Coarse-grained Potentials Research Articles

Multi-scale coarse-grained molecular dynamics simulation to investigate the thermo-mechanical behavior of shape-memory polyurethane copolymers

Shape-memory polyurethanes (SMPUs) are smart semi-crystalline polymers with heat-induced shape memory. The segmented SMPU copolymer simulated in this study consisted of an isocyanate (hard segment) that acts as a netpoint to stabilize the network, and a polyol (soft segment) that, owing to polymer crystallization, acts as a molecular switch. The ratio of hard to soft segments is a determining factor in the thermo-mechanical behavior and shape-memory performance of SMPU copolymers. However, the limitations of the scale of the conventional all-atom molecular dynamics simulation makes it difficult to observe mesoscale phenomena such as the phase-segregated morphology and polymer crystallization. To address this problem, we have developed a coarse-grained (CG) molecular dynamics (MD) model with fewer degrees of freedom by treating multiple atoms as a single bead. We derived the CG intra- and inter-bead potentials of the CG MD model such that the structural and thermodynamic properties would be identical to those of the all-atom reference model. Consequently, polymer crystallization was verified to occur at room temperature with the developed CG potentials. We subsequently investigated the effects of hard-segment content (HSC) on the thermal transition at SMPU melting temperature. We also investigated the influence of HSC on the thermo-elastic behavior and shape-memory properties of SMPU copolymers by simulating a 4-step thermo-mechanical cycle. The results revealed that the microstructure significantly affects macroscopic shape-memory behavior. We expect that this study will be used to improve the prediction and design of the thermo-mechanical behavior of segmented polyurethane or other semi-crystalline polymers.

Mechanics of 2D Materials-Based Cellular Kirigami Structures: A Computational Study

We develop a generic coarse-grained potential for a general group of 2D materials to study the mechanical performance of 2D materials-based cellular kirigami structures for understanding of the relation between the mechanical properties and structure pattern as well as the material component. By patterning the structure lattice cell, the mechanical properties of 2D materials-based structures show a very wide range from almost zero to those of the pristine 2D materials by orders of magnitude. Moreover, results indicate that there are two distinct stress–strain stages associated with density, J-shape non-linear and linear elasticity. Results also indicate that hole-in structures show better ductility performance than no-hole structures. In addition, the material effect on mechanical performance of 2D materials-based cellular kirigami is significant, exemplified by the graphene-based structure outperforming those made of other 2D materials. Overall, this study provides a computational basis for designing future kirigami structures with outstanding properties and functions.

Learning composition-transferable coarse-grained models: Designing external potential ensembles to maximize thermodynamic information.

Achieving thermodynamic faithfulness and transferability across state points is an outstanding challenge in the bottom-up coarse graining of molecular models, with many efforts focusing on augmenting the form of coarse-grained interaction potentials to improve transferability. Here, we revisit the critical role of the simulation ensemble and the possibility that even simple models can be made more predictive through a smarter choice of ensemble. We highlight the efficacy of coarse graining from ensembles where variables conjugate to the thermodynamic quantities of interest are forced to respond to applied perturbations. For example, to learn activity coefficients, it is natural to coarse grain from ensembles with spatially varying external potentials applied to one species to force local composition variations and fluctuations. We apply this strategy to coarse grain both an atomistic model of water and methanol and a binary mixture of spheres interacting via Gaussian repulsions and demonstrate near-quantitative capture of activity coefficients across the whole composition range. Furthermore, the approach is able to do so without explicitly measuring and targeting activity coefficients during the coarse graining process; activity coefficients are only computed after-the-fact to assess accuracy. We hypothesize that ensembles with applied thermodynamic potentials are more "thermodynamically informative." We quantify this notion of informativeness using the Fisher information metric, which enables the systematic design of optimal bias potentials that promote the learning of thermodynamically faithful models. The Fisher information is related to variances of structural variables, highlighting the physical basis underlying the Fisher information's utility in improving coarse-grained models.

Temperature and Phase Transferable Bottom-up Coarse-Grained Models.

Despite the high fidelity of bottom-up coarse-grained (CG) approaches to recapitulate the structural correlations in atomistic simulations, the general use of bottom-up CG methods is limited because of the nontransferable nature of these CG models under different thermodynamic conditions. Because bottom-up CG potentials usually correspond to configuration-dependent free energies of the system, recent studies have focused on adjusting enthalpic or entropic contributions to account for issues with transferability. However, these approaches can require a manual adjustment of the CG interaction a priori and are usually limited to constant volume ensembles. To overcome these limitations, we construct temperature and phase transferable CG models under constant pressure by developing the ultra-coarse-graining (UCG) methodology in the mean-field limit. In the mean-field ansatz, an embedded semi-global order parameter recapitulates global changes to the system by automatically adjusting the effective CG interactions, thus bridging free energy decompositions with UCG theory. The method presented is designed to faithfully capture structural correlations under different thermodynamic conditions, using a single UCG model. Specifically, we test the applicability of the developed theory in three distinct cases: (1) different temperatures at constant pressure in liquids, (2) different temperatures across thermodynamic phases, and (3) liquid/vapor interfaces. We demonstrate that the systematic construction of both temperature and phase transferable bottom-up CG models is possible using this generalized UCG theory. Based on our findings, this approach significantly extends the transferability and applicability of the bottom-up CG theory and method.

Learning Coarse-Grained Potentials for Binary Fluids.

For a multiple-fluid system, CG models capable of accurately predicting the interfacial properties as a function of curvature are still lacking. In this work, we propose a new probabilistic machine learning (ML) model for learning CG potentials for binary fluids. The water-hexane mixture is selected as a typical immiscible binary liquid-liquid system. We develop a new CG force field (FF) using the Shinoda-DeVane-Klein (SDK) FF framework and compute parameters in this CG FF using the proposed probabilistic ML method. It is shown that a standard response-surface approach does not provide a unique set of parameters, as it results in a loss function with multiple shallow minima. To address this challenge, we develop a probabilistic ML approach where we compute the probability density function (PDF) of parameters that minimize the loss function. The PDF has a well-defined peak corresponding to a unique set of parameters in the CG FF that reproduces the desired properties of a liquid-liquid interface. We compare the performance of the new CG FF with several existing FFs for the water-hexane mixture, including two atomistic and three CG FFs with respect to modeling the interface structure and thermodynamic properties. It is demonstrated that the new FF significantly improves the CG model prediction of both the interfacial tension and structure for the water-hexane mixture.

Predicting optical spectra for optoelectronic polymers using coarse-grained models and recurrent neural networks

Coarse-grained modeling of conjugated polymers has become an increasingly popular route to investigate the physics of organic optoelectronic materials. While ultraviolet (UV)-vis spectroscopy remains one of the key experimental methods for the interrogation of these materials, a rigorous bridge between simulated coarse-grained structures and spectroscopy has not been established. Here, we address this challenge by developing a method that can predict spectra of conjugated polymers directly from coarse-grained representations while avoiding repetitive procedures such as ad hoc back-mapping from coarse-grained to atomistic representations followed by spectral computation using quantum chemistry. Our approach is based on a generative deep-learning model: the long-short-term memory recurrent neural network (LSTM-RNN). The latter is suggested by the apparent similarity between natural languages and the mathematical structure of perturbative expansions of, in our case, excited-state energies perturbed by conformational fluctuations. We also use this model to explore the level of sensitivity of spectra to the coarse-grained representation back-mapping protocol. Our approach presents a tool uniquely suited for improving postsimulation analysis protocols, as well as, potentially, for including spectral data as input in the refinement of coarse-grained potentials.

A composition transferable and time-scale consistent coarse-grained model for cis-polyisoprene and vinyl-polybutadiene oligomeric blends

We study a coarse-grained model for a binary blend system composed of cis-polyisoprene and vinyl-polybutadiene. Since the slow relaxation dynamics of polymers may require very long simulation times, coarse-grained descriptions are regularly used in order to reduce computational cost while keeping the essential physics. Relaxation dynamics of a coarse-grained model is sometimes accelerated by the smooth coarse-grained potentials. However, the magnitude of the acceleration may be different in different components in a multi-component system. In order to simulate a time-scale consistent dynamics, the acceleration effects should be the same across the different components. Here, we investigate a time-scale consistent coarse-grained model for a binary polymer blend. For the coarse-grained equation of motion, we adopt the Langevin equation and adjust the friction coefficients by focusing on the relaxation times of the first normal mode of the polymers. A united-atom model is used as a reference system of the coarse-graining. Since it is found that the solubility parameter of the atomistic model is much larger than the experimental result, our simulation model is not applicable for the quantitative predictions, but we utilize it as a example system to study a time scale mismatch of a coarse-grained model. We find that the coarse-grained potentials and the friction coefficients derived for one blend composition captures different compositions of the blend. Furthermore, it is found that the magnitude of the acceleration effects of the blend rarely depends on the composition ratio. This implies that our coarse-grained model can be used for inhomogeneous systems.

Molecular-weight dependence of simulated glass transition temperature for isolated poly(ethylene oxide) chain

ABSTRACT Molecular dynamics simulations have been performed with chemically realistic coarse-grained potentials to assess the effects of molecular weight on the glass transition temperatures (Tg ) of single-chain particle of poly(ethylene oxide) in a vacuum. It is found that all the long isolated chains form impact globule like configurations, and higher molecular weight and lower temperature lead to more perfect sphericity. With increasing molecular weight, the simulated Tg of the isolated chain tends to increase whereas the Tg of the bulk undergoes a slight change. The confinement effects are associated with localisation of chain ends at the surface and specific surface areas. More importantly, the Tg shift can be quantified by the solubility parameter that includes the contribution of conformational change. As compared to the conventional definition that only sums intermolecular interactions, such solubility parameter is a better metric in simulations to explain the confinement effects since it does not depend upon the degree of equilibration as the Tg . These results can be quite valuable to clarifying glass transition behaviour of polymers films.

Combining molecular dynamics simulations with small-angle X-ray and neutron scattering data to study multi-domain proteins in solution.

Many proteins contain multiple folded domains separated by flexible linkers, and the ability to describe the structure and conformational heterogeneity of such flexible systems pushes the limits of structural biology. Using the three-domain protein TIA-1 as an example, we here combine coarse-grained molecular dynamics simulations with previously measured small-angle scattering data to study the conformation of TIA-1 in solution. We show that while the coarse-grained potential (Martini) in itself leads to too compact conformations, increasing the strength of protein-water interactions results in ensembles that are in very good agreement with experiments. We show how these ensembles can be refined further using a Bayesian/Maximum Entropy approach, and examine the robustness to errors in the energy function. In particular we find that as long as the initial simulation is relatively good, reweighting against experiments is very robust. We also study the relative information in X-ray and neutron scattering experiments and find that refining against the SAXS experiments leads to improvement in the SANS data. Our results suggest a general strategy for studying the conformation of multi-domain proteins in solution that combines coarse-grained simulations with small-angle X-ray scattering data that are generally most easy to obtain. These results may in turn be used to design further small-angle neutron scattering experiments that exploit contrast variation through 1H/2H isotope substitutions.

Coarse-grained molecular dynamics simulations of poly(ethylene terephthalate).

We have constructed efficient coarse-grained (CG) models of poly(ethylene terephthalate) (PET), using three mapping schemes, in which a repeat unit is lumped into either three or four beads. The CG potentials are parameterized to reproduce target distributions of an underlying accurate atomistic model [H. Eslami and F. Müller-Plathe, Macromolecules 42, 8241-8250 (2009)]. The CG simulations allow equilibration of long PET chains at all length scales. The CG results on the density of PET in melt and glassy states, chain dimension, local packing, and structure factor are in good agreement with experiment. We have established a link between the glass transition temperature and the local movements including conformational transitions and mean-square displacements of chain segments. Temperature transferabilities of the three proposed models were studied by comparing CG results on the static and thermodynamic properties of a polymer with atomistic and experimental findings. One of the three CG models has a good degree of transferability, following all inter- and intra-structural rearrangements of the atomistic model, over a broad range of temperature. Furthermore, as a distinct point of strength of CG, over atomistic, simulations, we have examined the dynamics of PET long chains, consisting of 100 repeat units, over a regime where entanglements dominate the dynamics. Performing long-time (550 ns) CG simulations, we have noticed the signature of a crossover from Rouse to reptation dynamics. However, a clear separation between the Rouse and the reptation dynamics needs much longer time simulations, confirming the experimental findings that the crossover to full reptation dynamics is very protracted.

Reactive Coarse-Grained Molecular Dynamics.

Coarse-grained (CG) models have allowed for the study of long time and length scale properties of a variety of systems. However, when a system undergoes chemical reactions, current CG models are not able to capture this behavior because of their fixed bonding topology. In order to develop CG models capable of taking into account such chemical changes, a model must be able to adapt its bonding topology and CG site-site interactions to switch between multiple bonding structures (i.e., topologies). This challenge particularly impacts "bottom-up" CG models developed from the fundamental underlying atomistic-scale interactions. In this paper, a reactive coarse-grained (RCG) method is developed which utilizes all-atom (AA) data to create a CG model able to represent chemical reactions by undergoing changes in bonding topology. As an example, the RCG method was applied to a model of SN2 reactions of 1-chlorobutane with a chloride ion and 1-iodobutane with an iodide ion in a methanol solvent. An asymmetric reaction was also modeled by incorporating a constant energy offset to the 1-iodobutane model. In each case, the calculated CG potential of mean force (PMF) results in good agreement with the fully AA PMF for the reactions.

Determination of Protein Coarse-Grained Potentials by Machine Learning Approaches

Determination of Protein Coarse-Grained Potentials by Machine Learning Approaches

Data-driven coarse-grained modeling of polymers in solution with structural and dynamic properties conserved.

We present data-driven coarse-grained (CG) modeling for polymers in solution, which conserves the dynamic as well as structural properties of the underlying atomistic system. The CG modeling is built upon the framework of the generalized Langevin equation (GLE). The key is to determine each term in the GLE by directly linking it to atomistic data. In particular, we propose a two-stage Gaussian process-based Bayesian optimization method to infer the non-Markovian memory kernel from the data of the velocity autocorrelation function (VACF). Considering that the long-time behaviors of the VACF and memory kernel for polymer solutions can exhibit hydrodynamic scaling (algebraic decay with time), we further develop an active learning method to determine the emergence of hydrodynamic scaling, which can accelerate the inference process of the memory kernel. The proposed methods do not rely on how the mean force or CG potential in the GLE is constructed. Thus, we also compare two methods for constructing the CG potential: a deep learning method and the iterative Boltzmann inversion method. With the memory kernel and CG potential determined, the GLE is mapped onto an extended Markovian process to circumvent the expensive cost of directly solving the GLE. The accuracy and computational efficiency of the proposed CG modeling are assessed in a model star-polymer solution system at three representative concentrations. By comparing with the reference atomistic simulation results, we demonstrate that the proposed CG modeling can robustly and accurately reproduce the dynamic and structural properties of polymers in solution.

The coarse-grained models of poly(ethylene oxide) and poly(propylene oxide) homopolymers and poloxamers in big multipole water (BMW) and MARTINI frameworks.

Polyethylene oxide (PEO) and poly(propylene oxide) (PPO), especially their tri-block copolymers PEO-PPO-PEO (poloxamers), have a broad range of applications in biotechnology and medical science. Understanding their specific interactions with biomembranes is the key to unveil the unique features of poloxamers either as membrane-healing or membrane pore-forming agents. Based on the coarse-graining convention of the MARTINI force field and the big multipole water (BMW) model, which has a three charged site topology and can reproduce the correct dipole moment of four-water clusters, we generated coarse-grained (CG) models with analytical and numerical potentials for PEO and PPO homopolymers and poloxamers in dilute solution. The effective bonded interaction potentials between CG beads were determined from the probability distributions of bond lengths, angles and dihedrals that are determined from atomistic simulations. The nonbonded interaction parameters were fine-tuned to reproduce the conformational properties of atomistic PEO and PPO homopolymers and poloxamers via extensive CG simulations of PEO and PPO homopolymers and poloxamers in a BMW water environment. The reported CG models provide a promising framework for a comprehensive understanding of the microstructural, conformational, and dynamic properties of poloxamers and their delicate interactions with other species in an explicit water environment.

A coarse-grained potential for liquid water by spherically projected hydrogen-bonding interactions

A procedure for generating a coarse-grained spherically symmetric potential in order to reproduce the structure of liquid water is developed noniteratively through an all-atom Monte Carlo simulation. This procedure for determining the spherically averaged potential (SAP) extracts the effective potential of the molecular pairs from the simulation. The SAP procedure is then modified by projecting the hydrogen-bonding interactions during the all-atom simulation onto the spherically symmetric interaction. The projection suppresses the excessively attractive interaction at small intermolecular distances and allows one to derive the spherically projected potential (SPP). Although the rotation of the all-atom water molecule is accompanied by large energy fluctuations, this is not the case for the spherically symmetric potential. Given the decrease in the number of energy fluctuations in the case of coarse-graining, we scale both the SAP and the SPP. The scaled potentials for the SAP and SPP are referred to as the SAPw and SPPw, respectively. While the SAPw reproduces the liquid structure qualitatively, the SPPw reproduces the liquid structure well compared to the SAPw. Furthermore, the SAP procedure can be applied to any system involving interactions between spheres. By successively using the SAP procedure for the initial SPPw, we show that the obtained coarse-grained potentials produce a liquid structure that is similar to the initial one. Hence, this investigation provides novel insights into the characteristics of coarse-grained potentials.

Docking proteins and peptides under evolutionary constraints in Critical Assessment of PRediction of Interactions rounds 38 to 45.

Computational structural prediction of macromolecular interactions is a fundamental tool toward the global understanding of cellular processes. The Critical Assessment of PRediction of Interactions (CAPRI) community-wide experiment provides excellent opportunities for blind testing computational docking methods and includes original targets, thus widening the range of docking applications. Our participation in CAPRI rounds 38 to 45 enabled us to expand the way we include evolutionary information in structural predictions beyond our standard free docking InterEvDock pipeline. InterEvDock integrates a coarse-grained potential that accounts for interface coevolution based on joint multiple sequence alignments of two protein partners (co-alignments). However, even though such co-alignments could be built for none of the CAPRI targets in rounds 38 to 45, including host-pathogen and protein-oligosaccharide complexes and a redesigned interface, we identified multiple strategies that can be used to incorporate evolutionary constraints, which helped us to identify the most likely macromolecular binding modes. These strategies include template-based modeling where only local adjustments should be applied when query-template sequence identity is above 30% and larger perturbations are needed below this threshold; covariation-based structure prediction for individual protein partners; and the identification of evolutionarily conserved and structurally recurrent anchoring interface motifs. Overall, we submitted correct predictions among the top 5 models for 12 out of 19 interface challenges, including four High- and five Medium-quality predictions. Our top 20 models included correct predictions for three out of the five targets we missed in the top 5, including two targets for which misleading biological data led us to downgrade correct free docking models.

A coarse-grained deep neural network model for liquid water

We introduce a coarse-grained deep neural network (CG-DNN) model for liquid water that utilizes 50 rotational and translational invariant coordinates and is trained exclusively against energies of ∼30 000 bulk water configurations. Our CG-DNN potential accurately predicts both the energies and the molecular forces of water, within 0.9 meV/molecule and 54 meV/Å of a reference (coarse-grained bond-order potential) model. The CG-DNN water model also provides good prediction of several structural, thermodynamic, and temperature dependent properties of liquid water, with values close to those obtained from the reference model. More importantly, CG-DNN captures the well-known density anomaly of liquid water observed in experiments. Our work lays the groundwork for a scheme where existing empirical water models can be utilized to develop a fully flexible neural network framework that can subsequently be trained against sparse data from high-fidelity albeit expensive beyond-DFT calculations.

Dual-potential approach for coarse-grained implicit solvent models with accurate, internally consistent energetics and predictive transferability.

The dual-potential approach promises coarse-grained (CG) models that accurately reproduce both structural and energetic properties, while simultaneously providing predictive estimates for the temperature-dependence of the effective CG potentials. In this work, we examine the dual-potential approach for implicit solvent CG models that reflect large entropic effects from the eliminated solvent. Specifically, we construct implicit solvent models at various resolutions, R, by retaining a fraction 0.10 ≤ R ≤ 0.95 of the molecules from a simple fluid of Lennard-Jones spheres. We consider the dual-potential approach in both the constant volume and constant pressure ensembles across a relatively wide range of temperatures. We approximate the many-body potential of mean force for the remaining solutes with pair and volume potentials, which we determine via multiscale coarse-graining and self-consistent pressure-matching, respectively. Interestingly, with increasing temperature, the pair potentials appear increasingly attractive, while the volume potentials become increasingly repulsive. The dual-potential approach not only reproduces the atomic energetics but also quite accurately predicts this temperature-dependence. We also derive an exact relationship between the thermodynamic specific heat of an atomic model and the energetic fluctuations that are observable at the CG resolution. With this generalized fluctuation relationship, the approximate CG models quite accurately reproduce the thermodynamic specific heat of the underlying atomic model.

Transferable coarse-grained models for poly(ethylene oxide)/poly(methyl methacrylate) blends

The recently developed multiscale scheme has been extended to parameterize the coarse-grained (CG) potentials for simulating the two binary blends comprised of poly(ethylene oxide) (PEO) and isotactic or syndiotactic poly(methyl methacrylate) (iPMMA, sPMMA). The specific volumes and the non-bonded interaction energies reveal a single glass transition temperature (Tg), and the dynamical Tg and chain dimension exhibit a strong composition-dependence, and the scale-dependent miscibility is confirmed. As inferred from the intermolecular radial distribution function (RDF), sPMMA is more miscible with PEO than is iPMMA. For any of these systems, the heats and free energies of mixing are most negative at the middle composition. More negative free energy of mixing at lower temperature predicts a lower critical solution temperature. All these simulated results are in good agreements with the experimental observations, validating the multiscale scheme with the ability to derive the transferable CG potentials.

Scaling-Up Simulations of Diffusion in Microporous Materials.

We introduce and demonstrate the coarse-graining of static and dynamical properties of host-guest systems constituted by methane in two different microporous materials. The reference systems are mapped to occupancy-based pore-scale lattice models. Each coarse-grained model is equipped with an appropriate coarse-grained potential and a local dynamical operator, which represents the probability of interpore molecular jumps between different cages. Coarse-grained thermodynamics and dynamics are both defined based on small-scale atomistic simulations of the reference systems. We considered two host materials: the widely studied ITQ-29 zeolite and the LTA-zeolite-templated carbon, which was recently theorized. Our method allows for representing with satisfactory accuracy and a considerably reduced computational effort the reference systems while providing new interesting physical insights in terms of static and diffusive properties.