Dynamics in atomistic simulations of phospholipid membranes: Nuclear magnetic resonance relaxation rates and lateral diffusion

Brownian motion of soft particles near a fluctuating lipid bilayer

The dynamics of a soft particle suspended in a viscous fluid can be changed by the presence of an elastic boundary. Understanding the mechanisms and dynamics of soft-soft surface interactions can provide valuable insights into many important research fields, including biomedical engineering, soft robotics development, and materials science. This work investigates the anomalous transport properties of a soft nanoparticle near a visco-elastic interface, where the particle consists of a polymer assembly in the form of a micelle and the interface is represented by a lipid bilayer membrane. Mesoscopic simulations using a dissipative particle dynamics model are performed to examine the impact of micelle's proximity to the membrane on its Brownian motion. Two different sizes are considered, which correspond to ≈10-20nm in physical units. The wavelengths typically seen by the largest micelle fall within the range of wavenumbers where the Helfrich model captures fairly well the bilayer mechanical properties. Several independent simulations allowed us to compute the micelle trajectories during an observation time smaller than the diffusive time scale (whose order of magnitude is similar to the membrane relaxation time of the largest wavelengths), this time scale being hardly accessible by experiments. From the probability density function of the micelle normal position with respect to the membrane, it is observed that the position remains close to the starting position during ≈0.05τd (where τd corresponds to the diffusion time), which allowed us to compare the negative excess of mean-square displacement (MSD) to existing theories. In that time range, the MSD exhibits different behaviors along parallel and perpendicular directions. When the micelle is sufficiently close to the bilayer (its initial distance from the bilayer equals approximately twice its gyration radius), the micelle motion becomes quickly subdiffusive in the normal direction. Moreover, the temporal evolution of the micelle MSD excess in the perpendicular direction follows that of a nanoparticle near an elastic membrane. However, in the parallel direction, the MSD excess is rather similar to that of a nanoparticle near a liquid interface.

Free Energy Surface and Molecular Mechanism of Slow Structural Transitions in Lipid Bilayers

Lipid membrane remodeling, crucial for many cellular processes, is governed by the coupling of membrane structure and shape fluctuations. Given the importance of the ∼ nm length scale, details of the transition intermediates for conformational change are not fully captured by a continuum-mechanical description. Slow dynamics and the lack of knowledge of reaction coordinates (RCs) for biasing methods pose a challenge for all-atom (AA) simulations. Here, we map system dynamics on Langevin dynamics in a normal mode space determined from an elastic network model representation for the lipid-water Hamiltonian. AA molecular dynamics (MD) simulations are used to determine model parameters, and Langevin dynamics predictions for bilayer structural, mechanical, and dynamic properties are validated against MD simulations and experiments. Transferability to describe the dynamics of a larger lipid bilayer and a heterogeneous membrane-protein system is assessed. A set of generic RCs for pore formation in two tensionless bilayers is obtained by coupling Langevin dynamics to the underlying energy landscape for membrane deformations. Structure evolution is carried out by AA MD, wherein the generic RCs are used in a path metadynamics or an umbrella sampling simulation to determine the thermodynamics of pore formation and its molecular determinants, such as the role of distinct bilayer motions, lipid solvation, and lipid packing.

Standard Binding Free Energy and Membrane Desorption Mechanism for a Phospholipase C

Peripheral membrane proteins (PMPs) bind temporarily to cellular membranes and play important roles in signaling, lipid metabolism, and membrane trafficking. Obtaining accurate membrane-PMP affinities using experimental techniques is more challenging than for protein-ligand affinities in an aqueous solution. At the theoretical level, calculation of the standard protein-membrane binding free energy using molecular dynamics simulations remains a daunting challenge owing to the size of the biological objects at play, the slow lipid diffusion, and the large variation in configurational entropy that accompanies the binding process. To overcome these challenges, we used a computational framework relying on a series of potential-of-mean-force (PMF) calculations including a set of geometrical restraints on collective variables. This methodology allowed us to determine the standard binding free energy of a PMP to a phospholipid bilayer using an all-atom force field. Bacillus thuringiensis phosphatidylinositol-specific phospholipase C (BtPI-PLC) was chosen due to its importance as a virulence factor and owing to the host of experimental affinity data available. We computed a standard binding free energy of -8.2 ± 1.4 kcal/mol in reasonable agreement with the reported experimental values (-6.6 ± 0.2 kcal/mol). In light of the 2.3-μs separation PMF calculation, we investigated the mechanism whereby BtPI-PLC disengages from interactions with the lipid bilayer during separation. We describe how a short amphipathic helix engages in transitory interactions to ease the passage of its hydrophobes through the interfacial region upon desorption from the bilayer.

Computational study of DMPC liposomes loaded with the N-(2-Hydroxyphenyl)-2-propylpentanamide (HO-AAVPA) and determination of its antiproliferative activity in vitro in NIH-3T3 cells

N-(2-Hydroxyphenyl)-2-propylpentanamide (HO-AAVPA) is a valproic acid (VPA) derivative that has shown promising antiproliferative effects in different cancer cell lines, such as A204, HeLa, and MDA-MB-231. However, its low water solubility could reduce its therapeutic effectiveness. To solve this problem, in this work, we incorporated HO-AAVPA into dimyristoyl-phosphatidylcholine (DMPC) liposomes in the presence or absence of cholesterol (CHOL). Using differential scanning calorimetry (DSC), we found that the transition enthalpy (ΔH_tr) of DMPC liposomes is reduced in the presence of CHOL and/or HO-AAVPA, indicating the favorable interactions between CHOL and/or HO-AAVPA and DMPC. Further, by molecular dynamics simulations it was possible to observed that HO-AAVPA migrates from the center of the bilayer toward the water and lipid interface of the DPMC bilayer systems exposing the amine group to water and the aliphatic chain toward the interior of the bilayer. As a consequence, we observed an ordering of the lipid bilayer. Moreover, CHOL harbors into the inner bilayer membrane, increasing the order parameter of the system. The liposomal solutions loaded with HO-AAVPA were tested in the NIH3T3 cell line, showing a reduction in cell proliferation compared to those cells presented without liposomes.Communicated by Ramaswamy H. Sarma.

Dielectric dispersion characteristics of the phospholipid bilayer with subnanometer resolution from terahertz to mid-infrared

There is growing interest in whether the myelinated nerve fiber acts as a dielectric waveguide to propagate terahertz to mid-infrared electromagnetic waves, which are presumed stable signal carrier for neurotransmission. The myelin sheath is formed as a multilamellar biomembrane structure, hence insights into the dielectric properties of the phospholipid bilayer is essential for a complete understanding of the myelinated fiber functioning. In this work, by means of atomistic molecular dynamics simulations of the dimyristoylphosphatidylcholine (DMPC) bilayer in water and numerical calculations of carefully layered molecules along with calibration of optical dielectric constants, we for the first time demonstrate the spatially resolved (in sub-nm) dielectric spectrum of the phospholipid bilayer in a remarkably wide range from terahertz to mid-infrared. More specifically, the membrane head regions exhibit both larger real and imaginary permittivities than that of the tail counterparts in the majority of the 1–100 THz band. In addition, the spatial variation of dielectric properties suggests advantageous propagation characteristics of the phospholipid bilayer in a relatively wide band of 55–85 THz, where the electromagnetic waves are well confined within the head regions.

Orientation dependence of inhomogeneous magnetization transfer and dipolar order relaxation rate in phospholipid bilayers

Inhomogeneous magnetization transfer (ihMT) is a novel MRI technique used to measure white matter myelination in the brain and spinal cord. In the brain, ihMT has a strong orientation dependence which is likely to arise from the anisotropy of dipolar couplings between protons on oriented lipids in the myelin bilayers. We measured the orientation dependence of the second moment (M₂) of the lineshape, dipolar order relaxation rate (R_1D), and ihMT ratio (ihMTR) in an oriented phospholipid bilayer at 9.4 T. We found a strong orientation dependence in all three parameters. ihMTR and R_1D were maximized when the bilayers were aligned perpendicular to B₀ and minimized near the magic angle (∼54.7°). M₂ followed an orientation dependence given by the second Legendre polynomial squared as predicted by the form of the secular dipolar Hamiltonian. These results were used to calculate the orientation dependence of R_1D and ihMTR in a diffusionless myelin sheath model, which showed ihMTR was maximised for fibers perpendicular to B₀ and minimised at 45°, similar to ex-vivo spinal cord with a larger prepulse frequency offset, but in contrast to in vivo brain findings. Adding fiber dispersion to this model smoothed the orientation dependence curve as expected. Our results suggest the importance of the effects of lipid diffusion and prepulse offset frequency on ihMTR.

Design and simulation of the liposomal model by using a coarse-grained molecular dynamics approach towards drug delivery goals

The simulated liposome models provide events in molecular biological science and cellular biology. These models may help to understand the cell membrane mechanisms, biological cell interactions, and drug delivery systems. In addition, the liposomes model may resolve specific issues such as membrane transports, ion channels, drug penetration in the membrane, vesicle formation, membrane fusion, and membrane protein function mechanism. One of the approaches to investigate the lipid membranes and the mechanism of their formation is by molecular dynamics (MD) simulations. In this study, we used the coarse-grained MD simulation approach and designed a liposome model system. To simulate the liposome model, we used phospholipids that are present in the structure of natural cell membranes (1,2-Dioleoyl-sn-glycero-3-phosphocholine (DOPC) and 1,2-Dioleoyl-sn-glycero-3-phosphoethanolamine (DOPE)). Simulation conditions such as temperature, ions, water, lipid concentration were performed based on experimental conditions. Our results showed a liposome model (ellipse vesicle structure) during the 2100 ns was formed. Moreover, the analysis confirmed that the stretched and ellipse structure is the best structure that could be formed. The eukaryotic and even the bacterial cells have elliptical and flexible structures. Usually, an elliptical structure is more stable than other assembled structures. The results indicated the assembly of the lipids is directed through short-range interactions (electrostatic interactions and, van der Waals interactions). Total energy (Van der Waals and electrostatic interaction energy) confirmed the designed elliptical liposome structure has suitable stability at the end of the simulation process. Our findings confirmed that phospholipids DOPC and DOPE have a good tendency to form bilayer membranes (liposomal structure) based on their geometric shapes and chemical-physical properties. Finally, we expected the simulated liposomal structure as a simple model to be useful in understanding the function and structure of biological cell membranes. Furthermore, it is useful to design optimal, suitable, and biocompatible liposomes as potential drug carriers.

How stereochemistry of lipid components can affect lipid organization and the route of liposome internalization into cells

Though liposome-based drugs are in clinical use, the mechanism of cell internalization of liposomes is yet an object of controversy. The present experimental investigation, carried out on human glioblastoma cells, indicated different internalization routes for two diastereomeric liposomes. Molecular dynamics simulations of the lipid bilayers of the two formulations indicated that the different stereochemistry of a lipid component controls some parameters such as area per lipid molecule and fluidity of lipid membranes, surface potential and water organization at the lipid/water interface, all of which affect the interaction with biomolecules and cell components.

Optimization of Slipids Force Field Parameters Describing Headgroups of Phospholipids

The molecular mechanics force field Slipids developed in a series of works by Jämbeck and Lyubartsev (J. Phys. Chem. B 2012, 116, 3164-3179; J. Chem. Theory Comput. 2012, 8, 2938-2948) generally provides a good description of various lipid bilayer systems. However, it was also found that order parameters of C-H bonds in the glycerol moiety of the phosphatidylcholine headgroup deviate significantly from NMR results. In this work, the dihedral force field parameters have been reparameterized in order to improve the agreement with experiment. For this purpose, we have computed energies for a large amount of lipid headgroup conformations using density functional theory on the B3P86/cc-pvqz level and optimized dihedral angle parameters simultaneously to provide the best fit to the quantum chemical energies. The new parameter set was validated for three lipid bilayer systems against a number of experimental properties including order parameters, area per lipid, scattering form factors, bilayer thickness, area compressibility and lateral diffusion coefficients. In addition, the order parameter dependence on cholesterol content in the POPC bilayer was investigated. It is shown that the new force field significantly improves agreement with the experimental order parameters for the lipid headgroup while keeping good agreement with other experimentally measured properties.

Accelerating Membrane Simulations with Hydrogen Mass Repartitioning

The time step of atomistic molecular dynamics (MD) simulations is determined by the fastest motions in the system and is typically limited to 2 fs. An increasingly popular approach is to increase the mass of the hydrogen atoms to ∼3 amu and decrease the mass of the parent atom by an equivalent amount. This approach, known as hydrogen-mass repartitioning (HMR), permits time steps up to 4 fs with reasonable simulation stability. While HMR has been applied in many published studies to date, it has not been extensively tested for membrane-containing systems. Here, we compare the results of simulations of a variety of membranes and membrane-protein systems run using a 2 fs time step and a 4 fs time step with HMR. For pure membrane systems, we find almost no difference in structural properties, such as area-per-lipid, electron density profiles, and order parameters, although there are differences in kinetic properties such as the diffusion constant. Conductance through a porin in an applied field, partitioning of a small peptide, hydrogen-bond dynamics, and membrane mixing show very little dependence on HMR and the time step. We also tested a 9 Å cutoff as compared to the standard CHARMM cutoff of 12 Å, finding significant deviations in many properties tested. We conclude that HMR is a valid approach for membrane systems, but a 9 Å cutoff is not.

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

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

Entropic effects enable life at extreme temperatures

Maintaining membrane integrity is a challenge at extreme temperatures. Biochemical synthesis of membrane-spanning lipids is one adaptation that organisms such as thermophilic archaea have evolved to meet this challenge and preserve vital cellular function at high temperatures. The molecular-level details of how these tethered lipids affect membrane dynamics and function, however, remain unclear. Using synthetic monolayer-forming lipids with transmembrane tethers, here, we reveal that lipid tethering makes membrane permeation an entropically controlled process that helps to limit membrane leakage at elevated temperatures relative to bilayer-forming lipid membranes. All-atom molecular dynamics simulations support a view that permeation through membranes made of tethered lipids reduces the torsional entropy of the lipids and leads to tighter lipid packing, providing a molecular interpretation for the increased transition-state entropy of leakage.

Lipid lateral self-diffusion drop at liquid-gel phase transition

A drop of lipid lateral self-diffusion coefficient at the liquid-gel phase transition in lipid membranes is calculated. So far this drop was missing theoretical description. Our microscopic model captures so-called subdiffusion regime, which takes place on 1 ps-100 ns timescale and reveals a jump of self-diffusion coefficient. Calculation of the jump is based on our recent study of liquid-gel phase transition. Subdiffusive regime is described within the free volume theory. Calculated values of self-diffusion coefficient are in agreement with quasielastic neutron scattering measurements. Self-diffusion coefficient is found to be composed of two factors: one is related to an area per lipid change at the phase transition, and the other one is due to an order of magnitude change in the stiffness of entropic repulsive potential.

Rapid diffusion of cholesterol along polyunsaturated membranes via deep dives

Cholesterol regulates the function of membrane proteins either via direct or membrane-mediated effects. Therefore, its ready availability is crucial for many protein-governed cellular processes. Recent studies suggest that cholesterol can partition to the core of polyunsaturated membranes, where cholesterol binding sites of many membrane proteins are also located. This core region is characterized by a lower viscosity. Therefore, we hypothesized that cholesterol partitioning into the membrane interior increases the rate of its diffusion in polyunsaturated membrane environments. We studied the behavior of cholesterol in membranes with increasing level of lipid chain unsaturation using a combination of atomistic and coarse-grained molecular dynamics simulations. Our simulations suggest a strong correlation between entropy-driven enhanced cholesterol partitioning to the membrane core and its faster lateral diffusion, which indicates that the less viscous membrane core indeed provides an efficient means for cholesterol movement in polyunsaturated membrane environments.

Calcium-Induced Lipid Nanocluster Structures: Sculpturing of the Plasma Membrane

The plasma membrane of the cell is a complex, tightly regulated, heterogeneous environment shaped by proteins, lipids, and small molecules. Ca²⁺ ions are important cellular messengers, spatially separated from anionic lipids. After cell injury, disease, or apoptotic events, anionic lipids are externalized to the outer leaflet of the plasma membrane and encounter Ca²⁺, resulting in dramatic changes in the plasma membrane structure and initiation of signaling cascades. Despite the high chemical and biological significance, the structures of lipid-Ca²⁺ nanoclusters are still not known. Previously, we demonstrated by solid-state nuclear magnetic resonance (NMR) spectroscopy that upon binding to Ca²⁺, individual phosphatidylserine lipids populate two distinct yet-to-be-characterized structural environments. Here, we concurrently employ extensive all-atom molecular dynamics (MD) simulations with our accelerated membrane mimetic and detailed NMR measurements to identify lipid-Ca²⁺ nanocluster conformations. We find that major structural characteristics of these nanoclusters, including interlipid pair distances and chemical shifts, agree with observable NMR parameters. Simulations reveal that lipid-ion nanoclusters are shaped by two characteristic, long-lived lipid structures induced by divalent Ca²⁺. Using ab initio quantum mechanical calculations of chemical shifts on MD-captured lipid-ion complexes, we show that computationally observed conformations are validated by experimental NMR data. Both NMR measurements of diluted specifically labeled lipids and MD simulations reveal that the basic structural unit that reshapes the membrane is a Ca²⁺-coordinated phosphatidylserine tetramer. Our combined computational and experimental approach presented here can be applied to other complex systems in which charged membrane-active molecular agents leave structural signatures on lipids.

Molecular dynamics approach to probe the antigenicity of PagN - an outer membrane protein of Salmonella Typhi

PagN is a highly immunogenic 27-kDa outer membrane adhesin present in Salmonella Typhi. It plays a major role in the pathogenesis of typhoid fever and has emerged as a strong vaccine candidate. In this report, we predict the three-dimensional structure of PagN and describe the conformational dynamics associated with its four extracellular loops based on two 100-ns molecular dynamics simulations at 300 and 310 K. The formation and deformation of the secondary structures on these loops were also investigated during the simulations which revealed loops L1 and L2 to be highly flexible, whereas the relative flexibility of loops L3 and L4 was minimal. Essential dynamics and principal component analysis deciphered more realistic dynamic behaviours of the loops, particularly at 310 K. Moreover, our epitope predictions suggest that the antigenic peptides for B-cell recognition are located within the loops L1 and L2, while those for T-cell recognition are located within the loops L3 and L4. The binding specificities of the antigenic peptides towards specific human MHC-I and MHC-II HLA alleles closely resembled the stability of the loops L3 and L4 inferred from the simulations. Finally, we identified potential antigenic peptides in the flexible (L1 and L2) as well as stable (L3 and L4) regions of PagN for both B- and T-cell recognitions, which can help in developing effective sub-unit vaccines.

Extension of the Highly Mobile Membrane Mimetic to Transmembrane Systems through Customized in Silico Solvents

The mechanics of the protein-lipid interactions of transmembrane proteins are difficult to capture with conventional atomic molecular dynamics, due to the slow lateral diffusion of lipids restricting sampling to states near the initial membrane configuration. The highly mobile membrane mimetic (HMMM) model accelerates lipid dynamics by modeling the acyl tails nearest to the membrane center as a fluid organic solvent while maintaining an atomic description of the lipid headgroups and short acyl tails. The HMMM has been applied to many peripheral protein systems; however, the organic solvent used to date caused deformations in transmembrane proteins by intercalating into the protein and disrupting interactions between individual side chains. We ameliorate the effect of the solvent on transmembrane protein structure through the development of two new in silico Lennard-Jones solvents. The parameters for the new solvents were determined through an extensive parameter search in order to match the bulk properties of alkanes in a highly simplified model. Using these new solvents, we substantially improve the insertion free energy profiles of 10 protein side chain analogues across the entire bilayer. In addition, we reduce the intercalation of solvent into transmembrane systems, resulting in native-like transmembrane protein structures from five different topological classes within a HMMM bilayer. The parametrization of the solvents, in addition to their computed physical properties, is discussed. By combining high lipid lateral diffusion with intact transmembrane proteins, we foresee the developed solvents being useful to efficiently identify membrane composition inhomogeneities and lipid binding caused by the presence of membrane proteins.

Molecular dynamics study of lipid bilayers modeling the plasma membranes of mouse hepatocytes and hepatomas

Molecular dynamics (MD) calculations of lipid bilayers modeling the plasma membranes of normal mouse hepatocytes and hepatomas in water have been performed under physiological isothermal-isobaric conditions (310.15 K and 1 atm). The changes in the membrane properties induced by hepatic canceration were investigated and were compared with previous MD calculations included in our previous study of the changes in membrane properties induced by murine thymic canceration. The calculated model membranes for normal hepatocytes and hepatomas comprised 23 and 24 kinds of lipids, respectively. These included phosphatidylcholine, phosphatidylethanolamine, phosphatidylserine, phosphatidylinositol, sphingomyelin, lysophospholipids, and cholesterol. We referred to previously published experimental values for the mole fraction of the lipids adopted in the present calculations. The calculated structural and dynamic properties of the membranes such as lateral structure, order parameters, lateral self-diffusion constants, and rotational correlation times all showed that hepatic canceration causes plasma membranes to become more ordered laterally and less fluid. Interestingly, this finding contrasts with the less ordered structure and increased fluidity of plasma membranes induced by thymic canceration observed in our previous MD study.

Atomic-level description of protein-lipid interactions using an accelerated membrane model

Peripheral membrane proteins are structurally diverse proteins that are involved in fundamental cellular processes. Their activity of these proteins is frequently modulated through their interaction with cellular membranes, and as a result techniques to study the interfacial interaction between peripheral proteins and the membrane are in high demand. Due to the fluid nature of the membrane and the reversibility of protein-membrane interactions, the experimental study of these systems remains a challenging task. Molecular dynamics simulations offer a suitable approach to study protein-lipid interactions; however, the slow dynamics of the lipids often prevents sufficient sampling of specific membrane-protein interactions in atomistic simulations. To increase lipid dynamics while preserving the atomistic detail of protein-lipid interactions, in the highly mobile membrane-mimetic (HMMM) model the membrane core is replaced by an organic solvent, while short-tailed lipids provide a nearly complete representation of natural lipids at the organic solvent/water interface. Here, we present a brief introduction and a summary of recent applications of the HMMM to study different membrane proteins, complementing the experimental characterization of the presented systems, and we offer a perspective of future applications of the HMMM to study other classes of membrane proteins. This article is part of a Special Issue entitled: Membrane proteins edited by J.C. Gumbart and Sergei Noskov.

Effects of Lipid Tethering in Extremophile-Inspired Membranes on H(+)/OH(-) Flux at Room Temperature

This work explores the proton/hydroxide permeability (PH+/OH-) of membranes that were made of synthetic extremophile-inspired phospholipids with systematically varied structural elements. A fluorescence-based permeability assay was optimized to determine the effects on the PH+/OH- through liposome membranes with variations in the following lipid attributes: transmembrane tethering, tether length, and the presence of isoprenoid methyl groups on one or both lipid tails. All permeability assays were performed in the presence of a low concentration of valinomycin (10 nM) to prevent buildup of a membrane potential without artificially increasing the measured PH+/OH-. Surprisingly, the presence of a transmembrane tether did not impact PH+/OH- at room temperature. Among tethered lipid monolayers, PH+/OH- increased with increasing tether length if the number of carbons in the untethered acyl tail was constant. Untethered lipids with two isoprenoid methyl tails led to lower PH+/OH- values than lipids with only one or no isoprenoid tails. Molecular dynamics simulations revealed a strong positive correlation between the probability of observing water molecules in the hydrophobic core of these lipid membranes and their proton permeability. We propose that water penetration as revealed by molecular dynamics may provide a general strategy for predicting proton permeability through various lipid membranes without the need for experimentation.

Chloroform alters interleaflet coupling in lipid bilayers: an entropic mechanism

The interaction of the two leaflets of the plasmatic cell membrane is conjectured to play an important role in many cell processes. Experimental and computational studies have investigated the mechanisms that modulate the interaction between the two membrane leaflets. Here, by means of coarse-grained molecular dynamics simulations, we show that the addition of a small and polar compound such as chloroform alters interleaflet coupling by promoting domain registration. This is interpreted in terms of an entropic gain that would favour frequent chloroform commuting between the two leaflets. The implication of this effect is discussed in relation to the general anaesthetic action.

Atomistic resolution structure and dynamics of lipid bilayers in simulations and experiments

Accurate details on the sampled atomistic resolution structures of lipid bilayers can be experimentally obtained by measuring C-H bond order parameters, spin relaxation rates and scattering form factors. These parameters can be also directly calculated from the classical atomistic resolution molecular dynamics simulations (MD) and compared to the experimentally achieved results. This comparison measures the simulation model quality with respect to 'reality'. If agreement is sufficient, the simulation model gives an atomistic structural interpretation of the acquired experimental data. Significant advance of MD models is made by jointly interpreting different experiments using the same structural model. Here we focus on phosphatidylcholine lipid bilayers, which out of all model membranes have been studied mostly by experiments and simulations, leading to the largest available dataset. From the applied comparisons we conclude that the acyl chain region structure and rotational dynamics are generally well described in simulation models. Also changes with temperature, dehydration and cholesterol concentration are qualitatively correctly reproduced. However, the quality of the underlying atomistic resolution structural changes is uncertain. Even worse, when focusing on the lipid bilayer properties at the interfacial region, e.g. glycerol backbone and choline structures, and cation binding, many simulation models produce an inaccurate description of experimental data. Thus extreme care must be applied when simulations are applied to understand phenomena where the interfacial region plays a significant role. This work is done by the NMRlipids Open Collaboration project running at https://nmrlipids.blogspot.fi and https://github.com/NMRLipids. This article is part of a Special Issue entitled: Biosimulations edited by Ilpo Vattulainen and Tomasz Róg.

Calculation of Lipid-Bilayer Permeabilities Using an Average Force

Calculations of lipid bilayer permeabilities from first principles, using molecular simulations, would be valuable to rapidly assess the bioavailability of drug candidates, as well as to decipher, at the atomic level, the mechanisms that underlie the translocation of permeants. The most common theoretical approach, the solubility-diffusion model, requires determination of the free energy and the diffusivity as functions of the position of the permeant. Quantitative predictions of permeability have, however, been stymied by acute difficulties in calculating the diffusivity, inadequate sampling, and, most insidiously, systematic biases due to imperfections in the force field, simulation parameters, and the inherent limitations of the diffusive model. In the present work, we combine importance-sampling simulations employing an adaptive biasing force with a Bayesian-inference algorithm to determine the free energy and diffusivity with noteworthy precision and spatial resolution. In multimicrosecond simulations, we probe the sensitivity of the permeability estimates to different aspects of the methodology, including the truncation of short-range interactions, the thermostat, the force-field parameters of the permeant, the time scale over which the diffusivity is estimated, and the size of the simulated system. The force-field parameters and time scale dependence of the diffusivities impose the greatest uncertainties on the permeability estimates. Our simulations highlight the importance of membrane distortion due to the presence of the permeant, which may be partially suppressed if the bilayer patch is not large enough. We suggest that improvements to force fields and more robust kinetic models may be needed to reduce systematic errors below a factor of two.

Parametrization and Validation of Intramolecular Force Fields Derived from DFT Calculations

The energy and its first and second geometrical derivatives obtained by DFT calculations for a number of conformations of a single molecule are used to parametrize intramolecular force fields, suitable for computer simulations. A systematic procedure is proposed to adequately treat either fully atomistic or more simplified force fields, as within the united atom approach or other coarse grained models. The proposed method is tested and validated by performing molecular dynamics simulations on several different molecules, comparing the results with literature force fields and relevant experimental data. Particular emphasis is given to the united atom approach for flexible molecules characterized by "soft" torsional potentials which are known to retain a high degree of chemical specificity.

Mixed Mechanism of Lubrication by Lipid Bilayer Stacks

Although the key role of lipid bilayer stacks in biological lubrication is generally accepted, the mechanisms underlying their extreme efficiency remain elusive. In this article, we report molecular dynamics simulations of lipid bilayer stacks undergoing load and shear. When the hydration level is reduced, the velocity accommodation mechanism changes from viscous shear in hydration water to interlayer sliding in the bilayers. This enables stacks of hydrated lipid bilayers to act as efficient boundary lubricants for various hydration conditions, structures, and mechanical loads. We also propose an estimation for the friction coefficient; thanks to the strong hydration forces between lipid bilayers, the high local viscosity is not in contradiction with low friction coefficients.

Efficient Exploration of Membrane-Associated Phenomena at Atomic Resolution

Biological membranes constitute a critical component in all living cells. In addition to providing a conducive environment to a wide range of cellular processes, including transport and signaling, mounting evidence has established active participation of specific lipids in modulating membrane protein function through various mechanisms. Understanding lipid-protein interactions underlying these mechanisms at a sufficiently high resolution has proven extremely challenging, partly due to the semi-fluid nature of the membrane. In order to address this challenge computationally, multiple methods have been developed, including an alternative membrane representation termed highly mobile membrane mimetic (HMMM) in which lateral lipid diffusion has been significantly enhanced without compromising atomic details. The model allows for efficient sampling of lipid-protein interactions at atomic resolution, thereby significantly enhancing the effectiveness of molecular dynamics simulations in capturing membrane-associated phenomena. In this review, after providing an overview of HMMM model development, we will describe briefly successful application of the model to study a variety of membrane processes, including lipid-dependent binding and insertion of peripheral proteins, the mechanism of phospholipid insertion into lipid bilayers, and characterization of optimal tilt angle of transmembrane helices. We conclude with practical recommendations for proper usage of the model in simulation studies of membrane processes.

Model-free estimation of the effective correlation time for C-H bond reorientation in amphiphilic bilayers: (1)H-(13)C solid-state NMR and MD simulations

Molecular dynamics (MD) simulations give atomically detailed information on structure and dynamics in amphiphilic bilayer systems on timescales up to about 1 μs. The reorientational dynamics of the C-H bonds is conventionally verified by measurements of (13)C or (2)H nuclear magnetic resonance (NMR) longitudinal relaxation rates R1, which are more sensitive to motional processes with correlation times close to the inverse Larmor frequency, typically around 1-10 ns on standard NMR instrumentation, and are thus less sensitive to the 10-1000 ns timescale motion that can be observed in the MD simulations. We propose an experimental procedure for atomically resolved model-free estimation of the C-H bond effective reorientational correlation time τe, which includes contributions from the entire range of all-atom MD timescales and that can be calculated directly from the MD trajectories. The approach is based on measurements of (13)C R1 and R1ρ relaxation rates, as well as (1)H-(13)C dipolar couplings, and is applicable to anisotropic liquid crystalline lipid or surfactant systems using a conventional solid-state NMR spectrometer and samples with natural isotopic composition. The procedure is demonstrated on a fully hydrated lamellar phase of 1-palmitoyl-2-oleoyl-phosphatidylcholine, yielding values of τe from 0.1 ns for the methyl groups in the choline moiety and at the end of the acyl chains to 3 ns for the g1 methylene group of the glycerol backbone. MD simulations performed with a widely used united-atom force-field reproduce the τe-profile of the major part of the acyl chains but underestimate the dynamics of the glycerol backbone and adjacent molecular segments. The measurement of experimental τe-profiles can be used to study subtle effects on C-H bond reorientational motions in anisotropic liquid crystals, as well as to validate the C-H bond reorientation dynamics predicted in MD simulations of amphiphilic bilayers such as lipid membranes.

Modeling lipid raft domains containing a mono-unsaturated phosphatidylethanolamine species

An advanced coarse-grained model for “atypical” lipid rafts was built and validated to be employed in studies of membrane-protein interactions.

Conformational heterogeneity of α-synuclein in membrane

α-Synuclein (αS) is a natively disordered protein in solution, thought to be involved in the fusion of neurotransmitter vesicles to cellular membranes during neurotransmission. Monomeric αS has been previously characterized in two distinct membrane-associated conformations: a broken-helix structure, and an extended helix. By employing atomistic molecular dynamics and a novel membrane representation with significantly enhanced lipid mobility (HMMM), we investigate the process of spontaneous membrane binding of αS and the conformational dynamics of monomeric αS in its membrane-bound form. By repeatedly placing helical αS monomers in solution above a planar lipid bilayer and observing their spontaneous association and its spontaneous insertion into the membrane during twenty independent unbiased simulations, we are able to characterize αS in its membrane-bound state, suggesting that αS has a highly variable membrane insertion depth at equilibrium. Our simulations also capture two distinct states of αS, the starting broken-helix conformation seen in the micelle bound NMR structures, and a semi-extended helix. Analysis of lipid distributions near αS monomers indicates that the transition to a semi-extended helix is facilitated by concentration of phosphatidyl-serine headgroups along the inner edge of the protein. Such a lipid-mediated transition between helix-turn-helix and extended conformations of αS may also occur in vivo, and may be important for the physiological function of αS.

Diffusion and spectroscopy of water and lipids in fully hydrated dimyristoylphosphatidylcholine bilayer membranes

Microscopic structure and dynamics of water and lipids in a fully hydrated dimyristoylphosphatidylcholine phospholipid lipid bilayer membrane in the liquid-crystalline phase have been analyzed with all-atom molecular dynamics simulations based on the recently parameterized CHARMM36 force field. The diffusive dynamics of the membrane lipids and of its hydration water, their reorientational motions as well as their corresponding spectral densities, related to the absorption of radiation, have been considered for the first time using the present force field. In addition, structural properties such as density and pressure profiles, a deuterium-order parameter, surface tension, and the extent of water penetration in the membrane have been analyzed. Molecular self-diffusion, reorientational motions, and spectral densities of atomic species reveal a variety of time scales playing a role in membrane dynamics. The mechanisms of lipid motion strongly depend on the time scale considered, from fast ballistic translation at the scale of picoseconds (effective diffusion coefficients of the order of 10(-5) cm(2)/s) to diffusive flow of a few lipids forming nanodomains at the scale of hundreds of nanoseconds (diffusion coefficients of the order of 10(-8) cm(2)/s). In the intermediate regime of sub-diffusion, collisions with nearest neighbors prevent the lipids to achieve full diffusion. Lipid reorientations along selected directions agree well with reported nuclear magnetic resonance data and indicate two different time scales, one about 1 ns and a second one in the range of 2-8 ns. We associated the two time scales of reorientational motions with angular distributions of selected vectors. Calculated spectral densities corresponding to lipid and water reveal an overall good qualitative agreement with Fourier transform infrared spectroscopy experiments. Our simulations indicate a blue-shift of the low frequency spectral bands of hydration water as a result of its interaction with lipids. We have thoroughly analyzed the physical meaning of all spectral features from lipid atomic sites and correlated them with experimental data. Our findings include a "wagging of the tails" frequency around 30 cm(-1), which essentially corresponds to motions of the tail-group along the instantaneous plane formed by the two lipid tails, i.e., in-plane oscillations are clearly of bigger importance than those along the normal-to-the plane direction.

Ambidextrous binding of cell and membrane bilayers by soluble matrix metalloproteinase-12

Matrix metalloproteinases (MMPs) regulate tissue remodelling, inflammation and disease progression. Some soluble MMPs are inexplicably active near cell surfaces. Here we demonstrate the binding of MMP-12 directly to bilayers and cellular membranes using paramagnetic NMR and fluorescence. Opposing sides of the catalytic domain engage spin-labelled membrane mimics. Loops project from the β-sheet interface to contact the phospholipid bilayer with basic and hydrophobic residues. The distal membrane interface comprises loops on the other side of the catalytic cleft. Both interfaces mediate MMP-12 association with vesicles and cell membranes. MMP-12 binds plasma membranes and is internalized to hydrophobic perinuclear features, the nuclear membrane and inside the nucleus within minutes. While binding of TIMP-2 to MMP-12 hinders membrane interactions beside the active site, TIMP-2-inhibited MMP-12 binds vesicles and cells, suggesting compensatory rotation of its membrane approaches. MMP-12 association with diverse cell membranes may target its activities to modulate innate immune responses and inflammation.

Dynamics of lipids, cholesterol, and transmembrane α-helices from microsecond molecular dynamics simulations

Extensive all-atom molecular dynamics (∼24 μs total) allowed exploration of configurational space and calculation of lateral diffusion coefficients of the components of a protein-embedded, cholesterol-containing model bilayer. The three model membranes are composed of an ∼50/50 (by mole) dipalmitoylphosphatidylcholine (DPPC)/cholesterol bilayer and contained an α-helical transmembrane protein (HIV-1 gp41 TM). Despite the high concentration of cholesterol, normal Brownian motion was observed and the calculated diffusion coefficients (on the order of 10(-9) cm(2)/s) are consistent with experiments. Diffusion is sensitive to a variety of parameters, and a temperature difference of ∼4 K from thermostat artifacts resulted in 2-10-fold differences in diffusion coefficients and significant differences in lipid order, membrane thickness, and unit cell area. Also, the specific peptide sequence likely underlies the consistently observed faster diffusion in one leaflet. Although the simulations here present molecular dynamics (MD) an order of magnitude longer than those from previous studies, the three systems did not approach ergodicity. The distributions of cholesterol and DPPC around the peptides changed on the microsecond time scale, but not significantly enough to thoroughly explore configurational space. These simulations support conclusions of other recent microsecond MD in that even longer time scales are needed for equilibration of model membranes and simulations of more realistic cellular or viral bilayers.

Fast cholesterol flip-flop and lack of swelling in skin lipid multilayers

Atomistic simulations were performed on hydrated model lipid multilayers that are representative of the lipid matrix in the outer skin (stratum corneum). We find that cholesterol transfers easily between adjacent leaflets belonging to the same bilayer via fast orientational diffusion (tumbling) in the inter-leaflet disordered region, while at the same time there is a large free energy cost against swelling. This fast flip-flop may play an important role in accommodating the variety of curvatures that would be required in the three dimensional arrangement of the lipid multilayers in skin, and for enabling mechanical or hydration induced strains without large curvature elastic costs.

Assessing the efficiency of polymeric excipients by atomistic molecular dynamics simulations

We have performed all-atom molecular dynamics simulations of aqueous solutions of model oligomers of hydroxypropyl methylcellulose (HPMC) and hydroxypropyl methylcellulose acetate succinate (HPMCAS) excipients interacting with a representative poorly soluble active pharmaceutical ingredient (API), phenytoin. Simulations reveal formation of excipient-API complexes for some of the oligomers, which results in a reduction of API aggregation. API aggregation and diffusivity decreased with an increase in excipient content. Excipients form a "gel-like" phase spanning the simulation box beyond ∼10 wt %; API diffusivity within this gel phase is much smaller than API diffusivity without excipient, and decreases exponentially, by 5 orders of magnitude, with increased polymer concentration. Substantial differences are observed with variations in methyl, hydroxypropyl, acetate, and succinate substitution levels in the model oligomers and with the deprotonation state of succinate groups, with strongest interactions with hydrophobic phenytoin observed in the case of acetate substitution. These are used to develop quantitative measures of excipient-API interactions and excipient efficiency in the inhibition of API aggregation. We also find that for model oligomers based on Methocel E (manufactured by Dow Pharma & Food Solutions) chemistry, oligomers of length 10 monomers and simulation boxes of size 7 nm give results similar to those for longer oligomers and bigger boxes. The quantitative measures developed in this study are expected to prove useful as computational screening tools in excipient design.

Lipid14: The Amber Lipid Force Field

The AMBER lipid force field has been updated to create Lipid14, allowing tensionless simulation of a number of lipid types with the AMBER MD package. The modular nature of this force field allows numerous combinations of head and tail groups to create different lipid types, enabling the easy insertion of new lipid species. The Lennard-Jones and torsion parameters of both the head and tail groups have been revised and updated partial charges calculated. The force field has been validated by simulating bilayers of six different lipid types for a total of 0.5 μs each without applying a surface tension; with favorable comparison to experiment for properties such as area per lipid, volume per lipid, bilayer thickness, NMR order parameters, scattering data, and lipid lateral diffusion. As the derivation of this force field is consistent with the AMBER development philosophy, Lipid14 is compatible with the AMBER protein, nucleic acid, carbohydrate, and small molecule force fields.

Water channel formation and ion transport in linear and branched lipid bilayers

The lipid bilayer stability and water channel morphologies are affected by the presence of methyl branches on lipid tails.

Conical lipids in flat bilayers induce packing defects similar to that induced by positive curvature

In biological membranes, changes in lipid composition or mechanical deformations produce defects in the geometrical arrangement of lipids, thus allowing the adsorption of certain peripheral proteins. Here, we perform molecular dynamics simulations on bilayers containing a cylindrical lipid (PC) and a conical lipid (DOG). Profiles of atomic density and lateral pressure across the bilayer show differences in the acyl chain region due to deeper partitioning of DOG compared to PC. However, such analyses are less informative for the interfacial region where peripheral proteins adsorb. To circumvent this limitation, we develop, to our knowledge, a new method of membrane surface analysis. This method allows the identification of chemical defects, where hydrocarbon chains are accessible to the solvent, and geometrical defects, i.e., voids deeper than the glycerol backbone. The size and number of both types of defects increase with the number of monounsaturated acyl chains in PC and with the introduction of DOG, although the defects do not colocalize with the conical lipid. Interestingly, the size and probability of the defects promoted by DOG resemble those induced by positive curvature, thus explaining why conical lipids and positive curvature can both drive the adsorption of peripheral proteins that use hydrophobic residues as membrane anchors.