Generic Adaptive Resolution Method for Reverse Mapping of Polymers from Coarse-Grained to Atomistic Descriptions

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.

Integrating Machine Learning in the Coarse-Grained Molecular Simulation of Polymers

Machine learning (ML) is having an increasing impact on the physical sciences, engineering, and technology and its integration into molecular simulation frameworks holds great potential to expand their scope of applicability to complex materials and facilitate fundamental knowledge and reliable property predictions, contributing to the development of efficient materials design routes. The application of ML in materials informatics in general, and polymer informatics in particular, has led to interesting results, however great untapped potential lies in the integration of ML techniques into the multiscale molecular simulation methods for the study of macromolecular systems, specifically in the context of Coarse Grained (CG) simulations. In this Perspective, we aim at presenting the pioneering recent research efforts in this direction and discussing how these new ML-based techniques can contribute to critical aspects of the development of multiscale molecular simulation methods for bulk complex chemical systems, especially polymers. Prerequisites for the implementation of such ML-integrated methods and open challenges that need to be met toward the development of general systematic ML-based coarse graining schemes for polymers are discussed.

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.

Modelling Sorption and Transport of Gases in Polymeric Membranes across Different Scales: A Review

Professor Giulio C. Sarti has provided outstanding contributions to the modelling of fluid sorption and transport in polymeric materials, with a special eye on industrial applications such as membrane separation, due to his Chemical Engineering background. He was the co-creator of innovative theories such as the Non-Equilibrium Theory for Glassy Polymers (NET-GP), a flexible tool to estimate the solubility of pure and mixed fluids in a wide range of polymers, and of the Standard Transport Model (STM) for estimating membrane permeability and selectivity. In this review, inspired by his rigorous and original approach to representing membrane fundamentals, we provide an overview of the most significant and up-to-date modeling tools available to estimate the main properties governing polymeric membranes in fluid separation, namely solubility and diffusivity. The paper is not meant to be comprehensive, but it focuses on those contributions that are most relevant or that show the potential to be relevant in the future. We do not restrict our view to the field of macroscopic modelling, which was the main playground of professor Sarti, but also devote our attention to Molecular and Multiscale Hierarchical Modeling. This work proposes a critical evaluation of the different approaches considered, along with their limitations and potentiality.

Solvent-scaling as an alternative to coarse-graining in adaptive-resolution simulations: The adaptive solvent-scaling (AdSoS) scheme

A new approach termed Adaptive Solvent-Scaling (AdSoS) is introduced for performing simulations of a solute embedded in a fine-grained (FG) solvent region itself surrounded by a coarse-grained (CG) solvent region, with a continuous FG ↔ CG switching of the solvent resolution across a buffer layer. Instead of relying on a distinct CG solvent model, the AdSoS scheme is based on CG models defined by a dimensional scaling of the FG solvent by a factor s, accompanied by an s-dependent modulation of the atomic masses and interaction parameters. The latter changes are designed to achieve an isomorphism between the dynamics of the FG and CG models, and to preserve the dispersive and dielectric solvation properties of the solvent with respect to a solute at FG resolution. This scaling approach offers a number of advantages compared to traditional coarse-graining: (i) the CG parameters are immediately related to those of the FG model (no need to parameterize a distinct CG model); (ii) nearly ideal mixing is expected for CG variants with similar s-values (ideal mixing holding in the limit of identical s-values); (iii) the solvent relaxation timescales should be preserved (no dynamical acceleration typical for coarse-graining); (iv) the graining level N_G (number of FG molecules represented by one CG molecule) can be chosen arbitrarily (in particular, N_G = s³ is not necessarily an integer); and (v) in an adaptive-resolution scheme, this level can be varied continuously as a function of the position (without requiring a bundling mechanism), and this variation occurs at a constant number of particles per molecule (no occurrence of fractional degrees of freedom in the buffer layer). By construction, the AdSoS scheme minimizes the thermodynamic mismatch between the different regions of the adaptive-resolution system, leading to a nearly homogeneous scaled solvent density s³ρ. Residual density artifacts in and at the surface of the boundary layer can easily be corrected by means of a grid-based biasing potential constructed in a preliminary pure-solvent simulation. This article introduces the AdSoS scheme and provides an initial application to pure atomic liquids (no solute) with Lennard-Jones plus Coulomb interactions in a slab geometry.

Molecular Modeling and Simulations of Peptide–Polymer Conjugates

Peptide–polymer conjugates are a class of soft materials composed of covalently linked blocks of protein/polypeptides and synthetic/natural polymers. These materials are practically useful in biological applications, such as drug delivery, DNA/gene delivery, and antimicrobial coatings, as well as nonbiological applications, such as electronics, separations, optics, and sensing. Given their broad applicability, there is motivation to understand the molecular and macroscale structure, dynamics, and thermodynamic behavior exhibited by such materials. We focus on the past and ongoing molecular simulation studies aimed at obtaining such fundamental understanding and predicting molecular design rules for the target function. We describe briefly the experimental work in this field that validates or motivates these computational studies. We also describe the various models (e.g., atomistic, coarse-grained, or hybrid) and simulation methods (e.g., stochastic versus deterministic, enhanced sampling) that have been used and the types of questions that have been answered using these computational approaches.

Temporally Coarse-Grained All-Atom Molecular Dynamics Achieved via Stochastic Padé Approximants

A Padé approximant scheme for realizing the discrete-time evolution of the state of a many-atom system is introduced. This temporal coarse-graining scheme accounts for the underlying Newtonian physics and avoids the need for construction of spatially coarse-grained variables. Newtonian physics is incorporated through short molecular dynamics simulations at the beginning of each of the large coarse-grained timesteps. The balance between stochastic and coherent dynamics expressed by many-atom systems is captured via incorporation of the Ito formula into a Padé approximant for the time dependence of individual atom positions over large timesteps. Since the time for a many-atom system to express a characteristic ensemble of atomic velocity fluctuations is typically short relative to the characteristic time of large-scale atomic displacements, a computationally efficient and accurate temporal coarse-graining of the atom-resolved Newtonian dynamics is formulated, denoted all-atom Padé-Ito molecular dynamics (APIMD). Evolution of the system over a time step much longer than that required for standard molecular dynamics (MD) is achieved via incorporation of information from the short MD simulations into a Padé approximant extrapolation in time. The extrapolated atomic configuration is subjected to energy minimization and, when needed, thermal equilibration so as to avoid occasional unphysical close encounters deriving from the Padé approximant extrapolation and to represent configurations appropriate for the temperature of interest. APIMD is implemented and tested via comparison with traditional MD simulations of five phenomena: (1) pertussis toxin subunit deformation, (2) structural transition in a T = 1 capsid-like structure of HPV16 L1 protein, (3) coalescence of argon nanodroplets, and structural transitions in dialanine in (4) vacuum, and (5) water. Accuracy of APIMD is demonstrated using semimicroscopic descriptors (rmsd, radius of gyration, residue-residue contact maps, and densities) and the free energy. Significant computational acceleration relative to traditional molecular dynamics is illustrated.

Atomic-level reconstruction of biomolecules by a rigid-fragment- and local-frame-based (RF-LF) strategy

Coarse-grained (CG) model has been a powerful tool in bridging the gap between theoretical studies and experimental phenomena in biological computing field. The reconstruction from a CG model to an atomic-detail structure is especially important in CG studies of biological systems. In this work, a rigid-fragment- and local-frame-based (RF-LF) backmapping method was proposed to achieve reverse mapping from CG models to atomic-level structures. The initial atomic-level structures were further refined to yield the final backmapping ones. With the popular Martini force field, the performance of the RF-LF method was extensively examined in the CG → AA (CG to AA) backmapping of protein/DNA/RNA systems. Besides, the RF-LF method was also extended to the backmapping of the TMFF model. Numerical results illustrate that the RF-LF backmapping method is generic and parameter-free and can provide a promising way to tackle atomic-level studies in CG models.

Molecular Modeling Investigations of Sorption and Diffusion of Small Molecules in Glassy Polymers

With a wide range of applications, from energy and environmental engineering, such as in gas separations and water purification, to biomedical engineering and packaging, glassy polymeric materials remain in the core of novel membrane and state-of the art barrier technologies. This review focuses on molecular simulation methodologies implemented for the study of sorption and diffusion of small molecules in dense glassy polymeric systems. Basic concepts are introduced and systematic methods for the generation of realistic polymer configurations are briefly presented. Challenges related to the long length and time scale phenomena that govern the permeation process in the glassy polymer matrix are described and molecular simulation approaches developed to address the multiscale problem at hand are discussed.

SWINGER: a clustering algorithm for concurrent coupling of atomistic and supramolecular liquids

In this contribution, we review recent developments and applications of a dynamic clustering algorithm SWINGER tailored for the multiscale molecular simulations of biomolecular systems. The algorithm on-the-fly redistributes solvent molecules among supramolecular clusters. In particular, we focus on its applications in combination with the adaptive resolution scheme, which concurrently couples atomistic and coarse-grained molecular representations. We showcase the versatility of our multiscale approach on a few applications to biomolecular systems coupling atomistic and supramolecular water models such as the well-established MARTINI and dissipative particle dynamics models and provide an outlook for future work.

Multiscale Simulation of Protein Hydration Using the SWINGER Dynamical Clustering Algorithm

To perform computationally efficient concurrent multiscale simulations of biological macromolecules in solution, where the all-atom (AT) models are coupled to supramolecular coarse-grained (SCG) solvent models, previous studies resorted to modified AT water models, such as the bundled-simple point charge (SPC) models, that use semiharmonic springs to restrict the relative movement of water molecules within a cluster. Those models can have a significant impact on the simulated biomolecules and can lead, for example, to a partial unfolding of a protein. In this work, we employ the recently developed alternative approach with a dynamical clustering algorithm, SWINGER, which enables a direct coupling of original unmodified AT and SCG water models. We perform an adaptive resolution molecular dynamics simulation of a Trp-Cage miniprotein in multiscale water, where the standard SPC water model is interfaced with the widely used MARTINI SCG model, and demonstrate that, compared to the corresponding full-blown AT simulations, the structural and dynamic properties of the solvated protein and surrounding solvent are well reproduced by our approach.

Reverse mapping method for complex polymer systems

We present a comprehensive approach for reverse mapping of complex polymer systems in which the connectivity is created by the simulation of chemical reactions at the coarse-grained scale. Within the work, we use a recently developed generic adaptive reverse mapping procedure that we adapt to handle the varying connectivity structure resulting from the chemical reactions. The method is independent of the coarse-grained and fine-grained force-fields by design and relies only on a single control parameter. We employ the approach to reverse map four different systems: a three-component epoxy network, a trimethylol melamine network, a hyperbranched polymer, and a polyethylene terephthalate. In the case of the epoxy network, we use two fine-scale representations: fully atomistic and united-atom. Whereas the trimethylol melamine network the hyperbranched polymer and the polyethylene terephthalate are reverse mapped to the fully atomistic description. After the reverse mapping, we examine the fine-grained structure by comparing the radial distribution functions with respect to the control parameter. Moreover, in the case of the epoxy we perform tensile-test experiments and examine the resulting Young's modulus. In all cases, we show how the properties of the reverse mapped systems depend on the control parameters. In general, we see that the results are relatively insensitive to the control parameter and the resulting atomistic systems are stable. Only for the trimethylol melamine network, we notice chemically incorrect conformations when the reverse mapping is performed too fast. We provide a remedy for this issue. © 2017 Wiley Periodicals, Inc.

Molecular Structuring and Percolation Transition in Hydrated Sulfonated Poly(ether ether ketone) Membranes

The extent of phase separation and water percolation in sulfonated membranes are the key to their performance in fuel cells. Toward this, the effect of hydration on the morphology and transport characteristics of sulfonated poly(ether ether ketone), sPEEK, membrane is investigated using atomistic molecular dynamics simulation at various hydration levels(λ: number of water molecules per sulfonate group). The evolution of local morphology is investigated using structural correlations and minimum pair distances. Transport properties are probed using mean squared displacements and diffusion coefficients. The water-sulfonate interaction in sPEEK is found to be stronger than that in Nafion, as observed in experiments. Analyses indicate the presence of narrow connected path of water and hydronium at λ = 4 and large domains, spanning half the simulation box, at λ = 15. The behavior of membrane water remains far from bulk as indicated by its diffusion coefficient. The persistence of small isolated water clusters demonstrates the extent of phase separation in sPEEK to be lesser than that in Nafion. Analyses at molecular and collective levels suggest the occurrence of a percolation transition between λ = 8 and 10, which leads to a connected network of water channels in the membrane, thereby boosting the hydronium mobility.