment in the mechanical resistance of the bilayer, as revealed by measurements of the breakthrough force applied with AFM and ζ potential measurements at high temperature, and a rearrangement of the spatial distances between ganglioside and cholesterol molecules in the LUVs, as determined by FRET measurements. These physicochemical changes are all known to impair the interaction of misfolded oligomers with cell membranes, protecting them from their toxicity. Taken together, our results illustrate how the incorporation in cell membranes of sterol molecules modified by the addition of polyamine tails leads to the modulation of physicochemical properties of the cell membranes themselves, making them more resistant to protein aggregates associated with neurodegeneration. More generally, they suggest that therapeutic strategies can be developed to reinforce cell membranes against protein misfolded assemblies.

Confinement in Nanodiscs Anisotropically Modifies Lipid Bilayer Elastic Properties

Lipid nanodiscs are small synthetic lipid bilayer structures that are stabilized in solution by special circumscribing (or scaffolding) proteins or polymers. Because they create native-like environments for transmembrane proteins, lipid nanodiscs have become a powerful tool for structural determination of this class of systems when combined with cryo-electron microscopy or nuclear magnetic resonance. The elastic properties of lipid bilayers determine how the lipid environment responds to membrane protein perturbations, and how the lipid in turn modifies the conformational state of the embedded protein. However, despite the abundant use of nanodiscs in determining membrane protein structure, the elastic material properties of even pure lipid nanodiscs (i.e., without embedded proteins) have not yet been quantitatively investigated. A major hurdle is due to the inherently nonlocal treatment of the elastic properties of lipid systems implemented by most existing methods, both experimental and computational. In addition, these methods are best suited for very large “infinite” size lipidic assemblies, or ones that contain periodicity, in the case of simulations. We have previously described a computational analysis of molecular dynamics simulations designed to overcome these limitations, so it allows quantification of the bending rigidity (K_C) and tilt modulus (κ_t) on a local scale even for finite, nonperiodic systems, such as lipid nanodiscs. Here we use this computational approach to extract values of K_C and κ_t for a set of lipid nanodisc systems that vary in size and lipid composition. We find that the material properties of lipid nanodiscs are different from those of infinite bilayers of corresponding lipid composition, highlighting the effect of nanodisc confinement. Nanodiscs tend to show higher stiffness than their corresponding macroscopic bilayers, and moreover, their material properties vary spatially within them. For small-size MSP1 nanodiscs, the stiffness decreases radially, from a value that is larger in their center than the moduli of the corresponding bilayers by a factor of ∼2–3. The larger nanodiscs (MSP1E3D1 and MSP2N2) show milder spatial changes of moduli that are composition dependent and can be maximal in the center or at some distance from it. These trends in moduli correlate with spatially varying structural properties, including the area per lipid and the nanodisc thickness. Finally, as has previously been reported, nanodiscs tend to show deformations from perfectly flat circular geometries to varying degrees, depending on size and lipid composition. The modulations of lipid elastic properties that we find should be carefully considered when making structural and functional inferences concerning embedded proteins.

Lipid Head Group Parameterization for GROMOS 54A8: A Consistent Approach with Protein Force Field Description

Membranes are a crucial component of both bacterial and mammalian cells, being involved in signaling, transport, and compartmentalization. This versatility requires a variety of lipid species to tailor the membrane’s behavior as needed, increasing the complexity of the system. Molecular dynamics simulations have been successfully applied to study model membranes and their interactions with proteins, elucidating some crucial mechanisms at the atomistic detail and thus complementing experimental techniques. An accurate description of the functional interplay of the diverse membrane components crucially depends on the selected parameters that define the adopted force field. A coherent parameterization for lipids and proteins is therefore needed. In this work, we propose and validate new lipid head group parameters for the GROMOS 54A8 force field, making use of recently published parametrizations for key chemical moieties present in lipids. We make use additionally of a new canonical set of partial charges for lipids, chosen to be consistent with the parameterization of soluble molecules such as proteins. We test the derived parameters on five phosphocholine model bilayers, composed of lipid patches four times larger than the ones used in previous studies, and run 500 ns long simulations of each system. Reproduction of experimental data like area per lipid and deuterium order parameters is good and comparable with previous parameterizations, as well as the description of liquid crystal to gel-phase transition. On the other hand, the orientational behavior of the head groups is more realistic for this new parameter set, and this can be crucial in the description of interactions with other polar molecules. For that reason, we tested the interaction of the antimicrobial peptide lactoferricin with two model membranes showing that the new parameters lead to a weaker peptide–membrane binding and give a more realistic outcome in comparing binding to antimicrobial versus mammal membranes.

Determination of bending rigidity and tilt modulus of lipid membranes from real-space fluctuation analysis of molecular dynamics simulations

We have recently developed a novel computational methodology (termed RSF for Real-Space Fluctuations) to quantify the bending rigidity and tilt modulus of lipid membranes from real-space analysis of fluctuations in the tilt and splay degrees of freedom as sampled in molecular dynamics (MD) simulations. In this article, we present a comprehensive study that combines results from the application of the RSF method to a wide range of lipid bilayer systems that encompass membranes of different fluidities and sizes, including lipids with saturated and unsaturated lipid tails, single and multi-component lipid systems, as well as non-standard lipids such as the four-tailed cardiolipin. By comparing the material properties calculated with the RSF method to those obtained from experimental data and from other computational methodologies, we rigorously demonstrate the validity of our approach and show its robustness. This should allow for future applications of even more complex lipidic assemblies, whose material properties are not tractable by other computational techniques. In addition, we discuss the relationship between different definitions of the tilt modulus appearing in current literature to address some important unresolved discrepancies in the field.