Coarse-grained model for phospholipid/cholesterol bilayer

Soft Matter under Pressure: Pushing Particle-Field Molecular Dynamics to the Isobaric Ensemble

Hamiltonian hybrid particle-field molecular dynamics is a computationally efficient method to study large soft matter systems. In this work, we extend this approach to constant-pressure (NPT) simulations. We reformulate the calculation of internal pressure from the density field by taking into account the intrinsic spread of the particles in space, which naturally leads to a direct anisotropy in the pressure tensor. The anisotropic contribution is crucial for reliably describing the physics of systems under pressure, as demonstrated by a series of tests on analytical and monatomic model systems as well as realistic water/lipid biphasic systems. Using Bayesian optimization, we parametrize the field interactions of phospholipids to reproduce the structural properties of their lamellar phases, including area per lipid, and local density profiles. The resulting model excels in providing pressure profiles in qualitative agreement with all-atom modeling, and surface tension and area compressibility in quantitative agreement with experimental values, indicating the correct description of long-wavelength undulations in large membranes. Finally, we demonstrate that the model is capable of reproducing the formation of lipid droplets inside a lipid bilayer.

Brillouin Spectroscopy of Binary Phospholipid-Cholesterol Bilayers

Multicomponent lipid bilayers are used as models for searching the origin of spatial heterogeneities in biomembranes called lipid rafts, implying the coexistence of domains of different phases and compositions within the lipid bilayer. The spatial organization of multicomponent lipid bilayers on a scale of a hundred nanometers remains unknown. Brillouin spectroscopy providing information about the acoustic phonons with the wavelength of several hundred nanometers has an unexplored potential for this problem. Here, we applied Brillouin spectroscopy for three binary bilayers composed of 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC), 1,2-palmitoyl-sn-glycero-3-phosphocholine (DPPC), and cholesterol. The Brillouin experiment for the oriented planar multibilayers was realized for two scattering geometries involving phonons for the lateral and normal directions of the propagation. The DPPC-DOPC mixtures known for the coexistence of the solid-ordered and liquid-disordered phases had bimodal Brillouin peaks, revealing the phase domains with sizes more than a hundred nanometers. Analysis of the Brillouin data for the binary mixtures concluded that the lateral phonons are preferable for testing the lateral homogeneity of the bilayers, while the phonons spreading across the bilayers are sensitive to the layered packing at the mesoscopic scale.

Coarse-Grained Water Model Development for Accurate Dynamics and Structure Prediction

Several coarse-graining (CG) methods have been combined to develop a CG model of water capable of the accurate prediction of structure and dynamics properties. The multiscale coarse-graining (MS-CG) method based on force matching and the PDF-based coarse-graining method were used for accurate dynamics prediction. The iterative Boltzmann inversion (IBI) method was added for accurate structure representation. The approach is applied to bulk water, and the results show close reproduction of the CG structure when compared with the reference atomistic data. The combination of MS-CG and IBI methods facilitates the development of CG force fields at different temperatures based on a single MS-CG coarse-graining procedure. The dynamic properties of the CG water model closely match those obtained from the reference atomistic system. The general application of this approach to any existing coarse-graining methods is discussed.

The Critical Diameter for Continuous Evaporation Is between 3 and 4 nm for Hydrophilic Nanopores

Evaporation studies of water using classical molecular dynamics simulations are largely limited due to their high computational expense. This study addresses that issue by developing coarse-grained molecular dynamics models based on Morse potential. Models are optimized based on multi-temperature and at room temperature using machine learning techniques like Genetic Algorithm, Nelder-Mead algorithm, and Strength Pareto Evolutionary Algorithm. The multi-temperature-based model named as Morse-D is found to be more accurate than the single temperature model in representing the water properties at higher temperatures. Using this Morse-D water model, evaporation from hydrophilic nanopores with pore diameter varying from 2 to 5 nm is studied. Our results show that the critical diameter to initiate continuous evaporation at nanopores lies between 3 and 4 nm. A maximum heat flux of 21.3 kW/cm² is observed for a pore diameter of 4.5 nm and a maximum mass flow rate of 16.2 ng/s for a pore diameter of 5 nm. The observed heat flux is an order of magnitude times larger than the currently reported values from experiments in the literature for water, which indicates that we need to focus on nanoscale evaporation to enhance the critical heat flux.

Review on the QM/MM Methodologies and Their Application to Metalloproteins

The multiscaling quantum mechanics/molecular mechanics (QM/MM) approach was introduced in 1976, while the extensive acceptance of this methodology started in the 1990s. The combination of QM/MM approach with molecular dynamics (MD) simulation, otherwise known as the QM/MM/MD approach, is a powerful and promising tool for the investigation of chemical reactions’ mechanism of complex molecular systems, drug delivery, properties of molecular devices, organic electronics, etc. In the present review, the main methodologies in the multiscaling approaches, i.e., density functional theory (DFT), semiempirical methodologies (SE), MD simulations, MM, and their new advances are discussed in short. Then, a review on calculations and reactions on metalloproteins is presented, where particular attention is given to nitrogenase that catalyzes the conversion of atmospheric nitrogen molecules N₂ into NH₃ through the process known as nitrogen fixation and the FeMo-cofactor.

Cations Regulate Membrane Attachment and Functionality of DNA Nanostructures

The interplay between nucleic acids and lipids underpins several key processes in molecular biology, synthetic biotechnology, vaccine technology, and nanomedicine. These interactions are often electrostatic in nature, and much of their rich phenomenology remains unexplored in view of the chemical diversity of lipids, the heterogeneity of their phases, and the broad range of relevant solvent conditions. Here we unravel the electrostatic interactions between zwitterionic lipid membranes and DNA nanostructures in the presence of physiologically relevant cations, with the purpose of identifying new routes to program DNA–lipid complexation and membrane-active nanodevices. We demonstrate that this interplay is influenced by both the phase of the lipid membranes and the valency of the ions and observe divalent cation bridging between nucleic acids and gel-phase bilayers. Furthermore, even in the presence of hydrophobic modifications on the DNA, we find that cations are still required to enable DNA adhesion to liquid-phase membranes. We show that the latter mechanism can be exploited to control the degree of attachment of cholesterol-modified DNA nanostructures by modifying their overall hydrophobicity and charge. Besides their biological relevance, the interaction mechanisms we explored hold great practical potential in the design of biomimetic nanodevices, as we show by constructing an ion-regulated DNA-based synthetic enzyme.

Modelling lipid systems in fluid with Lattice Boltzmann Molecular Dynamics simulations and hydrodynamics

In this work we present the coupling between Dry Martini, an efficient implicit solvent coarse-grained model for lipids, and the Lattice Boltzmann Molecular Dynamics (LBMD) simulation technique in order to include naturally hydrodynamic interactions in implicit solvent simulations of lipid systems. After validating the implementation of the model, we explored several systems where the action of a perturbing fluid plays an important role. Namely, we investigated the role of an external shear flow on the dynamics of a vesicle, the dynamics of substrate release under shear, and inquired the dynamics of proteins and substrates confined inside the core of a vesicle. Our methodology enables future exploration of a large variety of biological entities and processes involving lipid systems at the mesoscopic scale where hydrodynamics plays an essential role, e.g. by modulating the migration of proteins in the proximity of membranes, the dynamics of vesicle-based drug delivery systems, or, more generally, the behaviour of proteins in cellular compartments.

Coarse-Grained Double-Stranded RNA Model from Quantum-Mechanical Calculations

A coarse-grained model for simulating structural properties of double-stranded RNA is developed with parameters obtained from quantum-mechanical calculations. This model follows previous parametrization for double-stranded DNA, which is based on mapping the all-atom picture to a coarse-grained four-bead scheme. Chemical and structural differences between RNA and DNA have been taken into account for the model development. The parametrization is based on simulations using density functional theory (DFT) on separate units of the RNA molecule without implementing experimental data. The total energy is decomposed into four terms of physical significance: hydrogen bonding interaction, stacking interactions, backbone interactions, and electrostatic interactions. The first three interactions are treated within DFT, whereas the last one is included within a mean field approximation. Our double-stranded RNA coarse-grained model predicts stable helical structures for RNA. Other characteristics, such as structural or mechanical properties are reproduced with a very good accuracy. The development of the coarse-grained model for RNA allows extending the spatial and temporal length scales accessed by computer simulations and being able to model RNA-related biophysical processes, as well as novel RNA nanostructures.

Quantum theory of multiscale coarse-graining

Coarse-grained (CG) models serve as a powerful tool to simulate molecular systems at much longer temporal and spatial scales. Previously, CG models and methods have been built upon classical statistical mechanics. The present paper develops a theory and numerical methodology for coarse-graining in quantum statistical mechanics, by generalizing the multiscale coarse-graining (MS-CG) method to quantum Boltzmann statistics. A rigorous derivation of the sufficient thermodynamic consistency condition is first presented via imaginary time Feynman path integrals. It identifies the optimal choice of CG action functional and effective quantum CG (qCG) force field to generate a quantum MS-CG (qMS-CG) description of the equilibrium system that is consistent with the quantum fine-grained model projected onto the CG variables. A variational principle then provides a class of algorithms for optimally approximating the qMS-CG force fields. Specifically, a variational method based on force matching, which was also adopted in the classical MS-CG theory, is generalized to quantum Boltzmann statistics. The qMS-CG numerical algorithms and practical issues in implementing this variational minimization procedure are also discussed. Then, two numerical examples are presented to demonstrate the method. Finally, as an alternative strategy, a quasi-classical approximation for the thermal density matrix expressed in the CG variables is derived. This approach provides an interesting physical picture for coarse-graining in quantum Boltzmann statistical mechanics in which the consistency with the quantum particle delocalization is obviously manifest, and it opens up an avenue for using path integral centroid-based effective classical force fields in a coarse-graining methodology.

Artificial biomembrane morphology: a dissipative particle dynamics study

Artificial membranes mimicking biological structures are rapidly breaking new ground in the areas of medicine and soft-matter physics. In this endeavor, we use dissipative particle dynamics simulation to investigate the morphology and behavior of lipid-based biomembranes under conditions of varied lipid density and self-interaction. Our results show that a less-than-normal initial lipid density does not create the traditional membrane; but instead results in the formation of a 'net', or at very low densities, a series of disparate 'clumps' similar to the micelles formed by lipids in nature. When the initial lipid density is high, a membrane forms, but due to the large number of lipids, the naturally formed membrane would be larger than the simulation box, leading to 'rippling' behavior as the excess repulsive force of the membrane interior overcomes the bending energy of the membrane. Once the density reaches a certain point however, 'bubbles' appear inside the membrane, reducing the rippling behavior and eventually generating a relatively flat, but thick, structure with micelles of water inside the membrane itself. Our simulations also demonstrate that the interaction parameter between individual lipids plays a significant role in the formation and behavior of lipid membrane assemblies, creating similar structures as the initial lipid density distribution. This work provides a comprehensive approach to the intricacies of lipid membranes, and offers a guideline to design biological or polymeric membranes through self-assembly processes as well as develop novel cellular manipulation and destruction techniques.

Energy-conserving coarse-graining of complex molecules

Coarse-graining (CG) of complex molecules is a method to reach time scales that would be impossible to access through brute force molecular simulations. In this paper, we formulate a coarse-grained model for complex molecules using first principles caculations that ensures energy conservation. Each molecule is described in a coarse way by a thermal blob characterized by the position and momentum of the center of mass of the molecule, together with its internal energy as an additional degree of freedom. This level of description gives rise to an entropy-based framework instead of the usual one based on the configurational free energy (i.e. potential of mean force). The resulting dynamic equations, which account for an appropriate description of heat transfer at the coarse-grained level, have the structure of the dissipative particle dynamics with energy conservation (DPDE) model but with a clear microscopic underpinning. Under suitable approximations, we provide explicit microscopic expressions for each component (entropy, mean force, friction and conductivity coefficients) appearing in the coarse-grained model. These quantities can be computed directly using MD simulations. The proposed non-isothermal coarse-grained model is thermodynamically consistent and opens up a first principles CG strategy for the study of energy transport issues that are not accessible using current isothermal models.

A Coarse-Grained Molecular Dynamics Study of Carbon Nanoparticle Aggregation

A multiscale coarse-graining procedure is used to study carbonaceous nanoparticle assembly. The computational methodology is applied to an ensemble of 10 000 nanoparticles (or effectively 2 million total carbon atoms) to simulate the agglomeration of carbonaceous nanoparticles using coarse-grained atomistic-scale information. In particular, with the coarse-graining approach, we are able to assess the influence of nanoparticle morphology and temperature on the agglomeration process. The coarse-graining of the interparticle force field is accomplished applying a force-matching procedure to data obtained from trajectories and forces from all-atom molecular dynamics simulation. The coarse-grained molecular dynamics results show rich and varied clustering behaviors for different particle morphologies. They are shown to reproduce accurately the structural properties of the nanoparticles systems studied, while allowing for molecular dynamics simulations of much larger self-assembled nanoparticles systems.

Multiscale Coarse-Graining of Mixed Phospholipid/Cholesterol Bilayers

Coarse-grained (CG) models for mixed dimyristoylphosphatidylcholine (DMPC)/cholesterol lipid bilayers are constructed using the recently developed multiscale coarse-graining (MS-CG) method. The MS-CG method permits a systematic fit of the bonded and nonbonded interactions and system pressure to trajectory and force data derived from an underlying reference all-atom molecular dynamics (MD) simulation. The CG sites for lipid and cholesterol molecules are associated with the centers-of-mass of atomic groups because of the simplicity in the evaluation of the forces acting on them from the atomistic MD data. Corresponding models with four-site and seven-site representations of the cholesterol molecule were also developed. The latter CG models differed by the bonding scheme of CG sites to represent intramolecular interactions. A one-site MS-CG model based on the TIP3P potential was used for water, with the interaction site placed at the molecular geometrical center, and the analytical fit of the model is presented. The MS-CG models were then used to conduct simulations in the constant NPT ensemble which reproduce accurately the structural properties as seen in the full all-atom MD simulation.

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.

The structure and interaction mechanism of a polyelectrolyte complex: a dissipative particle dynamics study

The mechanism of complex formation of two oppositely charged linear polyelectrolytes dispersed in a solvent is investigated by using dissipative particle dynamics (DPD) simulation. In the polyelectrolyte solution, the size of the cationic polyelectrolyte remains constant while the size of the anionic chain increases. We analyze the influence of the anionic polyelectrolyte size and salt effect (ionic strength) on the conformational changes of the chains during complex formation. The behavior of the radial distribution function, the end-to-end distance and the radius of gyration of each polyelectrolyte is examined. These results showed that the effectiveness of complex formation is strongly influenced by the process of counterion release from the polyelectrolyte chains. The radius of gyration of the complex is estimated using the Fox-Flory equation for a wormlike polymer in a theta solvent. The addition of salts in the medium accelerates the complex formation process, affecting its radius of gyration. Depending on the ratio of chain lengths a compact complex or a loosely bound elongated structure can be formed.

Parametrization of Backbone Flexibility in a Coarse-Grained Force Field for Proteins (COFFDROP) Derived from All-Atom Explicit-Solvent Molecular Dynamics Simulations of All Possible Two-Residue Peptides

Recently, we reported the parametrization of a set of coarse-grained (CG) nonbonded potential functions, derived from all-atom explicit-solvent molecular dynamics (MD) simulations of amino acid pairs and designed for use in (implicit-solvent) Brownian dynamics (BD) simulations of proteins; this force field was named COFFDROP (COarse-grained Force Field for Dynamic Representations Of Proteins). Here, we describe the extension of COFFDROP to include bonded backbone terms derived from fitting to results of explicit-solvent MD simulations of all possible two-residue peptides containing the 20 standard amino acids, with histidine modeled in both its protonated and neutral forms. The iterative Boltzmann inversion (IBI) method was used to optimize new CG potential functions for backbone-related terms by attempting to reproduce angle, dihedral, and distance probability distributions generated by the MD simulations. In a simple test of the transferability of the extended force field, the angle, dihedral, and distance probability distributions obtained from BD simulations of 56 three-residue peptides were compared to results from corresponding explicit-solvent MD simulations. In a more challenging test of the COFFDROP force field, it was used to simulate eight intrinsically disordered proteins and was shown to quite accurately reproduce the experimental hydrodynamic radii (Rhydro), provided that the favorable nonbonded interactions of the force field were uniformly scaled downward in magnitude. Overall, the results indicate that the COFFDROP force field is likely to find use in modeling the conformational behavior of intrinsically disordered proteins and multidomain proteins connected by flexible linkers.

Molecular dynamics simulations of membrane proteins

Membrane protein structures are underrepresented in the Protein Data Bank (PDB) due to difficulties associated with expression and crystallization. As such, it is one area where computational studies, particularly Molecular Dynamics (MD) simulations, can provide useful additional information. Recently, there has been substantial progress in the simulation of lipid bilayers and membrane proteins embedded within them. Initial efforts at simulating membrane proteins embedded within a lipid bilayer were relatively slow and interactive processes, but recent advances now mean that the setup and running of membrane protein simulations is somewhat more straightforward, though not without its problems. In this chapter, we outline practical methods for setting up and running MD simulations of a membrane protein embedded within a lipid bilayer and discuss methodologies that are likely to contribute future improvements.

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.

Mesoscale computational studies of membrane bilayer remodeling by curvature-inducing proteins

Biological membranes constitute boundaries of cells and cell organelles. These membranes are soft fluid interfaces whose thermodynamic states are dictated by bending moduli, induced curvature fields, and thermal fluctuations. Recently, there has been a flood of experimental evidence highlighting active roles for these structures in many cellular processes ranging from trafficking of cargo to cell motility. It is believed that the local membrane curvature, which is continuously altered due to its interactions with myriad proteins and other macromolecules attached to its surface, holds the key to the emergent functionality in these cellular processes. Mechanisms at the atomic scale are dictated by protein-lipid interaction strength, lipid composition, lipid distribution in the vicinity of the protein, shape and amino acid composition of the protein, and its amino acid contents. The specificity of molecular interactions together with the cooperativity of multiple proteins induce and stabilize complex membrane shapes at the mesoscale. These shapes span a wide spectrum ranging from the spherical plasma membrane to the complex cisternae of the Golgi apparatus. Mapping the relation between the protein-induced deformations at the molecular scale and the resulting mesoscale morphologies is key to bridging cellular experiments across the various length scales. In this review, we focus on the theoretical and computational methods used to understand the phenomenology underlying protein-driven membrane remodeling. Interactions at the molecular scale can be computationally probed by all atom and coarse grained molecular dynamics (MD, CGMD), as well as dissipative particle dynamics (DPD) simulations, which we only describe in passing. We choose to focus on several continuum approaches extending the Canham - Helfrich elastic energy model for membranes to include the effect of curvature-inducing proteins and explore the conformational phase space of such systems. In this description, the protein is expressed in the form of a spontaneous curvature field. The approaches include field theoretical methods limited to the small deformation regime, triangulated surfaces and particle-based computational models to investigate the large-deformation regimes observed in the natural state of many biological membranes. Applications of these methods to understand the properties of biological membranes in homogeneous and inhomogeneous environments of proteins, whose underlying curvature fields are either isotropic or anisotropic, are discussed. The diversity in the curvature fields elicits a rich variety of morphological states, including tubes, discs, branched tubes, and caveola. Mapping the thermodynamic stability of these states as a function of tuning parameters such as concentration and strength of curvature induction of the proteins is discussed. The relative stabilities of these self-organized shapes are examined through free-energy calculations. The suite of methods discussed here can be tailored to applications in specific cellular settings such as endocytosis during cargo trafficking and tubulation of filopodial structures in migrating cells, which makes these methods a powerful complement to experimental studies.

Investigation of coarse-grained mappings via an iterative generalized Yvon-Born-Green method

Low resolution coarse-grained (CG) models enable highly efficient simulations of complex systems. The interactions in CG models are often iteratively refined over multiple simulations until they reproduce the one-dimensional (1-D) distribution functions, e.g., radial distribution functions (rdfs), of an all-atom (AA) model. In contrast, the multiscale coarse-graining (MS-CG) method employs a generalized Yvon-Born-Green (g-YBG) relation to determine CG potentials directly (i.e., without iteration) from the correlations observed for the AA model. However, MS-CG models do not necessarily reproduce the 1-D distribution functions of the AA model. Consequently, recent studies have incorporated the g-YBG equation into iterative methods for more accurately reproducing AA rdfs. In this work, we consider a theoretical framework for an iterative g-YBG method. We numerically demonstrate that the method robustly determines accurate models for both hexane and also a more complex molecule, 3-hexylthiophene. By examining the MS-CG and iterative g-YBG models for several distinct CG representations of both molecules, we investigate the approximations of the MS-CG method and their sensitivity to the CG mapping. More generally, we explicitly demonstrate that CG models often reproduce 1-D distribution functions of AA models at the expense of distorting the cross-correlations between the corresponding degrees of freedom. In particular, CG models that accurately reproduce intramolecular 1-D distribution functions may still provide a poor description of the molecular conformations sampled by the AA model. We demonstrate a simple and predictive analysis for determining CG mappings that promote an accurate description of these molecular conformations.

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.

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.

Thermomechanical properties and deformation of coarse-grained models of hard-soft block copolymers

In this paper, we investigate the enhancement mechanism of the mechanical properties for hard-soft block copolymers by using molecular dynamics simulations at various temperatures. A coarse-grained approach is adopted to study sufficiently generic models. Our numerical experiments demonstrate that the nonbond potential plays a more significant role in mechanical properties compared to the bond potential. This finding serves as a cornerstone to understand the hard-soft materials. To explore the effect of hard segments, four copolymers with different concentrations and energy factors that describe the interaction between hard beads are conducted. Simulation results show that the mechanical performances of the system with large attractive force and small concentration of hard segments could be improved dramatically in conjunction with a moderate increment of the glass transition temperature. In particular, the energy factor shows a substantial influence in determining the microphase separation as well as the morphology of hard domains. These observations are believed to provide design guidelines for polymeric materials in engineering practice.

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.

Role of neutral lipids in tear fluid lipid layer: coarse-grained simulation study

Tear fluid lipid layer (TFLL) residing at the air-water interface of tears has been recognized to play an important role in the development of dry eye syndrome. Yet, the composition, structure, and mechanical properties of TFLL are only partly known. Here, we report results of coarse-grained simulations of a lipid layer comprising phospholipids, free fatty acids, cholesteryl esters, and triglycerides at the air-water interface to shed light on the properties of TFLL. We consider structural as well as dynamical properties of the lipid layer as a function of surface pressure. Simulations revealed that neutral lipids reside heterogeneously between phospholipids at relatively low pressures but form a separate hydrophobic phase with increasing surface pressure, transforming the initial lipid monolayer to a two-layered structure. When the model of TFLL was compared to a one-component phospholipid monolayer system, we found drastic differences in both structural and dynamical properties that explain the prominent role of neutral lipids as stabilizers of the TFLL. Based on our results, we suggest that neutral lipids are able to increase the stability of the TFLL by modulating its dynamical and structural behavior, which is important for the proper function of tear film.

Effects of cholesterol on pore formation in lipid bilayers induced by human islet amyloid polypeptide fragments: a coarse-grained molecular dynamics study

Disruption of the cellular membrane by the amyloidogenic peptide, islet amyloid polypeptide (IAPP), has been considered as one of the mechanisms of β-cell death during type 2 diabetes. The N-terminal region (residues 1-19) of the human version of IAPP is suggested to be primarily responsible for the membrane-disrupting effect of the full-length hIAPP peptide. However, the detailed assembly mode of hIAPP1-19 with membrane remains unclear. To gain insight into the interactions of hIAPP1-19 oligomer with the model membrane, we have employed coarse-grained molecular dynamics self-assembly simulations to study the aggregation of hIAPP1-19 fragments in the binary lipid made of zwitterionic dipalmitoylphosphatidylcholine (DPPC) and anionic dipalmitoylphosphatidylserine (DPPS) in the presence and absence of different levels of cholesterol content. The membrane-destabilizing effect of hIAPP1-19 is found to be modulated by the presence of cholesterol. In the absence of cholesterol, hIAPP1-19 aggregates prefer to locate inside the bilayer, forming pore-like assemblies. While in the presence of cholesterol molecules, the lipid bilayer becomes more ordered and stiff, and the hIAPP1-19 aggregates are dominantly positioned at the bilayer-water interface. The action of cholesterol may suggest a possible way to maintain the membrane integrity by small molecule interference.

Obtaining fully dynamic coarse-grained models from MD

We present a general method to obtain parametrised models for the drift and diffusion terms of the Fokker-Planck equation of a coarse-grained description of molecular systems. The method is based on the minimisation of the relative entropy defined in terms of the two-time joint probability and thus captures the full dynamics of the coarse-grained description. In addition, we show an alternative Bayesian argument that starts from the path probability of a diffusion process which allows one to obtain the best parametrised model that fits an actual observed path of the coarse-grained variables. Both approaches lead to exactly the same optimisation function giving strong support to the methodology. We provide an heuristic argument that explains how both approaches are connected.

A structurally relevant coarse-grained model for cholesterol

Detailed atomistic computer simulations are now widely used to study biological membranes, including increasingly mixed lipid systems that involve, for example, cholesterol, which is a key membrane lipid. Typically, simulations of these systems start from a preassembled bilayer because the timescale on which self-assembly occurs in mixed lipid systems is beyond the practical abilities of fully atomistic simulations. To overcome this limitation and study bilayer self-assembly, coarse-grained models have been developed. Although there are several coarse-grained models for cholesterol reported in the literature, these generally fail to account explicitly for the unique molecular features of cholesterol that relate to its function and role as a membrane lipid. In this work, we propose a new coarse-grained model for cholesterol that retains the molecule's unique features and, as a result, can be used to study crystalline structures of cholesterol. In the development of the model, two levels of coarse-graining are explored and the importance of retaining key molecular features in the coarse-grained model that are relevant to structural properties is investigated.

A coarse-grained model for amorphous and crystalline fatty acids

Fatty acids constitute one of the main components of the lipid lamellae in the top layer of the skin, known as the stratum corneum, which acts as a barrier to foreign substances entering the body and to water leaving the body. To better understand the mechanics of the skin, a molecular-level understanding of the structure of the lamellae needs to be investigated. As a first step toward this goal, the current work involves the development of a coarse-grained model for fatty acids in an amorphous and a crystalline state. In order to retain the structural details of the atomistic molecules, radial distribution functions have been used to provide target data against which the coarse-grained force field is optimized. The optimization was achieved using the method developed by Reith, Putz, and Muller-Plathe with a damping factor introduced into the updating scheme to facilitate the convergence against the crystalline radial distribution functions. Using this approach, a transferable force field has been developed for both crystalline and amorphous systems that can be used to describe fatty acids of different chain lengths. We are unaware of any other coarse-grained model in the literature that has been developed to study solid phases. Additionally, the amorphous force field has been shown to accurately model mixtures of different free fatty acids based on the potentials derived from pure lipid systems.

Molecular dynamics simulations of the dimerization of transmembrane alpha-helices

Membrane proteins account for nearly a quarter of all genes, but their structure and function remain incompletely understood. Most membrane proteins have transmembrane (TM) domains made up of bundles of hydrophobic alpha-helices. The lateral association of TM helices within the lipid bilayer is a key stage in the folding of membrane proteins. It may also play a role in signaling across cell membranes. Dimerization of TM helices is a simple example of such lateral association. Molecular dynamics (MD) simulations have been used for over a decade to study membrane proteins in a lipid bilayer environment. However, direct atomistic (AT) MD simulation of self-assembly of a TM helix bundle remains challenging. AT-MD may be complemented by coarse-grained (CG) simulations, in which small numbers of atoms are grouped together into particles. In this Account, we demonstrate how CG-MD may be used to simulate formation of dimers of TM helices. We also show how a serial combination of CG and AT simulation provides a multiscale approach for generating and refining models of TM helix dimers. The glycophorin A (GpA) TM helix dimer represents a paradigm for helix-helix packing, mediated by a GxxxG sequence motif. It is well characterized experimentally and so is a good test case for evaluating computational methods. CG-MD simulations in which two separate TM helices are inserted in a lipid bilayer result in spontaneous formation of a right-handed GpA dimer, in agreement with NMR structures. CG-MD models were evaluated via comparison with data on destabilizing mutants of GpA. Such mutants increased the conformational flexibility and the dissociation constants of helix dimers. GpA dimers have been used to evaluate a multiscale approach: A CG model is converted to an AT model, which is used as the basis of an AT-MD simulation. Comparison of three AT-MD simulations of GpA, one starting from a CG model and two starting from NMR structures, leads to convergence to a common refined structure for the dimer. CG-MD self-assembly has also been used to model dimerization of the TM domain of the syndecan-2 receptor protein. This TM helix contains a GxxxG motif, which mediates right-handed helix packing comparable to that of the GxxxG motif in GpA. The multiscale approach has been applied to a more complex system, the heterodimeric alphaIIb/beta3 integrin TM helix dimer. In CG-MD, both right-handed and left-handed structures were formed. Subsequent AT-MD simulations showed that the right-handed structure was more stable, yielding a dimer in which the GxxxG motif of the alphaIIb TM helix packed against a hydrophobic surface of the beta3 helix in a manner comparable to that observed in two recent NMR studies. This work demonstrates that the multiscale simulation approach can be used to model simple membrane proteins. The method may be applied to more complex proteins, such as the influenza M2 channel protein. Future refinements, such as extending the multiscale approach to a wider range of scales (from CG through QM/MM simulations, for example), will expand the range of applications and the accuracy of the resultant models.

Mori-Zwanzig formalism as a practical computational tool

An operational procedure is presented to compute explicitly the different terms in the generalized Langevin equation (GLE) for a few relevant variables obtained within Mori-Zwanzig formalism. The procedure amounts to introducing an artificial controlled parameter which can be tuned in such a way that the so-called projected dynamics becomes explicit and the GLE reduces to a Markovian equation. The projected dynamics can be realised in practice by introducing constraints, and it is shown that the Green-Kubo formulae computed with these dynamics do not suffer from the plateau problem. The methodology is illustrated in the example of star polymer molecules in a melt using their center of mass as relevant variables. Through this example, we show that not only the effective potentials, but also the friction forces and the noise play a very important role in the dynamics.

Versatile Object-Oriented Toolkit for Coarse-Graining Applications

Coarse-graining is a systematic way of reducing the number of degrees of freedom representing a system of interest. Several coarse-graining techniques have so far been developed, such as iterative Boltzmann inversion, force-matching, and inverse Monte Carlo. However, there is no unified framework that implements these methods and that allows their direct comparison. We present a versatile object-oriented toolkit for coarse-graining applications (VOTCA) that implements these techniques and that provides a flexible modular platform for the further development of coarse-graining techniques. All methods are illustrated and compared by coarse-graining the SPC/E water model, liquid methanol, liquid propane, and a single molecule of hexane.

Peptide nanopores and lipid bilayers: interactions by coarse-grained molecular-dynamics simulations

A set of 49 protein nanopore-lipid bilayer systems was explored by means of coarse-grained molecular-dynamics simulations to study the interactions between nanopores and the lipid bilayers in which they are embedded. The seven nanopore species investigated represent the two main structural classes of membrane proteins (alpha-helical and beta-barrel), and the seven different bilayer systems range in thickness from approximately 28 to approximately 43 A. The study focuses on the local effects of hydrophobic mismatch between the nanopore and the lipid bilayer. The effects of nanopore insertion on lipid bilayer thickness, the dependence between hydrophobic thickness and the observed nanopore tilt angle, and the local distribution of lipid types around a nanopore in mixed-lipid bilayers are all analyzed. Different behavior for nanopores of similar hydrophobic length but different geometry is observed. The local lipid bilayer perturbation caused by the inserted nanopores suggests possible mechanisms for both lipid bilayer-induced protein sorting and protein-induced lipid sorting. A correlation between smaller lipid bilayer thickness (larger hydrophobic mismatch) and larger nanopore tilt angle is observed and, in the case of larger hydrophobic mismatches, the simulated tilt angle distribution seems to broaden. Furthermore, both nanopore size and key residue types (e.g., tryptophan) seem to influence the level of protein tilt, emphasizing the reciprocal nature of nanopore-lipid bilayer interactions.

Dynamics of vesicle formation from lipid droplets: mechanism and controllability

A coarse-grained model developed by Marrink et al. [J. Phys. Chem. B 111, 7812 (2007)] is applied to investigate vesiculation of lipid [dipalmitoylphosphatidylcholine (DPPC)] droplets in water. Three kinds of morphologies of micelles are found with increasing lipid droplet size. When the initial lipid droplet is smaller, the equilibrium structure of the droplet is a spherical micelle. When the initial lipid droplet is larger, the lipid ball starts to transform into a disk micelle or vesicle. The mechanism of vesicle formation from a lipid ball is analyzed from the self-assembly of DPPC on the molecular level, and the morphological transition from disk to vesicle with increasing droplet size is demonstrated. Importantly, we discover that the transition point is not very sharp, and for a fixed-size lipid ball, the disk and vesicle appear with certain probabilities. The splitting phenomenon, i.e., the formation of a disk/vesicle structure from a lipid droplet, is explained by applying a hybrid model of the Helfrich membrane theory. The elastic module of the DPPC bilayer and the smallest size of a lipid droplet for certain formation of a vesicle are successfully predicted.

Coarse-grained modeling of lipids

Molecular modeling of phospholipids on many scales has progressed significantly over the last years. Here we review several membrane models on intermediate to large length scales restricting ourselves to particle based coarse-grained models with implicit and explicit solvent. We explain similarities and differences as well as their connection to experiments and fine-grained models. We neglect any field descriptions on larger scales. We discuss then a few examples where we focus on studies of lipid phase behavior as well as supported lipid bilayers as these examples can only be meaningfully studied using large-scale models to date.