Coarse-grained Force Research Articles

Development of accurate coarse-grained force fields for weakly polar groups by an indirect parameterization strategy.

Coarse-grained (CG) molecular dynamics simulations are widely used to predict morphological structures and interpret mechanisms of mesoscopic behavior between the scope of traditional experiments and all-atom simulations. However, most current CG force fields (FFs) are not precise enough, especially for polar molecules or functional groups. A main obstacle in developing accurate CG FFs for polar molecules is the freezing problem met at room temperature. In this work, we introduce an indirect parametrization strategy for weakly polar groups by considering their short-chain homologs to avoid freezing. Here, a polar group containing three to four heavy atoms is mapped into one CG bead that is connected to one alkyl bead composed of three or four carbons. The CG beads interact via 4-parameter nonbonded Morse potentials and harmonic bonded potentials. An efficient meta-multilinear interpolation parameterization algorithm, as recently developed by us, is used to rigorously optimize the force parameters. Satisfactory accuracy is witnessed in terms of the density, heat of vaporization, surface tension, and solvation free energy of the homologs of twelve polar molecules, all deviating from the experiment by less than 5%. The transferability of the current FF is indicated by the predicted density, heat of vaporization, and end-to-end distance distributions of fatty acid methyl esters composed of multiple functional groups parameterized in this work.

Development of coarse-grained force field for alcohols: an efficient meta-multilinear interpolation parameterization algorithm.

Coarse-grained (CG) molecular dynamics are powerful tools to access a mesoscopic phenomenon and simultaneously record microscopic details, but currently the CG force fields (FFs) are still limited by low parameterization efficiency and poor accuracy especially for polar molecules. In this work, we developed a Meta-Multilinear Interpolation Parameterization (Meta-MIP) algorithm to optimize the CG FFs for alcohols. This algorithm significantly boosts parameterization efficiency by constructing on-the-fly local databases to cover the global optimal parameterization path. In specific, an alcohol molecule is mapped to a heterologous model composed of an OH bead and a hydrocarbon portion which consists of alkane beads representing two to four carbon atoms. Non-bonded potentials are described by soft Morse functions that have no tail-corrections but can still retain good continuities at truncation distance. Nearly all of the properties in terms of density, heat of vaporization, surface tension, and solvation free energy for alcohols predicted by the current FFs deviate from experimental values by less than 7%. This Meta-MIP algorithm can be readily applied to force field development for a wide variety of molecules or functional groups, in many situations including but not limited to CG FFs.

Estimating the accuracy of the MARTINI model towards the investigation of peripheral protein-membrane interactions.

Peripheral membrane proteins play a major role in numerous biological processes by transiently associating with cellular membranes, often with extreme membrane specificity. Because of the short-lived nature of these interactions, molecular dynamics (MD) simulations have emerged as an appealing tool to characterize at the structural level the molecular details of the protein-membrane interface. Transferable coarse-grained (CG) MD simulations, in particular, offer the possibility to investigate the spontaneous association of peripheral proteins with lipid bilayers of different compositions at limited computational cost, but they are hampered by the lack of a reliable a priori estimation of their accuracy and thus typically require a posteriori experimental validation. In this article, we investigate the ability of the MARTINI CG force field, specifically the 3 open-beta version, to reproduce known experimental observations regarding the membrane binding behavior of 12 peripheral membrane proteins and peptides. Based on observations of multiple binding and unbinding events in several independent replicas, we found that, despite the presence of false positives and false negatives, this model is mostly able to correctly characterize the membrane binding behavior of peripheral proteins, and to identify key residues found to disrupt membrane binding in mutagenesis experiments. While preliminary, our investigations suggest that transferable chemical-specific CG force fields have enormous potential in the characterization of the membrane binding process by peripheral proteins, and that the identification of negative results could help drive future force field development efforts.

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.

Coarse-grained conformational surface hopping: Methodology and transferability.

Coarse-grained (CG) conformational surface hopping (SH) adapts the concept of multisurface dynamics, initially developed to describe electronic transitions in chemical reactions, to accurately describe classical molecular dynamics at a reduced level. The SH scheme couples distinct conformational basins (states), each described by its own force field (surface), resulting in a significant improvement of the approximation to the many-body potential of mean force [T. Bereau and J. F. Rudzinski, Phys. Rev. Lett. 121, 256002 (2018)]. The present study first describes CG SH in more detail, through both a toy model and a three-bead model of hexane. We further extend the methodology to non-bonded interactions and report its impact on liquid properties. Finally, we investigate the transferability of the surfaces to distinct systems and thermodynamic state points, through a simple tuning of the state probabilities. In particular, applications to variations in temperature and chemical composition show good agreement with reference atomistic calculations, introducing a promising "weak-transferability regime," where CG force fields can be shared across thermodynamic and chemical neighborhoods.

Recent Open Issues in Coarse Grained Force Fields.

This viewpoint intends to show recent open issues of using coarse grained models in molecular dynamics simulation. It reviews the current knowledge of the comparison between experimental and simulation data of structural and physical chemical properties that depend on the hydrophilic and hydrophobic behavior of the molecule.

Coarse-Grained Parameters for Divalent Cations within the SIRAH Force Field.

Although molecular dynamics simulations allow for the study of interactions among virtually all biomolecular entities, metal ions still pose significant challenges in achieving an accurate structural and dynamical description of many biological assemblies, particularly to coarse-grained (CG) models. Although the reduced computational cost of CG methods often makes them the technique of choice for the study of large biomolecular systems, the parameterization of metal ions is still very crude or not available for the vast majority of CG force fields. Here, we show that incorporating statistical data retrieved from the Protein Data Bank (PDB) to set specific Lennard-Jones interactions can produce structurally accurate CG molecular dynamics simulations using the SIRAH force field. We provide a set of interaction parameters for calcium, magnesium, and zinc ions, which cover more than 80% of the metal-bound structures reported in the PDB. Simulations performed on several proteins and DNA systems show that it is possible to preclude the use of topological constraints by modifying specific Lennard-Jones interactions.

Effect of Protein Flexibility from Coarse-Grained Elastic Network Parameterizations on the Calculation of Free Energy Profiles of Ligand Binding.

The characterization of the affinity and binding mechanism of specific molecules to a protein active site is scientifically and industrially relevant for many applications. In principle, this information can be obtained using molecular dynamics (MD) simulations by calculating the free energy profile of the process. However, this is a computationally demanding calculation. Currently, coarse-grained (CG) force fields are very well implemented for MD simulations of biomolecular systems. These computationally efficient force fields are a major advantage to the study of large model systems and/or those requiring long simulation times. The Martini model is currently one of the most popular CG force fields for these systems. For the specific case of protein simulations, to correctly maintain the macromolecular three-dimensional structure, the Martini model needs to include an elastic network (EN). In this work, the effect of protein flexibility, as induced by three EN models compatible with the Martini force field, was tested on the calculation of free energy profiles for protein-ligand binding. The EN models used were ElNeDyn, GoMartini, and GEN. The binding of triolein (TOG) and triacetin (TAG) to a lipase protein (thermomyces lanuginosa lipase-TLL) was used as a case study. The results show that inclusion of greater flexibility in the CG parameterization of proteins is of high importance in the calculation of the free energy profiles of protein-ligand systems. However, care must be taken in order to avoid unjustified large protein deformations. In addition, due to molecular flexibility there may be no absolute need for the center of the ligand to reach the center of the protein-binding site. The calculation of the energy profile to a distance of about 0.5 nm from the active site center can be sufficient to differentiate the affinity of different ligands to a protein.

Development of a coarse-grained force field model of polymeric 1-vinyl-3-ethylimidazolium tetrafluoroborate ionic liquids

A novel coarse-grained (CG) model for poly (1-vinyl-3-ethylimidazolium) tetrafluoroborate ([PVEim][BF4]) was developed with the all-atom (AA) molecular dynamics simulations as a benchmark. In this model, the bonded and non-bonded potential parameters of CG force field were obtained by Boltzmann and iterative Boltzmann inversion, respectively. The simulation results show that the novel CG model can accurately describe the structural characteristics and reproduce the thermodynamic properties comparing with the AA force field model. The deviation of densities values between CG model and experiment was within 5% at 298 K. This work can be a useful guide to the computational for large-scale PILs systems.

Dual Resolution Membrane Simulations Using Virtual Sites.

All-atomistic (AA) and coarse-grain (CG) simulations have been successfully applied to investigate a broad range of biomolecular processes. However, the accessible time and length scales of AA simulation are limited and the specific molecular details of CG simulation are simplified. Here, we propose a virtual site (VS) based hybrid scheme that can concurrently couple AA and CG resolutions in a single membrane simulation, mitigating the shortcomings of either representation. With some adjustments to make the AA and CG force fields compatible, we demonstrate that lipid bilayer properties are well kept in our hybrid approach. Our VS hybrid method was also applied to simulate a small lipid vesicle, with the inner leaflet and interior solvent represented in AA, and the outer leaflet together with exterior solvent at the CG level. Our multiscale method opens the way to investigate biomembrane properties at increased computational efficiency, in particular applications involving large solvent filled regions.

Arbitrary Resolution with Two Bead Types Coarse-Grained Strategy and Applications to Protein Recognition.

Molecular recognition is a fundamental step in essentially any biological process. However, the kinetic processes during association and dissociation are difficult to be efficiently sampled by direct all-atom molecular dynamics simulations because of the large spatial and temporal scales. Here we propose an arbitrary resolution with two bead types (ART) coarse-grained (CG) strategy that is adept in molecular recognition. ART is a universal user-customized CG strategy that can generate a system-specific CG force field anytime and be applied to any system with an arbitrary CG resolution according to research requirements. ART CG simulations can be very efficiently performed with implicit solvation in prevalent simulation packages and provide interfaces for any enhanced sampling method. We used three applications, HLA-HIV epitope recognition, barnase-barstar association, and trimeric TRAF2 self-assembly, to validate the feasibility of the ART CG strategy, its advantages in protein recognition, and its high performance in simulations. Regular CG simulations can successfully achieve valid protein recognitions without any prior bound structure.

A novel multiscale scheme to accelerate atomistic simulations of bio-macromolecules by adaptively driving coarse-grained coordinates.

All-atom molecular dynamics (MD) simulations of bio-macromolecules can yield relatively accurate results while suffering from the limitation of insufficient conformational sampling. On the other hand, the coarse-grained (CG) MD simulations efficiently accelerate conformational changes in biomolecules but lose atomistic details and accuracy. Here, we propose a novel multiscale simulation method called the adaptively driving multiscale simulation (ADMS)-it efficiently accelerates biomolecular dynamics by adaptively driving virtual CG atoms on the fly while maintaining the atomistic details and focusing on important conformations of the original system with irrelevant conformations rarely sampled. Herein, the "adaptive driving" is based on the short-time-averaging response of the system (i.e., an approximate free energy surface of the original system), without requiring the construction of the CG force field. We apply the ADMS to two peptides (deca-alanine and Ace-GGPGGG-Nme) and one small protein (HP35) as illustrations. The simulations show that the ADMS not only efficiently captures important conformational states of biomolecules and drives fast interstate transitions but also yields, although it might be in part, reliable protein folding pathways. Remarkably, a ∼100-ns explicit-solvent ADMS trajectory of HP35 with three CG atoms realizes folding and unfolding repeatedly and captures the important states comparable to those from a 398-µs standard all-atom MD simulation.

Molecular dynamics trajectories for 630 coarse-grained drug-membrane permeations

The permeation of small-molecule drugs across a phospholipid membrane bears much interest both in the pharmaceutical sciences and in physical chemistry. Connecting the chemistry of the drug and the lipids to the resulting thermodynamic properties remains of immediate importance. Here we report molecular dynamics (MD) simulation trajectories using the coarse-grained (CG) Martini force field. A wide, representative coverage of chemistry is provided: across solutes—exhaustively enumerating all 105 CG dimers—and across six phospholipids. For each combination, umbrella-sampling simulations provide detailed structural information of the solute at all depths from the bilayer midplane to bulk water, allowing a precise reconstruction of the potential of mean force. Overall, the present database contains trajectories from 15,120 MD simulations. This database may serve the further identification of structure-property relationships between compound chemistry and drug permeability.

Martini Force Field for Protonated Polyethyleneimine.

Polyethyleneimine (PEI), one of the most widely used nonviral gene carriers, was investigated in the presented work at coarse-grained (CG) level. The main focus was on elaborating a realistic CG force field (FF) aimed to reproduce dynamic structural features of protonated PEI chains and, furthermore, to enable massive simulations of DNA-PEI complex formation and condensation. We parametrized CG Martini FF models for PEI in polarizable and nonpolarizable water by applying Boltzmann inversion techniques to all-atom (AA) probability distributions for distances, angles, and dihedrals of entire monomers. The fine-tuning of the FFs was achieved by fitting simulated CG gyration radii and end-to-end distances to their AA counterparts. The developed Martini FF models are shown to be well suited for realistic large-scale simulations of size/protonation-dependent behavior of solvated PEI chains, either individually or as part of DNA-PEI systems. © 2019 Wiley Periodicals, Inc.

Recent Progress towards Chemically-Specific Coarse-Grained Simulation Models with Consistent Dynamical Properties

Coarse-grained (CG) models can provide computationally efficient and conceptually simple characterizations of soft matter systems. While generic models probe the underlying physics governing an entire family of free-energy landscapes, bottom-up CG models are systematically constructed from a higher-resolution model to retain a high level of chemical specificity. The removal of degrees of freedom from the system modifies the relationship between the relative time scales of distinct dynamical processes through both a loss of friction and a “smoothing” of the free-energy landscape. While these effects typically result in faster dynamics, decreasing the computational expense of the model, they also obscure the connection to the true dynamics of the system. The lack of consistent dynamics is a serious limitation for CG models, which not only prevents quantitatively accurate predictions of dynamical observables but can also lead to qualitatively incorrect descriptions of the characteristic dynamical processes. With many methods available for optimizing the structural and thermodynamic properties of chemically-specific CG models, recent years have seen a stark increase in investigations addressing the accurate description of dynamical properties generated from CG simulations. In this review, we present an overview of these efforts, ranging from bottom-up parameterizations of generalized Langevin equations to refinements of the CG force field based on a Markov state modeling framework. We aim to make connections between seemingly disparate approaches, while laying out some of the major challenges as well as potential directions for future efforts.

(Invited) Multiscale Molecular Modeling for Polymer Electrolyte Membrane for Fuel Cell

Multi-scale “molecular” modeling approach has been developed and applied to polymer electrolyte membrane. The goal of this work is to investigate the possible morphology, structure, dynamics, and mechanical properties of perfluorosulfonic acid (PFSA) membrane with realistic polymer chain lengths (>100 monomer units) by molecular dynamics (MD) simulations. First, we have carried out a series of all-atom (AA) MD simulations of PFSA polymer with a short chain length (10 monomer units) to yield reference structural data for building a coarse-grained (CG) molecular model. Although many phenomenological modeling based on dissipative particle dynamics has been proposed previously, a chemically accurate CG model should be beneficial to investigate the morphology in realistic membranes and to provide a concrete molecular design. Thus, we attempted to construct a predictive CG model for the structure and morphology of PFSA membranes that is compatible with the SDK CG water model. [1] As a first trial, we extended the parameter set in the SDK CG force field to examine a hydrated PFSA membrane based on thermodynamic and structural data from experiments and AA-MD simulations. However, a noticeable degradation of the morphology was detected, which motivated us to improve the structural properties by a combination with the iterative Boltzmann inversion (IBI) approach. The hybrid SDK/IBI model was determined to reasonably reproduce both the thermodynamic and structural properties of the PFSA membrane for all examined water contents. [2] In addition, the obtained CG model demonstrated good transferability. Then, we used the CG-MD to simulate realistic long-chained (including more than 120 monomer units) PFSA membranes. We obtained successfully a well converged structure for this long-chained membrane system. We also developed a reverse-mapping method and successfully used it to produce a well-equilibrated structure at all-atom resolution. We further investigated the mechanical properties of this realistic PSFA membranes at AA resolution. The uniaxial tension tests were conducted to understand the mechanical behavior of hydrated PEM membranes, especially the failure mechanism of the membranes. It was observed that the results (Poisson's ratio, free volume) of the uniaxial deformation were sensitive to the hydration level. This computational methodology will provide more chemically realistic predictions of the PEM membrane properties and give an insight into how to develop the large-scale atomistic PEM model in a multi-scale framework. We will further discuss the effect of equivalent weight (EW) and side chain length on morphology and dynamics of PFSA membranes.[3,4][1] Shinoda et al., Mol. Simul. 33, 27 (2007).[2] Kuo et al., J. Chem. Phys. 147, 094904 (2017).[3] Kuo et al., J. Phys. Chem. C 120, 25832 (2016).[4] Kuo et al., Polymer, 146, 53 (2018).

Developing a Transferable Coarse-Grained Model for the Prediction of Thermodynamic, Structural, and Mechanical Properties of Polyimides at Different Thermodynamic State Points

In the present work, we develop a coarse-grained (CG) model for polyimide (PI) at 800 K and 1 atm by applying iterative Boltzmann inversion (IBI) and the density correction method to derive the bonded and nonbonded interaction potentials. Although the CG force field is built at a single thermodynamic state point without any temperature correction, the CG model possesses a rather favorable temperature transferability in a wide temperature range of 300-800 K at P = 1 atm and a good pressure transferability to some extent in a certain pressure range from 0.1 to 30 MPa. In addition to the local conformation and local packing distribution functions, the thermodynamic properties such as the glass transition temperature and the coefficient of linear thermal expansion are predicted correctly by the CG model, and the isothermal compressibility coefficients calculated from both atomic and CG models are on the same order of magnitude. Additionally, the stress-strain behavior under compression or tension of the CG model shows a qualitative agreement with the atomistic results, and the corresponding values of the elastic modulus of the CG model at different temperatures roughly match with those of the atomistic model.

Realistic Coarse-Grain Model ofcis-1,4-Polybutadiene: From Chemistry to Rheology

We present a practical coarse-grain (CG) force field for dissipative particle dynamics (DPD) simulations of cis-1,4-polybutadiene (cPB). The parametrization of the model was realized using the recent Bayesian bottom-up scheme based on trajectory matching. The CG force field enables the correct description of cPB melts in a broad range of temperatures and pressures. We demonstrate its robustness by measuring the thermal expansion coefficient and isothermal compressibility consistent with experimental values. By reducing the computational cost by a factor 21 with respect to classical united-atom force fields while keeping accuracy, we can reach larger time and length scales suitable for the investigation of the rheological and the mechanical properties of such polymeric systems. In particular, the rubbery plateau and the entanglement mass for monodisperse cPB entangled melts are quantitatively predicted using this CG model.

The SIRAH 2.0 Force Field: Altius, Fortius, Citius.

A new version of the coarse-grained (CG) SIRAH force field for proteins has been developed. Modifications to bonded and non-bonded interactions on the existing molecular topologies significantly ameliorate the structural description and flexibility of a non-redundant set of proteins. The SIRAH 2.0 force field has also been ported to the popular simulation package AMBER, which along with the former implementation in GROMACS expands significantly the potential range of users and performance of this CG force field on CPU/GPU codes. As a non-trivial example of its application, we undertook the structural and dynamical analysis of the most abundant and conserved calcium-binding protein, calmodulin (CaM). CaM is composed of two calcium-binding motifs called EF-hands, which in the presence of calcium specifically recognize a cognate peptide by embracing it. CG simulations of CaM bound to four calcium ions in the presence or absence of a binding peptide (holo and apo forms, respectively) resulted in good and stable ion coordination. The simulation of the holo form starting from an experimental structure sampled near-native conformations, retrieving quasi-atomistic precision. Removing the binding peptide enabled the EF-hands to perform large reciprocal movements, comparable to those observed in NMR structures. On the other hand, the isolated peptide starting from the helical conformation experienced spontaneous unfolding, in agreement with previous experimental data. However, repositioning the peptide in the neighborhood of one EF-hand not only prevented the peptide from unfolding but also drove CaM to a fully bound conformation, with both EF-hands embracing the cognate peptide, resembling the experimental holo structure. Therefore, SIRAH 2.0 shows the capacity to handle a number of structurally and dynamically challenging situations, including metal ion coordination, unbiased conformational sampling, and specific protein-peptide recognition.

Styrene/Maleic Acid Copolymers Form SMALPs by Pulling Lipid Patches out of the Lipid Bilayer.

Amphiphilic copolymers composed of styrene and maleic acid (SMA) monomers caused a major methodical breakthrough in the study of membrane proteins. They were found to directly release phospholipids and membrane proteins both from artificial and natural lipid bilayers, yielding stable water-soluble discoidal SMA/lipid particles (SMALPs) of uniform size. Although many empirical studies indicate the great potency of SMALPs for membrane protein research, the mechanisms of their formation remain obscure. It is unknown which factors account for the very assembly of SMALPs and govern their uniform size. We have developed a coarse-grained (CG) molecular model of SMA copolymers based on the MARTINI CG force field and used it to probe the behavior of SMA copolymers with varying composition/charge/concentration in solution as well as their interaction with lipid membranes. First, we found that SMA copolymers tend to aggregate in solution into clusters, which could account for the uniform size of SMALPs. Next, molecular dynamics (MD) simulations showed that periodic SMA copolymers with styrene/maleic acid ratios of 2:1 ([SSM] n) and 3:1 ([SSSM] n) differently interacted with lipid bilayers. While clusters of 2:1 SMA copolymers induced membrane poration, the clusters of 3:1 SMA copolymers extracted lipid patches from the membrane yielding SMALP-like structures. Extraction of lipid patches was also observed when we simulated the behavior of 3:1 copolymers with varying lengths and statistical distribution of styrene and MA units. Analysis of MD simulation trajectories and comparison with experimental data indicate that the formation of SMALPs requires copolymer molecules with a sufficient number of units made of more than two sequential styrene monomers.