Multiscale Coarse-Graining of Mixed Phospholipid/Cholesterol Bilayers

Can Coarse-Grained Molecular Dynamics Simulations Predict Pharmaceutical Crystal Growth?

To investigate the ability of coarse-grained molecular dynamics simulations to predict the relative growth rates of crystal facets of pharmaceutical molecules, we apply two coarse-graining strategies to two drug molecules, phenytoin and carbamazepine. In the first method, we map an atomistic model to a MARTINI-level coarse-grained (CG) force field that uses 2 or 3 heavy atoms per bead. This is followed by applying Particle Swarm Optimization (PSO), a global optimum searching algorithm, to the CG Lennard-Jones intermolecular potentials to fit the radial distribution functions of both the crystalline and melt structures. In the second, a coarser-grained method, we map 5 or more heavy atoms into one bead with the help of the Iterative Boltzmann Inversion (IBI) method to derive a tabulated longer-range force field (FF). Simulations using the FF's derived from both strategies were able to stabilize the crystal in the correct structure and to predict crystal growth from the melt with modest computational resources. We evaluate the advantages and limitations of both methods and compare the relative growth rates of various facets of both drug crystals with those predicted by the Bravais-Friedel-Donnay-Harker (BFDH) and attachment energy (AE) theories. While all methods, except for the simulations conducted with the coarser-grained IBI-generated model, produced similarly good results for phenytoin, the finer-grained PSO-generated FF using MARTINI mapping rules outperformed the other methods in its prediction of the facet growth rates and resulting crystalline morphology for carbamazepine.

Martini 3 coarse-grained model of enzymes: Framework with validation by all-atom simulations and x-ray diffraction measurements

Recent experiments have shown that complexation with a stabilizing compound can preserve enzyme activity in harsh environments. Such complexation is believed to be driven by noncovalent interactions at the enzyme surface, including hydrophobicity and electrostatics. Molecular modeling of these interactions is costly at the all-atom scale due to the long time scales and large particle counts needed to characterize binding. Protein structure at the scale of amino acid residues is parsimoniously represented by a coarse-grained model in which one particle represents several atoms, significantly reducing the cost of simulation. Coarse-grained models may then be used to generate reduced surface descriptions to underlie detailed theories of surface adhesion. In this study, we present two coarse-grained enzyme models-lipase and dehalogenase-that have been prepared using the Martini 3 top-down modeling framework. We simulate each enzyme in aqueous solution and calculate the statistics of protein surface features and shape descriptors. The values from the coarse-grained data are compared with the same calculations performed on all-atom reference systems, revealing key similarities of surface chemistry at the two scales. Structural measures are calculated from the all-atom reference systems and compared with estimates from small-angle x-ray scattering experiments, with good agreement between the two. The described procedures of modeling and analysis comprise a framework for the development of coarse-grained models of protein surfaces with validation to experiment.

Tracking Cholesterol Flip-Flop in Mammalian Plasma Membrane through Coarse-Grained Molecular Dynamics Simulations

Plasma membrane (PM) simulations at longer length and time scales at nearly atomistic resolution can provide invaluable insights into cell signaling, apoptosis, lipid trafficking, and lipid raft formation. We propose a coarse-grained (CG) model of a mammalian PM considering major lipid head groups distributed asymmetrically across the membrane bilayer and validate the model against bilayer structural properties from atomistic simulation. Using the proposed CG model, we identify a recurring pattern in the passive collective cholesterol transbilayer motion and study the individual cholesterol flip-flop events and associated pathways along with lateral ordering in the bilayer during a flip-flop event. We identify two discrete cholesterol flip-flop pathways: (i) a systematic rototranslational pathway and (ii) intraleaflet inversion followed by interleaflet translation (or reverse). We observe a periodic cholesterol enrichment in the exoplasmic leaflet of the PM bilayer and examine the underlying cholesterol-lipid affinities. We observe closer association between cholesterol and palmitoylsphingomyelin (PSM) lipid, relative to other lipids, and conclude that the cholesterol enrichment in the exoplasmic leaflet can be attributed to higher PSM content in that leaflet, together leading to formation of short-lived PSM-cholesterol-rich domains.

A Neural-Network-Based Mapping and Optimization Framework for High-Precision Coarse-Grained Simulation

The accuracy and efficiency of a coarse-grained (CG) force field are pivotal for high-precision molecular simulations of large systems with complex molecules. We present an automated mapping and optimization framework for molecular simulation (AMOFMS), which is designed to streamline and improve the force field optimization process. It features a neural-network-based mapping function, DSGPM-TP (deep supervised graph partitioning model with type prediction). This model can accurately and efficiently convert atomistic structures to CG mappings, reducing the need for manual intervention. By integrating bottom-up and top-down methodologies, AMOFMS allows users to freely combine these approaches or use them independently as optimization targets. Moreover, users can select and combine different optimizers to meet their specific mission. With its parallel optimizer, AMOFMS significantly accelerates the optimization process, reducing the time required to achieve optimal results. Successful applications of AMOFMS include parameter optimizations for systems such as POPC and PEO, demonstrating its robustness and effectiveness. Overall, AMOFMS provides a general and flexible framework for the automated development of high-precision CG force fields.

Bottom-up Coarse-Graining: Principles and Perspectives

Large-scale computational molecular models provide scientists a means to investigate the effect of microscopic details on emergent mesoscopic behavior. Elucidating the relationship between variations on the molecular scale and macroscopic observable properties facilitates an understanding of the molecular interactions driving the properties of real world materials and complex systems (e.g., those found in biology, chemistry, and materials science). As a result, discovering an explicit, systematic connection between microscopic nature and emergent mesoscopic behavior is a fundamental goal for this type of investigation. The molecular forces critical to driving the behavior of complex heterogeneous systems are often unclear. More problematically, simulations of representative model systems are often prohibitively expensive from both spatial and temporal perspectives, impeding straightforward investigations over possible hypotheses characterizing molecular behavior. While the reduction in resolution of a study, such as moving from an atomistic simulation to that of the resolution of large coarse-grained (CG) groups of atoms, can partially ameliorate the cost of individual simulations, the relationship between the proposed microscopic details and this intermediate resolution is nontrivial and presents new obstacles to study. Small portions of these complex systems can be realistically simulated. Alone, these smaller simulations likely do not provide insight into collectively emergent behavior. However, by proposing that the driving forces in both smaller and larger systems (containing many related copies of the smaller system) have an explicit connection, systematic bottom-up CG techniques can be used to transfer CG hypotheses discovered using a smaller scale system to a larger system of primary interest. The proposed connection between different CG systems is prescribed by (i) the CG representation (mapping) and (ii) the functional form and parameters used to represent the CG energetics, which approximate potentials of mean force (PMFs). As a result, the design of CG methods that facilitate a variety of physically relevant representations, approximations, and force fields is critical to moving the frontier of systematic CG forward. Crucially, the proposed connection between the system used for parametrization and the system of interest is orthogonal to the optimization used to approximate the potential of mean force present in all systematic CG methods. The empirical efficacy of machine learning techniques on a variety of tasks provides strong motivation to consider these approaches for approximating the PMF and analyzing these approximations.

Automatic multi-objective optimization of coarse-grained lipid force fields using SwarmCG

The development of coarse-grained (CG) molecular models typically requires a time-consuming iterative tuning of parameters in order to have the approximated CG models behave correctly and consistently with, e.g., available higher-resolution simulation data and/or experimental observables. Automatic data-driven approaches are increasingly used to develop accurate models for molecular dynamics simulations. However, the parameters obtained via such automatic methods often make use of specifically designed interaction potentials and are typically poorly transferable to molecular systems or conditions other than those used for training them. Using a multi-objective approach in combination with an automatic optimization engine (SwarmCG), here, we show that it is possible to optimize CG models that are also transferable, obtaining optimized CG force fields (FFs). As a proof of concept, here, we use lipids for which we can avail reference experimental data (area per lipid and bilayer thickness) and reliable atomistic simulations to guide the optimization. Once the resolution of the CG models (mapping) is set as an input, SwarmCG optimizes the parameters of the CG lipid models iteratively and simultaneously against higher-resolution simulations (bottom-up) and experimental data (top-down references). Including different types of lipid bilayers in the training set in a parallel optimization guarantees the transferability of the optimized lipid FF parameters. We demonstrate that SwarmCG can reach satisfactory agreement with experimental data for different resolution CG FFs. We also obtain stimulating insights into the precision-resolution balance of the FFs. The approach is general and can be effectively used to develop new FFs and to improve the existing ones.

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.

Swarm-CG: Automatic Parametrization of Bonded Terms in MARTINI-Based Coarse-Grained Models of Simple to Complex Molecules via Fuzzy Self-Tuning Particle Swarm Optimization

We present Swarm-CG, a versatile software for the automatic iterative parametrization of bonded parameters in coarse-grained (CG) models, ideal in combination with popular CG force fields such as MARTINI. By coupling fuzzy self-tuning particle swarm optimization to Boltzmann inversion, Swarm-CG performs accurate bottom-up parametrization of bonded terms in CG models composed of up to 200 pseudo atoms within 4-24 h on standard desktop machines, using default settings. The software benefits from a user-friendly interface and two different usage modes (default and advanced). We particularly expect Swarm-CG to support and facilitate the development of new CG models for the study of complex molecular systems interesting for bio- and nanotechnology. Excellent performances are demonstrated using a benchmark of 9 molecules of diverse nature, structural complexity, and size. Swarm-CG is available with all its dependencies via the Python Package Index (PIP package: swarm-cg). Demonstration data are available at: www.github.com/GMPavanLab/SwarmCG.

Extension of transferable coarse-grained models to dicationic ionic liquids

In this study, we extended the previously developed coarse-grained (CG) models of mono-cationic ionic liquids (MILs) to di-cationic ILs (DILs). To achieve this purpose, the MD simulations in three different mapping schemes of CG were done and the results of RDF (as a structural property), density (as a volumetric property) and the diffusion coefficient (as a dynamical property) were compared with the corresponding results of the all-atom (AA) simulations for [C₅(mim)₂][BF₄]₂. The previously developed CG models for MILs with the least refinement in parameters were used to extend the CG models for DILs. Since, the first mapping scheme of the CG model showed the best agreement with the results of the AA simulations for the three mentioned studied properties, this scheme was selected to simulate DILs using the CG model. The transferability of the selected CG model to DILs was investigated by comparing the different volumetric, structural and dynamical properties of [C_n(mim)₂][BF₄]₂ (with n = 3, 6, 9, and 12) obtained from the CG model with those obtained using the corresponding atomistic simulations at different thermodynamic state points. The average deviation for the densities of the CG model with respect to the AA results is less than 2%. Furthermore, in both CG and AA models, the densities and isobaric expansion coefficients decrease with increasing temperature and linkage alkyl chain. The structural properties of the studied DILs, i.e. RDFs, nano segregation of domains, heterogeneity order parameters (HOPs) and angle distributions showed good agreements between the results of the CG and AA models. The CG-based calculated diffusion coefficients of the studied DILs at different temperatures showed that this model leads to faster dynamics with respect to the AA model due to the sacrifice of some degrees of freedom in this model. However, the trend of increasing diffusion coefficients with increasing temperature and linkage alkyl chain length is the same in both CG and AA models. Also, there are good agreements between the results of these two models for other dynamical properties, i.e. electrical conductivity, transference numbers and non-Gaussian parameter with increasing linkage alkyl chain and at various temperatures.

Nanoscale Probing of Cholesterol-Rich Domains in Single Bilayer Dimyristoyl-Phosphocholine Membranes Using Near-Field Spectroscopic Imaging

Cholesterol is believed to induce the formation of membrane domains, "rafts", which are implicated in a range of natural and pathologic membrane processes. Therefore, it is important to understand the role that cholesterol plays in the formation of these structures. Here, we use label-free spectroscopic imaging to investigate cholesterol fractioning in supported bilayer membranes at nanoscale. Scattering-type scanning near-field optical microscopy (s-SNOM) was used to visualize the formation of cholesterol-induced domains in 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) membranes. Our results revealed the coexistence of phase separated domains in DMPC lipids with 10 mol % cholesterol content, whereas a mostly homogeneous bilayer was found at low (5 mol %) and high (15 mol %) cholesterol content. Near-field nano-FTIR spectroscopy was used to identify the cholesterol-rich domains based on their qualitative chemical compositions. It was determined that cholesterol binds to phosphodiester and alkyl glycerol ester moieties, likely via hydrogen bonding of the alcohol to either of the ester oxygens. The results also confirm the existence of an ideal cholesterol-lipid mixture ratio (∼15:85) with a geometrically defined packing. At lower cholesterol content there is phase separation between liquid ordered and almost neat DMPC domains. Thus, the liquid ordered phase exists at an energy minimum at a given lipid-cholesterol ratio.

Bottom-up derived flexible water model with dipole and quadrupole moments for coarse-grained molecular simulations

A bottom-up CG water model is developed to capture the electrostatic multipoles, structural correlation and thermodynamics of water.

Computational studies of peptide-induced membrane pore formation

A variety of peptides induce pores in biological membranes; the most common ones are naturally produced antimicrobial peptides (AMPs), which are small, usually cationic, and defend diverse organisms against biological threats. Because it is not possible to observe these pores directly on a molecular scale, the structure of AMP-induced pores and the exact sequence of steps leading to their formation remain uncertain. Hence, these questions have been investigated via molecular modelling. In this article, we review computational studies of AMP pore formation using all-atom, coarse-grained, and implicit solvent models; evaluate the results obtained and suggest future research directions to further elucidate the pore formation mechanism of AMPs.This article is part of the themed issue 'Membrane pores: from structure and assembly, to medicine and technology'.

Predicting ligand binding poses for low-resolution membrane protein models: Perspectives from multiscale simulations

Membrane receptors constitute major targets for pharmaceutical intervention. Drug design efforts rely on the identification of ligand binding poses. However, the limited experimental structural information available may make this extremely challenging, especially when only low-resolution homology models are accessible. In these cases, the predictions may be improved by molecular dynamics simulation approaches. Here we review recent developments of multiscale, hybrid molecular mechanics/coarse-grained (MM/CG) methods applied to membrane proteins. In particular, we focus on our in-house MM/CG approach. It is especially tailored for G-protein coupled receptors, the largest membrane receptor family in humans. We show that our MM/CG approach is able to capture the atomistic details of the receptor/ligand binding interactions, while keeping the computational cost low by representing the protein frame and the membrane environment in a highly simplified manner. We close this review by discussing ongoing improvements and challenges of the current implementation of our MM/CG code.

On the Calculation of Acyl Chain Order Parameters from Lipid Simulations

For molecular dynamics simulations of biological membrane systems to live up to the potential of providing accurate atomic level detail into membrane properties and functions, it is essential that the force fields used to model such systems are as accurate as possible. One membrane property that is often used to assess force field accuracy is the carbon-hydrogen (or carbon-deuterium) order parameters of the lipid tails, which can be accurately measured using experimental NMR techniques. There are a variety of analysis tools available to calculate these order parameters from simulations and it is essential that these computational tools work correctly to ensure the accurate assessment of the simulation force fields. In this work we compare many of these computational tools for calculating the order parameters of POPC membranes. While tools that work on all-atom systems and tools that work on saturated lipid tails in general work extremely well, we demonstrate that the majority of the tested tools that calculate the order parameters for unsaturated united-atom lipid tails do so incorrectly. We identify tools that do perform accurate calculations and include one such program with this work, enabling rapid and accurate calculation of united-atom lipid order parameters. Furthermore, we discuss cases in which it is nontrivial to appropriately predict the unsaturated carbon order parameters in united-atom systems. Finally, we examine order parameter splitting for carbon 2 in sn-2 lipid chains, demonstrating substantial deviations from experimental values in several all-atom and united-atom lipid force fields.

How Water's Properties Are Encoded in Its Molecular Structure and Energies

How are water's material properties encoded within the structure of the water molecule? This is pertinent to understanding Earth's living systems, its materials, its geochemistry and geophysics, and a broad spectrum of its industrial chemistry. Water has distinctive liquid and solid properties: It is highly cohesive. It has volumetric anomalies-water's solid (ice) floats on its liquid; pressure can melt the solid rather than freezing the liquid; heating can shrink the liquid. It has more solid phases than other materials. Its supercooled liquid has divergent thermodynamic response functions. Its glassy state is neither fragile nor strong. Its component ions-hydroxide and protons-diffuse much faster than other ions. Aqueous solvation of ions or oils entails large entropies and heat capacities. We review how these properties are encoded within water's molecular structure and energies, as understood from theories, simulations, and experiments. Like simpler liquids, water molecules are nearly spherical and interact with each other through van der Waals forces. Unlike simpler liquids, water's orientation-dependent hydrogen bonding leads to open tetrahedral cage-like structuring that contributes to its remarkable volumetric and thermal properties.

Effects of Coarse Graining and Saturation of Hydrocarbon Chains on Structure and Dynamics of Simulated Lipid Molecules

Molecular dynamics simulations are used extensively to study the processes on biological membranes. The simulations can be conducted at different levels of resolution: all atom (AA), where all atomistic details are provided; united atom (UA), where hydrogen atoms are treated inseparably of corresponding heavy atoms; and coarse grained (CG), where atoms are grouped into larger particles. Here, we study the behavior of model bilayers consisting of saturated and unsaturated lipids DOPC, SOPC, OSPC and DSPC in simulations performed using all atom CHARMM36 and coarse grained Martini force fields. Using principal components analysis, we show that the structural and dynamical properties of the lipids are similar, both in AA and CG simulations, although the unsaturated molecules are more dynamic and favor more extended conformations. We find that CG simulations capture 75 to 100% of the major collective motions, overestimate short range ordering, result in more flexible molecules and 5–7 fold faster sampling. We expect that the results reported here will be useful for comprehensive quantitative comparisons of simulations conducted at different resolution levels and for further development and improvement of CG force fields.

Adaptive resolution simulations of biomolecular systems

In this review article, we discuss and analyze some recently developed hybrid atomistic-mesoscopic solvent models for multiscale biomolecular simulations. We focus on the biomolecular applications of the adaptive resolution scheme (AdResS), which allows solvent molecules to change their resolution back and forth between atomistic and coarse-grained representations according to their positions in the system. First, we discuss coupling of atomistic and coarse-grained models of salt solution using a 1-to-1 molecular mapping-i.e., one coarse-grained bead represents one water molecule-for development of a multiscale salt solution model. In order to make use of coarse-grained molecular models that are compatible with the MARTINI force field, one has to resort to a supramolecular mapping, in particular to a 4-to-1 mapping, where four water molecules are represented with one coarse-grained bead. To this end, bundled atomistic water models are employed, i.e., the relative movement of water molecules that are mapped to the same coarse-grained bead is restricted by employing harmonic springs. Supramolecular coupling has recently also been extended to polarizable coarse-grained water models with explicit charges. Since these coarse-grained models consist of several interaction sites, orientational degrees of freedom of the atomistic and coarse-grained representations are coupled via a harmonic energy penalty term. The latter aligns the dipole moments of both representations. The reviewed multiscale solvent models are ready to be used in biomolecular simulations, as illustrated in a few examples.

Biomembrane solubilization mechanism by Triton X-100: a computational study of the three stage model

The solubilization mechanism of lipid membranes in the presence of Triton X-100 (TX-100) is investigated at molecular resolution using hybrid particle field–self consistence field simulations.

Hysteresis and the Cholesterol Dependent Phase Transition in Binary Lipid Mixtures with the Martini Model

Extensive Martini simulation data, totaling 5 ms, is presented for binary mixtures of dipalmitoylphosphatidylcholine (DPPC) and cholesterol. Using simulation initiated from both gel (s_o) and liquid-disordered (L_d) phases, significant and strongly cholesterol-dependent hysteresis in the enthalpy as a function of temperature is observed for cholesterol mole fractions from 0 to 20 mol %. Although the precise phase transition temperature cannot be determined due to the hysteresis, the data are consistent with a first order gel to fluid transition, which increases in temperature with cholesterol. At 30 mol % cholesterol, no hysteresis is observed, and there is no evidence for a continuous transition, in either structural parameters like the area per lipid or in the heat capacity as a function of temperature. The results are consistent with a single uniform phase above a critical cholesterol composition between 20 and 30 mol % in Martini, while highlighting the importance and difficulty of obtaining the equilibrium averages to locate phase boundaries precisely in computational models of lipid bilayers.

Multiscale coarse-grained modelling of chromatin components: DNA and the nucleosome

To model large biomolecular systems, such as cell and organelles an atomistic description is not currently achievable and is not generally practical. Therefore, simplified coarse-grained (CG) modelling becomes a necessity. One of the most important cellular components is chromatin, a large DNA-protein complex where DNA is highly compacted. Recent progress in coarse graining modelling of the major chromatin components, double helical DNA and the nucleosome core particle (NCP) is presented. First, general principles and approaches allowing rigorous bottom-to-top generation of interaction potentials in the CG models are presented. Then, recent CG models of DNA are reviewed and their adequacy is benchmarked against experimental data on the salt dependence of DNA flexibility (persistence length). Furthermore, a few recent CG models of the NCP are described and their application for studying salt-dependent NCP-NCP interaction is discussed. An example of a multiscale approach to CG modelling of chromatin is presented where interactions and self-assembly of thousands of NCPs in solution are observed.

Force Field Development for Lipid Membrane Simulations

With the rapid development of computer power and wide availability of modelling software computer simulations of realistic models of lipid membranes, including their interactions with various molecular species, polypeptides and membrane proteins have become feasible for many research groups. The crucial issue of the reliability of such simulations is the quality of the force field, and many efforts, especially in the latest several years, have been devoted to parametrization and optimization of the force fields for biomembrane modelling. In this review, we give account of the recent development in this area, covering different classes of force fields, principles of the force field parametrization, comparison of the force fields, and their experimental validation. This article is part of a Special Issue entitled: Biosimulations edited by Ilpo Vattulainen and Tomasz Róg.

Toward a Coarse-Grained Protein Model Coupled with a Coarse-Grained Solvent Model: Solvation Free Energies of Amino Acid Side Chains

Recently, we reported that molecular dynamics (MD) simulations using a coarse-grained (CG) peptide model coupled with a CG water model are able to reproduce many of the structural and thermodynamic features of short peptides with nonpolar side chains at 10(3) times the normal speed (JCTC, 2007, 3, 2146-2161). To further develop a CG protein model for MD simulations, we systematically parametrized the side chains of all 20 naturally occurring amino acids. We developed the parameters by fitting the dihedral potentials of 13 small molecules, the densities and self-solvation free energies of liquids of eight organic molecules, and the hydration free energies of 35 small organic molecules. In a set of 11 classes of compounds (105 in total) including alkanes, alcohols, ethers, ketones/aldehydes, amines, amides, aromatics, carboxylic acids, sulfides/thiols, alkyl ammoniums, and carboxylate ions, the average error in the calculated hydration free energies compared with experimental results is about 1.4 kJ/mol. The average error in the calculated transfer free energies of the 19 side-chain analogues of amino acids from cyclohexane to water is about 2.2 kJ/mol. These results are comparable to the results of all-atom models.

A Nonradial Coarse-Grained Potential for Proteins Produces Naturally Stable Secondary Structure Elements

We introduce a nonradial potential term for coarse-grained (CG) molecular simulations of proteins. This term mimics the backbone dipole-dipole interactions and accounts for the needed directionality to form stable folded secondary structure elements. We show that α-helical and β-sheet peptide chains are correctly described in dynamics without the need of introducing any a priori bias potentials or ad hoc parametrizations, which limit broader applicability of CG simulations for proteins. Moreover, our model is able to catch the formation of supersecondary structural motifs, like transitions from long single α-helices to helix-coil-helix or β-hairpin assemblies. This novel scheme requires the structural information of Cα beads only; it does not introduce any additional degrees of freedom to the system and has a general formulation, which allows it to be used in synergy with various CG protocols, leading to an improved description of the structural and dynamic properties of protein assemblies and networks.

Biomembranes in atomistic and coarse-grained simulations

The architecture of biological membranes is tightly coupled to the localization, organization, and function of membrane proteins. The organelle-specific distribution of lipids allows for the formation of functional microdomains (also called rafts) that facilitate the segregation and aggregation of membrane proteins and thus shape their function. Molecular dynamics simulations enable to directly access the formation, structure, and dynamics of membrane microdomains at the molecular scale and the specific interactions among lipids and proteins on timescales from picoseconds to microseconds. This review focuses on the latest developments of biomembrane force fields for both atomistic and coarse-grained molecular dynamics (MD) simulations, and the different levels of coarsening of biomolecular structures. It also briefly introduces scale-bridging methods applicable to biomembrane studies, and highlights selected recent applications.

Modeling kinetics and equilibrium of membranes with fields: milestoning analysis and implication to permeation

Coarse graining of membrane simulations by translating atomistic dynamics to densities and fields with Milestoning is discussed. The space of the membrane system is divided into cells and the different cells are characterized by order parameters presenting the number densities. The dynamics of the order parameters are probed with Milestoning. The methodology is illustrated here for a phospholipid membrane system (a hydrated bilayer of DOPC (1,2-dioleoyl-sn-glycero-3-phosphocholine) lipid molecules). Significant inhomogeneity in membrane internal number density leads to complex free energy landscape and local maps of transition times. Dynamics and distributions of cavities within the membrane assist the permeation of nonpolar solutes such as xenon atoms. It is illustrated that quantitative and detailed dynamics of water transport through DOPC membrane can be analyzed using Milestoning with fields. The reaction space for water transport includes at least two slow variables: the normal to the membrane plane, and the water density.

Microsecond molecular dynamics simulations of lipid mixing

Molecular dynamics (MD) simulations of membranes are often hindered by the slow lateral diffusion of lipids and the limited time scale of MD. In order to study the dynamics of mixing and characterize the lateral distribution of lipids in converged mixtures, we report microsecond-long all-atom MD simulations performed on the special-purpose machine Anton. Two types of mixed bilayers, POPE:POPG (3:1) and POPC:cholesterol (2:1), as well as a pure POPC bilayer, were each simulated for up to 2 μs. These simulations show that POPE:POPG and POPC:cholesterol are each fully miscible at the simulated conditions, with the final states of the mixed bilayers similar to a random mixture. By simulating three POPE:POPG bilayers at different NaCl concentrations (0, 0.15, and 1 M), we also examined the effect of salt concentration on lipid mixing. While an increase in NaCl concentration is shown to affect the area per lipid, tail order, and lipid lateral diffusion, the final states of mixing remain unaltered, which is explained by the largely uniform increase in Na(+) ions around POPE and POPG. Direct measurement of water permeation reveals that the POPE:POPG bilayer with 1 M NaCl has reduced water permeability compared with those at zero or low salt concentration. Our calculations provide a benchmark to estimate the convergence time scale of all-atom MD simulations of lipid mixing. Additionally, equilibrated structures of POPE:POPG and POPC:cholesterol, which are frequently used to mimic bacterial and mammalian membranes, respectively, can be used as starting points of simulations involving these membranes.

COFFDROP: A Coarse-Grained Nonbonded Force Field for Proteins Derived from All-Atom Explicit-Solvent Molecular Dynamics Simulations of Amino Acids

We describe the derivation of a set of bonded and nonbonded coarse-grained (CG) potential functions for use in implicit-solvent Brownian dynamics (BD) simulations of proteins derived from all-atom explicit-solvent molecular dynamics (MD) simulations of amino acids. Bonded potential functions were derived from 1 μs MD simulations of each of the 20 canonical amino acids, with histidine modeled in both its protonated and neutral forms; nonbonded potential functions were derived from 1 μs MD simulations of every possible pairing of the amino acids (231 different systems). The angle and dihedral probability distributions and radial distribution functions sampled during MD were used to optimize a set of CG potential functions through use of the iterative Boltzmann inversion (IBI) method. The optimized set of potential functions—which we term COFFDROP (COarse-grained Force Field for Dynamic Representation Of Proteins)—quantitatively reproduced all of the “target” MD distributions. In a first test of the force field, it was used to predict the clustering behavior of concentrated amino acid solutions; the predictions were directly compared with the results of corresponding all-atom explicit-solvent MD simulations and found to be in excellent agreement. In a second test, BD simulations of the small protein villin headpiece were carried out at concentrations that have recently been studied in all-atom explicit-solvent MD simulations by Petrov and Zagrovic (PLoS Comput. Biol.2014, 5, e1003638). The anomalously strong intermolecular interactions seen in the MD study were reproduced in the COFFDROP simulations; a simple scaling of COFFDROP’s nonbonded parameters, however, produced results in better accordance with experiment. Overall, our results suggest that potential functions derived from simulations of pairwise amino acid interactions might be of quite broad applicability, with COFFDROP likely to be especially useful for modeling unfolded or intrinsically disordered proteins.

Transferring the PRIMO Coarse-Grained Force Field to the Membrane Environment: Simulations of Membrane Proteins and Helix-Helix Association

An extension of the recently developed PRIMO coarse-grained force field to membrane environments, PRIMO-M, is described. The membrane environment is modeled with the heterogeneous dielectric generalized Born (HDGB) methodology that simply replaces the standard generalized Born model in PRIMO without further parametrization. The resulting model was validated by comparing amino acid insertion free energy profiles and application in molecular dynamics simulations of membrane proteins and membrane-interacting peptides. Membrane proteins with 148–661 amino acids show stable root-mean-squared-deviations (RMSD) between 2 and 4 Å for most systems. Transmembrane helical peptides maintain helical shape and exhibit tilt angles in good agreement with experimental or other simulation data. The association of two glycophorin A (GpA) helices was simulated using replica exchange molecular dynamics simulations yielding the correct dimer structure with a crossing angle in agreement with previous studies. Finally, conformational sampling of the influenza fusion peptide also generates structures in agreement with previous studies. Overall, these findings suggest that PRIMO-M can be used to study membrane bound peptides and proteins and validates the transferable nature of the PRIMO coarse-grained force field.

The power of coarse graining in biomolecular simulations

Computational modeling of biological systems is challenging because of the multitude of spatial and temporal scales involved. Replacing atomistic detail with lower resolution, coarse grained (CG), beads has opened the way to simulate large-scale biomolecular processes on time scales inaccessible to all-atom models. We provide an overview of some of the more popular CG models used in biomolecular applications to date, focusing on models that retain chemical specificity. A few state-of-the-art examples of protein folding, membrane protein gating and self-assembly, DNA hybridization, and modeling of carbohydrate fibers are used to illustrate the power and diversity of current CG modeling.

Refined OPLS all-atom force field for saturated phosphatidylcholine bilayers at full hydration

We report parametrization of dipalmitoyl-phosphatidylcholine (DPPC) in the framework of the Optimized Parameters for Liquid Simulations all-atom (OPLS-AA) force field. We chose DPPC as it is one of the most studied phospholipid species and thus has plenty of experimental data necessary for model validation, and it is also one of the highly important and abundant lipid types, e.g., in lung surfactant. Overall, PCs have not been previously parametrized in the OPLS-AA force field; thus, there is a need to derive its bonding and nonbonding parameters for both the polar and nonpolar parts of the molecule. In the present study, we determined the parameters for torsion angles in the phosphatidylcholine and glycerol moieties and in the acyl chains, as well the partial atomic charges. In these calculations, we used three methods: (1) Hartree-Fock (HF), (2) second order Møller-Plesset perturbation theory (MP2), and (3) density functional theory (DFT). We also tested the effect of the polar environment by using the polarizable continuum model (PCM), and for acyl chains the van der Waals parameters were also adjusted. In effect, six parameter sets were generated and tested on a DPPC bilayer. Out of these six sets, only one was found to be able to satisfactorily reproduce experimental data for the lipid bilayer. The successful DPPC model was obtained from MP2 calculations in an implicit polar environment (PCM).

Perspective: Coarse-grained models for biomolecular systems

By focusing on essential features, while averaging over less important details, coarse-grained (CG) models provide significant computational and conceptual advantages with respect to more detailed models. Consequently, despite dramatic advances in computational methodologies and resources, CG models enjoy surging popularity and are becoming increasingly equal partners to atomically detailed models. This perspective surveys the rapidly developing landscape of CG models for biomolecular systems. In particular, this review seeks to provide a balanced, coherent, and unified presentation of several distinct approaches for developing CG models, including top-down, network-based, native-centric, knowledge-based, and bottom-up modeling strategies. The review summarizes their basic philosophies, theoretical foundations, typical applications, and recent developments. Additionally, the review identifies fundamental inter-relationships among the diverse approaches and discusses outstanding challenges in the field. When carefully applied and assessed, current CG models provide highly efficient means for investigating the biological consequences of basic physicochemical principles. Moreover, rigorous bottom-up approaches hold great promise for further improving the accuracy and scope of CG models for biomolecular systems.

Coarse-grained molecular dynamics simulations of photoswitchable assembly and disassembly

The supramolecular self-assembly and disassembly that are responsive to external stimuli are of critical importance to the design and synthesis of functional supramolecular materials. In this work, we performed a coarse-grained molecular dynamics study of photo-controlled assembly and disassembly on a timescale of ten microseconds. The spontaneous assembly of cis-AzoC10, trans-AzoC10, and cis-AzoC10/α-CD into micelle-like aggregates, and the disassembly of trans-AzoC10/α-CD starting from a pre-assembled micelle were directly simulated. Our results of simulations have revealed a significant size and shape dependence of aggregates on the molecular structure and concentrations of monomers. As demonstrated, with careful design, coarse-grained molecular dynamics simulations are useful in the study of controlled assembly and disassembly to bridge the gap between atomistic simulations and experiments.

MagiC: Software Package for Multiscale Modeling

We present software package MagiC, which is designed to perform systematic structure-based coarse graining of molecular models. The effective pairwise potentials between coarse-grained sites of low-resolution molecular models are constructed to reproduce structural distribution functions obtained from the modeling of the system in a high resolution (atomistic) description. The software supports coarse-grained tabulated intramolecular bond and angle interactions, as well as tabulated nonbonded interactions between different site types in the coarse-grained system, with the treatment of long-range electrostatic forces by the Ewald summation. Two methods of effective potential refinement are implemented: iterative Boltzmann inversion and inverse Monte Carlo, the latter accounting for cross-correlations between pair interactions. MagiC uses its own Metropolis Monte Carlo sampling engine, allowing parallel simulation of many copies of the system with subsequent averaging of the properties, which provides fast convergence of the method with nearly linear scaling at parallel execution.

Systematic methods for structurally consistent coarse-grained models

This chapter provides a primer on theories for coarse-grained (CG) modeling and, in particular, reviews several systematic methods for determining effective potentials for CG models. The chapter first reviews a statistical mechanics framework for relating atomistic and CG models. This framework naturally leads to a quantitative criterion for CG models that are "consistent" with a particular atomistic model for the same system. This consistency criterion is equivalent to minimizing the relative entropy between the two models. This criterion implies that a many-body PMF is the appropriate potential for a CG model that is consistent with a particular atomistic model. This chapter then presents a unified exposition of the theory and numerical methods for several approaches for approximating this many-body PMF. Finally, this chapter closes with a brief discussion of a few of the outstanding challenges facing the field of systematic coarse-graining.

A Hybrid Approach for Highly Coarse-grained Lipid Bilayer Models

We present a systematic methodology to develop highly coarse-grained (CG) lipid models for large scale bio-membrane simulations, in which we derive CG interactions using a powerful combination of the multiscale coarse-graining (MS-CG) method, and an analytical form of the CG potential to model interactions at short range. The resulting hybrid coarse-graining (HCG) methodology is used to develop a three-site solvent-free model for 1,2-dilauroyl-sn-glycero-3-phosphocholine (DLPC), 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC), and a 1:1 mixture of 1,2-dioleoyl-sn-glycero-3-phospho-L-serine (DOPS) and DOPC. In addition, we developed a four-site model of DOPC, demonstrating the capability of the HCG methodology in designing model lipid systems of a desired resolution. We carried out microsecond-scale molecular dynamics (MD) simulations of large vesicles, highlighting the ability of the model to study systems at mesoscopic length and time scales. The models of DLPC, DOPC and DOPC-DOPS have elastic properties consistent with experiment and structural properties such as the radial distribution functions (RDF), bond and angle distributions, and the z-density distributions that compare well with reference all-atom systems.

Concentration and temperature dependences of polyglutamine aggregation by multiscale coarse-graining molecular dynamics simulations

The solvent-free multiscale coarse-graining model of polyglutamine was employed to study polyglutamine aggregation at different concentrations and temperatures by means of molecular dynamics simulation. The heterogeneity order parameter (HOP) was used to quantify the polyglutamine aggregation. Our simulation results demonstrate that polyglutamine aggregation is sensitive to concentration and temperature changes. In equilibrium states, polyglutamine molecules fluctuate between aggregating tightly and distributing uniformly. The degree of aggregation monotonically increases with decreasing temperature, but the fluctuation of HOP reaches its maximum at an intermediate temperature. With increasing concentration, the distribution of polyglutamines first changes from more uniform to more nonuniform and then changes back to be more uniform, and the HOP has the widest distribution at the turning point. Simulations with different system sizes indicate that the finite-size effect is trivial and do not change the conclusions drawn for the polyglutamine system. In addition, the composition of the potential energies has been analyzed to confirm that the nonbonded interactions dominate the aggregation of polyglutamines. These results can be thermodynamically understood by considering the competition between the system entropy and molecular interactions, and a statistical model based on HOP has been developed to explain the microscopic mechanism of polyglutamine aggregation.