Mechanical properties of lipid bilayers from molecular dynamics simulation

Biomembranes balance many types of leaflet asymmetries

Many biological membranes host different lipid species in their two leaflets. Since their spontaneous curvatures are typically not the same, this compositional asymmetry generally entails bending torques, which can be counteracted by differential stress-the difference between the two leaflet tensions. This stress, in turn, can affect elastic parameters or phase behavior of the membrane or each individual leaflet, or push easily flippable species, especially cholesterol, from the compressed leaflet into the tense leaflet. In short, breaking the symmetry of a single observable (to wit: composition), essentially breaks all other symmetries as well, with many potentially interesting consequences. This brief report examines the elastic aspects of this interplay, focusing on some elementary conditions of mechanical and thermodynamic equilibrium, but also shows how this poses novel questions that we are only beginning to appreciate.

Investigating the Influence of Photoswitchable Lipids on the Structure and Dynamics of Lipid Membranes: Fundamentals and Potential Applications

In this work, we delve into the impact of photoisomerization of photoswitchable lipids (PSLs) on the membrane structure and dynamics at a molecular level. Through all-atom molecular dynamics simulations, we explore how UV irradiation-induced trans-to-cis isomerization of these lipids, particularly the azobenzene-derivatized phosphatidylcholine (AzoPC) lipid, influences the structure and dynamics of a simplified lipid membrane, mimicking those of E. coli bacteria across different temperatures. Our findings align with previous experimental observations regarding membrane properties and offer insights into localized effects and microscopic heterogeneity. Additionally, we estimate the relaxation time scale of the lipid membrane following AzoPC photoisomerization. Moreover, we demonstrate the feasibility of photoactivated drug release, exemplified by the controlled liberation of doxorubicin, an anticancer agent, through the membrane, suggesting the potential of PSLs in engineering photoactivated liposomes, coined as photoazosomes, for precise targeted drug delivery applications.

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.

Protonation State of a Bioactive Compound Regulates Its Release from Lamellar Gel-Phase Bilayers

Lamellar gel networks (LGNs) in personal care or pharmaceutical lotions and creams provide an opaque cream appearance and a creamy texture to these products. Within the LGNs, the lamellar gel (Lβ) phase composed of regularly spaced bilayers of surfactants and long-chain fatty alcohols is predominately responsible for the unique rheological properties of the LGNs. To extend the shelf life of LGN-containing products, bioactive compounds with antimicrobial properties are often incorporated into the formulation. However, how the protonation state of the bioactive compounds regulates their release from the Lβ-phase bilayers is currently unknown. Using molecular dynamics simulations, we found that the protonated (neutral) form of cinnamic acid, a common antimicrobial food additive, has a retention ratio higher than that of its deprotonated (charged) counterpart in the Lβ-phase bilayer. From free energy calculations, we determined that not only is the protonated molecule more stable in the hydrophobic interior of the bilayer but also the formation of hydrogen-bonded dimers significantly enhances its stability within the bilayer. Thus, the protonation state has a profound impact on bioavailability of the compounds. Our results also highlight the importance of considering possible oligomeric states of molecules when performing calculations to estimate the permeability of molecules within various bilayers.

Dynamics of an aqueous suspension of short hyaluronic acid chains near a DPPC bilayer

The synergy between hyaluronic acid (HA) and lipid molecules plays a crucial role in synovial fluids, cell coatings, etc. Diseased cells in cancer and arthritis show changes in HA concentration and chain size, impacting the viscoelastic and mechanical properties of the cells. Although the solution behavior of HA is known in experiments, a molecular-level understanding of the role of HA in the dynamics at the interface of HA-water and the cellular boundary is lacking. Here, we perform atomistic molecular dynamics simulation of short HA chains in an explicit water solvent in the presence of a DPPC bilayer, relevant in pathological cases. We identify a stable interface between HA-water and the bilayer where the water molecules are in contact with the bilayer and the HA chains are located away without any direct contact. Both translation and rotation of the interfacial waters in contact with the lipid bilayer and translation of the HA chains exhibit subdiffusive behavior. The diffusive behavior sets in slightly away from the bilayer, where the diffusion coefficients of water and HA decrease monotonically with increase in HA concentration. On the contrary, the dependence on HA chain size is only marginal due to enhanced chain flexibility as their size increases.

Molecular dynamics simulations reliably identify vibrational modes in far-IR spectra of phospholipids

The properties of self-assembled phospholipid membranes are of essential importance in biochemistry and physical chemistry, providing a platform for many cellular life functions. Far-infrared (far-IR) vibrational spectroscopy, on the other hand, is a highly information-rich method to characterize intermolecular interactions and collective behaviour of lipids that can help explain, e.g., chain packing, thermodynamic phase behaviour, and sequestration. However, reliable interpretation of the far-IR spectra is still lacking. Here we present a molecular dynamics (MD) based approach to simulate vibrational modes of individual lipids and in an ensemble. The results are a good match to synchrotron far-IR measurements and enable identification of the molecular motions corresponding to each vibrational mode, thus allowing the correct interpretation of membrane spectra with high accuracy and resolving the longstanding ambiguities in the literature in this regard. Our results demonstrate the feasibility of using MD simulations for interpreting far-IR spectra broadly, opening new avenues for practical use of this powerful method.

Softening in Two-Component Lipid Mixtures by Spontaneous Curvature Variance

The bending modulus of a lipid bilayer quantifies its mechanical resistance to curvature. It is typically understood in terms of thickness; e.g., thicker bilayers are usually stiffer. Here, we describe an additional and powerful molecular determinant of stiffness─the variance in the distribution of curvature sensitivity of lipids and lipid conformations. Zwitterionic choline and ethanolamine headgroups of glycerophospholipids dynamically explore inter- and intraspecies interactions, leading to transient clustering. We demonstrate that these clusters couple strongly to negative curvature, exciting undulatory membrane modes and reducing the apparent bending modulus. Three force fields (Martini 2, Martini 3, and all-atom CHARMM C36) each show the effect to a different extent, with the coarse-grained Martini models showing the most clustering and thus the most softening. The theory is a guide to understanding the stiffness of biological membranes with their complex composition, as well as how choices of force field parameterization are translated into mechanical stiffness.

Molecular behavior of silicone adhesive at buried polymer interface studied by molecular dynamics simulation and sum frequency generation vibrational spectroscopy

Silicones have excellent material properties and are used extensively in many applications, ranging from adhesives and lubricants to electrical insulation. To ensure strong adhesion of silicone adhesives to a wide variety of substrates, silane-based adhesion promotors are typically blended into the silicone adhesive formulation. However, little is known at the molecular level about the true silane adhesion promotion mechanism, which limits the ability to develop even more effective adhesion promoters. To understand the adhesion promotion mechanism of silane molecules at the molecular level, this study has used sum frequency generation vibrational spectroscopy (SFG) to determine the behavior of (3-glycidoxypropyl)trimethoxy silane (γ-GPS) at the buried interface between poly(ethylene terephthalate) (PET) and a bulk silicone adhesive. To complement and extend the SFG results, atomistic molecular dynamics (MD) simulations were applied to investigate molecular behavior and interfacial interaction of γ-GPS at the silicone/PET interface. Free energy computations were used to study the γ-GPS interaction in the sample system and determine the γ-GPS interfacial segregation mechanism. Both experiments and simulations consistently show that γ-GPS molecules prefer to segregate at the interface between PET and PDMS. The methoxy groups on γ-GPS molecules orient toward the PDMS polymer phase. The consistent picture of interfacial structure emerging from both simulation and experiment provides enhanced insight on how γ-GPS behaves in the silicone - PET system and illustrates why γ-GPS could improve the adhesion of silicone adhesive, leading to further understanding of silicone adhesion mechanisms useful in the design of silicone adhesives with improved performance.

Study on the Cross-Scale Effects of Microscopic Interactions and Mechanical Properties of Rigid Polyurethane Foam Driven by Negative-Temperature Environments

In order to investigate the cross-scale effects of the interaction between the hard and soft segments of stiff polyurethane foam on the material's mesoscopic pore structure and macroscopic compression characteristics in various negative-temperature environments, this paper used molecular dynamics to calculate the interaction differences between hard and soft segments in different negative-temperature environments. The effects of various negative-temperature settings on the cell structure of stiff polyurethane foam were investigated using scanning electron microscopy and Image J software. Finally, macro experiments were used to determine the influence of a negative-temperature environment on the characteristics of stiff polyurethane foam (such as compressibility). The molecular simulation calculation results show that in a negative-temperature environment, decreasing temperature gradually increases the interaction between hard segment molecules and soft segment molecules, resulting in an increase in the molecules' modulus and cohesive energy density. The scanning electron microscope results reveal that a negative-temperature environment gradually increases the pore diameter of stiff polyurethane foam. The compression experiment findings demonstrate that, for the same service duration, the compressive strength in the -20 °C environment is 27.53% higher than that in the 0 °C environment. The study's findings reveal a microscopic mechanism for the following receiving alterations and toughness enhancement of rigid polyurethane foam throughout service in negative-temperature conditions.

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.

Dynamic framework for large-scale modeling of membranes and peripheral proteins

In this chapter, we present a novel computational framework to study the dynamic behavior of extensive membrane systems, potentially in interaction with peripheral proteins, as an alternative to conventional simulation methods. The framework effectively describes the complex dynamics in protein-membrane systems in a mesoscopic particle-based setup. Furthermore, leveraging the hydrodynamic coupling between the membrane and its surrounding solvent, the coarse-grained model grounds its dynamics in macroscopic kinetic properties such as viscosity and diffusion coefficients, marrying the advantages of continuum- and particle-based approaches. We introduce the theoretical background and the parameter-space optimization method in a step-by-step fashion, present the hydrodynamic coupling method in detail, and demonstrate the application of the model at each stage through illuminating examples. We believe this modeling framework to hold great potential for simulating membrane and protein systems at biological spatiotemporal scales, and offer substantial flexibility for further development and parametrization.

Simulating asymmetric membranes using P21 periodic boundary conditions

Molecular dynamics (MD) simulations of symmetric lipid bilayers are now well established, while those of asymmetric ones are considerably less developed. This disjunction arises in part because the surface tensions of leaflets in asymmetric bilayers can differ (unlike those of symmetric ones), and there is no simple way to determine them without assumptions. This chapter describes the use of P21 periodic boundary conditions (PBC), which allow lipids to switch leaflets, to generate asymmetric bilayers under the assumption of equal chemical potentials of lipids in opposing leaflets. A series of examples, ranging from bilayers with one lipid type to those with peptides and proteins, provides a guide for the use of P21 PBC. Critical properties of asymmetric membranes, such as spontaneous curvature, are highly sensitive to differences in the leaflet surface tensions (or differential stress), and equilibration with P21 PBC substantially reduces differential stress of asymmetric bilayers assembled with surface area-based methods. Limitations of the method are discussed. Technically, the nonstandard unit cell is difficult to parallelize and to incorporate restraints. Inherently, the assumption of equal chemical potentials, and therefore the method itself, is not applicable to all target systems. Despite these limitations, it is argued that P21 simulations should be considered when designing equilibration protocols for MD studies of most asymmetric membranes.

Efficient calculation of orientation-dependent lipid dynamics from membrane simulations

Molecular dynamics simulations of lipid membranes have become increasingly impactful in biophysics because they offer atomistic resolution of structural fluctuations in relation to their functional outputs. Yet quantitative characterization of multiscale processes is a formidable challenge due to the distribution of motions that evade analysis of discrete simulation data. Here we investigate the efficient calculation of CH bond relaxation rates from membrane simulations. Widely used computational approaches offer numerical simplicity but fall short of capturing crucial aspects of the orientation dependence of the dynamics. To circumvent this problem, we introduced a robust framework based on liquid crystal theory which considers explicitly the CH bond motions with respect to the director axis (bilayer normal). Analysis of the orientation dependence of the dynamics shows excellent agreement with experiment, illustrating how the ordering potential affects the calculated relaxation rates. Furthermore, a fit-based resampling of the autocorrelation function of the bond fluctuations validates the new approach for low-temporal resolution data. The recovered relaxation rates indicate that at short timescales, both with and without cholesterol, the local motions of CH bonds describe the bilayer microviscosity and resemble liquid hydrocarbons. Our results establish the critical role of the orientational anisotropy in analysis of membrane simulations, explain fundamental aspects of lipid dynamics, and provide guidelines for extracting information that can be compared to experimental data.

Spontaneous curvature generation by peptides in asymmetric bilayers

Peptides and proteins play crucial roles in membrane remodeling by inducing spontaneous curvature. However, extracting spontaneous curvatures from simulations of asymmetric bilayers is challenging because differential stress (i.e., the difference of the leaflet surface tensions) arising from leaflet area strains can vary substantially among initial conditions. This study investigates peptide-induced spontaneous curvatureδc 0 p in asymmetric bilayers consisting of a single lipid type and a peptide confined to one leaflet;δc 0 p is calculated from the Helfrich equation using the first moment of the lateral pressure tensor and an alternative expression using the differential stress. It is shown that differential stress introduced during initial system generation is effectively relaxed by equilibrating using P21 periodic boundary conditions, which allows lipids to switch leaflets across cell boundaries and equalize their chemical potentials across leaflets. This procedure leads to robust estimates ofδc 0 p for the systems simulated, and is recommended when equality of chemical potentials between the leaflets is a primary consideration.

Light-Activated Synthetic Rotary Motors in Lipid Membranes Induce Shape Changes Through Membrane Expansion

Membranes are the key structures to separate and spatially organize cellular systems. Their rich dynamics and transformations during the cell cycle are orchestrated by specific membrane-targeted molecular machineries, many of which operate through energy dissipation. Likewise, man-made light-activated molecular rotary motors have previously shown drastic effects on cellular systems, but their physical roles on and within lipid membranes remain largely unexplored. Here, the impact of rotary motors on well-defined biological membranes is systematically investigated. Notably, dramatic mechanical transformations are observed in these systems upon motor irradiation, indicative of motor-induced membrane expansion. The influence of several factors on this phenomenon is systematically explored, such as motor concentration and membrane composition., Membrane fluidity is found to play a crucial role in motor-induced deformations, while only minor contributions from local heating and singlet oxygen generation are observed. Most remarkably, the membrane area expansion under the influence of the motors continues as long as irradiation is maintained, and the system stays out-of-equilibrium. Overall, this research contributes to a comprehensive understanding of molecular motors interacting with biological membranes, elucidating the multifaceted factors that govern membrane responses and shape transitions in the presence of these remarkable molecular machines, thereby supporting their future applications in chemical biology.

Dynamic structure factor of undulating vesicles: finite-size and spherical geometry effects with application to neutron spin echo experiments

We consider the dynamic structure factor (DSF) of quasi-spherical vesicles and present a generalization of an expression that was originally formulated by Zilman and Granek (ZG) for scattering from isotropically oriented quasi-flat membrane plaquettes. The expression is obtained in the form of a multi-dimensional integral over the undulating membrane surface. The new expression reduces to the original stretched exponential form in the limit of sufficiently large vesicles, i.e., in the micron range or larger. For much smaller unilamellar vesicles, deviations from the asymptotic, stretched exponential equation are noticeable even if one assumes that the Seifert-Langer leaflet density mode is completely relaxed and membrane viscosity is neglected. To avoid the need for an exhaustive numerical integration while fitting to neutron spin echo (NSE) data, we provide a useful approximation for polydisperse systems that tests well against the numerical integration of the complete expression. To validate the new expression, we performed NSE experiments on variable-size vesicles made of a POPC/POPS lipid mixture and demonstrate an advantage over the original stretched exponential form or other manipulations of the original ZG expression that have been deployed over the years to fit the NSE data. In particular, values of the membrane bending rigidity extracted from the NSE data using the new approximations were insensitive to the vesicle radii and scattering wavenumber and compared very well with expected values of the effective bending modulus ([Formula: see text]) calculated from results in the literature. Moreover, the generalized scattering theory presented here for an undulating quasi-spherical shell can be easily extended to other models for the membrane undulation dynamics beyond the Helfrich Hamiltonian and thereby provides the foundation for the study of the nanoscale dynamics in more complex and biologically relevant model membrane systems.

Understanding the cell: Future views of structural biology

Determining the structure and mechanisms of all individual functional modules of cells at high molecular detail has often been seen as equal to understanding how cells work. Recent technical advances have led to a flush of high-resolution structures of various macromolecular machines, but despite this wealth of detailed information, our understanding of cellular function remains incomplete. Here, we discuss present-day limitations of structural biology and highlight novel technologies that may enable us to analyze molecular functions directly inside cells. We predict that the progression toward structural cell biology will involve a shift toward conceptualizing a 4D virtual reality of cells using digital twins. These will capture cellular segments in a highly enriched molecular detail, include dynamic changes, and facilitate simulations of molecular processes, leading to novel and experimentally testable predictions. Transferring biological questions into algorithms that learn from the existing wealth of data and explore novel solutions may ultimately unveil how cells work.

Antimicrobial peptide interactions with bacterial cell membranes

Antimicrobial peptides (AMPs) are potential alternatives for common antibiotics because of their greater activity and efficiency against a broad range of viruses, bacteria, fungi, and parasites. In this project, two antimicrobial peptides including magainin 2 and protegrin 1 with α-helix and β-sheet secondary structures were selected to investigate their interactions with different lipid bilayers such as 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC), 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphoserine (POPS), 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphoglycerol (POPG), and 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphoethanolamine (POPE), POPC/POPG (7:3), POPC/POPS (7:3), POPG/POPE(1:3), and POPG/POPE(3:1). The obtained structures of the AMPs illustrated that protegrin 1 cannot maintain its secondary structure in the solution phase in contrast to magainin 2. The head groups of the lipid units play a key role in the stability of the lipid bilayers. The head parts of the lipid membranes by increasing the internal H-bond contribute to membrane compactness. The POPG and POPS units inside the POPC/POPG and POPC/POPS membranes increase the order of the POPC units. The cationic residues of the AMPs form remarkable electrostatic interactions with the negatively charged membrane surfaces, which play a key role in the stabilization process of the peptide secondary structures. The Arg residues of protegrin 1 and the Gly1, Lys4, Lys10, Lys11, Lys14, and Glu19 of the magainin 2 have the most important roles in the complexation process. The values of Gibbs binding energies (ΔG) indicate that the complexation process between AMPs and different bacterial membranes is favorable from the thermodynamic viewpoint and AMPs could form stable complexes with the lipid bilayers. As a result of ΔG values, protegrin 1 forms a more stable complex with POPG/POPE(3:1), while the α-helix has more affinity to the POPG/POPE(1:3) bacterial membranes. Therefore, it can be considered that β-sheet and α-helix AMPs are more effective against gram-positive and gram-negative bacteria, respectively. The results of this study can provide useful details about the antimicrobial peptide interactions with the bacterial cell, which can be employed for designing new antimicrobial materials with greater efficiency.Communicated by Ramaswamy H. Sarma.

Exploring Cyclic Peptide Nanotube Stability Across Diverse Lipid Bilayers and Unveiling Water Transport Dynamics

Cyclic Peptide Nanotubes (CPNTs) have emerged as compelling candidates for various applications, particularly as nanochannels within lipid bilayers. In this study, the stability of two CPNTs, namely 8 × [(Cys-Gly-Met-Gly)2] and 8 × [(Gly-Leu)4], are comprehensively investigated across different lipid bilayers, including 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC), a mixed model membrane (POPE/POPG), and a realistic yeast model membrane. The results demonstrate that both CPNTs maintain their tubular structures in all lipid bilayers, with [(Cys-Gly-Met-Gly)2] showing increased stability over an extended period in these lipid membranes. The insertion of CPNTs shows negligible impact on lipid bilayer properties, including area per lipid, volume per lipid, and bilayer thickness. The study demonstrates that the CPNT preserves its two-line water movement pattern within all the lipid membranes, reaffirming their potential as water channels. The MSD curves further reveal that the dynamics of water molecules inside the nanotube are similar for all the bilayer systems with minor differences that arise due to different lipid environments.

Softening in two-component lipid mixtures by spontaneous curvature variance

The bending modulus of a lipid bilayer quantifies its mechanical resistance to curvature. It is typically understood in terms of thickness, e.g., thicker bilayers are stiffer. Here, we describe an additional and powerful molecular determinant of stiffness - the variance in the distribution of curvature sensitivity of lipids and lipid conformations. Zwitterionic choline and ethanolamine head-groups of glycero-phospholipids dynamically explore inter- and intra-species interactions, leading to transient clustering. We demonstrate that these clusters couple strongly to negative curvature, exciting undulatory membrane modes and reducing the apparent bending modulus. Three forcefields (Martini 2, Martini 3, and all-atom CHARMM C36) each show the effect to a different extent, with the coarse-grained Martini models showing the most clustering and thus the most softening. The theory is a guide to understanding the stiffness of biological membranes with their complex composition, as well as how choices of forcefield parameterization are translated into mechanical stiffness.

Modeling the Effect on a Novel Fungal Peptaibol Placed in an All-Atom Bacterial Membrane Mimicking System via Accelerated Molecular Dynamics Simulations

We previously reported on a novel peptaibol, named Tripleurin XIIc (TPN), an 18-residue long sequence produced by the fungus Trichoderma pleuroti. We elucidated its 3D structure via classical and accelerated molecular dynamics simulation (aMD) methods and reported the folding dynamics of TPN in water and chloroform solvents. Peptaibols, in general, are insoluble in water, as they are amphipathic and may prefer hydrophobic environments like transmembrane regions. In this study, we attempted to use aMD simulations to model an all-atom bacterial membrane system while placing a TPN molecule in its vicinity. The results highlighted that TPN was able to introduce some disorder into the membrane and caused lipid clustering. It could also enter the transmembrane region from the water-bilayer interface. The structural dynamics of TPN in the transmembrane region revealed a single energetically stable conformation similar to the one obtained from water and chloroform solvent simulations reported by us previously. However, this linear structure was found to be at the local energy minimum (stable) in water but at a metastable intermediate state (higher energy) in chloroform. Therefore, it could be said that the water solvent can be successfully used for folding simulations of peptaibols.

Anomalous lateral diffusion of lipids during the fluid/gel phase transition of a lipid membrane

A lipid membrane undergoes a phase transition from fluid to gel phase upon changing external thermodynamic conditions, such as decreasing temperature and increasing pressure. Extremophilic organisms face the challenge of preventing this deleterious phase transition. The main focus of their adaptive strategy is to facilitate effective temperature sensing through sensor proteins, relying on the drastic changes in packing density and membrane fluidity during the phase transition. Although the changes in packing density parameters due to the fluid/gel phase transition are studied in detail, the impact on membrane fluidity is less explored in the literature. Understanding the lateral diffusive dynamics of lipids in response to temperature, particularly during the fluid/gel phase transition, is albeit crucial. Here we have simulated the phase transition of a single component lipid membrane composed of dipalmitoylphosphatidylcholine (DPPC) lipids using a coarse-grained (CG) model and studied the changes of the structural and dynamical properties. It is observed that near the phase transition point, both fluid and gel phase domains coexist together. The dynamics remains highly non-Gaussian for a long time even when the mean square displacement reaches the Fickian regime at a much earlier time. This Fickian yet non-Gaussian diffusion (FnGD) is a characteristic of a highly heterogeneous system, previously observed for the lateral diffusion of lipids in raft mimetic membranes having liquid-ordered and liquid-disordered phases co-existing together. We have analyzed the molecular trajectories and calculated the jump-diffusion of the lipids, stemming from sudden jump translations, using a translational jump-diffusion (TJD) approach. An overwhelming contribution of the jump-diffusion of the lipids is observed suggesting anomalous diffusion of lipids during fluid/gel phase transition of the membrane. These results are important in unravelling the intricate nature of lipid diffusion during the phase transition of the membrane and open up a new possibility of investigating the most significant change of membrane properties during phase transition, which can be effectively sensed by proteins.

Molecular insights into the effects of focused ultrasound mechanotherapy on lipid bilayers: Unlocking the keys to design effective treatments

Administration of focused ultrasounds (US) represents an attractive complement to classical therapies for a wide range of maladies, from cancer to neurological pathologies, as they are non-invasive, easily targeted, their dosage is easy to control, and they involve low risks. Different mechanisms have been proposed for their activity but the direct effect of their interaction with cell membranes is not well understood at the molecular level. This is in part due to the difficulty of designing experiments able to probe the required spatio-temporal resolutions. Here we use Molecular Dynamics (MD) simulations at two resolution levels and machine learning (ML) classification tools to shed light on the effects that focused US mechanotherapy methods have over a range of lipid bilayers. Our results indicate that the dynamic-structural response of the membrane models to the mechanical perturbations caused by the sound waves strongly depends on the lipid composition. The analyses performed on the MD trajectories contribute to a better understanding of the behavior of lipid membranes, and to open up a path for the rational design of new therapies for the long list of diseases characterized by specific lipid profiles of pathological membrane cells.

Understanding the Mechanical Properties of Ultradeformable Liposomes Using Molecular Dynamics Simulations

Improving drug delivery efficiency to solid tumor sites is a central challenge in anticancer therapeutic research. Our previous experimental study (Guo et al., Nat. Commun. 2018, 9, 130) showed that soft, elastic liposomes had increased uptake and accumulation in cancer cells and tumors in vitro and in vivo respectively, relative to rigid particles. As a first step toward understanding how liposomes' molecular structure and composition modulates their elasticity, we performed all-atom and coarse-grained classical molecular dynamics (MD) simulations of lipid bilayers formed by mixing a long-tailed unsaturated phospholipid with a short-tailed saturated lipid with the same headgroup. The former types of phospholipids considered were 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) and 1,2-dipalmitoleoyl-sn-glycero-3-phosphocholine (termed here DPMPC). The shorter saturated lipids examined were 1,2-diheptanoyl-sn-glycero-3-phosphocholine (DHPC), 1,2-didecanoyl-sn-glycero-3-phosphocholine (DDPC), 1,2-dilauroyl-sn-glycero-3-phosphocholine (DLPC), and 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC). Several lipid concentrations and surface tensions were considered. Our results show that DOPC or DPMPC systems having 25-35 mol % of the shortest lipids DHPC or DDPC are the least rigid, having area compressibility moduli KA that are ∼10% smaller than the values observed in pure DOPC or DPMPC bilayers. These results agree with experimental measurements of the stretching modulus and lysis tension in liposomes with the same compositions. These mixed systems also have lower areas per lipid and form more uneven x-y interfaces with water, the tails of both primary and secondary lipids are more disordered, and the terminal methyl groups in the tails of the long lipid DOPC or DPMPC wriggle more in the vertical direction, compared to pure DOPC or DPMPC bilayers or their mixtures with the longer saturated lipid DLPC or DMPC. These observations confirm our hypothesis that adding increasing concentrations of the short unsaturated lipid DHPC or DDPC to DOPC or DPMPC bilayers alters lipid packing and thus makes the resulting liposomes more elastic and less rigid. No formation of lipid nanodomains was noted in our simulations, and no clear trends were observed in the lateral diffusivities of the lipids as the concentration, type of secondary lipid, and surface tension were varied.

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.

Integration of an LPAR1 Antagonist into Liposomes Enhances Their Internalization and Tumor Accumulation in an Animal Model of Human Metastatic Breast Cancer

Lysophosphatidic acid receptor 1 (LPAR1) is elevated in breast cancer. The deregulation of LPAR1, including the function and level of expression, is linked to cancer initiation, progression, and metastasis. LPAR1 antagonists, AM095 or Ki16425, may be effective therapeutic molecules, yet their limited water solubility hinders in vivo delivery. In this study, we report on the synthesis of two liposomal formulations incorporating AM095 or Ki16425, embedded within the lipid bilayer, as targeted nanocarriers for metastatic breast cancer (MBC). The data show that the Ki16425 liposomal formulation exhibited a 50% increase in internalization by MBC mouse epithelial cells (4T1) and a 100% increase in tumor accumulation in a mouse model of MBC compared with that of a blank liposomal formulation (control). At the same time, normal mouse epithelial cells (EpH-4Ev) internalized the Ki16425 liposomal formulation 25% lesser than the control formulation. Molecular dynamics simulations show that the integration of AM095 or Ki16425 modified the physical and mechanical properties of the lipid bilayer, making it more flexible in these liposomal formulations compared with liposomes without drug. The incorporation of an LPAR1 antagonist within a liposomal drug delivery system represents a viable therapeutic approach for targeting the LPA-LPAR1 axis, which may hinder the progression of MBC.

Passive Translocation of Phospholipids in Asymmetric Model Membranes: Solid-State 1H NMR Characterization of Flip-Flop Kinetics Using Deuterated Sphingomyelin and Phosphatidylcholine

Although lateral and inter-leaflet lipid-lipid interactions in cell membranes play roles in maintaining asymmetric lipid bilayers, the molecular basis of these interactions is largely unknown. Here, we established a method to determine the distribution ratio of phospholipids between the outer and inner leaflets of asymmetric large unilamellar vesicles (aLUVs). The trimethylammonium group, (CH3)3N+, in the choline headgroup of N-palmitoyl-sphingomyelin (PSM) and 1,2-dioleoyl-sn-glycero-3-phosphatidylcholine (DOPC) gave rise to a relatively sharp signal in magic-angle spinning solid-state 1H NMR (MAS-ss-1H NMR). PSM and DOPC have the same headgroup structure, but one phospholipid was selectively observed by deuterating the trimethylammonium group of the other phospholipid. The addition of Pr3+ to the medium surrounding aLUVs selectively shifted the chemical shift of the (CH3)3N+ group in the outer leaflet from that in the inner leaflet, which allowed estimation of the inter-leaflet distribution ratio of the unlabeled lipid in aLUVs. Using this method, we evaluated the translocation of PSM and DOPC between the outer and inner leaflets of the cholesterol-containing aLUVs, with PSM and DOPC mostly distributed in the outer and inner leaflets, respectively, immediately after aLUV preparation; their flip and flop rates were approximately 2.7 and 6.4 × 10-6 s-1, respectively. During the passive symmetrization of aLUVs, the lipid translocation rate was decreased due to changes in the membrane order, probably through the formation of the registered liquid-ordered domains. Comparison of the result with that of symmetric LUVs revealed that lipid asymmetry may not significantly affect the lipid translocation rates, while the lateral lipid-lipid interaction may be a dominant factor in lipid translocation under these conditions. These findings highlight the importance of considering the effects of lateral lipid interactions within the same leaflet on lipid flip-flop rates when evaluating the asymmetry of phospholipids in the cell membrane.

Origin of the nonlinear structural and mechanical properties in oppositely curved lipid mixtures

Structural and mechanical properties of membranes such as thickness, tail order, bending modulus and curvature energetics play crucial role in controlling various cellular functions that depend on the local lipid organization and membrane reshaping. While behavior of these biophysical properties are well understood in single component membranes, very little is known about how do they change in the mixed lipid membranes. Often various properties of the mixed lipid bilayers are assumed to change linearly with the mole fractions of the constituent lipids which, however, is true for "ideal" mixing only. In this study, using molecular dynamics simulations, we show that structural and mechanical properties of binary lipid mixture change nonlinearly with the lipid mole fractions, and the strength of the nonlinearity depends on two factors - spontaneous curvature difference and locally inhomogeneous interactions between the lipid components.

Combining SILCS and Artificial Intelligence for High-Throughput Prediction of the Passive Permeability of Drug Molecules

Membrane permeability of drug molecules plays a significant role in the development of new therapeutic agents. Accordingly, methods to predict the passive permeability of drug candidates during a medicinal chemistry campaign offer the potential to accelerate the drug design process. In this work, we combine the physics-based site identification by ligand competitive saturation (SILCS) method and data-driven artificial intelligence (AI) to create a high-throughput predictive model for the passive permeability of druglike molecules. In this study, we present a comparative analysis of four regression models to predict membrane permeabilities of small druglike molecules; of the tested models, Random Forest was the most predictive yielding an R2 of 0.81 for the independent data set. The input feature vector used to train the developed prediction model includes absolute free energy profiles of ligands through a POPC-cholesterol bilayer based on ligand grid free energy (LGFE) profiles obtained from the SILCS approach. The use of the membrane free energy profiles from SILCS offers information on the physical forces contributing to ligand permeability, while the use of AI yields a more predictive model trained on experimental PAMPA permeability data for a collection of 229 molecules. This combination allows for rapid estimations of ligand permeability at a level of accuracy beyond currently available predictive models while offering insights into the contributions of the functional groups in the ligands to the permeability barrier, thereby offering quantitative information to facilitate rational ligand design.

Membrane manipulation by free fatty acids improves microbial plant polyphenol synthesis

Microbial synthesis of nutraceutically and pharmaceutically interesting plant polyphenols represents a more environmentally friendly alternative to chemical synthesis or plant extraction. However, most polyphenols are cytotoxic for microorganisms as they are believed to negatively affect cell integrity and transport processes. To increase the production performance of engineered cell factories, strategies have to be developed to mitigate these detrimental effects. Here, we examine the accumulation of the stilbenoid resveratrol in the cell membrane and cell wall during its production using Corynebacterium glutamicum and uncover the membrane rigidifying effect of this stilbenoid experimentally and with molecular dynamics simulations. A screen of free fatty acid supplements identifies palmitelaidic acid and linoleic acid as suitable additives to attenuate resveratrol's cytotoxic effects resulting in a three-fold higher product titer. This cost-effective approach to counteract membrane-damaging effects of product accumulation is transferable to the microbial production of other polyphenols and may represent an engineering target for other membrane-active bioproducts.

Cristae formation is a mechanical buckling event controlled by the inner membrane lipidome

Cristae are high curvature structures in the inner mitochondrial membrane (IMM) that are crucial for ATP production. While cristae-shaping proteins have been defined, analogous mechanisms for lipids have yet to be elucidated. Here we combine experimental lipidome dissection with multi-scale modeling to investigate how lipid interactions dictate IMM morphology and ATP generation. When modulating phospholipid (PL) saturation in engineered yeast strains, we observed a surprisingly abrupt breakpoint in IMM topology driven by a continuous loss of ATP synthase organization at cristae ridges. We found that cardiolipin (CL) specifically buffers the IMM against curvature loss, an effect that is independent of ATP synthase dimerization. To explain this interaction, we developed a continuum model for cristae tubule formation that integrates both lipid and protein-mediated curvatures. The model highlighted a snapthrough instability, which drives IMM collapse upon small changes in membrane properties. We also showed that CL is essential in low oxygen conditions that promote PL saturation. These results demonstrate that the mechanical function of CL is dependent on the surrounding lipid and protein components of the IMM.

Membrane free-energy landscapes derived from atomistic dynamics explain nonuniversal cholesterol-induced stiffening

All lipid membranes have inherent morphological preferences and resist deformation. Yet adaptations in membrane shape can and do occur at multiple length scales. While this plasticity is crucial for cellular physiology, the factors controlling the morphological energetics of lipid bilayers and the dominant mechanisms of membrane remodeling remain to be fully understood. An ongoing debate regarding the universality of the stiffening effect of cholesterol underscores the challenges facing this field, both experimentally and theoretically, even for simple lipid mixtures. On the computational side, we have argued that enhanced-sampling all-atom molecular dynamics simulations are uniquely suited for the quantification of membrane conformational energetics, as they minimize a priori assumptions and permit analysis of bilayers in deformed states. To showcase this approach, we examine reported inconsistencies between alternative experimental measurements of bending moduli for cholesterol-enriched membranes. Specifically, we analyze lipid bilayers with different chain saturation and compute free-energy landscapes for curvature deformations distributed over areas from ∼5 to ∼60 nm2 . These enhanced simulations, totaling over 100 μs of sampling time, enable us to directly quantify both bending and tilt moduli and to dissect the contributing factors and molecular mechanisms of curvature generation at each length scale. Our results show that the effects of cholesterol on bending rigidity are lipid-specific and suggest that this specificity arises from differences in the torsional dynamics of the acyl chains. In summary, we demonstrate that quantitative relationships can now be established between lipid structure and bending energetics, paving the way for addressing open fundamental questions in cell membrane mechanics.

Utilizing Machine Learning to Greatly Expand the Range and Accuracy of Bottom-Up Coarse-Grained Models through Virtual Particles

Coarse-grained (CG) models parametrized using atomistic reference data, i.e., "bottom up" CG models, have proven useful in the study of biomolecules and other soft matter. However, the construction of highly accurate, low resolution CG models of biomolecules remains challenging. We demonstrate in this work how virtual particles, CG sites with no atomistic correspondence, can be incorporated into CG models within the context of relative entropy minimization (REM) as latent variables. The methodology presented, variational derivative relative entropy minimization (VD-REM), enables optimization of virtual particle interactions through a gradient descent algorithm aided by machine learning. We apply this methodology to the challenging case of a solvent-free CG model of a 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) lipid bilayer and demonstrate that introduction of virtual particles captures solvent-mediated behavior and higher-order correlations which REM alone cannot capture in a more standard CG model based only on the mapping of collections of atoms to the CG sites.

Simulated dynamic cholesterol redistribution favors membrane fusion pore constriction

Endo- and exocytosis proceed through a highly strained membrane fusion pore topology regardless of the aiding protein machinery. The membrane's lipid components bias fusion pores toward expansion or closure, modifying the necessary work done by proteins. Cholesterol, a key component of plasma membranes, promotes both inverted lipid phases with concave leaflets (i.e., negative total curvature, which thins the leaflet) and flat bilayer phases with thick, ordered hydrophobic interiors. We demonstrate by theory and simulation that both leaflets of nascent catenoidal fusion pores have negative total curvature. Furthermore, the hydrophobic core of bilayers with strong negative Gaussian curvature is thinned. Therefore, it is an open question whether cholesterol will be enriched in these regions because of the negative total curvature or depleted because of the membrane thinning. Here, we compare all-atom molecular dynamics simulations (built using a procedure to create specific fusion pore geometries) and theory to understand the underlying reasons for lipid redistribution on fusion pores. Our all-atom molecular dynamics simulations resolve this question by showing that cholesterol is strongly excluded from the thinned neck of fusion and fission pores, revealing that thickness (and/or lipid order) influences cholesterol distributions more than curvature. The results imply that cholesterol exclusion can drive fusion pore closure by creating a small, cholesterol-depleted zone in the neck. This model agrees with literature evidence that membrane reshaping is connected to cholesterol-dependent lateral phase separation.

Evolution of the Concepts of Architecture and Supramolecular Dynamics of the Plasma Membrane

The plasma membrane (PM) has undergone important conceptual changes during the history of scientific research, although it is undoubtedly a cellular organelle that constitutes the first defining characteristic of cellular life. Throughout history, the contributions of countless scientists have been published, each one of them with an enriching contribution to the knowledge of the structure-location and function of each structural component of this organelle, as well as the interaction between these and other structures. The first published contributions on the plasmatic membrane were the transport through it followed by the description of the structure: lipid bilayer, associated proteins, carbohydrates bound to both macromolecules, association with the cytoskeleton and dynamics of these components.. The data obtained experimentally from each researcher were represented in graphic configurations, as a language that facilitates the understanding of cellular structures and processes. This paper presents a review of some of the concepts and models proposed about the plasma membrane, emphasizing the components, the structure, the interaction between them and the dynamics. The work is illustrated with resignified 3D diagrams to visualize the changes that occurred during the history of the study of this organelle. Schemes were redrawn in 3D from the original articles...

Allosteric modulation of integral protein activity by differential stress in asymmetric membranes

The activity of integral membrane proteins is tightly coupled to the properties of the surrounding lipid matrix. In particular, transbilayer asymmetry, a hallmark of all plasma membranes, might be exploited to control membrane-protein activity. Here, we hypothesized that the membrane-embedded enzyme outer membrane phospholipase A (OmpLA) is susceptible to the lateral pressure differences that build up between such asymmetric membrane leaflets. Upon reconstituting OmpLA into synthetic, chemically well-defined phospholipid bilayers exhibiting different lateral pressure profiles, we indeed observed a substantial decrease in the enzyme's hydrolytic activity with increasing membrane asymmetry. No such effects were observed in symmetric mixtures of the same lipids. To quantitatively rationalize how the differential stress in asymmetric lipid bilayers inhibits OmpLA, we developed a simple allosteric model within the lateral pressure framework. Thus, we find that membrane asymmetry can serve as the dominant factor in controlling membrane-protein activity, even in the absence of specific, chemical cues or other physical membrane determinants such as hydrophobic mismatch.

Screening for bilayer-active and likely cytotoxic molecules reveals bilayer-mediated regulation of cell function

A perennial problem encountered when using small molecules (drugs) to manipulate cell or protein function is to assess whether observed changes in function result from specific interactions with a desired target or from less specific off-target mechanisms. This is important in laboratory research as well as in drug development, where the goal is to identify molecules that are unlikely to be successful therapeutics early in the process, thereby avoiding costly mistakes. We pursued this challenge from the perspective that many bioactive molecules (drugs) are amphiphiles that alter lipid bilayer elastic properties, which may cause indiscriminate changes in membrane protein (and cell) function and, in turn, cytotoxicity. Such drug-induced changes in bilayer properties can be quantified as changes in the monomer↔dimer equilibrium for bilayer-spanning gramicidin channels. Using this approach, we tested whether molecules in the Pathogen Box (a library of 400 drugs and drug-like molecules with confirmed activity against tropical diseases released by Medicines for Malaria Venture to encourage the development of therapies for neglected tropical diseases) are bilayer modifiers. 32% of the molecules in the Pathogen Box were bilayer modifiers, defined as molecules that at 10 µM shifted the monomer↔dimer equilibrium toward the conducting dimers by at least 50%. Correlation analysis of the molecules' reported HepG2 cell cytotoxicity to bilayer-modifying potency, quantified as the shift in the gramicidin monomer↔dimer equilibrium, revealed that molecules producing <25% change in the equilibrium had significantly lower probability of being cytotoxic than molecules producing >50% change. Neither cytotoxicity nor bilayer-modifying potency (quantified as the shift in the gramicidin monomer↔dimer equilibrium) was well predicted by conventional physico-chemical descriptors (hydrophobicity, polar surface area, etc.). We conclude that drug-induced changes in lipid bilayer properties are robust predictors of the likelihood of membrane-mediated off-target effects, including cytotoxicity.

OxPAPC stabilizes liquid-ordered domains in biomimetic membranes

Long-chain polyunsaturated fatty acids (PUFAs) are prone to nonenzymatic oxidation in response to differing environmental stressors and endogenous cellular sources. There is increasing evidence that phospholipids containing oxidized PUFA acyl chains control the inflammatory response. However, the underlying mechanism(s) of action by which oxidized PUFAs exert their functional effects remain unclear. Herein, we tested the hypothesis that replacement of 1-palmitoyl-2-arachidonyl-phosphatidylcholine (PAPC) with oxidized 1-palmitoyl-2-arachidonyl-phosphatidylcholine (oxPAPC) regulates membrane architecture. Specifically, with solid-state 2H NMR of biomimetic membranes, we investigated how substituting oxPAPC for PAPC modulates the molecular organization of liquid-ordered (Lo) domains. 2H NMR spectra for bilayer mixtures of 1,2-dipalmitoylphosphatidylcholine-d62 (an analog of DPPC deuterated throughout sn-1 and -2 chains) and cholesterol to which PAPC or oxPAPC was added revealed that replacing PAPC with oxPAPC disrupted molecular organization, indicating that oxPAPC does not mix favorably in a tightly packed Lo phase. Furthermore, unlike PAPC, adding oxPAPC stabilized 1,2-dipalmitoylphosphatidylcholine-d6-rich/cholesterol-rich Lo domains formed in mixtures with 1,2-dioleoylphosphatidylcholine while decreasing the molecular order within 1,2-dioleoylphosphatidylcholine-rich liquid-disordered regions of the membrane. Collectively, these results suggest a mechanism in which oxPAPC stabilizes Lo domains-by disordering the surrounding liquid-disordered region. Changes in the structure, and thereby functionality, of Lo domains may underly regulation of plasma membrane-based inflammatory signaling by oxPAPC.

Initiation and evolution of pores formed by influenza fusion peptides probed by lysolipid inclusion

The fusion peptide (FP) domain is necessary for the fusogenic activity of spike proteins in a variety of enveloped viruses, allowing the virus to infect the host cell, and is the only part of the protein that interacts directly with the target membrane lipid tails during fusion. There are consistent findings of poration by this domain in experimental model membrane systems, and, in certain conditions, the isolated FPs can generate pores. Here, we use molecular dynamics simulations to investigate the specifics of how these FP-induced pores form in membranes with different compositions of lysolipid and POPC. The simulations show that pores form spontaneously at high lysolipid concentrations via hybrid intermediates, where FP aggregates in the cis leaflet tilt to form a funnel-like structure that spans the leaflet and locally reduces the hydrophobic thickness that must be traversed by water to form a pore. By restraining a single FP within an FP aggregate to this tilted conformation, pores can be formed in lower-lysolipid-content membranes, including pure POPC, on the 100-ns timescale, much more rapidly than in unbiased simulations in bilayers with the same composition. The pore formation pathway is similar to the spontaneous formation in high lysolipid concentrations. Depending on the membrane composition, the pores can be metastable (as seen in POPC) or lead to membrane rupture.

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.

Surface viscosities of lipid bilayers determined from equilibrium molecular dynamics simulations

Lipid membrane viscosity is critical to biological function. Bacterial cells grown in different environments alter their lipid composition in order to maintain a specific viscosity, and membrane viscosity has been linked to the rate of cellular respiration. To understand the factors that determine the viscosity of a membrane, we ran equilibrium all-atom simulations of single component lipid bilayers and calculated their viscosities. The viscosity was calculated via a Green-Kubo relation, with the stress-tensor autocorrelation function modeled by a stretched exponential function. By simulating a series of lipids at different temperatures, we establish the dependence of viscosity on several aspects of lipid chemistry, including hydrocarbon chain length, unsaturation, and backbone structure. Sphingomyelin is found to have a remarkably high viscosity, roughly 20 times that of DPPC. Furthermore, we find that inclusion of the entire range of the dispersion interaction increases viscosity by up to 140%. The simulated viscosities are similar to experimental values obtained from the rotational dynamics of small chromophores and from the diffusion of integral membrane proteins but significantly lower than recent measurements based on the deformation of giant vesicles.

Membrane free-energy landscapes derived from atomistic dynamics explain nonuniversal cholesterol-induced stiffening

All lipid membranes have inherent morphological preferences and resist deformation. Yet adaptations in membrane shape can and do occur at multiple length scales. While this plasticity is crucial for cellular physiology, the factors controlling the morphological energetics of lipid bilayers and the dominant mechanisms of membrane remodeling remain unclear. An ongoing debate regarding the universality of the stiffening effect of cholesterol underscores the challenges facing this field, both experimentally and theoretically, even for simple lipid mixtures. On the computational side, we have argued that enhanced- sampling all-atom molecular dynamics simulations are uniquely suited for quantification of membrane conformational energetics, not only because they minimize a-priori assumptions, but also because they permit analysis of bilayers in deformed states. To showcase this approach, we examine reported inconsistencies between alternative experimental measurements of bending moduli for cholesterol-enriched membranes. Specifically, we analyze lipid bilayers with different chain saturation, and compute free-energy landscapes for curvature deformations distributed over areas from ∼5 to ∼60 nm 2 . These enhanced simulations, totaling over 100 microseconds of sampling time, enable us to directly quantify both bending and tilt moduli, and to dissect the contributing factors and molecular mechanisms of curvature generation at each length scale. Our results show that cholesterol effects are lipid-specific, in agreement with giantvesicle measurements, and explain why experiments probing nanometer scale lipid dynamics diverge. In summary, we demonstrate that quantitative structure-mechanics relationships can now be established for heterogenous membranes, paving the way for addressing open fundamental questions in cell membrane mechanics.

Significance

Elucidating the energetics and mechanisms of membrane remodeling is an essential step towards understanding cell physiology. This problem is challenging, however, because membrane bending involves both large-scale and atomic-level dynamics, which are difficult to measure simultaneously. A recent controversy regarding the stiffening effect of cholesterol, which is ubiquitous in animal cells, illustrates this challenge. We show how enhanced molecular-dynamics simulations can bridge this length-scale gap and reconcile seemingly incongruent observations. This approach facilitates a conceptual connection between lipid chemistry and membrane mechanics, thereby providing a solid basis for future research on remodeling phenomena, such as in membrane trafficking or viral infection.

Insights into autoregulation of a membrane protein complex by its cytoplasmic domains

Membrane transporters mediate the passage of molecules across membranes and are essential for cellular function. While the transmembrane region of these proteins is responsible for substrate transport, often the cytoplasmic regions are required for modulating their activity. However, it can be difficult to obtain atomic-resolution descriptions of these autoregulatory domains by classical structural biology techniques, especially if they lack a single, defined structure. The betaine permease, BetP, a homotrimer, is a prominent and well-studied example of a membrane protein whose autoregulation depends on cytoplasmic N- and C-terminal segments. These domains sense and transduce changes in K+ concentration and in lipid bilayer properties caused by osmotic stress. However, structural data for these terminal domains is incomplete, which hinders a clear description of the molecular mechanism of autoregulation. Here we used microsecond-scale molecular simulations of the BetP trimer to compare reported conformations of the 45-amino-acid long C-terminal tails. The simulations provide support for the idea that the conformation derived from electron microscopy (EM) data represents a more stable global orientation of the C-terminal segment under downregulating conditions while also providing a detailed molecular description of its dynamics and highlighting specific interactions with lipids, ions, and neighboring transporter subunits. A missing piece of the molecular puzzle is the N-terminal segment, whose dynamic nature has prevented structural characterization. Using Rosetta to generate ensembles of de novo conformations in the context of the EM-derived structure robustly identifies two features of the N-terminal tail, namely 1) short helical elements and 2) an orientation that would confine potential interactions to the protomer in the counterclockwise direction (viewed from the cytoplasm). Since each C-terminal tail only contacts the protomer in the clockwise direction, these results indicate an intricate interplay between the three protomers of BetP in the downregulated protein and a multidirectionality that may facilitate autoregulation of transport.

Brominated lipid probes expose structural asymmetries in constricted membranes

Lipids in biological membranes are thought to be functionally organized, but few experimental tools can probe nanoscale membrane structure. Using brominated lipids as contrast probes for cryo-EM and a model ESCRT-III membrane-remodeling system composed of human CHMP1B and IST1, we observed leaflet-level and protein-localized structural lipid patterns within highly constricted and thinned membrane nanotubes. These nanotubes differed markedly from protein-free, flat bilayers in leaflet thickness, lipid diffusion rates and lipid compositional and conformational asymmetries. Simulations and cryo-EM imaging of brominated stearoyl-docosahexanenoyl-phosphocholine showed how a pair of phenylalanine residues scored the outer leaflet with a helical hydrophobic defect where polyunsaturated docosahexaenoyl tails accumulated at the bilayer surface. Combining cryo-EM of halogenated lipids with molecular dynamics thus enables new characterizations of the composition and structure of membranes on molecular length scales.

Determination of elastic parameters of lipid membranes from simulation under varied external pressure

Many cellular processes such as endocytosis, exocytosis, and vesicle trafficking involve membrane deformations, which can be analyzed in the framework of the elastic theories of lipid membranes. These models operate with phenomenological elastic parameters. A connection between these parameters and the internal structure of lipid membranes can be provided by three-dimensional (3D) elastic theories. Considering a membrane as a 3D layer, Campelo et al. [F. Campelo et al., Adv. Colloid Interface Sci. 208, 25 (2014)10.1016/j.cis.2014.01.018] developed a theoretical basis for the calculation of elastic parameters. In this work we generalize and improve this approach by considering a more general condition of global incompressibility instead of local incompressibility. Crucially, we find an important correction to the theory of Campelo et al., which if not taken into account leads to a significant miscalculation of elastic parameters. With the total volume conservation taken into account, we derive an expression for the local Poisson's ratio, which determines how the local volume changes upon stretching and permits a more precise determination of elastic parameters. Also, we substantially simplify the procedure by calculating the derivatives of the moments of the local tension with respect to stretching instead of calculating the local stretching modulus. We obtain a relation between the Gaussian curvature modulus as a function of stretching and the bending modulus, showing that these two elastic parameters are not independent, as was previously assumed. The proposed algorithm is applied to membranes composed of pure dipalmitoylphosphatidylcholine (DPPC), dioleoylphosphatidylcholine (DOPC), and their mixture. The following elastic parameters of these systems are obtained: the monolayer bending and stretching moduli, spontaneous curvature, neutral surface position, and local Poisson's ratio. It is shown that the bending modulus of the DPPC/DOPC mixture follows a more complex trend than predicted by the classical Reuss averaging, which is often employed in theoretical frameworks.

Interactions of Surfactants with the Bacterial Cell Wall and Inner Membrane: Revealing the Link between Aggregation and Antimicrobial Activity

Surfactants with their intrinsic ability to solubilize lipid membranes are widely used as antibacterial agents, and their interactions with the bacterial cell envelope are complicated by their differential aggregation tendencies. We present a combined experimental and molecular dynamics investigation to unravel the molecular basis for the superior antimicrobial activity and faster kill kinetics of shorter-chain fatty acid surfactant, laurate, when compared with the longer-chain surfactants studied in contact time assays with live Escherichia coli (E. coli). From all-atom molecular dynamics simulations, translocation events across peptidoglycan were the highest for laurate followed by sodium dodecyl sulfate, myristate, palmitate, oleate, and stearate. The translocation kinetics were positively correlated with the critical micellar concentration, which determined the free monomer surfactant concentration available for translocation across peptidoglycan. Interestingly, aggregates showed a lower propensity to translocate across the peptidoglycan layer and longer translocation times were observed for oleate, thereby revealing an intrinsic sieving property of the bacterial cell wall. Molecular dynamics simulations with surfactant-incorporated bacterial inner membranes revealed the greatest hydrophobic mismatch and membrane thinning in the presence of laurate when compared with the other surfactants. The enhanced antimicrobial efficacy of laurate over oleate was further verified by experiments with giant unilamellar vesicles, and electroporation molecular dynamics simulations revealed greater inner membrane poration tendency in the presence of laurate when compared with the longer-chain surfactants. Our study provides molecular insights into surfactant translocation across peptidoglycan and chain length-induced structural disruption of the inner membrane, which correlate with contact time kill efficacies observed as a function of chain length with E. coli. The insights gained from our study uncover unexplored barrier properties of the bacterial cell envelope to rationalize the development of antimicrobial formulations and therapeutics.

Magainin 2 and PGLa in bacterial membrane mimics IV: Membrane curvature and partitioning

We previously reported that the synergistically enhanced antimicrobial activity of magainin 2 (MG2a) and PGLa is related to membrane adhesion and fusion. Here, we demonstrate that equimolar mixtures of MG2a and L18W-PGLa induce positive monolayer curvature stress and sense, at the same time, positive mean and Gaussian bilayer curvatures already at low amounts of bound peptide. The combination of both abilities-membrane curvature sensing and inducing-is most likely the base for the synergistically enhanced peptide activity. In addition, our coarse-grained simulations suggest that fusion stalks are promoted by decreasing the free-energy barrier for their formation rather than by stabilizing their shape. We also interrogated peptide partitioning as a function of lipid and peptide concentration using tryptophan fluorescence spectroscopy and peptide-induced leakage of dyes from lipid vesicles. In agreement with a previous report, we find increased membrane partitioning of L18W-PGLa in the presence of MG2a. However, this effect does not prevail to lipid concentrations higher than 1 mM, above which all peptides associate with the lipid bilayers. This implies that synergistic effects of MG2a and L18W-PGLa in previously reported experiments with lipid concentrations >1 mM are due to peptide-induced membrane remodeling and not their specific membrane partitioning.

Planar aggregation of the influenza viral fusion peptide alters membrane structure and hydration, promoting poration

To infect, enveloped viruses employ spike protein, spearheaded by its amphipathic fusion peptide (FP), that upon activation extends out from the viral surface to embed into the target cellular membrane. Here we report that synthesized influenza virus FPs are membrane active, generating pores in giant unilamellar vesicles (GUV), and thus potentially explain both influenza virus' hemolytic activity and the liposome poration seen in cryo-electron tomography. Experimentally, FPs are heterogeneously distributed on the GUV at the time of poration. Consistent with this heterogeneous distribution, molecular dynamics (MD) simulations of asymmetric bilayers with different numbers of FPs in one leaflet show FP aggregation. At the center of FP aggregates, a profound change in the membrane structure results in thinning, higher water permeability, and curvature. Ultimately, a hybrid bilayer nanodomain forms with one lipidic leaflet and one peptidic leaflet. Membrane elastic theory predicts a reduced barrier to water pore formation when even a dimer of FPs thins the membrane as above, and the FPs of that dimer tilt, to continue the leaflet bending initiated by the hydrophobic mismatch between the FP dimer and the surrounding lipid.

Remodeling of the Plasma Membrane by Surface-Bound Protein Monomers and Oligomers: The Critical Role of Intrinsically Disordered Regions

The plasma membrane (PM) of cells is a dynamic structure whose morphology and composition is in constant flux. PM morphologic changes are particularly relevant for the assembly and disassembly of signaling platforms involving surface-bound signaling proteins, as well as for many other mechanochemical processes that occur at the PM surface. Surface-bound membrane proteins (SBMP) require efficient association with the PM for their function, which is often achieved by the coordinated interactions of intrinsically disordered regions (IDRs) and globular domains with membrane lipids. This review focuses on the role of IDR-containing SBMPs in remodeling the composition and curvature of the PM. The ability of IDR-bearing SBMPs to remodel the Gaussian and mean curvature energies of the PM is intimately linked to their ability to sort subsets of phospholipids into nanoclusters. We therefore discuss how IDRs of many SBMPs encode lipid-binding specificity or facilitate cluster formation, both of which increase their membrane remodeling capacity, and how SBMP oligomers alter membrane shape by monolayer surface area expansion and molecular crowding.

Conformations of Three Types of Ultra-Long-Chain Fatty Acids in Multicomponent Lipid Bilayers

Ultra-long-chain fatty acids (ULCFAs) are biosynthesized in certain types of tissues, but their biological roles remain unknown. Here, we report how the conformation of ULCFAs depends on the length and unsaturated-bond ratio of the ultra-long chains and the composition of the host bilayer membrane using molecular dynamics simulations. The ultra-long chain of ULCFAs flips between the two leaflets and fluctuates among three conformations: elongated, L-shaped, and turned. Furthermore, we found that the saturated ultra-long chain exhibited an elongated conformation more frequently than the unsaturated chain. In addition, the truncation of the ultra-long chain at C26 had little effect on the remaining ULCFAs. ULCFAs respond to lipid-density differences in the two leaflets, and the ratio of the elongated and turned conformations changed to reduce this difference. However, in cholesterol-containing membranes, ULCFAs exhibit no density difference after the flip-flop of cholesterol removes the difference.