Equilibrium distributions of dipalmitoyl phosphatidylcholine and dilauroyl phosphatidylcholine in a mixed lipid bilayer: atomistic semigrand canonical ensemble simulations

Configurational Sampling of All-Atom Solvated Membranes Using Hybrid Nonequilibrium Molecular Dynamics Monte Carlo Simulations

All-atom simulations are a powerful approach to study the structure and dynamics of biological membranes. However, sampling the atomic configurations of inhomogeneous membranes can be challenging due to the slow lateral diffusion of the various constituents. To address this issue, a hybrid nonequilibrium molecular dynamics Monte Carlo (neMD/MC) simulation method is proposed in which randomly chosen lipid molecules are swapped to generate configurations that are subsequently accepted or rejected according to a Metropolis criterion based on the alchemical work for the attempted swap calculated via a short trajectory. A dual-topology framework constraining the common atoms of the exchanging molecules yields a good acceptance probability using switching trajectories as short as 10 ps. The performance of the hybrid neMD/MC algorithm and its ability to sample the distribution of lipids near a transmembrane helix carrying a net charge are illustrated for a binary mixture of charged and zwitterionic lipids.

Hydrophobic Matching Dictates over the Linear Rule of Mixtures in Binary Lipid Membranes

Biological membranes feature heterogeneous mixtures of lipids with different head and tail characteristics. Their biophysical properties are dictated by the intimate interaction among different constituent lipids. Previous studies suggest that the membrane area-per-lipid (APL) deviates from the linear rule of mixtures (LRM) for binary lipid membranes, but the underlying mechanism remains elusive. Our molecular dynamics (MD) simulations of binary lipid membranes consisting of lipids with different tail characteristics reveal a competitive mechanism whereby lipids tend to deform each other to minimize the hydrophobic mismatch between their tails. Depending on the relative tail lengths and saturation levels, this may result in an either positive or negative deviation of APL from the LRM. As lipid packing plays an essential role in membrane fusion and peptide-membrane binding, our findings may help guide the selection of lipids for the effective rational design of nanoliposomes and membrane-targeting peptides.

How Ethanolic Disinfectants Disintegrate Coronavirus Model Membranes: A Dissipative Particle Dynamics Simulation Study

We have developed dissipative particle dynamics models for pure dipalmitoylphosphatidylcholine (DPPC), dioleoylphosphatidylcholine (DOPC), and dimyristoylphosphatidylcholine (DMPC) as well as their binary and ternary mixed membranes, as coronavirus model membranes. The stabilities of pure and mixed membranes, surrounded by aqueous solutions containing up to 70 mol % ethanol (alcoholic disinfectants), have been investigated at room temperature. We found that aqueous solutions containing 5-10 mol % ethanol already have a significant weakening effect on the pure and mixed membranes. The magnitude of the effect depends on the membrane composition and the ethanol concentration. Ethanol permeabilizes the membrane, causing its lateral swelling and thickness shrinking and reducing the orientational order of the hydrocarbon tail of the bilayer. The free energy barrier for the permeation of ethanol in the bilayers is considerably reduced by the ethanol uptake. The rupture-critical ethanol concentrations causing the membrane failure are 20.7, 27.5, and 31.7 mol % in the aqueous phase surrounding pure DMPC, DOPC, and DPPC membranes, respectively. Characterizing the failure of lipid membranes by a machine-learning neural network framework, we found that all mixed binary and/or ternary membranes disrupt when immersed in an aqueous solution containing a rupture-critical ethanol concentration, ranging from 20.7 to 31.7 mol %, depending on the composition of the membrane; the DPPC-rich membranes are more intact, while the DMPC-rich membranes are least intact. Due to the tight packing of long, saturated hydrocarbon tails in DPPC, increasing the DPPC content of the mixed membrane increases its stability against the disinfectant. At high DPPC concentrations, where the DOPC and DMPC molecules are confined between the DPPC lipids, the ordered hydrocarbon tails of DPPC also induce order in the DOPC and DMPC molecules and, hence, stabilize the membrane more. Our simulations on pure and mixed membranes of a diversity of compositions reveal that a maximum ethanol concentration of 32 mol % (55 wt %) in the alcohol-based disinfectants is enough to disintegrate any membrane composed of these three lipids.

Dynamic "Molecular Portraits" of Biomembranes Drawn by Their Lateral Nanoscale Inhomogeneities

To date, it has been reliably shown that the lipid bilayer/water interface can be thoroughly characterized by a sophisticated so-called "dynamic molecular portrait". The latter reflects a combination of time-dependent surface distributions of various physicochemical properties, inherent in both model lipid bilayers and natural multi-component cell membranes. One of the most important features of biomembranes is their mosaicity, which is expressed in the constant presence of lateral inhomogeneities, the sizes and lifetimes of which vary in a wide range-from 1 to 10³ nm and from 0.1 ns to milliseconds. In addition to the relatively well-studied macroscopic domains (so-called "rafts"), the analysis of micro- and nanoclusters (or domains) that form an instantaneous picture of the distribution of structural, dynamic, hydrophobic, electrical, etc., properties at the membrane-water interface is attracting increasing interest. This is because such nanodomains (NDs) have been proven to be crucial for the proper membrane functioning in cells. Therefore, an understanding with atomistic details the phenomena associated with NDs is required. The present mini-review describes the recent results of experimental and in silico studies of spontaneously formed NDs in lipid membranes. The main attention is paid to the methods of ND detection, characterization of their spatiotemporal parameters, the elucidation of the molecular mechanisms of their formation. Biological role of NDs in cell membranes is briefly discussed. Understanding such effects creates the basis for rational design of new prospective drugs, therapeutic approaches, and artificial membrane materials with specified properties.

Scaling relationships for the elastic moduli and viscosity of mixed lipid membranes

The elastic and viscous properties of biological membranes play a vital role in controlling cell functions that require local reorganization of the membrane components as well as dramatic shape changes such as endocytosis, vesicular trafficking, and cell division. These properties are widely acknowledged to depend on the unique composition of lipids within the membrane, yet the effects of lipid mixing on the membrane biophysical properties remain poorly understood. Here, we present a comprehensive characterization of the structural, elastic, and viscous properties of fluid membranes composed of binary mixtures of lipids with different tail lengths. We show that the mixed lipid membrane properties are not simply additive quantities of the single-component analogs. Instead, the mixed membranes are more dynamic than either of their constituents, quantified as a decrease in their bending modulus, area compressibility modulus, and viscosity. While the enhanced dynamics are seemingly unexpected, we show that the measured moduli and viscosity for both the mixed and single-component bilayers all scale with the area per lipid and collapse onto respective master curves. This scaling links the increase in dynamics to mixing-induced changes in the lipid packing and membrane structure. More importantly, the results show that the membrane properties can be manipulated through lipid composition the same way bimodal blends of surfactants, liquid crystals, and polymers are used to engineer the mechanical properties of soft materials, with broad implications for understanding how lipid diversity relates to biomembrane function.

Measuring the composition-curvature coupling in binary lipid membranes by computer simulations

The coupling between local composition fluctuations in binary lipid membranes and curvature affects the lateral membrane structure. We propose an efficient method to compute the composition-curvature coupling in molecular simulations and apply it to two coarse-grained membrane models-a minimal, implicit-solvent model and the MARTINI model. Both the weak-curvature behavior that is typical for thermal fluctuations of planar bilayer membranes as well as the strong-curvature regime corresponding to narrow cylindrical membrane tubes are studied by molecular dynamics simulation. The simulation results are analyzed by using a phenomenological model of the thermodynamics of curved, mixed bilayer membranes that accounts for the change of the monolayer area upon bending. Additionally the role of thermodynamic characteristics such as the incompatibility between the two lipid species and asymmetry of composition are investigated.

Modeling Lipid-Lipid Correlations across a Bilayer Membrane Using the Quasi-chemical Approximation

Mixed fluid-like lipid membranes exhibit interactions not only among the lipids within a given leaflet but also across the bilayer. The ensuing collective interleaflet coupling of entire membrane domains has been modeled previously using various mean-field approaches. Yet, also on the level of individual lipids have correlations across the bilayer been observed experimentally for binary mixtures of charged/uncharged lipids with mismatching combinations of short and long acyl chain lengths. The present study proposes a lattice gas model to quantify these correlations. To this end, we represent a macroscopically homogeneous lipid bilayer by two coupled two-dimensional lattice gases that we study using the quasi-chemical approximation. We demonstrate that the rationalization of previous experimental results is only possible if besides two-body lipid-lipid interactions within and across the bilayer our model also accounts for an additional multibody interaction mechanism, namely the local hydrophobic height mismatch created by pairing short and long chain lipids together. The robustness of the quasi-chemical approximation is verified by comparison with Monte Carlo simulations.

Hydrophobic mismatch and lipid sorting near OmpA in mixed bilayers: atomistic and coarse-grained simulations

To understand the effects of lipid composition on membrane protein function in a mixture as complex as a biomembrane, one must know whether the lipid composition local to the protein differs from the mean lipid composition. In this study, we simulated the transmembrane domain of a β-barrel protein, OmpA, in mixtures of lipids of different tail lengths under conditions of negative hydrophobic mismatch, i.e., local bilayer thinning. We modeled the influence of OmpA on the local lipid composition both at a coarse-grained (CG) resolution using conventional molecular dynamics, and at an atomistic resolution within the semi-grand canonical ensemble using mutation moves to rapidly approach an equilibrium lateral distribution of lipids. Moderate enrichment of the shorter tail component (either DDPC in DDPC/DMPC mixtures or DMPC in DMPC/DSPC mixtures) extending 2-3 nm away from the protein surface was observed with both the atomistic and CG models. The similarity in trends suggests that the more computationally economical CG models capture the essential features of lipid sorting induced by hydrophobic mismatch.

Atomistic simulations of bicelle mixtures

Mixtures of long- and short-tail phosphatidylcholine lipids are known to self-assemble into a variety of aggregates combining flat bilayerlike and curved micellelike features, commonly called bicelles. Atomistic simulations of bilayer ribbons and perforated bilayers containing dimyristoylphosphatidylcholine (DMPC, di-C(14) tails) and dihexanoylphosphatidylcholine (DHPC, di-C(6) tails) have been carried out to investigate the partitioning of these components between flat and curved microenvironments and the stabilization of the bilayer edge by DHPC. To approach equilibrium partitioning of lipids on an achievable simulation timescale, configuration-bias Monte Carlo mutation moves were used to allow individual lipids to change tail length within a semigrand-canonical ensemble. Since acceptance probabilities for direct transitions between DMPC and DHPC were negligible, a third component with intermediate tail length (didecanoylphosphatidylcholine, di-C(10) tails) was included at a low concentration to serve as an intermediate for transitions between DMPC and DHPC. Strong enrichment of DHPC is seen at ribbon and pore edges, with an excess linear density of approximately 3 nm(-1). The simulation model yields estimates for the onset of edge stability with increasing bilayer DHPC content between 5% and 15% DHPC at 300 K and between 7% and 17% DHPC at 323 K, higher than experimental estimates. Local structure and composition at points of close contact between pores suggest a possible mechanism for effective attractions between pores, providing a rationalization for the tendency of bicelle mixtures to aggregate into perforated vesicles and perforated sheets.

On the Validation of Molecular Dynamics Simulations of Saturated and cis-Monounsaturated Phosphatidylcholine Lipid Bilayers: A Comparison with Experiment

Molecular dynamics simulations of fully hydrated pure bilayers of four widely studied phospholipids, 1,2-dilauroyl-sn-glycero-3-phosphocholine (DLPC), 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC), 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC), and 2-oleoyl-1-palmitoyl-sn-glycero-3-phosphocholine (POPC) using a recent revision of the GROMOS96 force field are reported. It is shown that the force field reproduces the structure and the hydration of bilayers formed by each of the four lipids with high accuracy. Specifically, the solvation and the orientation of the dipole of the phosphocholine headgroup and of the ester carbonyls show that the structure of the primary hydration shell in the simulations closely matches experimental findings. This work highlights the need to reproduce a broad range of properties beyond the area per lipid, which is poorly defined experimentally, and to consider the effect of system size and sampling times well beyond those commonly used.

Structural characterization on the gel to liquid-crystal phase transition of fully hydrated DSPC and DSPE bilayers

The structural properties of fully hydrated distearoylphosphatidylcholine (DSPC) and distearoylphosphatidylethanolamine (DSPE) bilayers near the main phase transition were investigated using molecular dynamics simulations on the basis of a united-atom model. Although largely similar in their molecular structures, the two lipids were found with different molecular packing modes at temperatures below the phase transition. For DSPC, three packing modes, namely, cross-tilt, partially interdigitated, and "mixed" gel phases, were observed, while, for DSPE, the lipid tails were almost perpendicular to the lipid surface. Above the main transition temperature, both lipid bilayers transformed into a disordered liquid-crystal phase with marked greater area per lipid and gauche % of the acyl chains and smaller bilayer thickness and order parameter, in comparison with the gel phase. The transformation process of liquid-crystal to gel phase was proved to experience the nucleation and growth stages in a hexagonal manner. The electron density profiles of some major components of both lipid bilayers at various temperatures have been calculated, and the results reveal that both lipid bilayers have less interdigitation around the main transition temperature.

Systematic coarse-graining of a multicomponent lipid bilayer

A solvent-free coarse-grained model for a 1:1 mixed dioleoylphosphatidylcholine (DOPC) and a dioleoylphospatidylethanolamine (DOPE) bilayer is developed using the multiscale coarse-graining (MS-CG) approach. B-spline basis functions are implemented instead of the original cubic spline basis functions in the MS-CG method. The new B-spline basis functions are able to dramatically reduce memory requirements and increase computational efficiency of the MS-CG calculation. Various structural properties from the CG simulations are compared with their corresponding all-atom counterpart in order to validate the CG model. The resulting CG structural properties agree well with atomistic results, which shows that the MS-CG force field can reasonably approximate the many-body potential of mean force in the coarse-grained coordinates. Fast lipid lateral diffusion in the CG simulations, as a result of smoother free energy landscape, makes the study of phase behavior of the binary mixture possible. Small clusters of distinct lipid composition are identified by analyzing the DOPC/DOPE lipid lateral distribution, indicating a nonuniform distribution for the mixed bilayer. The results of lipid phase behavior are compared to experimental results, and connections between the experimental and simulation conclusions are discussed.

Atomistic simulations of mixed-lipid bilayers in gel and fluid phases

The slow rate of diffusive mixing poses a challenge for molecular dynamics (MD) simulation studies of mixed-lipid bilayers. A mixed Monte Carlo-molecular dynamics (MC-MD) approach, which uses mutation moves to swap lipid types throughout the system within the semi-grand canonical ensemble, is here applied to a comparison of binary mixtures in the gel and liquid crystalline phases. The two lipid components modeled, distearoylphosphatidylcholine (DSPC) and dimyristoylphosphatidylcholine (DMPC), differ by four carbons in the lengths of their acyl tails and are investigated here at full hydration at a temperature (313 K) between their transition temperatures, where coexistence between a DSPC-rich gel phase and a DMPC-rich liquid crystalline phase is expected. An analysis of DSPC-DMPC mixtures in the gel phase indicates strong deviation from ideality in the thermodynamics of mixing, accompanied by a tendency of the shorter-tailed component DMPC to associate laterally and for DMPC headgroups to be displaced toward the bilayer midplane. The liquid crystal phase mixtures, in contrast, show more mild deviation from thermodynamically ideal mixing with no apparent tendency for similar lipids to cluster laterally and no difference in headgroup normal distribution profiles.

Bilayer edge and curvature effects on partitioning of lipids by tail length: atomistic simulations

The partitioning of lipids among different microenvironments in a bilayer is of considerable relevance to characterization of composition variations in biomembranes. Atomistic simulation has been ill-suited to model equilibrated lipid mixtures because the time required for diffusive exchange of lipids among microenvironments exceeds typical submicrosecond molecular dynamics trajectories. A method to facilitate local composition fluctuations, using Monte Carlo mutations to change lipid structures within the semigrand-canonical ensemble (at a fixed difference in component chemical potentials, Deltamu), was recently implemented to address this challenge. This technique was applied here to mixtures of dimyristoylphosphatidylcholine and a shorter-tail lipid, either symmetric (didecanoylphosphatidylcholine (DDPC)) or asymmetric (hexanoyl-myristoylphosphatidylcholine), arranged in two types of structure: bilayer ribbons and buckled bilayers. In ribbons, the shorter-tail component showed a clear enrichment at the highly curved rim, more so for hexanoyl-myristoylphosphatidylcholine than for DDPC. Results on buckled bilayers were variable. Overall, the DDPC content of buckled bilayers tended to exceed by several percent the DDPC content of flat ones simulated at the same Deltamu, but only for mixtures with low overall DDPC content. Within the buckled bilayer structure, no correlation could be resolved between the sign or magnitude of the local curvature of a leaflet and the mean local lipid composition. Results are discussed in terms of packing constraints, surface area/volume ratios, and curvature elasticity.

Molecular dynamics simulations of cardiolipin bilayers

Cardiolipin is a key lipid component in the inner mitochondrial membrane, where the lipid is involved in energy production, cristae structure, and mechanisms in the apoptotic pathway. In this article we used molecular dynamics computer simulations to investigate cardiolipin and its effect on the structure of lipid bilayers. Three cardiolipin/POPC bilayers with different lipid compositions were simulated: 100, 9.2, and 0% cardiolipin. We found strong association of sodium counterions to the carbonyl groups of both lipid types, leaving in the case of 9.2% cardiolipin virtually no ions in the aqueous compartment. Although binding occurred primarily at the carbonyl position, there was a preference to bind to the carbonyl groups of cardiolipin. Ion binding and the small headgroup of cardiolipin gave a strong ordering of the hydrocarbon chains. We found significant effects in the water dipole orientation and water dipole potential which can compensate for the electrostatic repulsion that otherwise should force charged lipids apart. Several parameters relevant for the molecular structure of cardiolipin were calculated and compared with results from analyses of coarse-grained simulations and available X-ray structural data.

Flexible chain molecules in the marginal and concentrated regimes: universal static scaling laws and cross-over predictions

We present predictions for the static scaling exponents and for the cross-over polymer volumetric fractions in the marginal and concentrated solution regimes. Corrections for finite chain length are made. Predictions are based on an analysis of correlated fluctuations in density and chain length, in a semigrand ensemble in which mers and solvent sites exchange identities. Cross-over volumetric fractions are found to be chain length independent to first order, although reciprocal-N corrections are also estimated. Predicted scaling exponents and cross-over regimes are compared with available data from extensive off-lattice Monte Carlo simulations [Karayiannis and Laso, Phys. Rev. Lett. 100, 050602 (2008)] on freely jointed, hard-sphere chains of average lengths from N=12-500 and at packing densities from dilute ones up to the maximally random jammed state.