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

Balancing Group I Monatomic Ion-Polar Compound Interactions for Condensed Phase Simulation in the Polarizable Drude Force Field

Molecular dynamics (MD) simulations are a commonly used method for investigating molecular behavior at the atomic level. Achieving reliable MD simulation results necessitates the use of an accurate force field. In the present work, we present a protocol to enhance the quality of group 1 monatomic ions (specifically Li+, Na+, K+, Rb+, and Cs+) with respect to their interactions with common polar model compounds in biomolecules in condensed phases in the context of the Drude polarizable force field. Instead of adjusting preexisting individual parameters for ions, model compounds, and water, we employ atom-pair specific Lennard-Jones (LJ) (known as NBFIX in CHARMM) and through-space Thole dipole screening (NBTHOLE) terms to fine-tune the balance of ion-model compound, ion-water, and model compound-water interactions. This involved establishing a protocol for the optimization of NBFIX and NBTHOLE parameters targeting the difference between molecular mechanical (MM) and quantum mechanical (QM) potential energy scans (PES). It is shown that targeting PES involving complexes that include multiple model compounds and/or ions as trimers and tetramers yields parameters that produce condensed phase properties in agreement with experimental data. Validation of this protocol involved the reproduction of experimental thermodynamic benchmarks, including solvation free energies of ions in methanol and N-methylacetamide, osmotic pressures, ionic conductivities, and diffusion coefficients within the condensed phase. These results show the importance of including more complex ion-model compound complexes beyond dimers in the QM target data to account for many-body effects during parameter fitting. The presented parameters represent a significant refinement of the Drude polarizable force field, which will lead to improved accuracy for modeling ion-biomolecular interactions.

Quantitative Comparison against Experiments Reveals Imperfections in Force Fields' Descriptions of POPC-Cholesterol Interactions

Cholesterol is a central building block in biomembranes, where it induces orientational order, slows diffusion, renders the membrane stiffer, and drives domain formation. Molecular dynamics (MD) simulations have played a crucial role in resolving these effects at the molecular level; yet, it has recently become evident that different MD force fields predict quantitatively different behavior. Although easily neglected, identifying such limitations is increasingly important as the field rapidly progresses toward simulations of complex membranes mimicking the in vivo conditions: pertinent multicomponent simulations must capture accurately the interactions between their fundamental building blocks, such as phospholipids and cholesterol. Here, we define quantitative quality measures for simulations of binary lipid mixtures in membranes against the C-H bond order parameters and lateral diffusion coefficients from NMR spectroscopy as well as the form factors from X-ray scattering. Based on these measures, we perform a systematic evaluation of the ability of commonly used force fields to describe the structure and dynamics of binary mixtures of palmitoyloleoylphosphatidylcholine (POPC) and cholesterol. None of the tested force fields clearly outperforms the others across the tested properties and conditions. Still, the Slipids parameters provide the best overall performance in our tests, especially when dynamic properties are included in the evaluation. The quality evaluation metrics introduced in this work will, particularly, foster future force field development and refinement for multicomponent membranes using automated approaches.

Calculations of Absolute Solvation Free Energies with Transformato─Application to the FreeSolv Database Using the CGenFF Force Field

We recently introduced transformato, an open-source Python package for the automated setup of large-scale calculations of relative solvation and binding free energy differences. Here, we extend the capabilities of transformato to the calculation of absolute solvation free energy differences. After careful validation against the literature results and reference calculations with the PERT module of CHARMM, we used transformato to compute absolute solvation free energies for most molecules in the FreeSolv database (621 out of 642). The force field parameters were obtained with the program cgenff (v2.5.1), which derives missing parameters from the CHARMM general force field (CGenFF v4.6). A long-range correction for the Lennard-Jones interactions was added to all computed solvation free energies. The mean absolute error compared to the experimental data is 1.12 kcal/mol. Our results allow a detailed comparison between the AMBER and CHARMM general force fields and provide a more in-depth understanding of the capabilities and limitations of the CGenFF small molecule parameters.

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.

Ceramide-1-phosphate transfer protein enhances lipid transport by disrupting hydrophobic lipid-membrane contacts

Cellular distributions of the sphingolipid ceramide-1-phosphate (C1P) impact essential biological processes. C1P levels are spatiotemporally regulated by ceramide-1-phosphate transfer protein (CPTP), which efficiently shuttles C1P between organelle membranes. Yet, how CPTP rapidly extracts and inserts C1P into a membrane remains unknown. Here, we devise a multiscale simulation approach to elucidate biophysical details of CPTP-mediated C1P transport. We find that CPTP binds a membrane poised to extract and insert C1P and that membrane binding promotes conformational changes in CPTP that facilitate C1P uptake and release. By significantly disrupting a lipid's local hydrophobic environment in the membrane, CPTP lowers the activation free energy barrier for passive C1P desorption and enhances C1P extraction from the membrane. Upon uptake of C1P, further conformational changes may aid membrane unbinding in a manner reminiscent of the electrostatic switching mechanism used by other lipid transfer proteins. Insertion of C1P into an acceptor membrane, eased by a decrease in membrane order by CPTP, restarts the transfer cycle. Most notably, we provide molecular evidence for CPTP's ability to catalyze C1P extraction by breaking hydrophobic C1P-membrane contacts with compensatory hydrophobic lipid-protein contacts. Our work, thus, provides biophysical insights into how CPTP efficiently traffics C1P between membranes to maintain sphingolipid homeostasis and, additionally, presents a simulation method aptly suited for uncovering the catalytic mechanisms of other lipid transfer proteins.

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.

Refinement of the Optimized Potentials for Liquid Simulations Force Field for Thermodynamics and Dynamics of Liquid Alkanes

Torsion and Lennard-Jones parameters of the optimized potentials for liquid simulations (OPLS) all-atom force field have been refined for describing thermodynamics and dynamics of a wide range of liquid alkanes. Monte Carlo statistical mechanics (MC) and molecular dynamics (MD) simulations were carried out. For thermodynamics properties, MC simulations with truncated electrostatic interactions performed very closely to MD simulations with a Verlet neighbor list and the particle mesh Ewald algorithm. The average errors in comparison with experimental data for computed properties were improved with the modified force field (OPLS/2020), especially for long-chain alkanes. For liquid densities, heats of vaporization, and free energies of hydration, the average errors are 0.01 g/cm³, 0.2 kcal/mol, and ca. 0.5 kcal/mol, respectively; significant gains were made for relative heats of vaporization of isomeric series. Results for self-diffusion coefficients also reproduce experimental data well for linear alkane liquids up to hexadecane. The new force field is suitable for use in improved modeling of myriad systems of importance in chemistry, biology, and materials science.

Computing the Work of Solid-Liquid Adhesion in Systems with Damped Coulomb Interactions via Molecular Dynamics: Approaches and Insights

Recently, the dry-surface method [Langmuir2016, 31, 8335−8345] has been developed to compute the work of adhesion of solid–liquid and other interfaces using molecular dynamics via thermodynamic integration. Unfortunately, when long-range Coulombic interactions are present in the interface, a special treatment is required, such as solving additional Poisson equations, which is usually not implemented in generic molecular dynamics software, or as fixing some groups of atoms in place, which is undesirable most of the time. In this work, we replace the long-range Coulombic interactions with damped Coulomb interactions, and explore several thermal integration paths. We demonstrate that regardless of the integration path, the same work of adhesion values are obtained as long as the path is reversible, but the numerical efficiency differs vastly. Simple scaling of the interactions is most efficient, requiring as little as 8 sampling points, followed by changing the Coulomb damping parameter, while modifying the Coulomb interaction cutoff length performs worst. We also demonstrate that switching long-range Coulombic interactions to damped ones results in a higher work of adhesion by about 10 mJ/m² because of slightly different liquid molecule orientation at the solid–liquid interface, and this value is mostly unchanged for surfaces with substantially different Coulombic interactions at the solid–liquid interface. Finally, even though it is possible to split the work of adhesion into van der Waals and Coulomb components, it is known that the specific per-component values are highly dependent on the integration path. We obtain an extreme case, which demonstrates that caution should be taken even when restricting to qualitative comparison.

Accurate Simulations of Lipid Monolayers Require a Water Model with Correct Surface Tension

Lipid monolayers provide our lungs and eyes their functionality and serve as proxy systems in biomembrane research. Therefore, lipid monolayers have been studied intensively including using molecular dynamics simulations, which are able to probe their lateral structure and interactions with, e.g., pharmaceuticals or nanoparticles. However, such simulations have struggled in describing the forces at the air-water interface. Particularly, the surface tension of water and long-range van der Waals interactions have been considered critical, but their importance in monolayer simulations has been evaluated only separately. Here, we combine the recent C36/LJ-PME lipid force field that includes long-range van der Waals forces with water models that reproduce experimental surface tensions to elucidate the importance of these contributions in monolayer simulations. Our results suggest that a water model with correct surface tension is necessary to reproduce experimental surface pressure-area isotherms and monolayer phase behavior. The latter includes the liquid expanded and liquid condensed phases, their coexistence, and the opening of pores at the correct area per lipid upon expansion. Despite these improvements of the C36/LJ-PME with certain water models, the standard cutoff-based CHARMM36 lipid model with the 4-point OPC water model still provides the best agreement with experiments. Our results emphasize the importance of using high-quality water models in applications and parameter development in molecular dynamics simulations of biomolecules.

All-Atom Modeling of Complex Cellular Membranes

Cell membranes are composed of a variety of lipids and proteins where they interact with each other to fulfill their roles. The first step in modeling these interactions in molecular simulations is to have reliable mimetics of the membrane's lipid environment. This Feature Article presents our recent efforts to model complex cellular membranes using all-atom force fields. A short review of the CHARMM36 (C36) lipid force field and its recent update to incorporate the long-range dispersion is presented. Key examples of model membranes mimicking various species and organelles are given. These include single-celled organisms such as bacteria (E. coli., chlamydia, and P. aeruginosa) and yeast (plasma membrane, endoplasmic reticulum, and trans-Golgi network) and more advanced ones such as plants (soybean and Arabidopsis thaliana) and mammals (ocular lens, stratum corneum, and peripheral nerve myelin). Leaflet asymmetry in composition has also been applied to some of these models. With the increased lipid diversity in the C36 lipid FF, these complex models can better reflect the structural, mechanical, and dynamic properties of realistic membranes and open an opportunity to study biological processes involving other molecules.

Recharging your fats: CHARMM36 parameters for neutral lipids triacylglycerol and diacylglycerol

Neutral lipids (NLs) are an abundant class of cellular lipids. They are characterized by the total lack of charged chemical groups in their structure, and, as a consequence, they play a major role in intracellular lipid storage. NLs that carry a glycerol backbone, such as triacylglycerols (TGs) and diacylglycerols (DGs), are also involved in the biosynthetic pathway of cellular phospholipids, and they have recently been the subject of numerous structural investigations by means of atomistic molecular dynamics simulations. However, conflicting results on the physicochemical behavior of NLs were observed depending on the nature of the atomistic force field used. Here, we show that current phospholipid-derived CHARMM36 parameters for DGs and TGs cannot adequately reproduce interfacial properties of these NLs because of excessive hydrophilicity at the glycerol-ester region. By following a CHARMM36-consistent parameterization strategy, we develop improved parameters for both TGs and DGs that are compatible with both cutoff-based and particle mesh Ewald schemes for the treatment of Lennard-Jones interactions. We show that our improved parameters can reproduce interfacial properties of NLs and their behavior in more complex lipid assemblies. We discuss the implications of our findings in the context of intracellular lipid storage and NLs’ cellular activity.

CHARMM-GUI Drude prepper for molecular dynamics simulation using the classical Drude polarizable force field

Explicit treatment of electronic polarizability in empirical force fields (FFs) represents an extension over a traditional additive or pairwise FF and provides a more realistic model of the variations in electronic structure in condensed phase, macromolecular simulations. To facilitate utilization of the polarizable FF based on the classical Drude oscillator model, Drude Prepper has been developed in CHARMM-GUI. Drude Prepper ingests additive CHARMM protein structures file (PSF) and pre-equilibrated coordinates in CHARMM, PDB, or NAMD format, from which the molecular components of the system are identified. These include all residues and patches connecting those residues along with water, ions, and other solute molecules. This information is then used to construct the Drude FF-based PSF using molecular generation capabilities in CHARMM, followed by minimization and equilibration. In addition, inputs are generated for molecular dynamics (MD) simulations using CHARMM, GROMACS, NAMD, and OpenMM. Validation of the Drude Prepper protocol and inputs is performed through conversion and MD simulations of various heterogeneous systems that include proteins, nucleic acids, lipids, polysaccharides, and atomic ions using the aforementioned simulation packages. Stable simulations are obtained in all studied systems, including 5 μs simulation of ubiquitin, verifying the integrity of the generated Drude PSFs. In addition, the ability of the Drude FF to model variations in electronic structure is shown through dipole moment analysis in selected systems. The capabilities and availability of Drude Prepper in CHARMM-GUI is anticipated to greatly facilitate the application of the Drude FF to a range of condensed phase, macromolecular systems.

Validating the CHARMM36m protein force field with LJ-PME reveals altered hydrogen bonding dynamics under elevated pressures

The pressure-temperature phase diagram is important to our understanding of the physics of biomolecules. Compared to studies on temperature effects, studies of the pressure dependence of protein dynamic are rather limited. Molecular dynamics (MD) simulations with fine-tuned force fields (FFs) offer a powerful tool to explore the influence of thermodynamic conditions on proteins. Here we evaluate the transferability of the CHARMM36m (C36m) protein force field at varied pressures compared with NMR data using ubiquitin as a model protein. The pressure dependences of J couplings for hydrogen bonds and order parameters for internal motion are in good agreement with experiment. We demonstrate that the C36m FF combined with the Lennard-Jones particle-mesh Ewald (LJ-PME) method is suitable for simulations in a wide range of temperature and pressure. As the ubiquitin remains stable up to 2500 bar, we identify the mobility and stability of different hydrogen bonds in response to pressure. Based on those results, C36m is expected to be applied to more proteins in the future to further investigate protein dynamics under elevated pressures.

Physical Characterization of Triolein and Implications for Its Role in Lipid Droplet Biogenesis

Lipid droplets (LDs) are neutral lipid-storing organelles surrounded by a phospholipid (PL) monolayer. At present, how LDs are formed in the endoplasmic reticulum (ER) bilayer is poorly understood. In this study, we present a revised all-atom (AA) triolein (TG) model, the main constituent of the LD core, and characterize its properties in a bilayer membrane to demonstrate the implications of its behavior in LD biogenesis. In bilayer simulations, TG resides at the surface, adopting PL-like conformations (denoted in this work as SURF-TG). Free energy sampling simulation results estimate the barrier for TG relocating from the bilayer surface to the bilayer center to be ∼2 kcal/mol in the absence of an oil lens. SURF-TG is able to modulate membrane properties by increasing PL ordering, decreasing bending modulus, and creating local negative curvature. The other neutral lipid, dioleoyl-glycerol (DAG), also reduces the membrane bending modulus and populates negative curvature regions. A phenomenological coarse-grained (CG) model is also developed to observe larger-scale SURF-TG-mediated membrane deformation. CG simulations confirm that TG nucleates between the bilayer leaflets at a critical concentration when SURF-TG is evenly distributed. However, when one monolayer contains more SURF-TG, the membrane bends toward the other leaflet, followed by TG nucleation if a concentration is higher than the critical threshold. The central conclusion of this study is that SURF-TG is a negative curvature inducer, as well as a membrane modulator. To this end, a model is proposed in which the accumulation of SURF-TG in the luminal leaflet bends the ER bilayer toward the cytosolic side, followed by TG nucleation.

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.

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.

Determination of van der Waals Parameters Using a Double Exponential Potential for Nonbonded Divalent Metal Cations in TIP3P Solvent

A double exponential (DE) functional form for Lennard-Jones (LJ) interactions, proposed in our previous study, has many advantages over LJ potentials including a natural softcore characteristic for the convenience of the pathway-based free-energy calculations, fast convergence, and flexibility in use. In this work, we put the first step on the application of the DE functional form by identifying a DE potential, coined DE-TIP3P, for molecular simulations using the TIP3P water model. The developed DE-TIP3 potential was better than LJ potential in reproducing the experimental water properties. Afterward, we developed the nonbonded models of 15 divalent metal ions, which frequently appear and play vital roles in biological systems, to be consistent with the DE-TIP3P potential and TIP3P water model. Our nonbonded models were as good as the complicated nonbonded dummy cationic models by Jiang et al. and the nonbonded 12-6-4 LJ models by Li and Merz in reproducing the experimental properties of those ions. Moreover, our nonbonded models achieved a better performance than the compromise (CM) LJ models and 12-6-4 LJ models, developed by Li and Merz, in reproducing the properties of MgCl₂ in aqueous solution.

A compression strategy for particle mesh Ewald theory

Particle Mesh Ewald (PME) has become a standard method for treating long-range electrostatics in molecular simulations. Although the method has inferior asymptotic computational complexity to its linear scaling competitors, it remains enormously popular due to its high efficiency, which stems from the use of fast Fourier transforms (FFTs). This use of FFTs provides great challenges for scaling the method up to massively parallel systems, in large part because of the need to transfer large amounts of data. In this work, we demonstrate that this data transfer volume can be greatly reduced as a natural consequence of the structure of the PME equations. We also suggest an alternative algorithm that supplants the FFT with a linear algebra approach, which further decreases communication costs at the expense of increased asymptotic computational complexity. This linear algebra based approach is demonstrated to have great potential for latency hiding by interleaving communication and computation steps of the short- and long-range electrostatic terms.

Update of the CHARMM36 United Atom Chain Model for Hydrocarbons and Phospholipids

Accurate lipid force field (FF) parameters used in molecular dynamics (MD) simulations are crucial for understanding the properties of lipid-containing systems and biological processes related to lipids. The last update of the CHARMM36 united atom chain model (C36UA) was in 2013 [Lee, S. J. Phys. Chem. B 2014, 118, 547 556]; it utilized CHARMM36 (C36) lipid FF parameters for headgroups and OPLS-UA Lennard-Jones (LJ) parameters for tails. Simulations with the FF were able to reproduce many experimental observables of lipid bilayers accurately, but to be more applicable for a wide range of lipids, additional FF parameter optimization was needed. In this work, we present an update of the model, named C36UAr. The parameterization included the LJ parameters for hydrocarbons and related dihedrals. Bulk liquid properties (density, heat of vaporization, isothermal compressibility, and diffusion constant) of model compounds were used as targets for the LJ parameter fitting, and dihedrals were fit to either quantum mechanical (QM) or potential of mean force (PMF) calculations using C36. Thermodynamic reweighting was used to further improve the parameters. Bilayer simulations of various lipid headgroups (phosphatidylcholine, phosphatidylethanolamine, and phosphatidylglycerol) and tails (saturated, monounsaturated, and polyunsaturated) were performed to validate the model, and significant improvements were seen in bilayer properties, including surface area, membrane thicknesses, NMR deuterium order parameters, and density profiles. C36UAr was also compared to the hydrogen mass repartitioning (HMR) method. The high accuracy and competitive efficiency shown in this study make C36UAr one of the best choices for studies of membrane structure and membrane-associated proteins.

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 Ų, a value that is 10% lower than the one determined experimentally by SDP analysis (61.9 Ų). Furthermore, scattering form factors calculated from the unconstrained simulations were in poor agreement with experimental form factors, even though segmental order parameter (S_CD) profiles calculated from the simulations were in relatively good agreement with S_CD profiles obtained from NMR experiments. Conversely, constrained area simulations at 61.9 Ų resulted in good agreement between the simulation and experimental scattering form factors, but not with S_CD 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.

A New Lipid Force Field (FUJI)

To explore inhomogeneous and anisotropic systems such as lipid bilayers, the Lennard-Jones particle mesh Ewald (LJ-PME) method has been applied without a conventional isotropic dispersion correction. As the popular AMBER and CHARMM lipid force fields were developed using a cutoff scheme, their lipid bilayers unacceptably shrink when using the LJ-PME method. In this study, a new all-atom lipid force field (FUJI) was developed on the basis of the AMBER force-field scheme including the Lipid14 van der Waals parameters. Point charges were calculated using the restrained electrostatic potentials of many lipid conformers. Further, torsion energy profiles were calculated using high-level ab initio molecular orbitals (LCCSD(T)/Aug-cc-pVTZ//LMP2/Aug-cc-pVTZ), following which the molecular mechanical dihedral parameters were derived through a fast Fourier transform. By incorporation of these parameters into a new lipid force field without fitting experimental data, the desired lipid characteristics such as the area per lipid and lateral diffusion coefficients were obtained through GROMACS molecular dynamics simulations using the LJ-PME method and virtual hydrogen sites. The calculated area per lipid and lateral diffusion coefficients showed satisfactory agreement with experimental data. Furthermore, the electron-density profiles along the membrane normal were calculated for pure lipid bilayers, and the resulting membrane thicknesses agreed well with the experimental values. As the new lipid force field is compatible with FUJI for protein and small molecules, the new FUJI force field will offer accurate modeling for complex systems consisting of various membrane proteins and lipids.

Predicting partition coefficients of drug-like molecules in the SAMPL6 challenge with Drude polarizable force fields

The water-octanol partition coefficient is an important physicochemical property for small molecule drug design. Here, we report our participation in the SAMPL6 logP prediction challenge with free energy perturbation (FEP) calculations in the water phase and in the 1-octanol phase using Drude polarizable force fields. Root mean square error (RMSE) and mean absolute error (MAE) of our prediction are equal to 1.85 and 1.25 logP units. The errors are not evenly distributed. Out of eleven SAMPL6 solutes, FEP/Drude performed very badly on three molecules (deviations all larger than 2 logP units) but good on the remaining eight (deviations all less than 1 logP unit). We find while FEP converges well within one nanosecond in water, simulations in 1-octanol need much longer simulation time and possibly more independent runs for sampling. We also find out that 1-octanol, albeit being a non-polar solvent, still polarizes solute molecules and forms stable hydrogen bonds with them. At the end, we attempt to reweight FEP trajectories with QM/Drude calculations and discuss possible caveats in our simulation setup.

Reaction-field electrostatics in molecular dynamics simulations: development of a conservative scheme compatible with an atomic cutoff

Shifting and switching schemes are developed to enable strict energy conservation in molecular dynamics simulations relying on reaction-field electrostatic (as well as Lennard-Jones) interactions with an atom-based cutoff truncation.

Surface Shear Viscosity and Interleaflet Friction from Nonequilibrium Simulations of Lipid Bilayers

Nonequilibrium simulation protocols based on shear deformations are applied to determine the surface viscosity and interleaflet friction of lipid bilayers. At high shear rates, a non-Newtonian shear thinning regime is observed, but lower shear rates yield a Newtonian plateau and results that are consistent with equilibrium measurements based on fluctuation-dissipation theorems. Application to all-atom bilayers modeled with the CHARMM36 parameter set yields values for the surface viscosity that are consistent with microscopic measurements based on membrane protein diffusion but are approximately 10 times lower than more macroscopic experimental measurements. The interleaflet friction is about 10 times lower than experimental measurements. Trends across different lipids, temperatures, and ternary liquid-disordered phase mixtures produce results that are consistent with experimental diffusion constants. Application of the protocol to the liquid-ordered phase fails to yield a Newtonian plateau, suggesting more complex rheology.

Accelerating Membrane Simulations with Hydrogen Mass Repartitioning

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

Molecular Dynamics Simulation of Pure n-Alkanes and Their Mixtures at Elevated Temperatures Using Atomistic and Coarse-Grained Force Fields

The properties of higher n-alkanes and their mixtures is a topic of significant interest for the oil and chemical industry. However, the experimental data at high temperatures are scarce. The present study focuses on simulating n-dodecane, n-octacosane, their binary mixture at a n-dodecane mole fraction of 0.3, and a model mixture of the commercially available hydrocarbon wax SX-70 to evaluate the performance of several force fields on the reproduction of properties such as liquid densities, surface tension, and viscosities. Molecular dynamics simulations over a broad temperature range from 323.15 to 573.15 K were employed in examining a broad set of atomistic molecular models assessed for the reproduction of experimental data. The well-established united atom TraPPE (TraPPE-UA) was compared against the all atom optimized potentials for liquid simulations (OPLS) reparametrization for long n-alkanes, L-OPLS, as well as Lipid14 and MARTINI force fields. All models qualitatively reproduce the temperature dependence of the aforementioned properties, but TraPPE-UA was found to reproduce liquid densities most accurately and consistently over the entire temperature range. TraPPE-UA and MARTINI were very successful in reproducing surface tensions, and L-OPLS was found to be the most accurate in reproducing the measured viscosities as compared to the other models. Our simulations show that these widely used force fields originating from the world of biomolecular simulations are suitable candidates in the study of n-alkane properties, both in the pure and mixture states.

AMOEBA+ Classical Potential for Modeling Molecular Interactions

Classical potentials based on isotropic and additive atomic charges have been widely used to model molecules in computers for the past few decades. The crude approximations in the underlying physics are hindering both their accuracy and transferability across chemical and physical environments. Here we present a new classical potential, AMOEBA+, to capture essential intermolecular forces, including permanent electrostatics, repulsion, dispersion, many-body polarization, short-range charge penetration, and charge transfer, by extending the polarizable multipole-based AMOEBA (Atomic Multipole Optimized Energetics for Biomolecular Applications) model. For a set of common organic molecules, we show that AMOEBA+ with general parameters can reproduce both quantum mechanical interactions and energy decompositions according to Symmetry-Adapted Perturbation Theory (SAPT). Additionally, a new water model based on the AMOEBA+ framework captures various liquid-phase properties in molecular dynamics simulations while remaining consistent with SAPT energy decompositions, utilizing both ab initio data and experimental liquid properties. Our results demonstrate that it is possible to improve the physical basis of classical force fields to advance their accuracy and general applicability.

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.

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.

Simulation Best Practices for Lipid Membranes [Article v1.0]

We establish a reliable and robust standardization of settings for practical molecular dynamics (MD) simulations of pure and mixed (single- and multi-component) lipid bilayer membranes. In lipid membranes research, particle-based molecular simulations are a powerful tool alongside continuum theory, lipidomics, and model, in vitro, and in vivo experiments. Molecular simulations can provide precise and reproducible spatiotemporal (atomic- and femtosecond-level) information about membrane structure, mechanics, thermodynamics, kinetics, and dynamics. Yet the simulation of lipid membranes can be a daunting task, given the uniqueness of lipid membranes relative to conventional liquid-liquid and solid-liquid interfaces, the immense and complex thermodynamic and statistical mechanical theory, the diversity of multiscale lipid models, limitations of modern computing power, the difficulty and ambiguity of simulation controls, finite size effects, competitive continuum simulation alternatives, and the desired application, including vesicle experiments and biological membranes. These issues can complicate an essential understanding of the field of lipid membranes, and create major bottlenecks to simulation advancement. In this article, we clarify these issues and present a consistent, thorough, and user-friendly framework for the design of state-of-the-art lipid membrane MD simulations. We hope to allow early-career researchers to quickly overcome common obstacles in the field of lipid membranes and reach maximal impact in their simulations.

Flexible lipid nanomaterials studied by NMR spectroscopy

Advances in solid-state nuclear magnetic resonance spectroscopy inform the emergence of material properties from atomistic-level interactions in membrane lipid nanostructures.

Force Fields for Small Molecules

Molecular dynamics (MD) simulations have been widely applied to computer-aided drug design (CADD). While MD has been used in a variety of applications such as free energy perturbation and long-time simulations, the accuracy of the results from those methods depends strongly on the force field used. Force fields for small molecules are crucial, as they not only serve as building blocks for developing force fields for larger biomolecules but also act as model compounds that will be transferred to ligands used in CADD. Currently, a wide range of small molecule force fields based on additive or nonpolarizable models have been developed. While these nonpolarizable force fields can produce reasonable estimations of physical properties and have shown success in a variety of systems, there is still room for improvements due to inherent limitations in these models including the lack of an electronic polarization response. For this reason, incorporating polarization effects into the energy function underlying a force field is believed to be an important step forward, giving rise to the development of polarizable force fields. Recent simulations of biological systems have indicated that polarizable force fields are able to provide a better physical representation of intermolecular interactions and, in many cases, better agreement with experimental properties than nonpolarizable, additive force fields. Therefore, this chapter focuses on the development of small molecule force fields with emphasis on polarizable models. It begins with a brief introduction on the importance of small molecule force fields and their evolution from additive to polarizable force fields. Emphasis is placed on the additive CHARMM General Force Field and the polarizable force field based on the classical Drude oscillator. The theory for the Drude polarizable force field and results for small molecules are presented showing their improvements over the additive model. The potential importance of polarization for their application in a wide range of biological systems including CADD is then discussed.

A physically grounded damped dispersion model with particle mesh Ewald summation

Accurate modeling of dispersion is critical to the goal of predictive biomolecular simulations. To achieve this accuracy, a model must be able to correctly capture both the short-range and asymptotic behavior of dispersion interactions. We present here a damped dispersion model based on the overlap of charge densities that correctly captures both regimes. The overlap damped dispersion model represents a classical physical interpretation of dispersion: the interaction between the instantaneous induced dipoles of two distinct charge distributions. This model is shown to be an excellent fit with symmetry adapted perturbation theory dispersion energy calculations, yielding an RMS error on the S101x7 database of 0.5 kcal/mol. Moreover, the damping function used in this model is wholly derived and parameterized from the electrostatic dipole-dipole interaction, making it not only physically grounded but transferable as well.

Parameterization of the CHARMM All-Atom Force Field for Ether Lipids and Model Linear Ethers

Linear ethers such as polyethylene glycol have extensive industrial and medical applications. Additionally, phospholipids containing an ether linkage between the glycerol backbone and hydrophobic tails are prevalent in human red blood cells and nerve tissue. This study uses ab initio results to revise the CHARMM additive (C36) partial-charge and dihedral parameters for linear ethers and develop parameters for the ether-linked phospholipid 1,2-di- O-hexadecyl- sn-glycero-3-phosphocholine (DHPC). The new force field, called C36e, more accurately represents the dihedral potential energy landscape and improves the densities and free energies of hydration of linear ethers. C36e allows more water to penetrate into a DHPC bilayer, increasing the surface area per lipid compared to simulations carried out with the original C36 ether parameters and improving the overall structural properties obtained from X-ray and neutron scattering. Comparison with an ester-linked DPPC bilayer (1,2-dipalmitoyl- sn-phosphatidylcholine) reveals that the ether linkage increases water organization in the headgroup region. This effect is a likely explanation for the experimentally lower water permeability of bilayers composed of ether-linked lipids.