Ion-Induced PIP2 Clustering with Martini3: Modification of Phosphate-Ion Interactions and Comparison with CHARMM36.

Phosphatidylinositol 4,5-bisphosphate (PIP2) is a critical lipid for cellular signaling. The specific phosphorylation of the inositol ring controls protein binding as well as clustering behavior. Two popular models to describe ion-mediated clustering of PIP2 are Martini3 (M3) and CHARMM36 (C36). Molecular dynamics simulations of PIP2-containing bilayers in solutions of potassium chloride, sodium chloride, and calcium chloride, and at two different resolutions are performed to understand the aggregation and the model parameters that drive it. The average M3 clusters of PIP2 in bilayers of 1-palmitoyl-2-oleoyl-glycero-3-phosphocholine and PIP2 bilayers in the presence of K+, Na+, or Ca2+ contained 2.2, 2.6, and 6.4 times more PIP2 than C36 clusters, respectively. Indeed, the Ca2+-containing systems often formed a single large aggregate. Reparametrization of the M3 ion-phosphate Lennard-Jones interaction energies to reproduce experimental osmotic pressure of sodium dimethyl phosphate (DMP), K[DMP], and Ca[DMP]2 solutions, the same experimental target as C36, yielded comparably sized PIP2 clusters for the two models. Furthermore, C36 and the modified M3 predict similar saturation of the phosphate groups with increasing Ca2+, although the coarse-grained model does not capture the cooperativity between K+ and Ca2+. This characterization of the M3 behavior in the presence of monovalent and divalent ions lays a foundation to study cation/protein/PIP2 clustering.

Drude Polarizable Lipid Force Field with Explicit Treatment of Long-Range Dispersion: Parametrization and Validation for Saturated and Monounsaturated Zwitterionic Lipids.

Accurate empirical force fields of lipid molecules are a critical component of molecular dynamics simulation studies aimed at investigating properties of monolayers, bilayers, micelles, vesicles, and liposomes, as well as heterogeneous systems, such as protein-membrane complexes, bacterial cell walls, and more. While the majority of lipid force field-based simulations have been performed using pairwise-additive nonpolarizable models, advances have been made in the development of the polarizable force field based on the classical Drude oscillator model. In the present study, we undertake further optimization of the Drude lipid force field, termed Drude2023, including improved treatment of the phosphate and glycerol linker region of PC and PE headgroups, additional optimization of the alkene group in monounsaturated lipids, and inclusion of long-range Lennard-Jones interactions using the particle-mesh Ewald method. Initial optimization targeted quantum mechanical (QM) data on small model compounds representative of the linker region. Subsequent optimization targeted QM data on larger model compounds, experimental data, and dihedral potentials of mean force from the CHARMM36 additive lipid force field using a parameter reweighting protocol. The use of both experimental and QM target data during the reweighting protocol is shown to produce physically reasonable parameters that reproduce a collection of experimental observables. Target data for optimization included surface area/lipid for DPPC, DSPC, DMPC, and DLPC bilayers and nuclear magnetic resonance (NMR) order parameters for DPPC bilayers. Validation data include prediction of membrane thickness, scattering form factors, electrostatic potential profiles, compressibility moduli, surface area per lipid, water permeability, NMR T1 relaxation times, diffusion constants, and monolayer surface tensions for a variety of saturated and unsaturated lipid mono- and bilayers. Overall, the agreement with experimental data is quite good, though the results are less satisfactory for the NMR T1 relaxation times for carbons near the ester groups. Notable improvements compared to the additive C36 force field were obtained for membrane dipole potentials, lipid diffusion coefficients, and water permeability with the exception of monounsaturated lipid bilayers. It is anticipated that the optimized polarizable Drude2023 force field will help generate more accurate molecular simulations of pure bilayers and heterogeneous systems containing membranes, advancing our understanding of the role of electronic polarization in these systems.

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.

Design principles of PI(4,5)P2 clustering under protein-free conditions: Specific cation effects and calcium-potassium synergy.

Phosphatidylinositol 4,5-bisphosphate (PIP2) clustering is a key component in cell signaling, yet little is known about the atomic-level features of this phenomenon. Network-theoretic analysis of multimicrosecond atomistic simulations of PIP2 containing asymmetric bilayers under protein-free conditions, presented here, reveals how design principles of PIP2 clustering are determined by the specific cation effects. Ca2+ generates large clusters (6% are pentamer or larger) by adding existing PIP2 dimers formed by strong O‒Ca2+‒O bridging interactions of unprotonated P4/P5 phosphates. In contrast, monovalent cations (Na+ and K+) form smaller and less-stable clusters by preferentially adding PIP2 monomers. Despite having the same net charge, the affinity to P4/P5 is higher for Na+, while affinity toward glycerol P1 is higher for K+. Consequently, a mixture of K+ and Ca2+ (as would be produced by Ca2+ influx) synergistically yields larger and more stable clusters than Ca2+ alone due to the different binding preferences of these cations.

Development of CHARMM Additive Potential Energy Parameters for α-Methyl Amino Acids.

Potential energy parameters for α-methyl amino acids were generated with ab initio calculations on α-methyl-N-acetylalanyl-N'-methylamide (the α-methyl "alanine dipeptide") which served as an input to a grid-based correction to the backbone torsional potential (known as CMAP) consistent with the CHARMM36m additive protein force field. The new parameters were validated by comparison with experimentally determined helicities of the 22 residue C-terminal peptide (H10) from apolipoprotein A1 and five α-methylated variants in water and 0.3:0.7 trifluoroethanol (TFE)/water. Conventional molecular dynamics simulation totaling 30 µs for each peptide is in overall good agreement with the experiment, including the increased helicity in 30% TFE. An additional 500 ns of simulation using two-dimensional dihedral biasing (bpCMAP) replica exchange reduced left-handed conformations, increased right-handed helices, and thereby mostly decreased agreement with the experiment. Analysis of side chain-side chain salt bridges suggests that the overestimation of the helical content may be, in part, due to such interactions. The increased helicity of the peptides in 30% TFE arises from decreased hydrogen bonding of the backbone atoms to water and a concomitant increase in intramolecular backbone hydrogen bonds.

CHARMM36 Lipid Force Field with Explicit Treatment of Long-Range Dispersion: Parametrization and Validation for Phosphatidylethanolamine, Phosphatidylglycerol, and Ether Lipids.

Long-range Lennard-Jones (LJ) interactions have been incorporated into the CHARMM36 (C36) lipid force field (FF) using the LJ particle-mesh Ewald (LJ-PME) method in order to remove the inconsistency of bilayer and monolayer properties arising from the exclusion of long-range dispersion [Yu, Y.; Semi-automated Optimization of the CHARMM36 Lipid Force Field to Include Explicit Treatment of Long-Range Dispersion. J. Chem. Theory Comput. 2021, 10.1021/acs.jctc.0c01326. (preceding article in this issue)]. The new FF is denoted C36/LJ-PME. While the first optimization was based on three phosphatidylcholines (PCs), this work extends the validation and parametrization to more lipids including PC, phosphatidylethanolamine (PE), phosphatidylglycerol (PG), and ether lipids. The agreement with experimental structure data is excellent for PC, PE, and ether lipids. C36/LJ-PME also compares favorably with scattering data of PG bilayers but less so with NMR deuterium order parameters of 1,2-dimyristoyl-sn-glycero-3-phospho-(1'-rac-glycerol) (DMPG) at 303.15 K, indicating a need for future optimization regarding PG-specific parameters. Frequency dependence of NMR T1 spin-lattice relaxation times is well-described by C36/LJ-PME, and the overall agreement with experiment is comparable to C36. Lipid diffusion is slower than C36 due to the added long-range dispersion causing a higher viscosity, although it is still too fast compared to experiment after correction for periodic boundary conditions. When using a 10 Å real-space cutoff, the simulation speed of C36/LJ-PME is roughly equal to C36. While more lipids will be incorporated into the FF in the future, C36/LJ-PME can be readily used for common lipids and extends the capability of the CHARMM FF by supporting monolayers and eliminating the cutoff dependence.

Semi-automated Optimization of the CHARMM36 Lipid Force Field to Include Explicit Treatment of Long-Range Dispersion.

The development of the CHARMM lipid force field (FF) can be traced back to the early 1990s with its current version denoted CHARMM36 (C36). The parametrization of C36 utilized high-level quantum mechanical data and free energy calculations of model compounds before parameters were manually adjusted to yield agreement with experimental properties of lipid bilayers. While such manual fine-tuning of FF parameters is based on intuition and trial-and-error, automated methods can identify beneficial modifications of the parameters via their sensitivities and thereby guide the optimization process. This work introduces a semi-automated approach to reparametrize the CHARMM lipid FF with consistent inclusion of long-range dispersion through the Lennard-Jones particle-mesh Ewald (LJ-PME) approach. The optimization method is based on thermodynamic reweighting with regularization with respect to the C36 set. Two independent optimizations with different topology restrictions are presented. Targets of the optimizations are primarily liquid crystalline phase properties of lipid bilayers and the compression isotherm of monolayers. Pair correlation functions between water and lipid functional groups in aqueous solution are also included to address headgroup hydration. While the physics of the reweighting strategy itself is well-understood, applying it to heterogeneous, complex anisotropic systems poses additional challenges. These were overcome through careful selection of target properties and reweighting settings allowing for the successful incorporation of the explicit treatment of long-range dispersion, and we denote the newly optimized lipid force field as C36/LJ-PME. The current implementation of the optimization protocol will facilitate the future development of the CHARMM and related lipid force fields.

Membrane permeability of small molecules from unbiased molecular dynamics simulations.

Permeation of many small molecules through lipid bilayers can be directly observed in molecular dynamics simulations on the nano- and microsecond timescale. While unbiased simulations provide an unobstructed view of the permeation process, their feasibility for computing permeability coefficients depends on various factors that differ for each permeant. The present work studies three small molecules for which unbiased simulations of permeation are feasible within less than a microsecond, one hydrophobic (oxygen), one hydrophilic (water), and one amphiphilic (ethanol). Permeabilities are computed using two approaches: counting methods and a maximum-likelihood estimation for the inhomogeneous solubility diffusion (ISD) model. Counting methods yield nearly model-free estimates of the permeability for all three permeants. While the ISD-based approach is reasonable for oxygen, it lacks precision for water due to insufficient sampling and results in misleading estimates for ethanol due to invalid model assumptions. It is also demonstrated that simulations using a Langevin thermostat with collision frequencies of 1/ps and 5/ps yield oxygen permeabilities and diffusion constants that are lower than those using Nosé-Hoover by statistically significant margins. In contrast, permeabilities from trajectories generated with Nosé-Hoover and the microcanonical ensemble do not show statistically significant differences. As molecular simulations become more affordable and accurate, calculation of permeability for an expanding range of molecules will be feasible using unbiased simulations. The present work summarizes theoretical underpinnings, identifies pitfalls, and develops best practices for such simulations.

Molecular Structure of Sphingomyelin in Fluid Phase Bilayers Determined by the Joint Analysis of Small-Angle Neutron and X-ray Scattering Data.

We have determined the fluid bilayer structure of palmitoyl sphingomyelin (PSM) and stearoyl sphingomyelin (SSM) by simultaneously analyzing small-angle neutron and X-ray scattering data. Using a newly developed scattering density profile (SDP) model for sphingomyelin lipids, we report structural parameters including the area per lipid, total bilayer thickness, and hydrocarbon thickness, in addition to lipid volumes determined by densitometry. Unconstrained all-atom simulations of PSM bilayers at 55 °C using the C36 CHARMM force field produced a lipid area of 56 Å2, a value that is 10% lower than the one determined experimentally by SDP analysis (61.9 Å2). Furthermore, scattering form factors calculated from the unconstrained simulations were in poor agreement with experimental form factors, even though segmental order parameter (SCD) profiles calculated from the simulations were in relatively good agreement with SCD profiles obtained from NMR experiments. Conversely, constrained area simulations at 61.9 Å2 resulted in good agreement between the simulation and experimental scattering form factors, but not with SCD profiles from NMR. We discuss possible reasons for the discrepancies between these two types of data that are frequently used as validation metrics for molecular dynamics force fields.

Permeability of membranes in the liquid ordered and liquid disordered phases.

The functional significance of ordered nanodomains (or rafts) in cholesterol rich eukaryotic cell membranes has only begun to be explored. This study exploits the correspondence of cellular rafts and liquid ordered (Lo) phases of three-component lipid bilayers to examine permeability. Molecular dynamics simulations of Lo phase dipalmitoylphosphatidylcholine (DPPC), dioleoylphosphatidylcholine (DOPC), and cholesterol show that oxygen and water transit a leaflet through the DOPC and cholesterol rich boundaries of hexagonally packed DPPC microdomains, freely diffuse along the bilayer midplane, and escape the membrane along the boundary regions. Electron paramagnetic resonance experiments provide critical validation: the measured ratio of oxygen concentrations near the midplanes of liquid disordered (Ld) and Lo bilayers of DPPC/DOPC/cholesterol is 1.75 ± 0.35, in very good agreement with 1.3 ± 0.3 obtained from simulation. The results show how cellular rafts can be structurally rigid signaling platforms while remaining nearly as permeable to small molecules as the Ld phase.

Interactions of Water and Alkanes: Modifying Additive Force Fields to Account for Polarization Effects.

Atomistic biomolecular simulations predominantly utilize additive force fields (FF), where the electrostatic potential is modeled by fixed point charges. Among other consequences, the lack of polarizability in these models undermines the balance of hydrophilic/hydrophobic nonbonded interactions. Simulations of water/alkane systems using the TIP3P water model and CHARMM36 parameters reveal a 1 kcal/mol overestimate of the experimental transfer free energy of water to hexadecane; more recent optimized water models (SPC/E, TIP4P/2005, TIP4P-Ew, TIP3P-FB, TIP4P-FB, OPC, TIP4P-D) overestimate this transfer free energy by approximately 2 kcal/mol. In contrast, the polarizable SWM4-NDP and SWM6 water models reproduce experimental values to within statistical error. As an alternative to explicitly modeling polarizability, this paper develops an efficient automated workflow to optimize pair-specific Lennard-Jones parameters within an additive FF. Water/hexadecane is used as a prototype and the free energy of water transfer to hexadecane as a target. The optimized model yields quantitative agreement with the experimental transfer free energy and improves the water/hexadecane interfacial tension by 6%. Simulations of five different lipid bilayers show a strong increase of water permeabilities compared to the unmodified CHARMM36 lipid FF which consistently improves match with experiment: the order-of-magnitude underestimate for monounsaturated bilayers is rectified and the factor of 2.8-4 underestimate for saturated bilayers is turned into a factor of 1.5-3 overestimate. While agreement with experiment is decreased for the diffusion constant of water in hexadecane, alkane transfer free energies, and the bilayers' area per lipid, the method provides a permeant-specific route to achieve a wide range of heterogeneous observables via rapidly optimized pairwise parameters.

Revisiting Volumes of Lipid Components in Bilayers.

In addition to obtaining the highly precise volumes of lipids in lipid bilayers, it has been desirable to obtain the volumes of parts of each lipid, such as the methylenes and terminal methyls on the hydrocarbon chains and the head group. Obtaining such component volumes from experiment and from simulations is re-examined, first by distinguishing methods based on apparent versus partial molar volumes. Although somewhat different, both these methods give results that are counterintuitive and that differ from results obtained by a more local method that can only be applied to simulations. These comparisons reveal differences in the average methylene component volume that result in larger differences in the head group component volumes. Literature experimental volume data for unsaturated phosphocholines and for alkanes have been used and new data have been acquired for saturated phosphocholines. Data and simulations cover extended ranges of temperature to assess both the temperature and chain length dependence of the component volumes. A new method to refine the determination of component volumes is proposed that uses experimental data for different chain lengths at temperatures guided by the temperature dependence determined in simulations. These refinements enable more precise comparisons of the component volumes of different lipids and alkanes in different phases. Finally, the notion of free volume is extended to components using the Lennard-Jones radii to estimate the excluded volume of each component. This analysis reveals that head group free volumes are relatively independent of thermodynamic phase, whereas both the methylene and methyl free volumes increase dramatically when bilayers transition from gel to fluid.

Molecular Dynamics Simulations of Membrane Permeability.

This Review illustrates the evaluation of permeability of lipid membranes from molecular dynamics (MD) simulation primarily using water and oxygen as examples. Membrane entrance, translocation, and exit of these simple permeants (one hydrophilic and one hydrophobic) can be simulated by conventional MD, and permeabilities can be evaluated directly by Fick's First Law, transition rates, and a global Bayesian analysis of the inhomogeneous solubility-diffusion model. The assorted results, many of which are applicable to simulations of nonbiological membranes, highlight the limitations of the homogeneous solubility diffusion model; support the utility of inhomogeneous solubility diffusion and compartmental models; underscore the need for comparison with experiment for both simple solvent systems (such as water/hexadecane) and well-characterized membranes; and demonstrate the need for microsecond simulations for even simple permeants like water and oxygen. Undulations, subdiffusion, fractional viscosity dependence, periodic boundary conditions, and recent developments in the field are also discussed. Last, while enhanced sampling methods and increasingly sophisticated treatments of diffusion add substantially to the repertoire of simulation-based approaches, they do not address directly the critical need for force fields with polarizability and multipoles, and constant pH methods.

Membrane Permeability: Characteristic Times and Lengths for Oxygen and a Simulation-Based Test of the Inhomogeneous Solubility-Diffusion Model.

The balance of normal and radial (lateral) diffusion of oxygen in phospholipid membranes is critical for biological function. Based on the Smoluchowski equation for the inhomogeneous solubility-diffusion model, Bayesian analysis (BA) can be applied to molecular dynamics trajectories of oxygen to extract the free energy and the normal and radial diffusion profiles. This paper derives a theoretical formalism to convert these profiles into characteristic times and lengths associated with entering, escaping, or completely crossing the membrane. The formalism computes mean first passage times and holds for any process described by rate equations between discrete states. BA of simulations of eight model membranes with varying lipid composition and temperature indicate that oxygen travels 3 to 5 times further in the radial than in the normal direction when crossing the membrane in a time of 15 to 32 ns, thereby confirming the anisotropy of passive oxygen transport in membranes. Moreover, the preceding times and distances estimated from the BA are compared to the aggregate of 280 membrane exits explicitly observed in the trajectories. BA predictions for the distances of oxygen radial diffusion within the membrane are statistically indistinguishable from the corresponding simulation values, yet BA oxygen exit times from the membrane interior are approximately 20% shorter than the simulation values, averaged over seven systems. The comparison supports the BA approach and, therefore, the applicability of the Smoluchowski equation to membrane diffusion. Given the shorter trajectories required for the BA, these results validate the BA as a computationally attractive alternative to direct observation of exits when estimating characteristic times and radial distances. The effect of collective membrane undulations on the BA is also discussed.

Graph-Theoretic Analysis of Monomethyl Phosphate Clustering in Ionic Solutions.

All-atom molecular dynamics simulations combined with graph-theoretic analysis reveal that clustering of monomethyl phosphate dianion (MMP2-) is strongly influenced by the types and combinations of cations in the aqueous solution. Although Ca2+ promotes the formation of stable and large MMP2- clusters, K+ alone does not. Nonetheless, clusters are larger and their link lifetimes are longer in mixtures of K+ and Ca2+. This "synergistic" effect depends sensitively on the Lennard-Jones interaction parameters between Ca2+ and the phosphorus oxygen and correlates with the hydration of the clusters. The pronounced MMP2- clustering effect of Ca2+ in the presence of K+ is confirmed by Fourier transform infrared spectroscopy. The characterization of the cation-dependent clustering of MMP2- provides a starting point for understanding cation-dependent clustering of phosphoinositides in cell membranes.

Comparison of Additive and Polarizable Models with Explicit Treatment of Long-Range Lennard-Jones Interactions Using Alkane Simulations.

Long-range Lennard-Jones (LJ) interactions have a significant impact on the structural and thermodynamic properties of nonpolar systems. While several methods have been introduced for the treatment of long-range LJ interactions in molecular dynamics (MD) simulations, increased accuracy and extended applicability is required for anisotropic systems such as lipid bilayers. The recently refined Lennard-Jones particle-mesh Ewald (LJ-PME) method extends the particle-mesh Ewald (PME) method to long-range LJ interactions and is suitable for use with anisotropic systems. Implementation of LJ-PME with the CHARMM36 (C36) additive and CHARMM Drude polarizable force fields improves agreement with experiment for density, isothermal compressibility, surface tension, viscosity, translational diffusion, and 13C T1 relaxation times of pure alkanes. Trends in the temperature dependence of the density and isothermal compressibility of hexadecane are also improved. While the C36 additive force field with LJ-PME remains a useful model for liquid alkanes, the Drude polarizable force field with LJ-PME is more accurate for nearly all quantities considered. LJ-PME is also preferable to the isotropic long-range correction for hexadecane because the molecular order extends to nearly 20 Å, well beyond the usual 10-12 Å cutoffs used in most simulations.

Position-Dependent Diffusion Tensors in Anisotropic Media from Simulation: Oxygen Transport in and through Membranes.

A Bayesian-based methodology is developed to estimate diffusion tensors from molecular dynamics simulations of permeants in anisotropic media, and is applied to oxygen in lipid bilayers. By a separation of variables in the Smoluchowski diffusion equation, the multidimensional diffusion is reduced to coupled one-dimensional diffusion problems that are treated by discretization. The resulting diffusivity profiles characterize the membrane transport dynamics as a function of the position across the membrane, discriminating between diffusion normal and parallel to the membrane. The methodology is first validated with neat water, neat hexadecane, and a hexadecane slab surrounded by water, the latter being a simple model for a lipid membrane. Next, a bilayer consisting of pure 1-palmitoyl 2-oleoylphosphatidylcholine (POPC), and a bilayer mimicking the lipid composition of the inner mitochondrial membrane, including cardiolipin, are investigated. We analyze the detailed time evolution of oxygen molecules, in terms of both normal diffusion through and radial diffusion inside the membrane. Diffusion is fast in the more loosely packed interleaflet region, and anisotropic, with oxygen spreading more rapidly in the membrane plane than normal to it. Visualization of the propagator shows that oxygen enters the membrane rapidly, reaching its thermodynamically favored center in about 1 ns, despite the free energy barrier at the headgroup region. Oxygen transport is quantified by computing the oxygen permeability of the membranes and the average radial diffusivity, which confirm the anisotropy of the diffusion. The position-dependent diffusion constants and free energies are used to construct compartmental models and test assumptions used in estimating permeability, including Overton's rule. In particular, a hexadecane slab surrounded by water is found to be a poor model of oxygen transport in membranes because the relevant energy barriers differ substantially.

Lipid and Peptide Diffusion in Bilayers: The Saffman-Delbrück Model and Periodic Boundary Conditions.

The periodic Saffman-Delbrück (PSD) model, an extension of the Saffman-Delbrück model developed to describe the effects of periodic boundary conditions on the diffusion constants of lipids and proteins obtained from simulation, is tested using the coarse-grained Martini and all-atom CHARMM36 (C36) force fields. Simulations of pure Martini dipalmitoylphosphatidylcholine (DPPC) bilayers and those with one embedded gramicidin A (gA) dimer or one gA monomer with sizes ranging from 512 to 2048 lipids support the PSD model. Underestimates of D∞ (the value of the diffusion constant for an infinite system) from the 512-lipid system are 35% for DPPC, 45% for the gA monomer, and 70% for the gA dimer. Simulations of all-atom DPPC and dioleoylphosphatidylcholine (DOPC) bilayers yield diffusion constants not far from experiment. However, the PSD model predicts that diffusion constants at the sizes of the simulation should underestimate experiment by approximately a factor of 3 for DPPC and 2 for DOPC. This likely implies a deficiency in the C36 force field. A Bayesian method for extrapolating diffusion constants of lipids and proteins in membranes obtained from simulation to infinite system size is provided.

Mechanical properties of lipid bilayers from molecular dynamics simulation.

Lipid areas (Aℓ), bilayer area compressibilities (KA), bilayer bending constants (KC), and monolayer spontaneous curvatures (c0) from simulations using the CHARMM36 force field are reported for 12 representative homogenous lipid bilayers. Aℓ (or their surrogate, the average deuterium order parameter in the "plateau region" of the chain) agree very well with experiment, as do the KA. Simulated KC are in near quantitative agreement with vesicle flicker experiments, but are somewhat larger than KC from X-ray, pipette aspiration, and neutron spin echo for saturated lipids. Spontaneous curvatures of bilayer leaflets from the simulations are approximately 30% smaller than experimental values of monolayers in the inverse hexagonal phase.

Determination of biomembrane bending moduli in fully atomistic simulations.

The bilayer bending modulus (Kc) is one of the most important physical constants characterizing lipid membranes, but precisely measuring it is a challenge, both experimentally and computationally. Experimental measurements on chemically identical bilayers often differ depending upon the techniques employed, and robust simulation results have previously been limited to coarse-grained models (at varying levels of resolution). This Communication demonstrates the extraction of Kc from fully atomistic molecular dynamics simulations for three different single-component lipid bilayers (DPPC, DOPC, and DOPE). The results agree quantitatively with experiments that measure thermal shape fluctuations in giant unilamellar vesicles. Lipid tilt, twist, and compression moduli are also reported.