Graph-Based Approach to Systematic Molecular Coarse-Graining

Data-Driven Design of Polymer-Based Biomaterials: High-throughput Simulation, Experimentation, and Machine Learning

Polymers, with the capacity to tunably alter properties and response based on manipulation of their chemical characteristics, are attractive components in biomaterials. Nevertheless, their potential as functional materials is also inhibited by their complexity, which complicates rational or brute-force design and realization. In recent years, machine learning has emerged as a useful tool for facilitating materials design via efficient modeling of structure-property relationships in the chemical domain of interest. In this Spotlight, we discuss the emergence of data-driven design of polymers that can be deployed in biomaterials with particular emphasis on complex copolymer systems. We outline recent developments, as well as our own contributions and takeaways, related to high-throughput data generation for polymer systems, methods for surrogate modeling by machine learning, and paradigms for property optimization and design. Throughout this discussion, we highlight key aspects of successful strategies and other considerations that will be relevant to the future design of polymer-based biomaterials with target properties.

Formalizing Coarse-Grained Representations of Anisotropic Interactions at Multimeric Protein Interfaces Using Virtual Sites

Molecular simulations of biomacromolecules that assemble into multimeric complexes remain a challenge due to computationally inaccessible length and time scales. Low-resolution and implicit-solvent coarse-grained modeling approaches using traditional nonbonded interactions (both pairwise and spherically isotropic) have been able to partially address this gap. However, these models may fail to capture the complex anisotropic interactions present at macromolecular interfaces unless higher-order interaction potentials are incorporated at the expense of the computational cost. In this work, we introduce an alternate and systematic approach to represent directional interactions at protein-protein interfaces by using virtual sites restricted to pairwise interactions. We show that virtual site interaction parameters can be optimized within a relative entropy minimization framework by using only information from known statistics between coarse-grained sites. We compare our virtual site models to traditional coarse-grained models using two case studies of multimeric protein assemblies and find that the virtual site models predict pairwise correlations with higher fidelity and, more importantly, assembly behavior that is morphologically consistent with experiments. Our study underscores the importance of anisotropic interaction representations and paves the way for more accurate yet computationally efficient coarse-grained simulations of macromolecular assembly in future research.

Surveying the energy landscape of coarse-grained mappings

Simulations of soft materials often adopt low-resolution coarse-grained (CG) models. However, the CG representation is not unique and its impact upon simulated properties is poorly understood. In this work, we investigate the space of CG representations for ubiquitin, which is a typical globular protein with 72 amino acids. We employ Monte Carlo methods to ergodically sample this space and to characterize its landscape. By adopting the Gaussian network model as an analytically tractable atomistic model for equilibrium fluctuations, we exactly assess the intrinsic quality of each CG representation without introducing any approximations in sampling configurations or in modeling interactions. We focus on two metrics, the spectral quality and the information content, that quantify the extent to which the CG representation preserves low-frequency, large-amplitude motions and configurational information, respectively. The spectral quality and information content are weakly correlated among high-resolution representations but become strongly anticorrelated among low-resolution representations. Representations with maximal spectral quality appear consistent with physical intuition, while low-resolution representations with maximal information content do not. Interestingly, quenching studies indicate that the energy landscape of mapping space is very smooth and highly connected. Moreover, our study suggests a critical resolution below which a "phase transition" qualitatively distinguishes good and bad representations.

Distilling coarse-grained representations of molecular electronic structure with continuously gated message passing

Bottom-up methods for coarse-grained (CG) molecular modeling are critically needed to establish rigorous links between atomistic reference data and reduced molecular representations. For a target molecule, the ideal reduced CG representation is a function of both the conformational ensemble of the system and the target physical observable(s) to be reproduced at the CG resolution. However, there is an absence of algorithms for selecting CG representations of molecules from which complex properties, including molecular electronic structure, can be accurately modeled. We introduce continuously gated message passing (CGMP), a graph neural network (GNN) method for atomically decomposing molecular electronic structure sampled over conformational ensembles. CGMP integrates 3D-invariant GNNs and a novel gated message passing system to continuously reduce the atomic degrees of freedom accessible for electronic predictions, resulting in a one-shot importance ranking of atoms contributing to a target molecular property. Moreover, CGMP provides the first approach by which to quantify the degeneracy of "good" CG representations conditioned on specific prediction targets, facilitating the development of more transferable CG representations. We further show how CGMP can be used to highlight multiatom correlations, illuminating a path to developing CG electronic Hamiltonians in terms of interpretable collective variables for arbitrarily complex molecules.

K-Means Clustering Coarse-Graining (KMC-CG): A Next Generation Methodology for Determining Optimal Coarse-Grained Mappings of Large Biomolecules

Coarse-grained (CG) molecular dynamics (MD) has become a method of choice for simulating various large scale biomolecular processes; therefore, the systematic definition of the CG mappings for biomolecules remains an important topic. Appropriate CG mappings can significantly enhance the representability of a CG model and improve its ability to capture critical features of large biomolecules. In this work, we present a systematic and more generalized method called K-means clustering coarse-graining (KMC-CG), which builds on the earlier approach of essential dynamics coarse-graining (ED-CG). KMC-CG removes the sequence-dependent constraints of ED-CG, allowing it to explore a more extensive space and thus enabling the discovery of more physically optimal CG mappings. Furthermore, the implementation of the K-means clustering algorithm can variationally optimize the CG mapping with efficiency and stability. This new method is tested in three cases: ATP-bound G-actin, the HIV-1 CA pentamer, and the Arp2/3 complex. In these examples, the CG models generated by KMC-CG are seen to better capture the structural, dynamic, and functional domains. KMC-CG therefore provides a robust and consistent approach to generating CG models of large biomolecules that can then be more accurately parametrized by either bottom-up or top-down CG force fields.

Automatic identification of chemical moieties

In recent years, the prediction of quantum mechanical observables with machine learning methods has become increasingly popular. Message-passing neural networks (MPNNs) solve this task by constructing atomic representations, from which the properties of interest are predicted. Here, we introduce a method to automatically identify chemical moieties (molecular building blocks) from such representations, enabling a variety of applications beyond property prediction, which otherwise rely on expert knowledge. The required representation can either be provided by a pretrained MPNN, or be learned from scratch using only structural information. Beyond the data-driven design of molecular fingerprints, the versatility of our approach is demonstrated by enabling the selection of representative entries in chemical databases, the automatic construction of coarse-grained force fields, as well as the identification of reaction coordinates.

Entanglements via Slip Springs with Soft, Coarse-Grained Models for Systems Having Explicit Liquid-Vapor Interfaces

Recent advances in nano-rheology require that new techniques and models be developed to precisely describe the equilibrium and non-equilibrium characteristics of entangled polymeric materials and their interfaces at a molecular level. In this study, a slip-spring (SLSP) model is proposed to capture the dynamics of entangled polymers at interfaces, including those between liquids, liquids and vapors, and liquids and solids. The SLSP model employs a highly coarse-grained approach, which allows for comprehensive simulations of entire nano-rheological characterization systems using a particle-level description. The model relies on many-body dissipative particle dynamics (MDPD) non-bonded interactions, which permit explicit description of liquid-vapor interfaces; a compensating potential is introduced to ensure an unbiased representation of the shape of the liquid-vapor interface within the SLSP model. The usefulness of the proposed MDPD + SLSP approach is illustrated by simulating a capillary breakup rheometer (CaBR) experiment, in which a liquid droplet splits into two segments under the influence of capillary forces. We find that the predictions of the MDPD + SLSP model are consistent with experimental measurements and theoretical predictions. The proposed model is also verified by comparison to the results of explicit molecular dynamics simulations of an entangled polymer melt using a Kremer-Grest chain representation, both at equilibrium and far from equilibrium. Taken together, the model and methods presented in this study provide a reliable framework for molecular-level interpretation of high-polymer dynamics in the presence of interfaces.

Automated Parameterization of Coarse-Grained Polyethylenimine under a Martini Framework

As a versatile polymer in many applications, synthesized polyethylenimine (PEI) is polydisperse with diverse branched structures that attain pH-dependent protonation states. Understanding the structure-function relationship of PEI is necessary for enhancing its efficacy in various applications. Coarse-grained (CG) simulations can be performed at length and time scales directly comparable with experimental data while maintaining the molecular perspective. However, manually developing CG forcefields for complex PEI structures is time-consuming and prone to human errors. This article presents a fully automated algorithm that can coarse-grain any branched architecture of PEI from its all-atom (AA) simulation trajectories and topology. The algorithm is demonstrated by coarse-graining a branched 2 kDa PEI, which can replicate the AA diffusion coefficient, radius of gyration, and end-to-end distance of the longest linear chain. Commercially available 25 and 2 kDa Millipore-Sigma PEIs are used for experimental validation. Specifically, branched PEI architectures are proposed, coarse-grained using the automated algorithm, and then simulated at different mass concentrations. The CG PEIs can reproduce existing experimental data on PEI's diffusion coefficient and Stokes-Einstein radius at infinite dilution as well as its intrinsic viscosity. This suggests a strategy where probable chemical structures of synthetic PEIs can be inferred computationally using the developed algorithm. The coarse-graining methodology presented here can also be extended to other polymers.

Hierarchical Machine Learning of Low-Resolution Coarse-Grained Free Energy Potentials

A force-matching-based method for supervised machine learning (ML) of coarse-grained (CG) free energy (FE) potentials─known as multiscale coarse-graining via force-matching (MSCG/FM)─is an efficient method to develop microscopically informed CG models that are thermodynamically and statistically equivalent to the reference microscopic models. For low-resolution models, when the coarse-graining is at supramolecular scales, objective-oriented clustering of nonbonded particles is required and the reduced description becomes a function of the clustering algorithm. In the present work, we explore the dependence of the ML of the CG Helmholtz FE potential on the clustering algorithm. We consider coarse-graining based on partitional (k-means, leading to Voronoi diagram) and hierarchical agglomerative (bottom-up) clustering algorithms common in unsupervised ML and develop theory connecting the MSCG/FM learned CG Helmholtz potential and the clustering statistics. By combining the agglomerative clustering and the MSCG/FM learning in a recursive manner, we propose an efficient ML methodology to develop the fine-to-low resolution hierarchies of the CG models. The methodology does not suffer from degrading accuracy or increased computational cost to construct larger hierarchies and as such does not impose an upper size limitation of the CG particles resulting from the extended hierarchies. The utility of the methodology is demonstrated by obtaining the bottom-up agglomerative hierarchy for liquid nitromethane from all-atom molecular dynamics (MD) simulations. For agglomerative hierarchies, we prove the existence of renormalization group transformations that indicate self-similarity and allow for learning the low-resolution MSCG/FM potentials at low computational cost by rescaling and renormalizing the certain finer-resolution members of the hierarchy. The hierarchies of the CG models can be used to carry out simulations under constant-pressure conditions.

Automatic Multiscale Method of Building up a Cross-linked Polymer Reaction System: Bridging SMILES to the Multiscale Molecular Dynamics Simulation

An automatic method is introduced to generate the initial configuration and input file from SMILES for multiscale molecular dynamics (MD) simulation of cross-linked polymer reaction systems. Inputs are a modified version of SMILES of all the components and conditions of coarse-grained (CG) and all-atom (AA) simulations. The overall process comprises the following steps: (1) Modified SMILES inputs of all the components are converted to 3-dimensional coordinates of molecular structures. (2) Molecular structures are mapped to the coarse-grained scale, followed by a CG reaction simulation. (3) CG beads are backmapped to the atomic scale after the CG reaction. (4) An AA productive run is finally performed to analyze volume shrinkage, glass transition, and atomic detail of network structure. The method is applied to two common epoxy resin reactions, that is, the cross-linking process of DGEVA (diglycidyl ether of vanillyl alcohol) and DHAVA (dihydroxyaminopropane of vanillyl alcohol) and that of DGEBA (diglycidyl ether of bisphenol A) and DETA (diethylenetriamine). These components form network structures after the CG cross-linking reaction and are then backmapped to calculate properties in the atomic scale. The result demonstrates that the method can accurately predict volume shrinkage, glass transition, and all-atom structure of cross-linked polymers. The method bridges from SMILES to MD simulation trajectories in an automatic way, which shortens the time of building up cross-linked polymer reaction model and suitable for high-throughput computations.

Computational Approaches for Organic Semiconductors: From Chemical and Physical Understanding to Predicting New Materials

While a complete understanding of organic semiconductor (OSC) design principles remains elusive, computational methods─ranging from techniques based in classical and quantum mechanics to more recent data-enabled models─can complement experimental observations and provide deep physicochemical insights into OSC structure-processing-property relationships, offering new capabilities for in silico OSC discovery and design. In this Review, we trace the evolution of these computational methods and their application to OSCs, beginning with early quantum-chemical methods to investigate resonance in benzene and building to recent machine-learning (ML) techniques and their application to ever more sophisticated OSC scientific and engineering challenges. Along the way, we highlight the limitations of the methods and how sophisticated physical and mathematical frameworks have been created to overcome those limitations. We illustrate applications of these methods to a range of specific challenges in OSCs derived from π-conjugated polymers and molecules, including predicting charge-carrier transport, modeling chain conformations and bulk morphology, estimating thermomechanical properties, and describing phonons and thermal transport, to name a few. Through these examples, we demonstrate how advances in computational methods accelerate the deployment of OSCsin wide-ranging technologies, such as organic photovoltaics (OPVs), organic light-emitting diodes (OLEDs), organic thermoelectrics, organic batteries, and organic (bio)sensors. We conclude by providing an outlook for the future development of computational techniques to discover and assess the properties of high-performing OSCs with greater accuracy.

Statistically Optimal Force Aggregation for Coarse-Graining Molecular Dynamics

Machine-learned coarse-grained (CG) models have the potential for simulating large molecular complexes beyond what is possible with atomistic molecular dynamics. However, training accurate CG models remains a challenge. A widely used methodology for learning bottom-up CG force fields maps forces from all-atom molecular dynamics to the CG representation and matches them with a CG force field on average. We show that there is flexibility in how to map all-atom forces to the CG representation and that the most commonly used mapping methods are statistically inefficient and potentially even incorrect in the presence of constraints in the all-atom simulation. We define an optimization statement for force mappings and demonstrate that substantially improved CG force fields can be learned from the same simulation data when using optimized force maps. The method is demonstrated on the miniproteins chignolin and tryptophan cage and published as open-source code.

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.

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.

Slicing and Dicing: Optimal Coarse-Grained Representation to Preserve Molecular Kinetics

The aim of molecular coarse-graining approaches is to recover relevant physical properties of the molecular system via a lower-resolution model that can be more efficiently simulated. Ideally, the lower resolution still accounts for the degrees of freedom necessary to recover the correct physical behavior. The selection of these degrees of freedom has often relied on the scientist's chemical and physical intuition. In this article, we make the argument that in soft matter contexts desirable coarse-grained models accurately reproduce the long-time dynamics of a system by correctly capturing the rare-event transitions. We propose a bottom-up coarse-graining scheme that correctly preserves the relevant slow degrees of freedom, and we test this idea for three systems of increasing complexity. We show that in contrast to this method existing coarse-graining schemes such as those from information theory or structure-based approaches are not able to recapitulate the slow time scales of the system.

Bottom-up Coarse-Graining: Principles and Perspectives

Large-scale computational molecular models provide scientists a means to investigate the effect of microscopic details on emergent mesoscopic behavior. Elucidating the relationship between variations on the molecular scale and macroscopic observable properties facilitates an understanding of the molecular interactions driving the properties of real world materials and complex systems (e.g., those found in biology, chemistry, and materials science). As a result, discovering an explicit, systematic connection between microscopic nature and emergent mesoscopic behavior is a fundamental goal for this type of investigation. The molecular forces critical to driving the behavior of complex heterogeneous systems are often unclear. More problematically, simulations of representative model systems are often prohibitively expensive from both spatial and temporal perspectives, impeding straightforward investigations over possible hypotheses characterizing molecular behavior. While the reduction in resolution of a study, such as moving from an atomistic simulation to that of the resolution of large coarse-grained (CG) groups of atoms, can partially ameliorate the cost of individual simulations, the relationship between the proposed microscopic details and this intermediate resolution is nontrivial and presents new obstacles to study. Small portions of these complex systems can be realistically simulated. Alone, these smaller simulations likely do not provide insight into collectively emergent behavior. However, by proposing that the driving forces in both smaller and larger systems (containing many related copies of the smaller system) have an explicit connection, systematic bottom-up CG techniques can be used to transfer CG hypotheses discovered using a smaller scale system to a larger system of primary interest. The proposed connection between different CG systems is prescribed by (i) the CG representation (mapping) and (ii) the functional form and parameters used to represent the CG energetics, which approximate potentials of mean force (PMFs). As a result, the design of CG methods that facilitate a variety of physically relevant representations, approximations, and force fields is critical to moving the frontier of systematic CG forward. Crucially, the proposed connection between the system used for parametrization and the system of interest is orthogonal to the optimization used to approximate the potential of mean force present in all systematic CG methods. The empirical efficacy of machine learning techniques on a variety of tasks provides strong motivation to consider these approaches for approximating the PMF and analyzing these approximations.

Effect of Slip-Spring Parameters on the Dynamics and Rheology of Soft, Coarse-Grained Polymer Models

Highly coarse-grained (hCG) linear polymer models allow for accessing long time and length scales by dissipative particle dynamics (DPD). This top-down strategy exploits the universal equilibrium behavior of long, flexible macromolecules by accounting only for the relevant interactions, such as molecular connectivity, and by parametrizing their strength via coarse-grained invariants, such as the mean-squared end-to-end distance. The description of the dynamics of long, entangled polymers, however, poses a challenge because (i) the noncrossability of the molecular backbones is not enforced by the soft interactions of an hCG model and (ii) the rheology involves multiple time and length scales, such as the Rouse-like dynamics on short scales and the reptation dynamics on long scales. One popular technique to effectively mimic the effect of entanglements in linear polymer melts via hCG models is slip-springs, and quantitative agreement with simulations that explicitly account for the noncrossability of molecular contours, experiments, and theoretical predictions has been achieved by identifying the time, length, and energy scales of the hCG model and adjusting the number of slip-springs per macromolecule. In the present work, we study how the spatial extent and the mobility of slip-springs affect the dynamics and discuss their implications in the choice of the degree of coarse-graining in computationally efficient hCG models.

Integration of Machine Learning and Coarse-Grained Molecular Simulations for Polymer Materials: Physical Understandings and Molecular Design

In recent years, the synthesis of monomer sequence-defined polymers has expanded into broad-spectrum applications in biomedical, chemical, and materials science fields. Pursuing the characterization and inverse design of these polymer systems requires our fundamental understanding not only at the individual monomer level, but also considering the chain scales, such as polymer configuration, self-assembly, and phase separation. However, our accessibility to this field is still rudimentary due to the limitations of traditional design approaches, the complexity of chemical space along with the burdened cost and time issues that prevent us from unveiling the underlying monomer sequence-structure-property relationships. Fortunately, thanks to the recent advancements in molecular dynamics simulations and machine learning (ML) algorithms, the bottlenecks in the tasks of establishing the structure-function correlation of the polymer chains can be overcome. In this review, we will discuss the applications of the integration between ML techniques and coarse-grained molecular dynamics (CGMD) simulations to solve the current issues in polymer science at the chain level. In particular, we focus on the case studies in three important topics—polymeric configuration characterization, feed-forward property prediction, and inverse design—in which CGMD simulations are leveraged to generate training datasets to develop ML-based surrogate models for specific polymer systems and designs. By doing so, this computational hybridization allows us to well establish the monomer sequence-functional behavior relationship of the polymers as well as guide us toward the best polymer chain candidates for the inverse design in undiscovered chemical space with reasonable computational cost and time. Even though there are still limitations and challenges ahead in this field, we finally conclude that this CGMD/ML integration is very promising, not only in the attempt of bridging the monomeric and macroscopic characterizations of polymer materials, but also enabling further tailored designs for sequence-specific polymers with superior properties in many practical applications.

Effective Industry-Academia Collaboration Driving Polymer Innovation

Polymer science is one of the few fundamental research fields where the results can be transferred into real-life products almost immediately. Industries need collaborations with the best researchers (universities or national laboratories) to elevate the field and favor the development of new materials, which will boost the chemical and materials business economy and ensure that innovative and sustainable polymer products are constantly being brought to the market. The mechanisms to ensure a seamless and fruitful collaboration are numerous, but few approaches really manage to incorporate the full range of polymer research from a molecular understanding to a macroscopic control of properties. We review some of the main components of standard industry-academia collaborations and propose to develop polymer open centers that put the business development objective as the starting point of the collaboration and allow those to gather and focus on different scientific fields toward a common objective.

Coarse-Grained Density Functional Theory Predictions via Deep Kernel Learning

Scalable electronic predictions are critical for soft materials design. Recently, the Electronic Coarse-Graining (ECG) method was introduced to renormalize all-atom quantum chemical (QC) predictions to coarse-grained (CG) resolutions using deep neural networks (DNNs). While DNNs can learn complex representations that prove challenging for kernel-based methods, they are susceptible to overfitting and the overconfidence of uncertainty estimations. Here, we develop ECG within a GPU-accelerated Deep Kernel Learning (DKL) framework to enable CG QC predictions using range-separated hybrid density functional theory (DFT), obtaining a 10⁷ speedup relative to naive all-atom QC. By treating the predicted electronic properties as random Gaussian Processes, DKL incorporates CG mapping degeneracy by learning the distribution of electronic energies as a function of CG configuration. DKL-ECG accurately reproduces molecular orbital energies from range-separated DFT while facilitating efficient training via active learning using the uncertainties provided by DKL. We show that while active learning algorithms enable efficient sampling of a more diverse configurational space relative to random sampling, all explored query methods exhibit comparable performance for the examined system. We attribute this result to the significant overlap of the feature space and output property distributions across multiple temperatures.

Neural Upscaling from Residue-Level Protein Structure Networks to Atomistic Structures

Coarse-graining is a powerful tool for extending the reach of dynamic models of proteins and other biological macromolecules. Topological coarse-graining, in which biomolecules or sets thereof are represented via graph structures, is a particularly useful way of obtaining highly compressed representations of molecular structures, and simulations operating via such representations can achieve substantial computational savings. A drawback of coarse-graining, however, is the loss of atomistic detail—an effect that is especially acute for topological representations such as protein structure networks (PSNs). Here, we introduce an approach based on a combination of machine learning and physically-guided refinement for inferring atomic coordinates from PSNs. This “neural upscaling” procedure exploits the constraints implied by PSNs on possible configurations, as well as differences in the likelihood of observing different configurations with the same PSN. Using a 1 μs atomistic molecular dynamics trajectory of Aβ1–40, we show that neural upscaling is able to effectively recapitulate detailed structural information for intrinsically disordered proteins, being particularly successful in recovering features such as transient secondary structure. These results suggest that scalable network-based models for protein structure and dynamics may be used in settings where atomistic detail is desired, with upscaling employed to impute atomic coordinates from PSNs.

Automated Coarse-Grained Mapping Algorithm for the Martini Force Field and Benchmarks for Membrane-Water Partitioning

With a view to high-throughput simulations, we present an automated system for mapping and parameterizing organic molecules for use with the coarse-grained Martini force field. The method scales to larger molecules and a broader chemical space than existing schemes. The core of the mapping process is a graph-based analysis of the molecule's bonding network, which has the advantages of being fast, general, and preserving symmetry. The parameterization process pays special attention to coarse-grained beads in aromatic rings. It also includes a method for building efficient and stable frameworks of constraints for molecules with structural rigidity. The performance of the method is tested on a diverse set of 87 neutral organic molecules and the ability of the resulting models to capture octanol-water and membrane-water partition coefficients. In the latter case, we introduce an adaptive method for extracting partition coefficients from free-energy profiles to take into account the interfacial region of the membrane. We also use the models to probe the response of membrane-water partitioning to the cholesterol content of the membrane.

Custom Tokenization Dictionary, CUSTODI: A General, Fast, and Reversible Data-Driven Representation and Regressor

Custom tokenization dictionary (CUSTODI) is introduced as a novel way for tackling the problem of molecular representations, and especially the challenge of molecular property prediction. Herein, the motivational theory and the actual representation and model are presented and shown to have performance that is in line with benchmark methodologies. The uniqueness of CUSTODI is its applicability on small training sets and the developed theory suggests its possible use for a-priori estimation of future fit quality on any given dataset, regardless of the method used for fitting.

"Dividing and Conquering" and "Caching" in Molecular Modeling

Molecular modeling is widely utilized in subjects including but not limited to physics, chemistry, biology, materials science and engineering. Impressive progress has been made in development of theories, algorithms and software packages. To divide and conquer, and to cache intermediate results have been long standing principles in development of algorithms. Not surprisingly, most important methodological advancements in more than half century of molecular modeling are various implementations of these two fundamental principles. In the mainstream classical computational molecular science, tremendous efforts have been invested on two lines of algorithm development. The first is coarse graining, which is to represent multiple basic particles in higher resolution modeling as a single larger and softer particle in lower resolution counterpart, with resulting force fields of partial transferability at the expense of some information loss. The second is enhanced sampling, which realizes "dividing and conquering" and/or "caching" in configurational space with focus either on reaction coordinates and collective variables as in metadynamics and related algorithms, or on the transition matrix and state discretization as in Markov state models. For this line of algorithms, spatial resolution is maintained but results are not transferable. Deep learning has been utilized to realize more efficient and accurate ways of "dividing and conquering" and "caching" along these two lines of algorithmic research. We proposed and demonstrated the local free energy landscape approach, a new framework for classical computational molecular science. This framework is based on a third class of algorithm that facilitates molecular modeling through partially transferable in resolution "caching" of distributions for local clusters of molecular degrees of freedom. Differences, connections and potential interactions among these three algorithmic directions are discussed, with the hope to stimulate development of more elegant, efficient and reliable formulations and algorithms for "dividing and conquering" and "caching" in complex molecular systems.

A Deep Graph Network-Enhanced Sampling Approach to Efficiently Explore the Space of Reduced Representations of Proteins

The limits of molecular dynamics (MD) simulations of macromolecules are steadily pushed forward by the relentless development of computer architectures and algorithms. The consequent explosion in the number and extent of MD trajectories induces the need for automated methods to rationalize the raw data and make quantitative sense of them. Recently, an algorithmic approach was introduced by some of us to identify the subset of a protein's atoms, or mapping, that enables the most informative description of the system. This method relies on the computation, for a given reduced representation, of the associated mapping entropy, that is, a measure of the information loss due to such simplification; albeit relatively straightforward, this calculation can be time-consuming. Here, we describe the implementation of a deep learning approach aimed at accelerating the calculation of the mapping entropy. We rely on Deep Graph Networks, which provide extreme flexibility in handling structured input data and whose predictions prove to be accurate and-remarkably efficient. The trained network produces a speedup factor as large as 105 with respect to the algorithmic computation of the mapping entropy, enabling the reconstruction of its landscape by means of the Wang-Landau sampling scheme. Applications of this method reach much further than this, as the proposed pipeline is easily transferable to the computation of arbitrary properties of a molecular structure.

Automation and data-driven design of polymer therapeutics

Polymers are uniquely suited for drug delivery and biomaterial applications due to tunable structural parameters such as length, composition, architecture, and valency. To facilitate designs, researchers may explore combinatorial libraries in a high throughput fashion to correlate structure to function. However, traditional polymerization reactions including controlled living radical polymerization (CLRP) and ring-opening polymerization (ROP) require inert reaction conditions and extensive expertise to implement. With the advent of air-tolerance and automation, several polymerization techniques are now compatible with well plates and can be carried out at the benchtop, making high throughput synthesis and high throughput screening (HTS) possible. To avoid HTS pitfalls often described as "fishing expeditions," it is crucial to employ intelligent and big data approaches to maximize experimental efficiency. This is where the disruptive technologies of machine learning (ML) and artificial intelligence (AI) will likely play a role. In fact, ML and AI are already impacting small molecule drug discovery and showing signs of emerging in drug delivery. In this review, we present state-of-the-art research in drug delivery, gene delivery, antimicrobial polymers, and bioactive polymers alongside data-driven developments in drug design and organic synthesis. From this insight, important lessons are revealed for the polymer therapeutics community including the value of a closed loop design-build-test-learn workflow. This is an exciting time as researchers will gain the ability to fully explore the polymer structural landscape and establish quantitative structure-property relationships (QSPRs) with biological significance.

Machine Learning of Coarse-Grained Models for Organic Molecules and Polymers: Progress, Opportunities, and Challenges

Machine learning (ML) has emerged as one of the most powerful tools transforming all areas of science and engineering. The nature of molecular dynamics (MD) simulations, complex and time-consuming calculations, makes them particularly suitable for ML research. This review article focuses on recent advancements in developing efficient and accurate coarse-grained (CG) models using various ML methods, in terms of regulating the coarse-graining process, constructing adequate descriptors/features, generating representative training data sets, and optimization of the loss function. Two classes of the CG models are introduced: bottom-up and top-down CG methods. To illustrate these methods and demonstrate the open methodological questions, we survey several important principles in constructing CG models and how these are incorporated into ML methods and improved with specific learning techniques. Finally, we discuss some key aspects of developing machine-learned CG models with high accuracy and efficiency. Besides, we describe how these aspects are tackled in state-of-the-art methods and which remain to be addressed in the near future. We expect that these machine-learned CG models can address thermodynamic consistent, transferable, and representative issues in classical CG models.

Coarse-Graining Organic Semiconductors: The Path to Multiscale Design

Four decades of molecular theory and computation have helped form the modern understanding of the physical chemistry of organic semiconductors. Whereas these efforts have historically centered around characterizations of electronic structure at the single-molecule or dimer scale, emerging trends in noncrystalline molecular and polymeric semiconductors are motivating the need for modeling techniques capable of morphological and electronic structure predictions at the mesoscale. Provided the challenges associated with these prediction tasks, the community has begun to evolve a computational toolkit for organic semiconductors incorporating techniques from the fields of soft matter, coarse-graining, and machine learning. Here, we highlight recent advances in coarse-grained methodologies aimed at the multiscale characterization of noncrystalline organic semiconductors. As organic semiconductor performance is dependent on the interplay of mesoscale morphology and molecular electronic structure, specific emphasis is placed on coarse-grained modeling approaches capable of both structural and electronic predictions without recourse to all-atom representations.

A journey through mapping space: characterising the statistical and metric properties of reduced representations of macromolecules

ABSTRACT

A mapping of a macromolecule is a prescription to construct a simplified representation of the system in which only a subset of its constituent atoms is retained. As the specific choice of the mapping affects the analysis of all-atom simulations as well as the construction of coarse-grained models, the characterisation of the mapping space has recently attracted increasing attention. We here introduce a notion of scalar product and distance between reduced representations, which allows the study of the metric and topological properties of their space in a quantitative manner. Making use of a Wang-Landau enhanced sampling algorithm, we exhaustively explore such space, and examine the qualitative features of mappings in terms of their squared norm. A one-to-one correspondence with an interacting lattice gas on a finite volume leads to the emergence of discontinuous phase transitions in mapping space, which mark the boundaries between qualitatively different reduced representations of the same molecule.

Airborne Transmission of COVID-19: Aerosol Dispersion, Lung Deposition, and Virus-Receptor Interactions

Coronavirus disease 2019 (COVID-19), due to infection by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), is now causing a global pandemic. Aerosol transmission of COVID-19, although plausible, has not been confirmed by the World Health Organization (WHO) as a general transmission route. Considering the rapid spread of SARS-CoV-2, especially nosocomial outbreaks and other superspreading events, there is an urgent need to study the possibility of airborne transmission and its impact on the lung, the primary body organ attacked by the virus. Here, we review the complete pathway of airborne transmission of SARS-CoV-2 from aerosol dispersion in air to subsequent biological uptake after inhalation. In particular, we first review the aerodynamic and colloidal mechanisms by which aerosols disperse and transmit in air and deposit onto surfaces. We then review the fundamental mechanisms that govern regional deposition of micro- and nanoparticles in the lung. Focus is given to biophysical interactions between particles and the pulmonary surfactant film, the initial alveolar-capillary barrier and first-line host defense system against inhaled particles and pathogens. Finally, we summarize the current understanding about the structural dynamics of the SARS-CoV-2 spike protein and its interactions with receptors at the atomistic and molecular scales, primarily as revealed by molecular dynamics simulations. This review provides urgent and multidisciplinary knowledge toward understanding the airborne transmission of SARS-CoV-2 and its health impact on the respiratory system.

An Information-Theory-Based Approach for Optimal Model Reduction of Biomolecules

In theoretical modeling of a physical system, a crucial step consists of the identification of those degrees of freedom that enable a synthetic yet informative representation of it. While in some cases this selection can be carried out on the basis of intuition and experience, straightforward discrimination of the important features from the negligible ones is difficult for many complex systems, most notably heteropolymers and large biomolecules. We here present a thermodynamics-based theoretical framework to gauge the effectiveness of a given simplified representation by measuring its information content. We employ this method to identify those reduced descriptions of proteins, in terms of a subset of their atoms, that retain the largest amount of information from the original model; we show that these highly informative representations share common features that are intrinsically related to the biological properties of the proteins under examination, thereby establishing a bridge between protein structure, energetics, and function.

Machine learning for condensed matter physics

Condensed matter physics (CMP) seeks to understand the microscopic interactions of matter at the quantum and atomistic levels, and describes how these interactions result in both mesoscopic and macroscopic properties. CMP overlaps with many other important branches of science, such as chemistry, materials science, statistical physics, and high-performance computing. With the advancements in modern machine learning (ML) technology, a keen interest in applying these algorithms to further CMP research has created a compelling new area of research at the intersection of both fields. In this review, we aim to explore the main areas within CMP, which have successfully applied ML techniques to further research, such as the description and use of ML schemes for potential energy surfaces, the characterization of topological phases of matter in lattice systems, the prediction of phase transitions in off-lattice and atomistic simulations, the interpretation of ML theories with physics-inspired frameworks and the enhancement of simulation methods with ML algorithms. We also discuss in detail the main challenges and drawbacks of using ML methods on CMP problems, as well as some perspectives for future developments.

Targeted sequence design within the coarse-grained polymer genome

The chemical design of polymers with target structural and/or functional properties represents a grand challenge in materials science. While data-driven design approaches are promising, success with polymers has been limited, largely due to limitations in data availability. Here, we demonstrate the targeted sequence design of single-chain structure in polymers by combining coarse-grained modeling, machine learning, and model optimization. Nearly 2000 unique coarse-grained polymers are simulated to construct and analyze machine learning models. We find that deep neural networks inexpensively and reliably predict structural properties with limited sequence information as input. By coupling trained ML models with sequential model-based optimization, polymer sequences are proposed to exhibit globular, swollen, or rod-like behaviors, which are verified by explicit simulations. This work highlights the promising integration of coarse-grained modeling with data-driven design and represents a necessary and crucial step toward more complex polymer design efforts.

Exploring the landscape of model representations

The success of any physical model critically depends upon adopting an appropriate representation for the phenomenon of interest. Unfortunately, it remains generally challenging to identify the essential degrees of freedom or, equivalently, the proper order parameters for describing complex phenomena. Here we develop a statistical physics framework for exploring and quantitatively characterizing the space of order parameters for representing physical systems. Specifically, we examine the space of low-resolution representations that correspond to particle-based coarse-grained (CG) models for a simple microscopic model of protein fluctuations. We employ Monte Carlo (MC) methods to sample this space and determine the density of states for CG representations as a function of their ability to preserve the configurational information, I, and large-scale fluctuations, Q, of the microscopic model. These two metrics are uncorrelated in high-resolution representations but become anticorrelated at lower resolutions. Moreover, our MC simulations suggest an emergent length scale for coarse-graining proteins, as well as a qualitative distinction between good and bad representations of proteins. Finally, we relate our work to recent approaches for clustering graphs and detecting communities in networks.

Graph neural network based coarse-grained mapping prediction

The selection of coarse-grained (CG) mapping operators is a critical step for CG molecular dynamics (MD) simulation. It is still an open question about what is optimal for this choice and there is a need for theory. The current state-of-the art method is mapping operators manually selected by experts. In this work, we demonstrate an automated approach by viewing this problem as supervised learning where we seek to reproduce the mapping operators produced by experts. We present a graph neural network based CG mapping predictor called Deep Supervised Graph Partitioning Model (DSGPM) that treats mapping operators as a graph segmentation problem. DSGPM is trained on a novel dataset, Human-annotated Mappings (HAM), consisting of 1180 molecules with expert annotated mapping operators. HAM can be used to facilitate further research in this area. Our model uses a novel metric learning objective to produce high-quality atomic features that are used in spectral clustering. The results show that the DSGPM outperforms state-of-the-art methods in the field of graph segmentation. Finally, we find that predicted CG mapping operators indeed result in good CG MD models when used in simulation.

We propose a scalable graph neural network-based method for automating coarse-grained mapping prediction for molecules.

Evidence of information limitations in coarse-grained models

Developing accurate coarse-grained (CG) models is critical for addressing long time and length scale phenomena with molecular simulations. Here, we distinguish and quantify two sources of error that are relevant to CG models in order to guide further methods development: "representability" errors, which result from the finite basis associated with the chosen functional form of the CG model and mapping operator, and "information" errors, which result from the limited kind and quantity of data supplied to the CG parameterization algorithm. We have performed a systematic investigation of these errors by generating all possible CG models of three liquids (butane, 1-butanol, and 1,3-propanediol) that conserve a set of chemically motivated locality and topology relationships. In turn, standard algorithms (iterative Boltzmann inversion, IBI, and multiscale coarse-graining, MSCG) were used to parameterize the models and the CG predictions were compared with atomistic results. For off-target properties, we observe a strong correlation between the accuracy and the resolution of the CG model, which suggests that the approximations represented by MSCG and IBI deteriorate with decreasing resolution. Conversely, on-target properties exhibit an extremely weak resolution dependence that suggests a limited role of representability errors in model accuracy. Taken together, these results suggest that simple CG models are capable of utilizing more information than is provided by standard parameterization algorithms, and that model accuracy can be improved by algorithm development rather than resorting to more complicated CG models.

Is preservation of symmetry necessary for coarse-graining?

This work investigates if preserving the symmetry of the underlying molecular graph of a given molecule when choosing a coarse-grained (CG) mapping significantly affects the CG model accuracy.

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.

Investigating the origin of high efficiency in confined multienzyme catalysis

Biomimetic strategies have successfully been applied to confine multiple enzymes on scaffolds to obtain higher catalytic efficiency of enzyme cascades than freely distributed enzymes. However, the origin of high efficiency is poorly understood. We developed a coarse-grained, particle-based model to understand the origin of high efficiency. We found that a reaction intermediate is the key in affecting reaction kinetics. In the case of unstable intermediates, the confinement of multiple enzymes in clusters enhanced the catalytic efficiency and a shorter distance between enzymes resulted in a higher reaction rate and yield. This understanding was verified by co-encapsulating multiple enzymes in metal-organic framework (MOF) nanocrystals as artificially confined multienzyme complexes. The activity enhancement of multiple enzymes in MOFs depended on the distance between enzymes, when the decay of intermediates existed. The finding of this study is useful for designing in vitro synthetic biology systems based on artificial multienzyme complexes.

Relative entropy indicates an ideal concentration for structure-based coarse graining of binary mixtures

Many methodological approaches have been proposed to improve systematic or bottom-up coarse-graining techniques to enhance the representability and transferability of the derived interaction potentials. Transferability describes the ability of a coarse-grained (CG) model to be predictive, i.e., to describe a system at state points different from those chosen for parametrization. Whereas the representability characterizes the accuracy of a CG model to reproduce target properties of the underlying reference or fine-grained model at a given state point. In this article, we shift the focus away from methodological aspects and rather raise the question whether we can overcome the disadvantages of a given method in terms of representability and transferability by systematically selecting the state point at which the CG model gets parametrized. We answer this question by applying the inverse Monte Carlo (IMC) approach-a structure-based coarse-graining method-to derive effective interactions for binary mixtures of simple Lennard-Jones (LJ) particles, which are different in size. For such simple systems we indeed can identify a concentration where the derived potentials show the best performance in terms of structural representability and transferability. This specific concentration is identified by computing the relative entropy which quantifies the information loss between different IMC models and the reference LJ model at varying mixture compositions. Further, we show that an IMC model for mixtures of n-hexane and n-perfluorohexane shows the same trend in transferability as the IMC models for the LJ system. All derived models are more transferable in the direction of increasing concentration of the larger-sized compound.

Electronic structure at coarse-grained resolutions from supervised machine learning

Computational studies aimed at understanding conformationally dependent electronic structure in soft materials require a combination of classical and quantum-mechanical simulations, for which the sampling of conformational space can be particularly demanding. Coarse-grained (CG) models provide a means of accessing relevant time scales, but CG configurations must be back-mapped into atomistic representations to perform quantum-chemical calculations, which is computationally intensive and inconsistent with the spatial resolution of the CG models. A machine learning approach, denoted as artificial neural network electronic coarse graining (ANN-ECG), is presented here in which the conformationally dependent electronic structure of a molecule is mapped directly to CG pseudo-atom configurations. By averaging over decimated degrees of freedom, ANN-ECG accelerates simulations by eliminating backmapping and repeated quantum-chemical calculations. The approach is accurate, consistent with the CG spatial resolution, and can be used to identify computationally optimal CG resolutions.