Coarse-grained Potentials Research Articles

Mechanical Properties of Polyethylene/Carbon Nanotube Composites from Coarse-Grained Simulations

Advanced nanocomposite membranes incorporate nanomaterials within a polymer matrix to augment the mechanical strength of the resultant product. Characterizing these membranes through molecular modeling necessitates specialized approaches to accurately capture the length scales, time scales, and structural complexities inherent in polymers. To address these requirements, an efficient simulation protocol is proposed, utilizing coarse-grained (CG) molecular dynamics simulations to examine the mechanical properties of polyethylene/single-walled carbon nanotube (PE/SWCNT) composites. This methodology integrates CG potentials derived from the statistical associating fluid theory (SAFT-γ Mie) equation of state and a modified Tersoff potential as a model for SWCNTs. A qualitative correspondence with benchmark classical all-atom models, as well as available experimental data, is observed, alongside enhanced computational efficiency. Employing this CG model, the focus is directed at exploring the mechanical properties of PE/SWCNT composites under both tensile and compressive loading conditions. The investigation covered the influence of SWCNT size, dispersion, and weight fraction. The findings indicate that although SWCNTs enhance the mechanical strength of PE, the extent of enhancement marginally depends on the dispersion, filler size, and weight fraction. Fracture strengths may be elevated by 20% with a minor incorporation of SWCNTs. Under compression, the incorporation of SWCNTs into the composites results in a transformation from brittle to tough materials. These insights contribute to the optimization of PE/SWCNT composites, emphasizing the importance of considering multiple factors to fine-tune the desired mechanical performance.

Mean-Field Coupling Between Local Interactions in Proteins in Relation to Chirality, Secondary, and Supersecondary Structure Formation, and Allostery.

Coarse graining is usually considered as a tool to extend the time and size scale of simulations. However, leaving out the atomistic details to keep their fingerprints in a coarse-grained model also enables us to understand better structure formation and dynamics. In this chapter, by using our scale-consistent theory of coarse graining, we demonstrate that the coarse-grained terms corresponding to the coupling between local conformational states of amino-acid residues explain secondary-structure propagation along polypeptide backbone to stabilize -helices and -strands in proteins and direct the loops preceding and following such segments of protein structure. These and related correlations are probably the still missing terms in both physics- and knowledge-based approaches to protein-structure modeling, including AlphaFold. We also show that the chirality of coarse-grained torsional potentials and, thereby, that of polypeptide backbone emerge from putting together achiral site-based torsional potentials given the phase shift due to residue chirality, and that the improper-torsional potentials that correspond to the coupling between local conformational states of the sites adjacent to a given -carbon atom enable us to model amino-acid-residue enantiomerization.

Coarse-grained molecular dynamic model and wettability simulation of graphite materials

Although progress has been made in high-performance computing, there are still limitations on temporal and spatial scales of molecular dynamic calculations. A major issue in molecular dynamic (MD) simulations is the computational cost, and coarse-grained methods can save computational costs and accelerate calculations by reducing the degrees of freedom in the system. This method takes a selected group of representative atoms in the atomic microstructure as a bead and uses the proportional relationship of atomic scale atomic potentials in MD simulation to define the interaction between beads and solve the motion equation of beads. This article proposed a coarse-grained potential for graphite based on the modification of Airebo potential, with an n3: 1 mapping, and established a corresponding n3: 1 coarse-grained model, where one bead represents the number of n3 atoms. The results indicated that the coarse-grained model well reflected the basic thermal and mechanical properties of graphite. In addition, this article also proposed a coarsening method for the Lennard–Jones (L–J) potential function parameters and established a coarse-grained wetting model with n = 2. The results indicate that the coarse-grained wetting model can effectively predict the wetting performance of copper droplets on graphite in only 60% of the time using the all-atom model. The coarsening potential function and model proposed in this article are also applicable to graphite with rough surfaces. It can be anticipated that coarse-grained molecular dynamics methods will have more applications in the future, as they can handle large-scale calculations more quickly.

Machine-learned coarse-grained potentials for particles with anisotropic shapes and interactions

Computational investigations of biological and soft-matter systems governed by strongly anisotropic interactions typically require resource-demanding methods such as atomistic simulations. However, these techniques frequently prove to be prohibitively expensive for accessing the long-time and large-length scales inherent to such systems. Conversely, coarse-grained models offer a computationally efficient alternative. Nonetheless, models of this type have seldom been developed to accurately represent anisotropic or directional interactions. In this work, we introduce a straightforward bottom-up, data-driven approach for constructing single-site coarse-grained potentials suitable for particles with arbitrary shapes and highly directional interactions. Our method for constructing these coarse-grained potentials relies on particle-centered descriptors of local structure that effectively encode dependencies on rotational degrees of freedom in the interactions. By using these descriptors as regressors in a linear model and employing a simple feature selection scheme, we construct single-site coarse-grained potentials for particles with anisotropic interactions, including surface-patterned particles and colloidal superballs in the presence of non-adsorbing polymers. We validate the efficacy of our models by accurately capturing the intricacies of the potential-energy surfaces from the underlying fine-grained models. Additionally, we demonstrate that this simple approach can accurately represent the contact function (shape) of non-spherical particles, which may be leveraged to construct continuous potentials suitable for large-scale simulations.

Energy landscapes for clusters of hexapeptides.

We present the results for energy landscapes of hexapeptides obtained using interfaces to the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) program. We have used basin-hopping global optimization and discrete path sampling to explore the landscapes of hexapeptide monomers, dimers, and oligomers containing 10, 100, and 200 monomers modeled using a residue-level coarse-grained potential, Mpipi, implemented in LAMMPS. We find that the dimers of peptides containing amino acid residues that are better at promoting phase separation, such as tyrosine and arginine, have melting peaks at higher temperature in their heat capacity compared to phenylalanine and lysine, respectively. This observation correlates with previous work on the same uncapped hexapeptide monomers modeled using atomistic potential. For oligomers, we compare the variation in monomer conformations with radial distance and observe trends for selected angles calculated for each monomer. The LAMMPS interfaces to the GMIN and OPTIM programs for landscape exploration offer new opportunities to investigate larger systems and provide access to the coarse-grained potentials implemented within LAMMPS.

A colloidal model for the equilibrium assembly and liquid-liquid phase separation of the reflectin A1 protein

Reflectin is an intrinsically disordered protein known for its ability to modulate the biophotonic camouflage of cephalopods based on its assembly-induced osmotic properties. Its reversible self-assembly into discrete, size-controlled clusters and condensed droplets are known to depend sensitively on the net protein charge, making reflectin stimuli-responsive to pH, phosphorylation, and electric fields. Despite considerable efforts to characterize this behavior, the detailed physical mechanisms of reflectin’s assembly are not yet fully understood. Here, we pursue a coarse-grained molecular understanding of reflectin assembly using a combination of experiments and simulations. We hypothesize that reflectin assembly and phase behavior can be explained from a remarkably simple colloidal model whereby individual protein monomers effectively interact via a short-range attractive and long-range repulsive (SA-LR) pair potential. We parameterize a coarse-grained SA-LR interaction potential for reflectin A1 from small-angle x-ray scattering measurements, and then extend it to a range of pH values using Gouy-Chapman theory to model monomer-monomer electrostatic interactions. The pH-dependent SA-LR interaction is then used in molecular dynamics simulations of reflectin assembly, which successfully capture a number of qualitative features of reflectin, including pH-dependent formation of discrete-sized nanoclusters and liquid-liquid phase separation at high pH, resulting in a putative phase diagram for reflectin. Importantly, we find that at low pH size-controlled reflectin clusters are equilibrium assemblies, which dynamically exchange protein monomers to maintain an equilibrium size distribution. These findings provide a mechanistic understanding of the equilibrium assembly of reflectin, and suggest that colloidal-scale models capture key driving forces and interactions to explain thermodynamic aspects of native reflectin behavior. Furthermore, the success of SA-LR interactions presented in this study demonstrates the potential of a colloidal interpretation of interactions and phenomena in a range of intrinsically disordered proteins.

Comparison of coarse-grained models for cis-1,4-polyisoprene-graphite system

ABSTRACT Structural and dynamical properties of cis-1,4-polyisoprene-graphite system were compared by four coarse-grained models. Coarse-graining of graphene layers replaced four carbon atoms by a single bead while four mapping schemes were used for the polymer. Pressure-correction was applied to the nonbonded part of the coarse-grained potential among coarse-grained polyisoprene beads. Among structural properties density profiles, bond orientation and conformation tensor as function of distance from the graphite surface were studied. Bulk values were achieved at around 2 nm from the graphite surface. Higher degree of coarse-graining showed comparatively larger fluctuations in data. Among dynamical properties mean square displacement and autocorrelation of end-to-end unit vectors for varied distances from the graphite surface were studied. Dynamics study indicated that pressure-correction method used to optimise pressure of the system resulted in slower dynamics for the higher degree of coarse-graining.

Synthetic Force-Field Database for Training Machine Learning Models to Predict Mobility-Preserving Coarse-Grained Molecular-Simulation Potentials.

Balancing accuracy and efficiency is a common problem in molecular simulation. This tradeoff is evident in coarse-grained molecular dynamics simulation, which prioritizes efficiency, and all-atom molecular simulation, which prioritizes accuracy. Despite continuous efforts, creating a coarse-grained model that accurately captures both the system's structure and dynamics remains elusive. In this article, we present a data-driven approach for constructing coarse-grained models that aim to describe both the structure and dynamics of the system equally well. While the development of machine learning models is well-received in the scientific community, the significance of dataset creation for these models is often overlooked. However, data-driven approaches cannot progress without a robust dataset. To address this, we construct a database of synthetic coarse-grained potentials generated from unphysical all-atom models. A neural network is trained with the generated database to predict the coarse-grained potentials of real liquids. We evaluate their quality by calculating the combined loss of structural and dynamical accuracy upon coarse-graining. When we compare our machine learning-based coarse-grained potential with the one from iterative Boltzmann inversion, the machine learning prediction turns out better for all eight hydrocarbon liquids we studied. As all-atom surfaces turn more nonspherical, both ways of coarse-graining degrade. Still, the neural network outperforms iterative Boltzmann inversion in constructing good quality coarse-grained models for such cases. The synthetic database and the developed machine learning models are freely available to the community, and we believe that our approach will generate interest in efficiently deriving accurate coarse-grained models for liquids.

Chemically Specific Systematic Coarse-Grained Polymer Model with Both Consistently Structural and Dynamical Properties.

The coarse-grained (CG) model serves as a powerful tool for the simulation of polymer systems; its reliability depends on the accurate representation of both structural and dynamical properties. However, strong correlations between structural and dynamical properties on different scales and also a strong memory effect, enforced by chain connectivity between monomers in polymer systems, render developing a chemically specific systematic CG model a formidable task. In this study, we report a systematic CG approach that combines the iterative Boltzmann inversion (IBI) method and the generalized Langevin equation (GLE) dynamics. Structural properties are ensured by using conservative CG potentials derived from the IBI method. To retrieve the correct dynamical properties in the system, we demonstrate that using a combination of a Rouse-type delta function and a time-dependent short-time kernel in the GLE simulation is practically efficient. The former can be used to adjust the long-time diffusion dynamics, and the latter can be reconstructed from an iterative procedure according to the velocity autocorrelation function (ACF) from all-atomistic (AA) simulations. Taking the polystyrene as an example, we show that not only structural properties of radial distribution function, intramolecular bond, and angle distributions can be reproduced but also dynamical properties of mean-square displacement, velocity ACF, and force ACF resulted from our CG model have quantitative agreement with the reference AA model. In addition, reasonable agreements are observed in other collective properties between our GLE-CG model and the AA simulations as well.

Temperature-Transferable Coarse-Grained Models for Volumetric Properties of Poly(lactic Acid).

A new coarse-grained (CG) model, for which each monomer is mapped as one bead at its center of mass, was developed for simulating the volumetric properties of the polylactide (PLA) bulk. The three bonded CG potentials are first parametrized against the strain energies of the dimer, trimer, and tetramer, and the nonbonded CG potentials are then optimized to match the melt densities of the decamer. With the derived CG potentials, molecular dynamics (MD) simulations are found to reproduce thermal expansion and glass transition. By rescaling the dihedral and nonbonded potentials with temperature-independent factors, the glass transition temperature (Tg) is also satisfactorily restored with little modifications on the volumetric expansive coefficients at both rubbery and glassy states. Therefore, the finally optimized CG potentials exhibit excellent temperature transferability, as rationalized by the Simha-Boyer relation. Furthermore, it is confirmed that the dihedral torsions and nonbonded interactions play key roles in glass transition. Also, the simulated bulk moduli and conformational properties in a wide temperature range compare well with the referenced data. The proposed multiscale scheme has great potential in simulating thermo-mechanical properties of PLA and other polymers.

Effect of surface roughness and morphology on the adsorption and transport of CH4/CO2 mixtures in nanoporous carbons

We report here molecular simulations of the adsorption and transport behaviour of CH4/CO2 mixtures in two types of non-ideal carbon nanopores. One model decorates an otherwise slit pore with surface imperfections which disrupt the smooth walls; a second model considers a disordered media, formed of randomly arranged coronene flakes, resulting in significant tortuosity. Boundary-Driven Non-Equilibrium Molecular Dynamics (BD-NEMD) and External Force Non-Equilibrium Molecular Dynamics (EF-NEMD) are used to study adsorption and transport properties in both types of pores with varying degrees of rugosity and tortuosity. Intermolecular interactions and bulk fluid properties are described by the statistical associating fluid theory (SAFT) coarse-grained Mie potential and equation of state respectively. Strong CO2 adsorption and fast CH4 transport are observed in smooth slit pores. Small instances of surface rugosity change the dynamics significantly, reducing the transport diffusivity by over an order of magnitude. The fast plug-like flow reported in slit pores dissipates with increasing rugosity, indicating a fundamental change in the flow pattern. Furthermore, rugose pores exhibit a lower capacity for CO2 adsorption, suggesting the performance of CO2 -enhanced oil recovery may be overestimated by the smooth pore models. A pore characteristic factor is shown to be appropriate to correlate the transport diffusivities in nano-pores.

Enhanced Coarse-Grained Molecular Dynamics Simulation with a Smoothed Hybrid Potential Using a Neural Network Model.

In all-atom (AA) molecular dynamics (MD) simulations, the rugged energy profile of the force field makes it challenging to reproduce spontaneous structural changes in biomolecules within a reasonable calculation time. Existing coarse-grained (CG) models, in which the energy profile is set to a global minimum around the initial structure, are unsuitable to explore the structural dynamics between metastable states far away from the initial structure without any bias. In this study, we developed a new hybrid potential composed of an artificial intelligence (AI) potential and minimal CG potential related to the statistical bond length and excluded volume interactions to accelerate the transition dynamics while maintaining the protein character. The AI potential is trained by energy matching using a diverse structural ensemble sampled via multicanonical (Mc) MD simulation and the corresponding AA force field energy, profile of which is smoothed by energy minimization. By applying the new methodology to chignolin and TrpCage, we showed that the AI potential can predict the AA energy with significantly high accuracy, as indicated by a correlation coefficient (R-value) between the true and predicted energies exceeding 0.89. In addition, we successfully demonstrated that CGMD simulation based on the smoothed hybrid potential can significantly enhance the transition dynamics between various metastable states while preserving protein properties compared to those obtained with conventional CGMD and AAMD.

Derived Coarse-Grained Potentials for Semicrystalline Polymers with a Blended Multistate Iterative Boltzmann Inversion Method.

In this article, we employ the multistate iterative Boltzmann inversion (MS-IBI) method to develop coarse-grained potentials capable of representing molecular structure in both the amorphous and crystalline phases of semicrystalline polymers with improved accuracy while allowing for tunable control over the dynamics governing the α-relaxation process. A unique feature of this method is that the potentials are blended using the product of the target structural distributions, for example, the radial density function, for each phase and a weighting factor. To demonstrate this approach, a family of potentials for polyethylene is developed where the weighting factor of the crystalline phase ranges is varied from zero, incorporating information only from the amorphous phase, to unity, where the model is trained from only the crystalline phase. The most accurate representation of structural distributions was obtained when the crystalline phases is weighted at 50%. However, we show that when the crystalline phase is weighted at 90%, the model more accurately represents dynamics of the α-relaxation process, with realistic predicted values of activation energy and diffusion rates, with relatively minor impact on accuracy in structure.

Coarse-Grained Many-Body Potentials of Ligand-Stabilized Nanoparticles from Machine-Learned Mean Forces.

Colloidal nanoparticles self-assemble into a variety of superstructures with distinctive optical, structural, and electronic properties. These nanoparticles are usually stabilized by a capping layer of organic ligands to prevent aggregation in the solvent. When the ligands are sufficiently long compared to the dimensions of the nanocrystal cores, the effective coarse-grained forces between pairs of nanoparticles are largely affected by the presence of neighboring particles. In order to efficiently investigate the self-assembly behavior of these complex colloidal systems, we propose a machine-learning approach to construct effective coarse-grained many-body interaction potentials. The multiscale methodology presented in this work constitutes a general bottom-up coarse-graining strategy where the coarse-grained forces acting on coarse-grained sites are extracted from measuring the vectorial mean forces on these sites in reference fine-grained simulations. These effective coarse-grained forces, i.e., gradients of the potential of mean force or of the free-energy surface, are represented by a simple linear model in terms of gradients of structural descriptors, which are scalar functions that are rotationally invariant. In this way, we also directly obtain the free-energy surface of the coarse-grained model as a function of all coarse-grained coordinates. We expect that this simple yet accurate coarse-graining framework for the many-body potential of mean force will enable the characterization, understanding, and prediction of the structure and phase behavior of relevant soft-matter systems by direct simulations. The key advantage of this method is its generality, which allows it to be applicable to a broad range of systems. To demonstrate the generality of our method, we also apply it to a colloid-polymer model system, where coarse-grained many-body interactions are pronounced.

Gaussian representation of coarse-grained interactions of liquids: Theory, parametrization, and transferability.

Coarse-grained (CG) interactions determined via bottom-up methodologies can faithfully reproduce the structural correlations observed in fine-grained (atomistic resolution) systems, yet they can suffer from limited extensibility due to complex many-body correlations. As part of an ongoing effort to understand and improve the applicability of bottom-up CG models, we propose an alternative approach to address both accuracy and transferability. Our main idea draws from classical perturbation theory to partition the hard sphere repulsive term from effective CG interactions. We then introduce Gaussian basis functions corresponding to the system's characteristic length by linking these Gaussian sub-interactions to the local particle densities at each coordination shell. The remaining perturbative long-range interaction can be treated as a collective solvation interaction, which we show exhibits a Gaussian form derived from integral equation theories. By applying this numerical parametrization protocol to CG liquid systems, our microscopic theory elucidates the emergence of Gaussian interactions in common phenomenological CG models. To facilitate transferability for these reduced descriptions, we further infer equations of state to determine the sub-interaction parameter as a function of the system variables. The reduced models exhibit excellent transferability across the thermodynamic state points. Furthermore, we propose a new strategy to design the cross-interactions between distinct CG sites in liquid mixtures. This involves combining each Gaussian in the proper radial domain, yielding accurate CG potentials of mean force and structural correlations for multi-component systems. Overall, our findings establish a solid foundation for constructing transferable bottom-up CG models of liquids with enhanced extensibility.

Center-of-mass momentum dependence of short-range correlations with the coarse-grained Granada potential

Center-of-mass momentum dependence of short-range correlations with the coarse-grained Granada potential

Computer modeling of thermotransport in a uniform binary liquid solution with equimolar n-alkane mixtures

By means of molecular dynamics (MD), two novel methods, a thermal mean-path that may outline temperature profiles effectively in the MD system and a modified coarse-grained force field potential (the MCG-FFP) that may depict inter/intra-molecular interactions fairly well among n-alkane species, are employed to simulate a thermotransport process in a uniform liquid solution with two equimolar n-pentane (nC-5) and n-decane (nC-10) mixtures. In addition, all the MD simulations are running under two constraints: a weak thermal gradient exerting on the MD system from its hot through cold boundary sides and the standard-state acting on the MD system from its outer environment. During the whole MD simulations, coefficients of thermal diffusion and mass mutual diffusion, and the Soret coefficient (SC) for the MD system are calculated by using the MCG-FFP. As a result, the MD simulations indicate that nC-5 species with light molar-mass would migrate toward the hot boundary region, while nC-10 species with heavy molar-mass would migrate toward the cold one. Coefficients calculated from the MCG-FFP are found to meet relevant experimental outputs fairly well. Furthermore, an empirical formula developed by means of relevant continuum methods is used for calculating coefficients of mass mutual diffusion in solutions mixing with multimolar nC-5 and nC-10 species. Its one output is found to corroborate pretty well with that from the MD simulations. This may expect that such the formula would perform universally when characterizing properties of mass mutual diffusion in binary liquid solutions with other multimolar alkane mixtures in the petroleum engineering.

Toward Consistent Physics-Based Modeling of Local Backbone Structures and Chirality Change of Proteins in Coarse-Grained Approaches.

A reliable representation of local interactions is critical for the accuracy of modeling protein structure and dynamics at both the all-atom and coarse-grained levels. The development of local (mainly torsional) potentials was focused on careful parametrization of the predetermined (usually Fourier) formulas rather than on their physics-based derivation. In this Perspective we discuss the state-of-the-art methods for modeling local interactions, including the scale-consistent theory developed in our laboratory, which implies that the coarse-grained torsional potentials inseparably depend on the virtual-bond angles adjacent to a given dihedral and that multitorsional terms should be considered. We extend the treatment to split the residue-based torsional potentials into the site-based regular and improper torsional potentials. These considerations are illustrated with the revised torsional potentials and improper-torsional potentials involving the l-alanine residue and the improper-torsional potential corresponding to serine-residue enantiomerization. Applications of the new approach in coarse-grained modeling and revising all-atom force fields are discussed.

Machine learning coarse-grained potentials of protein thermodynamics

A generalized understanding of protein dynamics is an unsolved scientific problem, the solution of which is critical to the interpretation of the structure-function relationships that govern essential biological processes. Here, we approach this problem by constructing coarse-grained molecular potentials based on artificial neural networks and grounded in statistical mechanics. For training, we build a unique dataset of unbiased all-atom molecular dynamics simulations of approximately 9 ms for twelve different proteins with multiple secondary structure arrangements. The coarse-grained models are capable of accelerating the dynamics by more than three orders of magnitude while preserving the thermodynamics of the systems. Coarse-grained simulations identify relevant structural states in the ensemble with comparable energetics to the all-atom systems. Furthermore, we show that a single coarse-grained potential can integrate all twelve proteins and can capture experimental structural features of mutated proteins. These results indicate that machine learning coarse-grained potentials could provide a feasible approach to simulate and understand protein dynamics.

Energy landscapes for proteins described by the UNRES coarse-grained potential

The self-assembly of proteins is encoded in the underlying potential energy surface (PES), from which we can predict structure, dynamics, and thermodynamic properties. However, the corresponding analysis becomes increasingly challenging with larger protein sizes, due to the computational time required, which grows significantly with the number of atoms. Coarse-grained models offer an attractive approach to reduce the computational cost. In this Feature Article, we describe our implementation of the UNited RESidue (UNRES) coarse-grained potential in the Cambridge energy landscapes software. We have applied this framework to explore the energy landscapes of four proteins that exhibit native states involving different secondary structures. Here we have tested the ability of the UNRES potential to represent the global energy landscape of proteins containing up to 100 amino acid residues. The resulting potential energy landscapes exhibit good agreement with experiment, with low-lying minima close to the PDB geometries and to results obtained using the all-atom AMBER force field. The new program interfaces will allow us to investigate larger biomolecules in future work, using the UNRES potential in combination with all the methodology available in the computational energy landscapes framework.