Chapter 1 Considerations for Lipid Force Field Development

Considerations of Recent All-Atom Lipid Force Field Development

Molecular simulations of biological molecules require an accurate description of molecular interactions through a force field (FF). The focus of this Perspective is on all-atom lipid FFs. Recent additions to the CHARMM36 lipid FF continue to expand a researcher's ability to probe membrane structure and function with a wide variety of biologically important lipids. Currently, there is an effort to reduce the assumptions in all-atom lipid FFs. The inclusion of long-range dispersion interaction through particle-mesh Ewald is allowing for more accurate descriptions of lipid bilayer and monolayer properties without additional computational cost. Soon, simulations with lipid FFs will no longer depend on short-range cutoffs and will accurately represent long-range dispersion. This requires efficient FF parametrization with an automated approach due to FF complexity. In addition, polarizable FFs for lipids will be important for the next generation of simulations that accurately represent how molecule interactions respond to a varied environment.

Are all-atom any better than united-atom force fields for the description of liquid properties of alkanes?

Alkanes are a fundamental part in empirical force fields (FF) not only due to their technological relevance, but also due to the prevalence of alkane moieties in organic molecules, e.g., compounds containing a saturated carbon chain. Therefore, a good description of alkane interactions is crucial for determining the quality of a FF. In this study, the performance of 12 empirical force fields (FF) was evaluated in the context of reproducing liquid properties of alkanes. More specifically, n-octane was chosen as a reference compound since it is a liquid in a broad temperature range and it has numerous experimental data for thermodynamic, transport, and structural properties, as well as for their temperature dependencies. A normalized root-mean-square deviation (NRMSD) analysis was used to rank the force fields in their ability to reproduce the experimental data. Five out of the six best force fields considered were united-atom models. The GROMOS force field showed the smallest deviation in terms of NRMSD, followed by TRAPPE-EH, NERD, CHARMM-UA, TRAPPE-UA, and OPLS-UA. This overall better performance of the united-atom force fields indicates that complexity does not always bring quality.

Exploring the impact of proteins on the line tension of a phase-separating ternary lipid mixture

The separation of lipid mixtures into thermodynamically stable phase-separated domains is dependent on lipid composition, temperature, and system size. Using molecular dynamics simulations, the line tension between thermodynamically stable lipid domains formed from ternary mixtures of di-C16:0 PC:di-C18:2 PC:cholesterol at 40:40:20 mol. % ratio was investigated via two theoretical approaches. The line tension was found to be 3.1 ± 0.2 pN by capillary wave theory and 4.7 ± 3.7 pN by pressure tensor anisotropy approaches for coarse-grained models based on the Martini force field. Using an all-atom model of the lipid membrane based on the CHARMM36 force field, the line tension was found to be 3.6 ± 0.9 pN using capillary wave theory and 1.8 ± 2.2 pN using pressure anisotropy approaches. The discrepancy between estimates of the line tension based on capillary wave theory and pressure tensor anisotropy methods is discussed. Inclusion of protein in Martini membrane lipid mixtures was found to reduce the line tension by 25%-35% as calculated by the capillary wave theory approach. To further understand and predict the behavior of proteins in phase-separated membranes, we have formulated an analytical Flory-Huggins model and parameterized it against the simulation results. Taken together these results suggest a general role for proteins in reducing the thermodynamic cost associated with domain formation in lipid mixtures and quantifies the thermodynamic driving force promoting the association of proteins to domain interfaces.

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.

Molecular dynamics simulations of lipid nanodiscs

A lipid nanodisc is a discoidal lipid bilayer stabilized by proteins, peptides, or polymers on its edge. Nanodiscs have two important connections to structural biology. The first is associated with high-density lipoprotein (HDL), a particle with a variety of functionalities including lipid transport. Nascent HDL (nHDL) is a nanodisc stabilized by Apolipoprotein A-I (APOA1). Determining the structure of APOA1 and its mimetic peptides in nanodiscs is crucial to understanding pathologies related to HDL maturation and designing effective therapies. Secondly, nanodiscs offer non-detergent membrane-mimicking environments and greatly facilitate structural studies of membrane proteins. Although seemingly similar, natural and synthetic nanodiscs are different in that nHDL is heterogeneous in size, due to APOA1 elasticity, and gradually matures to become spherical. Synthetic nanodiscs, in contrast, should be homogenous, stable, and size-tunable. This report reviews previous molecular dynamics (MD) simulation studies of nanodiscs and illustrates convergence and accuracy issues using results from new multi-microsecond atomistic MD simulations. These new simulations reveal that APOA1 helices take 10-20 μs to rearrange on the nanodisc, while peptides take 2 μs to migrate from the disc surfaces to the edge. These systems can also become kinetically trapped depending on the initial conditions. For example, APOA1 was trapped in a biologically irrelevant conformation for the duration of a 10 μs trajectory; the peptides were similarly trapped for 5 μs. It therefore remains essential to validate MD simulations of these systems with experiments due to convergence and accuracy issues. This article is part of a Special Issue entitled: Emergence of Complex Behavior in Biomembranes edited by Marjorie Longo.

Lipid Configurations from Molecular Dynamics Simulations

The extent to which current force fields faithfully reproduce conformational properties of lipids in bilayer membranes, and whether these reflect the structural principles established for phospholipids in bilayer crystals, are central to biomembrane simulations. We determine the distribution of dihedral angles in palmitoyl-oleoyl phosphatidylcholine from molecular dynamics simulations of hydrated fluid bilayer membranes. We compare results from the widely used lipid force field of Berger et al. with those from the most recent C36 release of the CHARMM force field for lipids. Only the CHARMM force field produces the chain inequivalence with sn-1 as leading chain that is characteristic of glycerolipid packing in fluid bilayers. The exposure and high partial charge of the backbone carbonyls in Berger lipids leads to artifactual binding of Na+ ions reported in the literature. Both force fields predict coupled, near-symmetrical distributions of headgroup dihedral angles, which is compatible with models of interconverting mirror-image conformations used originally to interpret NMR order parameters. The Berger force field produces rotamer populations that correspond to the headgroup conformation found in a phosphatidylcholine lipid bilayer crystal, whereas CHARMM36 rotamer populations are closer to the more relaxed crystal conformations of phosphatidylethanolamine and glycerophosphocholine. CHARMM36 alone predicts the correct relative signs of the time-average headgroup order parameters, and reasonably reproduces the full range of NMR data from the phosphate diester to the choline methyls. There is strong motivation to seek further experimental criteria for verifying predicted conformational distributions in the choline headgroup, including the 31P chemical shift anisotropy and 14N and CD3 NMR quadrupole splittings.

Drude Polarizable Force Field for Molecular Dynamics Simulations of Saturated and Unsaturated Zwitterionic Lipids

Additive force fields are designed to account for induced electronic polarization in a mean-field average way, using effective empirical fixed charges. The limitation of this approximation is cause for serious concerns, particularly in the case of lipid membranes, where the molecular environment undergoes dramatic variations over microscopic length scales. A polarizable force field based on the classical Drude oscillator offers a practical and computationally efficient framework for an improved representation of electrostatic interactions in molecular simulations. Building on the first-generation Drude polarizable force field for the dipalmitoylphosphatidylcholine 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) molecule, the present effort was undertaken to improve this initial model and expand the force field to a wider range of phospholipid molecules. New lipids parametrized include dimyristoylphosphatidylcholine (DMPC), dilauroylphosphatidylcholine (DLPC), 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC), 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC), dipalmitoylphosphatidylethanolamine (DPPE), 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphoethanolamine (POPE), and 1,2-dioleoyl-sn-glycero-3-phosphoethanolamine (DOPE). The iterative optimization protocol employed in this effort led to lipid models that achieve a good balance between reproducing quantum mechanical data on model compound representative of phospholipids and reproducing a range of experimental condensed phase properties of bilayers. A parametrization strategy based on a restrained ensemble-maximum entropy methodology was used to help accurately match the experimental NMR order parameters in the polar headgroup region. All the parameters were developed to be compatible with the remainder of the Drude polarizable force field, which includes water, ions, proteins, DNA, and selected carbohydrates.

Toward Chemically Resolved Computer Simulations of Dynamics and Remodeling of Biological Membranes

Cellular membranes are fundamental constituents of living organisms. Apart from defining the boundaries of the cells, they are involved in a wide range of biological functions, associated with both their structural and the dynamical properties. Biomembranes can undergo large-scale transformations when subject to specific environmental changes, including gel-liquid phase transitions, change of aggregation structure, formation of microtubules, or rupture into vesicles. All of these processes are dependent on a delicate interplay between intermolecular forces, molecular crowding, and entropy, and their understanding requires approaches that are able to capture and rationalize the details of all of the involved interactions. Molecular dynamics-based computational models at atom-level resolution are, in principle, the best way to perform such investigations. Unfortunately, the relevant spatial and time dimensionalities involved in membrane remodeling phenomena would require computational costs that are today unaffordable on a routinely basis. Such hurdles can be removed by coarse-graining the representations of the individual molecular components of the systems. This procedure anyway reduces the possibility of describing the chemical variations in the lipid mixtures composing biological membranes. New hybrid particle field multiscale approaches offer today a promising alternative to the more traditional particle-based simulations methods. By combining chemically distinguishable molecular representations with mesoscale-based computationally affordable potentials, they appear as one of the most promising ways to keep an accurate description of the chemical complexity of biological membranes and, at the same time, cover the required scales to describe remodeling events.

Detailed Structural Analysis of a Self-Assembled Vesicular Amphiphilic NCN-Pincer Palladium Complex by Using Wide-Angle X-Ray Scattering and Molecular Dynamics Calculations

Wide-angle X-ray scattering experiments and all-atomistic molecular dynamics calculations were performed to elucidate the detailed structure of bilayer vesicles constructed by self-assembly of an amphiphilic palladium NCN-pincer complex. We found an excellent agreement between the experimental and calculated X-ray spectra, and between the membrane thickness determined from a TEM image and that calculated from an electron-density profile, which indicated that the calculated structure was highly reliable. The analysis of the simulated bilayer structure showed that in general the membrane was softer than other phospholipid bilayer membranes. In this bilayer assemblage, the degree of alignment of complex molecules in the bilayer membrane was quite low. An analysis of the electron-density profile shows that the bilayer assemblage contains a space through which organic molecules can exit. Furthermore, the catalytically active center is near this space and is easily accessible by organic molecules, which permits the bilayer membrane to act as a nanoreactor. The free energy of permeation of water through the bilayer membrane of the amphiphilic complex was 12 kJ mol^-1 , which is much lower than that for phospholipid bilayer membranes in general. Organic molecules are expected to pass though the bilayer membrane. The self-assembled vesicles were shown to be catalytically active in a Miyaura-Michael reaction in water.

The Effect of Tethers on Artificial Cell Membranes: A Coarse-Grained Molecular Dynamics Study

Tethered bilayer lipid membranes (tBLMs) provide a stable platform for modeling the dynamics and order of biological membranes where the tethers mimic the cytoskeletal supports present in biological cell membranes. In this paper coarse-grained molecular dynamics (CGMD) is applied to study the effects of tethers on lipid membrane properties. Using results from the CGMD model and the overdamped Fokker-Planck equation, we show that the diffusion tensor and particle density of water in the tBLM is spatially dependent. Further, it is shown that the membrane thickness, lipid diffusion, defect density, free energy of lipid flip-flop, and membrane dielectric permittivity are all dependent on the tether density. The numerically computed results from the CGMD model are in agreement with the experimentally measured results from tBLMs containing different tether densities and lipids derived from Archaebacteria. Additionally, using experimental measurements from Escherichia coli bacteria and Saccharomyces Cerevisiae yeast tethered membranes, we illustrate how previous molecular dynamics results can be combined with the proposed model to estimate the dielectric permittivity and defect density of these membranes as a function of tether density.

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.

Toward Atomistic Resolution Structure of Phosphatidylcholine Headgroup and Glycerol Backbone at Different Ambient Conditions

Phospholipids are essential building blocks of biological membranes. Despite a vast amount of very accurate experimental data, the atomistic resolution structures sampled by the glycerol backbone and choline headgroup in phoshatidylcholine bilayers are not known. Atomistic resolution molecular dynamics simulations have the potential to resolve the structures, and to give an arrestingly intuitive interpretation of the experimental data, but only if the simulations reproduce the data within experimental accuracy. In the present work, we simulated phosphatidylcholine (PC) lipid bilayers with 13 different atomistic models, and compared simulations with NMR experiments in terms of the highly structurally sensitive C-H bond vector order parameters. Focusing on the glycerol backbone and choline headgroups, we showed that the order parameter comparison can be used to judge the atomistic resolution structural accuracy of the models. Accurate models, in turn, allow molecular dynamics simulations to be used as an interpretation tool that translates these NMR data into a dynamic three-dimensional representation of biomolecules in biologically relevant conditions. In addition to lipid bilayers in fully hydrated conditions, we reviewed previous experimental data for dehydrated bilayers and cholesterol-containing bilayers, and interpreted them with simulations. Although none of the existing models reached experimental accuracy, by critically comparing them we were able to distill relevant chemical information: (1) increase of choline order parameters indicates the P-N vector tilting more parallel to the membrane, and (2) cholesterol induces only minor changes to the PC (glycerol backbone) structure. This work has been done as a fully open collaboration, using nmrlipids.blogspot.fi as a communication platform; all the scientific contributions were made publicly on this blog. During the open research process, the repository holding our simulation trajectories and files ( https://zenodo.org/collection/user-nmrlipids ) has become the most extensive publicly available collection of molecular dynamics simulation trajectories of lipid bilayers.

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.

CHARMM all-atom additive force field for sphingomyelin: elucidation of hydrogen bonding and of positive curvature

The C36 CHARMM lipid force field has been extended to include sphingolipids, via a combination of high-level quantum mechanical calculations on small molecule fragments, and validation by extensive molecular dynamics simulations on N-palmitoyl and N-stearoyl sphingomyelin. NMR data on these two molecules from several studies in bilayers and micelles played a strong role in the development and testing of the force field parameters. Most previous force fields for sphingomyelins were developed before the availability of the detailed NMR data and relied on x-ray diffraction of bilayers alone for the validation; these are shown to be too dense in the bilayer plane based on published chain order parameter data from simulations and experiments. The present simulations reveal O-H:::O-P intralipid hydrogen bonding occurs 99% of the time, and interlipid N-H:::O=C (26-29%, depending on the lipid) and N-H:::O-H (17-19%). The interlipid hydrogen bonds are long lived, showing decay times of 50 ns, and forming strings of lipids, and leading to reorientational correlation time of nearly 100 ns. The spontaneous radius of curvature for pure N-palmitoyl sphingomyelin bilayers is estimated to be 43-100 Å, depending on the assumptions made in assigning a bending constant; this unusual positive curvature for a two-tailed neutral lipid is likely associated with hydrogen bond networks involving the NH of the sphingosine group.

Long-timescale motions in glycerol-monopalmitate lipid bilayers investigated using molecular dynamics simulation

The occurrence of long-timescale motions in glycerol-1-monopalmitate (GMP) lipid bilayers is investigated based on previously reported 600 ns molecular dynamics simulations of a 2×8×8 GMP bilayer patch in the temperature range 302-338 K, performed at three different hydration levels, or in the presence of the cosolutes methanol or trehalose at three different concentrations. The types of long-timescale motions considered are: (i) the possible phase transitions; (ii) the precession of the relative collective tilt-angle of the two leaflets in the gel phase; (iii) the trans-gauche isomerization of the dihedral angles within the lipid aliphatic tails; and (iv) the flipping of single lipids across the two leaflets. The results provide a picture of GMP bilayers involving a rich spectrum of events occurring on a wide range of timescales, from the 100-ps range isomerization of single dihedral angles, via the 100-ns range of tilt precession motions, to the multi-μs range of phase transitions and lipid-flipping events.

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.

CHARMM36 united atom chain model for lipids and surfactants

Molecular simulations of lipids and surfactants require accurate parameters to reproduce and predict experimental properties. Previously, a united atom (UA) chain model was developed for the CHARMM27/27r lipids (Hénin, J., et al. J. Phys. Chem. B. 2008, 112, 7008-7015) but suffers from the flaw that bilayer simulations using the model require an imposed surface area ensemble, which limits its use to pure bilayer systems. A UA-chain model has been developed based on the CHARMM36 (C36) all-atom lipid parameters, termed C36-UA, and agreed well with bulk, lipid membrane, and micelle formation of a surfactant. Molecular dynamics (MD) simulations of alkanes (heptane and pentadecane) were used to test the validity of C36-UA on density, heat of vaporization, and liquid self-diffusion constants. Then, simulations using C36-UA resulted in accurate properties (surface area per lipid, X-ray and neutron form factors, and chain order parameters) of various saturated- and unsaturated-chain bilayers. When mixed with the all-atom cholesterol model and tested with a series of 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC)/cholesterol mixtures, the C36-UA model performed well. Simulations of self-assembly of a surfactant (dodecylphosphocholine, DPC) using C36-UA suggest an aggregation number of 53 ± 11 DPC molecules at 0.45 M of DPC, which agrees well with experimental estimates. Therefore, the C36-UA force field offers a useful alternative to the all-atom C36 lipid force field by requiring less computational cost while still maintaining the same level of accuracy, which may prove useful for large systems with proteins.

Identification of novel cholesterol-binding regions in Kir2 channels

Inwardly rectifying potassium (Kir) channels play an important role in setting the resting membrane potential and modulating membrane excitability. We have recently shown that cholesterol regulates representative members of the Kir family and that in the majority of the cases, cholesterol suppresses channel function. Furthermore, recent data indicate that cholesterol regulates Kir channels by specific sterol-protein interactions, yet the location of the cholesterol binding site in Kir channels is unknown. Using a combined computational-experimental approach, we show that cholesterol may bind to two nonanular hydrophobic regions in the transmembrane domain of Kir2.1 located between adjacent subunits of the channel. The location of the binding regions suggests that cholesterol modulates channel function by affecting the hinging motion at the center of the pore-lining transmembrane helix that underlies channel gating either directly or through the interface between the N and C termini of the channel.

Simulations of anionic lipid membranes: development of interaction-specific ion parameters and validation using NMR data

Overbinding of ions to lipid head groups is a potentially serious artifact in simulations of charged lipid bilayers. In this study, the Lennard-Jones radii in the CHARMM force field for interactions of Na(+) and lipid oxygen atoms of carboxyl, phosphate, and ester groups were revised to match osmotic pressure data on sodium acetate and electrophoresis data on palmitoyloleoyl phosphatidylcholine (POPC) vesicles. The new parameters were then validated by successfully reproducing previously published experimental NMR deuterium order parameters for dimyristoyl phosphatidylglycerol (DMPG) and newly obtained values for palmitoyloleoyl phosphatidylserine (POPS). Although the increases in Lennard-Jones diameters are only 0.02-0.12 Å, they are sufficient to reduce Na+ binding, and thereby increase surface areas per lipid by 5-10% compared with the unmodified parameters.

A polarizable force field of dipalmitoylphosphatidylcholine based on the classical Drude model for molecular dynamics simulations of lipids

A polarizable force field of saturated phosphatidylcholine-containing lipids based on the classical Drude oscillator model is optimized and used in molecular dynamics simulations of bilayer and monolayer membranes. The hierarchical parametrization strategy involves the optimization of parameters for small molecules representative of lipid functional groups, followed by their application in larger model compounds and full lipids. The polar headgroup is based on molecular ions tetramethyl ammonium and dimethyl phosphate, the esterified glycerol backbone is based on methyl acetate, and the aliphatic lipid hydrocarbon tails are based on linear alkanes. Parameters, optimized to best represent a collection of gas and liquid properties for these compounds, are assembled into a complete model of dipalmitoylphosphatidylcholine (DPPC) lipids that is tested against the experimental properties of bilayer and monolayer membranes. The polarizable model yields average structural properties that are in broad accord with experimental data. The area per lipid of the model is 60 Å(2), slightly smaller than the experimental value of 63 Å(2). The order parameters from nuclear magnetic resonance deuterium quadrupolar splitting measures, the electron density profile, and the monolayer dipole potential are in reasonable agreement with experimental data, and with the nonpolarizable CHARMM C36 lipid force field.

Comparing simulations of lipid bilayers to scattering data: the GROMOS 43A1-S3 force field

Simulations of DOPC at T = 303 K were performed using the united atom force field 43A1-S3 at six fixed projected areas, A(P) = 62, 64, 66, 68, 70, and 72 Å(2), as well as a tensionless simulation that produced an average A(NPT) = 65.8 Å(2). After a small undulation correction for the system size consisting of 288 lipids, results were compared to experimental data. The best, and excellent, fit to neutron scattering data occurs at an interpolated A(N) = 66.6 Å(2) and the best, but not as good, fit to the more extensive X-ray scattering data occurs at A(X) = 68.7 Å(2). The distance ΔDB-H between the Gibbs dividing surface for water and the peak in the electron density profile agrees with scattering experiments. The calculated area compressibility K(A) = 277 ± 10 mN/m is in excellent agreement with the micromechanical experiment. The volume per lipid V(L) is smaller than volume experiments which suggests a workaround that raises all the areas by about 1.5%. Although A(X) ≠ A(N) ≠ A(NPT), this force field obtains acceptable agreement with experiment for A(L) = 67.5 Å(2) (68.5 Å(2) in the workaround), which we suggest is a better DOPC result from 43A1-S3 simulations than its value from the tensionless NPT simulation. However, nonsimulation modeling obtains better simultaneous fits to both kinds of scattering data, which suggests that the force fields can still be improved.

Lipid nanotechnology

Nanotechnology is a multidisciplinary field that covers a vast and diverse array of devices and machines derived from engineering, physics, materials science, chemistry and biology. These devices have found applications in biomedical sciences, such as targeted drug delivery, bio-imaging, sensing and diagnosis of pathologies at early stages. In these applications, nano-devices typically interface with the plasma membrane of cells. On the other hand, naturally occurring nanostructures in biology have been a source of inspiration for new nanotechnological designs and hybrid nanostructures made of biological and non-biological, organic and inorganic building blocks. Lipids, with their amphiphilicity, diversity of head and tail chemistry, and antifouling properties that block nonspecific binding to lipid-coated surfaces, provide a powerful toolbox for nanotechnology. This review discusses the progress in the emerging field of lipid nanotechnology.

The Role of Atomic Polarization in the Thermodynamics of Chloroform Partitioning to Lipid Bilayers

In spite of extensive research and use in medical practice, the precise molecular mechanism of volatile anesthetic action remains unknown. The distribution of anesthetics within lipid bilayers and potential targeting to membrane proteins is thought to be central to therapeutic function. Therefore, obtaining a molecular level understanding of volatile anesthetic partitioning into lipid bilayers is of vital importance to modern pharmacology. In this study we investigate the partitioning of the prototypical anesthetic, chloroform, into lipid bilayers and different organic solvents using molecular dynamics simulations with potential models ranging from simplified coarse-grained MARTINI to additive and polarizable CHARMM all-atom force fields. Many volatile anesthetics display significant inducible dipole moments, which correlate with their potency, yet the exact role of molecular polarizability in their stabilization within lipid bilayers remains unknown. We observe that explicit treatment of atomic polarizability makes it possible to accurately reproduce solvation free energies in solvents with different polarities, allowing for quantitative studies in heterogeneous molecular distributions, such as lipid bilayers. We calculate the free energy profiles for chloroform crossing lipid bilayers to reveal a role of polarizability in modulating chloroform partitioning thermodynamics via the chloroform-induced dipole moment and highlight competitive binding to the membrane core and toward the glycerol backbone that may have significant implications for understanding anesthetic action.

Update of the cholesterol force field parameters in CHARMM

A modification of the CHARMM36 lipid force field (C36) for cholesterol, henceforth, called C36c, is reported. A fused ring compound, decalin, was used to model the steroid section of cholesterol. For decalin, C36 inaccurately predicts the heat of vaporization (~10 kJ/mol) and molar volume (~10 cc/mol), but C36c resulted in near perfect comparison with experiment. MD simulations of decalin and heptane at various compositions were run to estimate the enthalpy and volumes of mixing to compare to experiment for this simple model of cholesterol in a chain environment. Superior estimates for these thermodynamic properties were obtained with C36c versus C36. These new parameters were applied to cholesterol, and quantum mechanical calculations were performed to modify the torsional potential of an acyl chain torsion for cholesterol. This model was tested through simulations of DMPC/10% cholesterol, DMPC/30% cholesterol, and DOPC/10% cholesterol. The C36 and C36c results were similar for surface areas per lipid, deuterium order parameters, electron density profiles, and atomic form factors and generally agree well with experiment. However, C36 and C36c produced slightly different cholesterol angle distributions with C36c adopting a more perpendicular orientation with respect to the bilayer plane. The new parameters in the C36c modification should enable more accurate simulations of lipid bilayers with cholesterol, especially for those interested in the free energy of lipid flip/flop or transfer of phospholipids and/or cholesterol.

Development of the CHARMM Force Field for Lipids

The development of the CHARMM additive all-atom lipid force field (FF) is traced from the early 1990's to the most recent version (C36) published in 2010. Though simulations with early versions yielded useful results, they failed to reproduce two important quantities: a zero surface tension at the experimental bilayer surface area, and the signature splitting of the deuterium order parameters in the glycerol and upper chain carbons. Systematic optimization of parameters based on high level quantum mechanical data and free energy simulations have resolved these issues, and bilayers with a wide range of lipids can be simulated in tensionless ensembles using C36. Issues associated with other all-atom lipid FFs, success and limitations in the C36 FF and ongoing developments are also discussed.

Chemical versus mechanical perturbations on the protonation state of arginine in complex lipid membranes: insights from microscopic pKa calculations

Charged amino acids such as Arginine play important roles in many membrane-mediated biological processes such as voltage gating of ion channels and membrane translocation of cell penetration peptides. It is well established that local membrane deformation and formation of water defects are crucial to the stabilization of charged species in contact with the membrane, which suggests that mechanical properties of the membrane are relevant although a clear connection has not been established. As a quantitative measure, we study how changes in the composition and therefore mechanical properties of a lipid bilayer influence the pK(a) of Arg in the membrane center using free energy simulations. Compared to previous studies in a single-component lipid bilayer containing saturated lipids or lipids with a modest degree of unsaturation, substantially larger pK(a) shifts are observed in the presence of highly unsaturated lipid tails and cholesterol. Moreover, the underlying molecular mechanisms for the pK(a) perturbation are distinct in different systems, with the unsaturated lipid tails mainly destabilizing the charged state of Arg and the cholesterol stabilizing the neutral state of Arg. The observed behaviors in both cases are at odds with predictions based on mechanical considerations at a mesoscopic level--highlighting that, while mechanical considerations are useful for stimulating hypothesis, their applicability to dissecting phenomena at the molecular-length scale is rather limited.

Force field dependence of phospholipid headgroup and acyl chain properties: comparative molecular dynamics simulations of DMPC bilayers

The reliability of molecular simulations largely depends on the quality of the empirical force field parameters. Force fields used in lipid simulations continue to be improved to enhance the agreement with experiments for a number of different properties. In this work, we have carried out molecular dynamics simulations of neat DMPC bilayers using united-atom Berger force field and three versions of all-atom CHARMM force fields. Three different systems consisting of 48, 72, and 96 lipids were studied. Both particle mesh Ewald (PME) and spherical cut-off schemes were used to evaluate the long-range electrostatic interactions. In total, 21 simulations were carried out and analyzed to find out the dependence of lipid properties on force fields, system size, and schemes to calculate long-range interactions. The acyl chain order parameters calculated from Berger and the recent versions of CHARMM simulations have shown generally good agreement with the experimental results. However, both sets of force fields deviate significantly from the experimentally observed P-C dipolar coupling values for the carbon atoms that link the choline and glycerol groups with the phosphate groups. Significant differences are also observed in several headgroup parameters between CHARMM and Berger simulations. Our results demonstrate that when changes were introduced to improve CHARMM force field using PME scheme, all the headgroup parameters have not been reoptimized. The headgroup properties are likely to play a significant role in lipid-lipid, protein-lipid, and ligand-lipid interactions and hence headgroup parameters in phospholipids require refinement for both Berger and CHARMM force fields.

Update of the CHARMM all-atom additive force field for lipids: validation on six lipid types

A significant modification to the additive all-atom CHARMM lipid force field (FF) is developed and applied to phospholipid bilayers with both choline and ethanolamine containing head groups and with both saturated and unsaturated aliphatic chains. Motivated by the current CHARMM lipid FF (C27 and C27r) systematically yielding values of the surface area per lipid that are smaller than experimental estimates and gel-like structures of bilayers well above the gel transition temperature, selected torsional, Lennard-Jones and partial atomic charge parameters were modified by targeting both quantum mechanical (QM) and experimental data. QM calculations ranging from high-level ab initio calculations on small molecules to semiempirical QM studies on a 1,2-dipalmitoyl-sn-phosphatidylcholine (DPPC) bilayer in combination with experimental thermodynamic data were used as target data for parameter optimization. These changes were tested with simulations of pure bilayers at high hydration of the following six lipids: DPPC, 1,2-dimyristoyl-sn-phosphatidylcholine (DMPC), 1,2-dilauroyl-sn-phosphatidylcholine (DLPC), 1-palmitoyl-2-oleoyl-sn-phosphatidylcholine (POPC), 1,2-dioleoyl-sn-phosphatidylcholine (DOPC), and 1-palmitoyl-2-oleoyl-sn-phosphatidylethanolamine (POPE); simulations of a low hydration DOPC bilayer were also performed. Agreement with experimental surface area is on average within 2%, and the density profiles agree well with neutron and X-ray diffraction experiments. NMR deuterium order parameters (S(CD)) are well predicted with the new FF, including proper splitting of the S(CD) for the aliphatic carbon adjacent to the carbonyl for DPPC, POPE, and POPC bilayers. The area compressibility modulus and frequency dependence of (13)C NMR relaxation rates of DPPC and the water distribution of low hydration DOPC bilayers also agree well with experiment. Accordingly, the presented lipid FF, referred to as C36, allows for molecular dynamics simulations to be run in the tensionless ensemble (NPT), and is anticipated to be of utility for simulations of pure lipid systems as well as heterogeneous systems including membrane proteins.

Structural aspects of lipid monolayers: computer simulation analyses

Extensive molecular dynamics simulations at room temperature were carried out for model films of two dissimilar lipids (DPPC and dicaprin) at the air/water interface. To study the peculiarities of the organization patterns at different average areas per molecule, surface concentrations corresponding to five almost equally spaced points along the isotherms of the two surfactants were considered. A variable of prime interest was the density distribution in a direction normal to the interface of the monolayer components: interfacial water and surfactant on one hand and the separate moieties of the lipids on the other hand. The packing pattern and cluster size dispersion were studied by means of Voronoi tessellation and radial distribution functions. Speculations regarding structural changes upon phase-state changes during film compression were made. Individual characteristics for surfactant heads and tails as well as for interfacial water were outlined and related to the available experimental data. An analysis of the diffusion coefficients revealed the limiting factors for lipid lateral and normal diffusion. Structural arguments in support of changes in monolayer dielectric properties with the area per molecule were provided.

Curvature generation and pressure profile modulation in membrane by lysolipids: insights from coarse-grained simulations

Although many membrane additives are known to modulate the activities of membrane proteins via perturbing the properties of lipid membrane, the underlying mechanism is often not precisely understood. In this study, we investigate the impact of asymmetrically incorporating single-tailed lysophosphatidylcholine (LPC) into a membrane bilayer using coarse-grained molecular dynamics simulations. Using a simple computational protocol designed to approximately mimic a micropipette setting, we show that asymmetric incorporation of LPC can lead to significant curvature in a bilayer. Detailed analysis of geometrical and mechanical properties (pressure profile) of the resulting mound structure indicates that the degree of pressure profile perturbation is determined not by the local curvature per se but by the packing of lipid headgroups (i.e., area-per-lipid). The findings help provide a concrete basis for understanding the activation mechanism of mechanosensitive channels by asymmetric incorporation of LPC into membrane patches in patch-clamp experiments. The calculated local pressure profiles are valuable to the construction of realistic membrane models for the analysis of mechanosensation in a continuum mechanics framework.

Lipids on the move: simulations of membrane pores, domains, stalks and curves

In this review we describe the state-of-the-art of computer simulation studies of lipid membranes. We focus on collective lipid-lipid and lipid-protein interactions that trigger deformations of the natural lamellar membrane state, showing that many important biological processes including self-aggregation of membrane components into domains, the formation of non-lamellar phases, and membrane poration and curving, are now amenable to detailed simulation studies.