Coarse-grained Configurations Research Articles

Analysis of mapping atomic models to coarse-grained resolution.

Low-resolution coarse-grained (CG) models provide significant computational and conceptual advantages for simulating soft materials. However, the properties of CG models depend quite sensitively upon the mapping, M, that maps each atomic configuration, r, to a CG configuration, R. In particular, M determines how the configurational information of the atomic model is partitioned between the mapped ensemble of CG configurations and the lost ensemble of atomic configurations that map to each R. In this work, we investigate how the mapping partitions the atomic configuration space into CG and intra-site components. We demonstrate that the corresponding coordinate transformation introduces a nontrivial Jacobian factor. This Jacobian factor defines a labeling entropy that corresponds to the uncertainty in the atoms that are associated with each CG site. Consequently, the labeling entropy effectively transfers configurational information from the lost ensemble into the mapped ensemble. Moreover, our analysis highlights the possibility of resonant mappings that separate the atomic potential into CG and intra-site contributions. We numerically illustrate these considerations with a Gaussian network model for the equilibrium fluctuations of actin. We demonstrate that the spectral quality, Q, provides a simple metric for identifying high quality representations for actin. Conversely, we find that neither maximizing nor minimizing the information content of the mapped ensemble results in high quality representations. However, if one accounts for the labeling uncertainty, Q(M) correlates quite well with the adjusted configurational information loss, Îmap(M), that results from the mapping.

Iterative site percolation on triangular lattice

The site percolation on the triangular lattice stands out as one of the few exactly solved statistical systems. By initially configuring critical percolation clusters of this model and randomly reassigning the color of each percolation cluster, we obtain coarse-grained configurations by merging adjacent clusters that share the same color. It is shown that the process can be infinitely iterated in the infinite-lattice limit, leading to an iterative site percolation model. We conjecture from the self-matching argument that percolation clusters remain fractal for any finite generation, which can even take any positive real number by a generalized process. Extensive simulations are performed, and, from the generation-dependent fractal dimension, a continuous family of previously unknown universalities is revealed. Published by the American Physical Society 2024

Physics-Informed Deep Learning Approach for Reintroducing Atomic Detail in Coarse-Grained Configurations of Multiple Poly(lactic acid) Stereoisomers.

Multiscale modeling of complex molecular systems, such as macromolecules, encompasses methods that combine information from fine and coarse representations of molecules to capture material properties over a wide range of spatiotemporal scales. Being able to exchange information between different levels of resolution is essential for the effective transfer of this information. The inverse problem of reintroducing atomistic degrees of freedom in coarse-grained (CG) molecular configurations is particularly challenging as, from a mathematical point of view, it is an ill-posed problem; the forward mapping from the atomistic to the CG description is typically defined via a deterministic operator ("one-to-one" problem), whereas the reversed mapping from the CG to the atomistic model refers to creating one representative configuration out of many possible ones ("one-to-many" problem). Most of the backmapping methods proposed so far balance accuracy, efficiency, and general applicability. This is particularly important for macromolecular systems with different types of isomers, i.e., molecules that have the same molecular formula and sequence of bonded atoms (constitution) but differ in the three-dimensional configurations of their atoms in space. Here, we introduce a versatile deep learning approach for backmapping multicomponent CG macromolecules with chiral centers, trained to learn structural correlations between polymer configurations at the atomistic level and their corresponding CG descriptions. This method is intended to be simple and flexible while presenting a generic solution for resolution transformation. In addition, the method is aimed to respect the structural features of the molecule, such as local packing, capturing therefore the physical properties of the material. As an illustrative example, we apply the model on linear poly(lactic acid) (PLA) in melt, which is one of the most popular biodegradable polymers. The framework is tested on a number of model systems starting from homopolymer stereoisomers of PLA to copolymers with randomly placed chiral centers. The results demonstrate the efficiency and efficacy of the new approach.

OpenABC enables flexible, simplified, and efficient GPU accelerated simulations of biomolecular condensates.

Biomolecular condensates are important structures in various cellular processes but are challenging to study using traditional experimental techniques. In silico simulations with residue-level coarse-grained models strike a balance between computational efficiency and chemical accuracy. They could offer valuable insights by connecting the emergent properties of these complex systems with molecular sequences. However, existing coarse-grained models often lack easy-to-follow tutorials and are implemented in software that is not optimal for condensate simulations. To address these issues, we introduce OpenABC, a software package that greatly simplifies the setup and execution of coarse-grained condensate simulations with multiple force fields using Python scripting. OpenABC seamlessly integrates with the OpenMM molecular dynamics engine, enabling efficient simulations with performance on a single GPU that rivals the speed achieved by hundreds of CPUs. We also provide tools that convert coarse-grained configurations to all-atom structures for atomistic simulations. We anticipate that OpenABC will significantly facilitate the adoption of in silico simulations by a broader community to investigate the structural and dynamical properties of condensates.

Ensuring thermodynamic consistency with invertible coarse-graining.

Coarse-grained models are a core computational tool in theoretical chemistry and biophysics. A judicious choice of a coarse-grained model can yield physical insights by isolating the essential degrees of freedom that dictate the thermodynamic properties of a complex, condensed-phase system. The reduced complexity of the model typically leads to lower computational costs and more efficient sampling compared with atomistic models. Designing "good" coarse-grained models is an art. Generally, the mapping from fine-grained configurations to coarse-grained configurations itself is not optimized in any way; instead, the energy function associated with the mapped configurations is. In this work, we explore the consequences of optimizing the coarse-grained representation alongside its potential energy function. We use a graph machine learning framework to embed atomic configurations into a low-dimensional space to produce efficient representations of the original molecular system. Because the representation we obtain is no longer directly interpretable as a real-space representation of the atomic coordinates, we also introduce an inversion process and an associated thermodynamic consistency relation that allows us to rigorously sample fine-grained configurations conditioned on the coarse-grained sampling. We show that this technique is robust, recovering the first two moments of the distribution of several observables in proteins such as chignolin and alanine dipeptide.

Deep convolutional neural networks for generating atomistic configurations of multi-component macromolecules from coarse-grained models.

Despite the modern advances in the available computational resources, the length and time scales of the physical systems that can be studied in full atomic detail, via molecular simulations, are still limited. To overcome such limitations, coarse-grained (CG) models have been developed to reduce the dimensionality of the physical system under study. However, to study such systems at the atomic level, it is necessary to re-introduce the atomistic details into the CG description. Such an ill-posed mathematical problem is typically treated via numerical algorithms, which need to balance accuracy, efficiency, and general applicability. Here, we introduce an efficient and versatile method for backmapping multi-component CG macromolecules of arbitrary microstructures. By utilizing deep learning algorithms, we train a convolutional neural network to learn structural correlations between polymer configurations at the atomistic and their corresponding CG descriptions, obtained from atomistic simulations. The trained model is then utilized to get predictions of atomistic structures from input CG configurations. As an illustrative example, we apply the convolutional neural network to polybutadiene copolymers of various microstructures, in which each monomer microstructure (i.e., cis-1,4, trans-1,4, and vinyl-1,2) is represented as a different CG particle type. The proposed methodology is transferable over molecular weight and various microstructures. Moreover, starting from a specific single CG configuration with a given microstructure, we show that by modifying its chemistry (i.e., CG particle types), we are able to obtain a set of well equilibrated polymer configurations of different microstructures (chemistry) than the one of the original CG configuration.

Backmapping coarse-grained macromolecules: An efficient and versatile machine learning approach.

Multiscale modeling of polymers exchanges information between coarse and fine representations of molecules to capture material properties over a wide range of spatial and temporal scales. Restoring details at a finer scale requires us to generate information following embedded physics and statistics of the models at two different levels of description. Techniques designed to address this persistent challenge balance among accuracy, efficiency, and general applicability. In this work, we present an image-based approach for structural backmapping from coarse-grained to atomistic models with cis-1,4 polyisoprene melts as an illustrative example. Through machine learning, we train conditional generative adversarial networks on the correspondence between configurations at the levels considered. The trained model is subsequently applied to provide predictions of atomistic structures from the input coarse-grained configurations. The effect of different data representation schemes on training and prediction quality is examined. Our proposed backmapping approach shows remarkable efficiency and transferability over different molecular weights in the melt based on training sets constructed from oligomeric compounds. We anticipate that this versatile backmapping approach can be readily extended to other complex systems to provide high-fidelity initial configurations with minimal human intervention.

Lithium ion conductivity and dielectric relaxation in dendritic nanostructured LiTaO3 glass–nanocrystal composites

Lithium tantalate in single-crystalline and coarse-grained configurations is a poor ionic conductor and does not qualify as a solid electrolyte for lithium-based batteries. In this work, ionic conductivity was sought to be enhanced by the use of nanocrystals of LiTaO3 embedded in a borate-based glass matrix. Glasses of composition 3Li2O–4B2O3–Ta2O5 were formed by melt-quenching. The crystallization process was described by using isothermal crystallization kinetics, invoking the Johnson–Mehl–Avrami–Kolmogorov equation, which indicated a three-dimensional growth with an Avrami exponent of 3.5 and an effective activation energy for crystallization of 735 ± 65 kJ mol–1. Heat treatment of the as-quenched glasses was performed between 530 and 560 °C, and the evolution of LiTaO3 phase was studied by X-ray powder diffraction, scanning electron microscopy, and transmission electron microscopy. The heat treatment yielded coalesced LiTaO3 nanocrystals of 18–32 nm size, forming dendritic structures in the glass matrix. Impedance analyses of the as-quenched and heat-treated glasses showed a dramatic improvement in dc conductivity (σdc), with a maximum around 3 × 10–3 S m−1 at 200 °C (σdcT = 1.5 S m−1 K) and activation energy of 0.54 eV for 530 °C/3 h heat-treated glasses. The values of σdc of the as-quenched glasses and of the 530 °C/3 h and 540 °C/3 h heat-treated glasses were about seven orders of magnitude higher than those of the single crystalline LiTaO3. Furthermore, the effect of heat treatment on lithium ion dynamics in the 40–200 °C temperature range was investigated by modulus formalism invoking the stretched exponential Kohlrausch–Williams–Watts function. The 7Li magic angle spinning NMR was used to investigate lithium self-diffusion in the nanostructured glass nanocrystal composites as a function of temperature between −10 °C and 60 °C.

Molecular modeling and simulation of atactic polystyrene/amorphous silica nanocomposites

The local structure, segmental dynamics, topological analysis of entanglement networks and mechanical properties of atactic polystyrene - amorphous silica nanocomposites are studied via molecular simulations using two interconnected levels of representation: (a) A coarse - grained level. Equilibration at all length scales at this level is achieved via connectivity - altering Monte Carlo simulations. (b) An atomistic level. Initial configurations for atomistic Molecular Dynamics (MD) simulations are obtained by reverse mapping well- equilibrated coarse-grained configurations. By analyzing atomistic MD trajectories, the polymer density profile is found to exhibit layering in the vicinity of the nanoparticle surface. The dynamics of polystyrene (in neat and filled melt systems) is characterized in terms of bond orientation. Well-equilibrated coarse-grained long-chain configurations are reduced to entanglement networks via topological analysis with the CReTA algorithm. Atomistic simulation results for the mechanical properties are compared to the experimental measurements and other computational works.

Molecular Modeling and Simulation of Polymer Nanocomposites at Multiple Length Scales

The complexity of intermolecular interactions and confinement in polymer—nanoparticle systems leads to spatial variations in structure and dynamics at both the meso and nanoscale. Molecular simulation holds great promise as a means of predicting these effects and understanding their microscopic origin. In order to shed some light onto local structure and segmental dynamics of atactic polystyrene/silica (PS/SiO2) and atactic polystyrene/fullerene (PS/C60) melt systems, molecular simulations have been conducted using two interconnected levels of representation: 1) A coarse-grained representation. Equilibration of coarse-grained polymer-nanoparticle systems at all length scales is achieved via connectivity-altering Monte Carlo simulations. 2) An atomistic representation. Initial configurations for atomistic molecular dynamics (MD) simulations are obtained by reverse mapping well-equilibrated coarse-grained configurations. The local structure around a silica nanoparticle immersed in the PS matrix, PS segmental, and local dynamics in both composites and mechanical properties and entanglements in PS/SiO2 are studied.

Influence of cross-linking rate on the structure of hypercrosslinked networks: Multiscale computer simulation

A multi-scale molecular dynamics simulation was implied to study the formation of hypercrosslinked polystyrene networks at different rates of cross-linking. The rate of cross-linking reaction was controlled by wide-range variation of the probability of chemical bonding between the particles within the reaction distance on individual step of the simulation. The cross-linking was performed in the framework of the coarse-grained model, with the force fields derived from atomistic simulations. The macroscopic properties of network were studied using the atomistic samples restored from the coarse-grained configurations by a reverse mapping procedure. It was shown that the rate of cross-linking influences the structure of “synthesized” hypercrosslinked networks: Slowly cross-linked polymer networks have smaller total specific surface, lower average density, larger pores than those cross-linked at high rate.

Multiscale simulations of PS-SiO2 nanocomposites: from melt to glassy state.

The interaction energetics, molecular packing, entanglement network properties, segmental dynamics, and elastic constants of atactic polystyrene-amorphous silica nanocomposites in the molten and the glassy state are studied via molecular simulations using two interconnected levels of representation: (a) a coarse-grained one, wherein each polystyrene repeat unit is mapped onto a single "superatom" and the silica nanoparticle is viewed as a solid sphere. Equilibration at all length scales at this level is achieved via connectivity-altering Monte Carlo simulations. (b) A united-atom (UA) level, wherein the polymer chains are represented in terms of a united-atom forcefield and the silica nanoparticle is represented in terms of a simplified, fully atomistic model. Initial configurations for UA molecular dynamics (MD) simulations are obtained by reverse mapping well-equilibrated coarse-grained configurations. By analysing microcanonical UA MD trajectories, the polymer density profile is studied and the polymer is found to exhibit layering in the vicinity of the nanoparticle surface. An estimate of the enthalpy of mixing between polymer and nanoparticles, derived from the UA simulations, compares favourably against available experimental values. The dynamical behaviour of polystyrene (in neat and filled melt systems) is characterized in terms of bond orientation and dihedral angle time autocorrelation functions. At low concentration in the molten polymer matrix, silica nanoparticles are found to cause a slight deceleration of the segmental dynamics close to their surface compared to the bulk polymer. Well-equilibrated coarse-grained long-chain configurations are reduced to entanglement networks via topological analysis with the CReTA algorithm, yielding a slightly lower density of entanglements in the filled than in the neat systems. UA melt configurations are glassified by MD cooling. The elastic moduli of the resulting glassy nanocomposites are computed through an analysis of strain fluctuations in the undeformed state and through explicit mechanical deformation by MD, showing a stiffening of the polymer in the presence of nanoparticles. UA simulation results for the elastic constants are compared to continuum micromechanical calculations invoked in homogenization models of the overall mechanical behaviour of heterogeneous materials. They can be interpreted in terms of the presence of an "interphase" of approximate thickness 2 nm around the nanoparticles, with elastic constants intermediate between those of the filler and the matrix.

High-Resolution Coarse-Grained Modeling Using Oriented Coarse-Grained Sites.

We introduce a method to bring nearly atomistic resolution to coarse-grained models, and we apply the method to proteins. Using a small number of coarse-grained sites (about one per eight atoms) but assigning an independent three-dimensional orientation to each site, we preferentially integrate out stiff degrees of freedom (bond lengths and angles, as well as dihedral angles in rings) that are accurately approximated by their average values, while retaining soft degrees of freedom (unconstrained dihedral angles) mostly responsible for conformational variability. We demonstrate that our scheme retains nearly atomistic resolution by mapping all experimental protein configurations in the Protein Data Bank onto coarse-grained configurations and then analytically backmapping those configurations back to all-atom configurations. This roundtrip mapping throws away all information associated with the eliminated (stiff) degrees of freedom except for their average values, which we use to construct optimal backmapping functions. Despite the 4:1 reduction in the number of degrees of freedom, we find that heavy atoms move only 0.051 Å on average during the roundtrip mapping, while hydrogens move 0.179 Å on average, an unprecedented combination of efficiency and accuracy among coarse-grained protein models. We discuss the advantages of such a high-resolution model for parametrizing effective interactions and accurately calculating observables through direct or multiscale simulations.

Equilibration of High Molecular Weight Polymer Melts: A Hierarchical Strategy

A strategy is developed for generating equilibrated high molecular weight polymer melts described with microscopic detail by sequentially backmapping coarse-grained (CG) configurations. The microscopic test model is generic but retains features like hard excluded volume interactions and realistic melt densities. The microscopic representation is mapped onto a model of soft spheres with fluctuating size, where each sphere represents a microscopic subchain with Nb monomers. By varying Nb, a hierarchy of CG representations at different resolutions is obtained. Within this hierarchy, CG configurations equilibrated with Monte Carlo at low resolution are sequentially fine-grained into CG melts described with higher resolution. A Molecular Dynamics scheme is employed to slowly introduce the microscopic details into the latter. All backmapping steps involve only local polymer relaxation; thus, the computational efficiency of the scheme is independent of molecular weight, being just proportional to system size. To demonstrate the robustness of the approach, microscopic configurations containing up to n = 1000 chains with polymerization degrees N = 2000 are generated and equilibration is confirmed by monitoring key structural and conformational properties. The extension to much longer chains or branched polymers is straightforward.

Local Segmental Dynamics and Stresses in Polystyrene–C60 Mixtures

The polymer dynamics of homogeneous C$_{60}$-polystyrene mixtures in the molten state are studied via molecular simulations using two interconnected levels of representation for polystyrene nanocomposites: (a) A coarse-grained representation, in which each polystyrene repeat unit is mapped into a single "superatom" and each fullerene is viewed as a spherical shell. Equilibration of coarse-grained polymer-nanoparticle systems at all length scales is achieved via connectivity-altering Monte Carlo simulations. (b) An atomistic representation, where both nanoparticles and polymer chains are represented in terms of united-atom forcefields. Initial configurations for atomistic Molecular Dynamics (MD) simulations are obtained by reverse mapping well-equilibrated coarse-grained configurations. By analyzing MD trajectories under constant energy, the segmental dynamics of polystyrene (for neat and filled systems) is characterized in terms of bond orientation time autocorrelation functions. Nanocomposite systems are found to exhibit slightly slower segmental dynamics than the unfilled ones, in good agreement with available experimental data. Moreover, by employing Voronoi tessellation of the simulation box, the mean-squared displacement of backbone carbon atoms is quantified in the vicinity of each fullerene molecule. Fullerenes are found to suppress the average motion of polymeric chains, in agreement with neutron scattering data, while slightly increasing the dynamic and stress heterogeneity of the melt. Atomic-level and local (per Voronoi cell) stress distributions are reported for the pure and the filled systems.

A multiscale approach to triglycerides simulations: from atomistic to coarse-grained models and back

The aim of this paper is to provide a simulation strategy to study the liquid-solid transition of triglycerides. The strategy is based on a multiscale approach. A coarse-grained model, parameterized on the basis of reference atomistic simulations, has been used to model the liquid-solid transition. A reverse mapping procedure has been proposed to reconstruct atomistic models from coarse-grained configurations and validated against experimental structural properties. The nucleation and growth of the crystalline order have been analysed in terms of several properties.

Interactions Between a Voltage Sensor and a Toxin via Multiscale Simulations

Gating-modifier toxins inhibit voltage-gated ion channels by binding the voltage sensors (VS) and altering the energetics of voltage-dependent gating. These toxins are thought to gain access to the VS via the membrane (i.e., by partitioning from water into the membrane before binding the VS). We used serial multiscale molecular-dynamics (MD) simulations, via a combination of coarse-grained (CG) and atomistic (AT) simulations, to study how the toxin VSTx1, which inhibits the archeabacterial voltage-gated potassium channel KvAP, interacts with an isolated membrane-embedded VS domain. In the CG simulations, VSTx1, which was initially located in water, partitioned into the headgroup/water interface of the lipid bilayer before binding the VS. The CG configurations were used to generate AT representations of the system, which were subjected to AT-MD to further evaluate the stability of the complex and refine the predicted VS/toxin interface. VSTx1 interacted with a binding site on the VS formed by the C-terminus of S1, the S1-S2 linker, and the N-terminus of S4. The predicted VS/toxin interactions are suggestive of toxin-mediated perturbations of the interaction between the VS and the pore domain of Kv channels, and of the membrane. Our simulations support a membrane-access mechanism of inhibition of Kv channels by VS toxins. Overall, the results show that serial multiscale MD simulations may be used to model a two-stage process of protein-bilayer and protein-protein interactions within a membrane.

Coarse-Grained and Reverse-Mapped United-Atom Simulations of Long-Chain Atactic Polystyrene Melts: Structure, Thermodynamic Properties, Chain Conformation, and Entanglements

A coarse-grained model of atactic polystyrene, in which meso and racemo diads are represented as single “superatoms,” parametrized using Iterative Boltzmann Inversion, has been subjected to connectivity-altering Monte Carlo simulations in order to simulate monodisperse atactic polystyrene melts of molar mass up to 210000 g mol-1 at 500 or 413 K and 1 bar. Analysis of the Monte Carlo results reveals excellent equilibration of chain conformations at all length scales. Chain dimensions, as determined from the mean square end-to-end distance, the mean square radius of gyration, and simulated Kratky plots of the single-chain scattering function, are in excellent agreement with experiment. The equilibrated long-chain configurations are reduced to entanglement networks via topological analysis with the CReTA algorithm. The resulting Kuhn length of primitive paths provides an excellent estimate of the molar mass between entanglements and of the entanglement tube diameter extracted from plateau modulus measurements. The distribution of strand lengths between entanglements, when appropriately reduced, follows the same master curve as previously determined distributions of polyethylene, cis-1,4 polybutadiene, and poly(ethylene terephthalate). A new strategy is introduced for reverse mapping the long-chain coarse-grained configurations into detailed united-atom configurations in a manner that preserves the sequence of diad types along the chains. This strategy employs local “flip” Monte Carlo moves to relax the reverse-mapped configurations. Relaxation starts using bonded interactions only, and proceeds by gradually introducing nonbonded interactions. Final relaxation is achieved via short-time canonical molecular dynamics simulation. Predicted wide-angle X-ray diffraction patterns from reverse-mapped configurations are indistinguishable from those of short-chain melts equilibrated directly in the united atom representation using molecular dynamics, and in favorable agreement with experiment. Distributions of torsion angles and pairs of successive torsion angles in the reverse-mapped configurations exhibit some deviations from the corresponding distributions of directly equilibrated short-chain united atom melts and from experimental NMR measurements.

Combined Coarse-Grained and Atomistic Simulation of Liquid Bisphenol A−Polycarbonate: Liquid Packing and Intramolecular Structure

We present a new coarse-graining scheme for efficient molecular dynamics simulations of polycarbonate liquids and compare its effectiveness to that of a previously presented model which uses a different coarse-grained representation. The effect of more realistically accounting for the excluded volume of the phenylene comonomeric units in the coarse-grained simulation is examined. The new treatment avoids artifacts arising from sphere-packing, which dominate the liquid structure and dynamics in the older scheme, leading to a significant improvement in the equilibration time, for systems run at the typical processing temperature of 570 K. However, we observe only a slight improvement (10-4 eV/atom) in the equilibration of atomistically detailed samples that are inverse-mapped from the equilibrated coarse-grained configurations. Distributions in the atomistically resolved backbone bond and torsion angles are identical using the two schemes, as are computed liquid coherent scattering functions. This indicates that artifacts present at the coarsened level are effectively erased by equilibration at full-blown atomistic resolution, at least for systems with relatively short chains well above the glass transition temperature.

Radiation breakage of DNA: a model based on random-walk chromatin structure.

Monte Carlo computer software, called DNAbreak, has recently been developed to analyze observed non-random clustering of DNA double strand breaks in chromatin after exposure to densely ionizing radiation. The software models coarse-grained configurations of chromatin and radiation tracks, small-scale details being suppressed in order to obtain statistical results for larger scales, up to the size of a whole chromosome. We here give an analytic counterpart of the numerical model, useful for benchmarks, for elucidating the numerical results, for analyzing the assumptions of a more general but less mechanistic "randomly-located-clusters" formalism, and, potentially, for speeding up the calculations. The equations characterize multi-track DNA fragment-size distributions in terms of one-track action; an important step in extrapolating high-dose laboratory results to the much lower doses of main interest in environmental or occupational risk estimation. The approach can utilize the experimental information on DNA fragment-size distributions to draw inferences about large-scale chromatin geometry during cell-cycle interphase.