An implicit solvent coarse-grained lipid model with correct stress profile

Utilizing Machine Learning to Greatly Expand the Range and Accuracy of Bottom-Up Coarse-Grained Models through Virtual Particles

Coarse-grained (CG) models parametrized using atomistic reference data, i.e., "bottom up" CG models, have proven useful in the study of biomolecules and other soft matter. However, the construction of highly accurate, low resolution CG models of biomolecules remains challenging. We demonstrate in this work how virtual particles, CG sites with no atomistic correspondence, can be incorporated into CG models within the context of relative entropy minimization (REM) as latent variables. The methodology presented, variational derivative relative entropy minimization (VD-REM), enables optimization of virtual particle interactions through a gradient descent algorithm aided by machine learning. We apply this methodology to the challenging case of a solvent-free CG model of a 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) lipid bilayer and demonstrate that introduction of virtual particles captures solvent-mediated behavior and higher-order correlations which REM alone cannot capture in a more standard CG model based only on the mapping of collections of atoms to the CG sites.

Coarse-grained implicit solvent lipid force field with a compatible resolution to the Cα protein representation

Biological membranes have been prominent targets for coarse-grained (CG) molecular dynamics simulations. While minimal CG lipid models with three beads per lipid and quantitative CG lipid models with >10 beads per lipid have been well studied, in between them, CG lipid models with a compatible resolution to residue-level CG protein models are much less developed. Here, we extended a previously developed three-bead lipid model into a five-bead model and parameterized it for two phospholipids, POPC (1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine) and DPPC (1,2-dipalmitoyl-sn-glycero-3-phosphatidylcholine). The developed model, iSoLF, reproduced the area per lipid, hydrophobic thickness, and phase behaviors of the target phospholipid bilayer membranes at the physiological temperature. The model POPC and DPPC membranes were in liquid and gel phases, respectively, in accordance with experiments. We further examined the spontaneous formation of a membrane bilayer, the temperature dependence of physical properties, the vesicle dynamics, and the POPC/DPPC two-component membrane dynamics of the CG lipid model, showing some promise. Once combined with standard Cα protein models, the iSoLF model will be a powerful tool to simulate large biological membrane systems made of lipids and proteins.

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.

Computational Modeling of Realistic Cell Membranes

Cell membranes contain a large variety of lipid types and are crowded with proteins, endowing them with the plasticity needed to fulfill their key roles in cell functioning. The compositional complexity of cellular membranes gives rise to a heterogeneous lateral organization, which is still poorly understood. Computational models, in particular molecular dynamics simulations and related techniques, have provided important insight into the organizational principles of cell membranes over the past decades. Now, we are witnessing a transition from simulations of simpler membrane models to multicomponent systems, culminating in realistic models of an increasing variety of cell types and organelles. Here, we review the state of the art in the field of realistic membrane simulations and discuss the current limitations and challenges ahead.

Implicit solvent systematic coarse-graining of dioleoylphosphatidylethanolamine lipids: From the inverted hexagonal to the bilayer structure

Lamellar and hexagonal lipid structures are of particular importance in the biological processes such as membrane fusion and budding. Atomistic simulations of formation of these phases and transitions between them are computationally prohibitive, hence development of coarse-grained models is an important part of the methodological development in this area. Here we apply systematic bottom-up coarse-graining to model different phase structures formed by 1,2-dioleoylphosphatidylethanolamine (DOPE) lipid molecules. We started from atomistic simulations of DOPE lipids in water carried out at two different water/lipid molar ratio corresponding to the lamellar L_α and inverted hexagonal H_II structures at low and high lipid concentrations respectively. The atomistic trajectories were mapped to coarse-grained trajectories, in which each lipid was represented by 14 coarse-grained sites. Then the inverse Monte Carlo method was used to compute the effective coarse-grained potentials which for the coarse-grain model reproduce the same structural properties as the atomistic simulations. The potentials derived from the low concentration atomistic simulation were only able to form a bilayer structure, while both L_α and H_II lipid phases were formed in simulations with potentials obtained at high concentration. The typical atomistic configurations of lipids at high concentration combine fragments of both lamellar and non-lamellar structures, that is reflected in the extracted coarse-grained potentials which become transferable and can form a wide range of structures including the inverted hexagonal, bilayer, tubule, vesicle and micellar structures.

Systematic Coarse-Grained Lipid Force Fields with Semiexplicit Solvation via Virtual Sites

Despite the central role of lipids in many biophysical functions, the molecular mechanisms that dictate macroscopic lipid behavior remain elusive to both experimental and computational approaches. As such, there has been much interest in the development of low-resolution, implicit-solvent coarse-grained (CG) models to dynamically simulate biologically relevant spatiotemporal scales with molecular fidelity. However, in the absence of solvent, a key challenge for CG models is to faithfully emulate solvent-mediated forces, which include both hydrophilic and hydrophobic interactions that drive lipid aggregation and self-assembly. In this work, we provide a new methodological framework to incorporate semiexplicit solvent effects through the use of virtual CG particles, which represent structural features of the solvent-lipid interface. To do so, we leverage two systematic coarse-graining approaches, multiscale coarse-graining (MS-CG) and relative entropy minimization (REM), in a hybrid fashion to construct our virtual-site CG (VCG) models. As a proof-of-concept, we focus our efforts on two lipid species, 1,2-dioleoyl- sn-glycero-3-phosphocholine (DOPC) and 1,2-dipalmitoyl- sn-glycero-3-phosphocholine (DPPC), which adopt a liquid-disordered and gel phase, respectively, at room temperature. Through our analysis, we also present, to our knowledge, the first direct comparison between the MS-CG and REM methods for a complex biomolecule and highlight each of their strengths and weaknesses. We further demonstrate that VCG models recapitulate the rich biophysics of lipids, which enable self-assembly, morphological diversity, and multiple phases. Our findings suggest that the VCG framework is a powerful approach for investigation into macromolecular biophysics.

Normal vibrations of ternary DOPC/DPPC/cholesterol lipid bilayers by low-frequency Raman spectroscopy

A lipid bilayer containing a ternary mixture of low- and high-melting lipids and cholesterol (Chol) can give rise to domain formation, referred to as lipid rafts. Low-frequency Raman spectroscopy at reduced temperatures allows detection of normal membrane mechanical vibrations. In this work, Raman spectra were obtained in the spectral range between 5 and 90 cm⁻¹ for bilayers prepared from dioleoyl-glycero-phosphocholine (DOPC), dipalmitoyl-glycero-phosphocholine (DPPC) and Chol. A narrow peak detected between 13 and 16 cm⁻¹ was attributed to the vibrational eigenmode of a lipid monolayer (a leaflet). For the equimolar DOPC/DPPC ratio, the Chol concentration dependence for the peak position, width and amplitude may be divided into three distinct ranges: below 9 mol%, the intermediate range between 9 mol% and 38 mol%, and above 38 mol%. In the intermediate range the peak position attains its minimum, and the peak width drops approximately by a factor of two as compared with the Chol-free bilayers. Meanwhile, this range is known for raft formation in a fluid state. The obtained results may be interpreted as evidence that bilayer structures in the raft-containing fluid state may be frozen at low temperatures. The drop of peak width indicates that at the spatial scale of the experiment (∼2.5 nm) the intermolecular bilayer structure with raft formation becomes more homogeneous and more cohesive.

Upon lipid raft formation, the Raman peak corresponding to monolayer normal mechanical vibrations drops remarkably in position and width.

Effect of head group orientation on phospholipid assembly

The relationship between bilayer stability and lipid head group orientation is reported. In this work, molecular-dynamics simulations are performed to analyze the structure-property relationship of lipid biomembranes, taking into account coarse-grained model lipid interactions. The work explains the molecular scale mechanism of the phase behavior of lipid systems due to ion-lipid or anesthetic-lipid interactions, where reorientations of dipoles play a key role in modifying lipid phases and thereby alter biomembrane function. Our study demonstrates that simple dipolar reorientation is indeed sufficient in tuning a bilayer to a randomly flipped nonbilayer lamellar phase. This study may be used to assess the impact of changes in lipid phase characteristics on biomembrane structure due to the presence of anesthetics and ions.

Solvent-free, molecular-level modeling of self-assembling amphiphiles in water

Aggregation mesophases of self-assembling amphiphiles in water are highly important in the context of biology (biomembranes), therapy (liposomes), industry (polymer surfactants), and condensed-matter physics (lyotropic liquid crystals). Besides helping to increase fundamental understanding of collective molecular behavior, simulations of these lyotropic phases are pivotal to technological and medical developments such as smart drug carriers for gene therapy. Implicit-solvent, coarse-grained, low resolution modeling with a simple pair potential is the key to realizing the larger length and time scales associated with such mesoscopic phenomena during a computer simulation. Modeling amphiphiles by directed, soft, ellipsoidal cores interacting via a computationally simple yet tunable anisotropic pair potential, we have come to such a single-site model amphiphile that can rapidly self-assemble to give diverse lyotropic phases (such as fluid bilayers, micelles, etc.) without requiring the explicit incorporation of solvent particles. The model directly represents a tunable packing parameter that manifests in the spontaneous curvature of the amphiphile aggregates. Besides the all-important hydrophobic interaction, the hydration force is also treated implicitly. Thanks to the efficient solvent-free molecular-level coarse graining, this model is suitable for generic mesoscale studies of phenomena such as self-assembly, amphiphile mixing, domain formation, fusion, elasticity, etc., in amphiphile aggregates.

On the dynamics of molecular self-assembly and the structural analysis of bilayer membranes using coarse-grained molecular dynamics simulations

We present a molecular dynamics simulation study of the self-assembly of coarse-grained lipid molecules from unbiased random initial configurations. Our lipid model is based on a well-tried CG polymer model with an additional potential that mimics the hydrophobic properties of lipid tails. We find that several stages of self-organization of lipid clusters are involved in the dynamics of bilayer formation and that the resulting equilibrium structures sensitively depend on the strength of hydrophobic interactions hc of the lipid tails and on temperature T. The obtained stable lipid membranes are quantitatively analyzed with respect to their local structure and their degree of order. At equilibrium, we obtain self-stabilizing bilayer membrane structures that exhibit a bending stiffness κB and compression modulus KC comparable to experimental measurements under physiological conditions. We present a phase diagram of our lipid model which covers a sol-gel transition, a liquid (or gel-like) phase including stable bilayer structures and vesicle formation, as well as a quasi-crystalline phase. We also determine the exact conditions for temperature T and degree of hydrophobicity hc for stable bilayer formation including closed vesicles.

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.

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.

Atomistic Monte Carlo simulation of lipid membranes

Biological membranes are complex assemblies of many different molecules of which analysis demands a variety of experimental and computational approaches. In this article, we explain challenges and advantages of atomistic Monte Carlo (MC) simulation of lipid membranes. We provide an introduction into the various move sets that are implemented in current MC methods for efficient conformational sampling of lipids and other molecules. In the second part, we demonstrate for a concrete example, how an atomistic local-move set can be implemented for MC simulations of phospholipid monomers and bilayer patches. We use our recently devised chain breakage/closure (CBC) local move set in the bond-/torsion angle space with the constant-bond-length approximation (CBLA) for the phospholipid dipalmitoylphosphatidylcholine (DPPC). We demonstrate rapid conformational equilibration for a single DPPC molecule, as assessed by calculation of molecular energies and entropies. We also show transition from a crystalline-like to a fluid DPPC bilayer by the CBC local-move MC method, as indicated by the electron density profile, head group orientation, area per lipid, and whole-lipid displacements. We discuss the potential of local-move MC methods in combination with molecular dynamics simulations, for example, for studying multi-component lipid membranes containing cholesterol.

Coarse-Grained Models for Protein-Cell Membrane Interactions

The physiological properties of biological soft matter are the product of collective interactions, which span many time and length scales. Recent computational modeling efforts have helped illuminate experiments that characterize the ways in which proteins modulate membrane physics. Linking these models across time and length scales in a multiscale model explains how atomistic information propagates to larger scales. This paper reviews continuum modeling and coarse-grained molecular dynamics methods, which connect atomistic simulations and single-molecule experiments with the observed microscopic or mesoscale properties of soft-matter systems essential to our understanding of cells, particularly those involved in sculpting and remodeling cell membranes.

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.

Determining the Gaussian curvature modulus of lipid membranes in simulations

The Gaussian curvature modulus κ¯ of lipid bilayers likely contributes more than 100 kcal/mol to every cellular fission or fusion event. This huge impact on membrane remodeling energetics might be a factor that codetermines the complex lipid composition of biomembranes through tuning of κ¯. Yet, its value has been measured only for a handful of simple lipids, and no simulation has so far determined it better than a factor of two, rendering a systematic investigation of such enticing speculations impossible. Here we propose a highly accurate method to determine κ¯ in computer simulations. It relies on the interplay between curvature stress and edge tension of partially curved axisymmetric membrane disks and requires determining their closing probability. For a simplified lipid model we obtain κ¯ and its relation to the normal bending modulus κ for membranes differing both in stiffness and spontaneous lipid curvature. The elastic ratio κ¯/κ can be determined with a few percent statistical accuracy. Its value agrees with the scarce experimental data, and its change with spontaneous lipid curvature is compatible with theoretical expectations, thereby granting additional information on monolayer properties. We also show that an alternative determination of these elastic parameters based on moments of the lateral stress profile gives markedly different and unphysical values.

Systematic implicit solvent coarse-graining of bilayer membranes: lipid and phase transferability of the force field

We study the lipid and phase transferability of our recently developed systematically coarse-grained solvent-free membrane model. The force field was explicitly parameterized to describe a fluid 1-palmitoyl-2-oleoyl-phosphatidylcholine (POPC) bilayer at 310 K with correct structure and area per lipid, while gaining at least three orders of magnitude in computational efficiency (see Wang and Deserno 2010 J. Phys. Chem. B 114 11207-20). Here, we show that exchanging CG tails, without any subsequent re-parameterization, creates reliable models of 1,2-dioleoylphosphatidylcholine (DOPC) and 1,2-dipalmitoylphosphatidylcholine (DPPC) lipids in terms of structure and area per lipid. Furthermore, all CG lipids undergo a liquid-gel transition upon cooling, with characteristics like those observed in experiments and all-atom simulations during phase transformation. These studies suggest a promising transferability of our force field parameters to different lipid species and thermodynamic state points, properties that are a prerequisite for even more complex systems, such as mixtures.