Generalized-Yvon-Born-Green Model of Toluene

Transferable Force Fields from Experimental Scattering Data with Machine Learning Assisted Structure Refinement

Deriving transferable pair potentials from experimental neutron and X-ray scattering measurements has been a longstanding challenge in condensed matter physics. State-of-the-art scattering analysis techniques estimate real-space microstructure from reciprocal-space total scattering data by refining pair potentials to obtain agreement between simulated and experimental results. Prior attempts to apply these potentials with molecular simulations have revealed inaccurate predictions of thermodynamic fluid properties. In this Letter, a machine learning assisted structure-inversion method applied to neutron scattering patterns of the noble gases (Ne, Ar, Kr, and Xe) is shown to recover transferable pair potentials that accurately reproduce both microstructure and vapor-liquid equilibria from the triple to critical point. Therefore, it is concluded that a single neutron scattering measurement is sufficient to predict macroscopic thermodynamic properties over a wide range of states and provide novel insight into local atomic forces in dense monatomic systems.

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.

A new one-site coarse-grained model for water: Bottom-up many-body projected water (BUMPer). I. General theory and model

Water is undoubtedly one of the most important molecules for a variety of chemical and physical systems, and constructing precise yet effective coarse-grained (CG) water models has been a high priority for computer simulations. To recapitulate important local correlations in the CG water model, explicit higher-order interactions are often included. However, the advantages of coarse-graining may then be offset by the larger computational cost in the model parameterization and simulation execution. To leverage both the computational efficiency of the CG simulation and the inclusion of higher-order interactions, we propose a new statistical mechanical theory that effectively projects many-body interactions onto pairwise basis sets. The many-body projection theory presented in this work shares similar physics from liquid state theory, providing an efficient approach to account for higher-order interactions within the reduced model. We apply this theory to project the widely used Stillinger-Weber three-body interaction onto a pairwise (two-body) interaction for water. Based on the projected interaction with the correct long-range behavior, we denote the new CG water model as the Bottom-Up Many-Body Projected Water (BUMPer) model, where the resultant CG interaction corresponds to a prior model, the iteratively force-matched model. Unlike other pairwise CG models, BUMPer provides high-fidelity recapitulation of pair correlation functions and three-body distributions, as well as N-body correlation functions. BUMPer extensively improves upon the existing bottom-up CG water models by extending the accuracy and applicability of such models while maintaining a reduced computational cost.

Direct route to reproducing pair distribution functions with coarse-grained models via transformed atomistic cross correlations

Coarse-grained (CG) models are often parameterized to reproduce one-dimensional structural correlation functions of an atomically detailed model along the degrees of freedom governing each interaction potential. While cross correlations between these degrees of freedom inform the optimal set of interaction parameters, the correlations generated from the higher-resolution simulations are often too complex to act as an accurate proxy for the CG correlations. Instead, the most popular methods determine the interaction parameters iteratively while assuming that individual interactions are uncorrelated. While these iterative methods have been validated for a wide range of systems, they also have disadvantages when parameterizing models for multicomponent systems or when refining previously established models to better reproduce particular structural features. In this work, we propose two distinct approaches for the direct (i.e., noniterative) parameterization of a CG model by adjusting the high-resolution cross correlations of an atomistic model in order to more accurately reflect correlations that will be generated by the resulting CG model. The derived models more accurately describe the low-order structural features of the underlying AA model while necessarily generating inherently distinct cross correlations compared with the atomically detailed reference model. We demonstrate the proposed methods for a one-site-per-molecule representation of liquid water, where pairwise interactions are incapable of reproducing the true tetrahedral solvation structure. We then investigate the precise role that distinct cross-correlation features play in determining the correct pair correlation functions, evaluating the importance of the placement of correlation features as well as the balance between features appearing in different solvation shells.

Accurate Structure-Based Coarse Graining Leads to Consistent Barrier-Crossing Dynamics

Structure-based coarse graining of molecular systems offers a systematic route to reproduce the many-body potential of mean force. Unfortunately, common strategies are inherently limited by the molecular mechanics force field employed. Here, we extend the concept of multisurface dynamics, initially developed to describe electronic transitions in chemical reactions, to accurately sample the conformational ensemble of a classical system in equilibrium. In analogy to describing different electronic configurations, a surface-hopping scheme couples distinct conformational basins beyond the additivity of the Hamiltonian. The incorporation of more surfaces leads systematically toward improved cross-correlations. The resulting models naturally achieve consistent long-time dynamics for systems governed by barrier-crossing events.

Investigation of coarse-grained mappings via an iterative generalized Yvon-Born-Green method

Low resolution coarse-grained (CG) models enable highly efficient simulations of complex systems. The interactions in CG models are often iteratively refined over multiple simulations until they reproduce the one-dimensional (1-D) distribution functions, e.g., radial distribution functions (rdfs), of an all-atom (AA) model. In contrast, the multiscale coarse-graining (MS-CG) method employs a generalized Yvon-Born-Green (g-YBG) relation to determine CG potentials directly (i.e., without iteration) from the correlations observed for the AA model. However, MS-CG models do not necessarily reproduce the 1-D distribution functions of the AA model. Consequently, recent studies have incorporated the g-YBG equation into iterative methods for more accurately reproducing AA rdfs. In this work, we consider a theoretical framework for an iterative g-YBG method. We numerically demonstrate that the method robustly determines accurate models for both hexane and also a more complex molecule, 3-hexylthiophene. By examining the MS-CG and iterative g-YBG models for several distinct CG representations of both molecules, we investigate the approximations of the MS-CG method and their sensitivity to the CG mapping. More generally, we explicitly demonstrate that CG models often reproduce 1-D distribution functions of AA models at the expense of distorting the cross-correlations between the corresponding degrees of freedom. In particular, CG models that accurately reproduce intramolecular 1-D distribution functions may still provide a poor description of the molecular conformations sampled by the AA model. We demonstrate a simple and predictive analysis for determining CG mappings that promote an accurate description of these molecular conformations.

Perspective: Coarse-grained models for biomolecular systems

By focusing on essential features, while averaging over less important details, coarse-grained (CG) models provide significant computational and conceptual advantages with respect to more detailed models. Consequently, despite dramatic advances in computational methodologies and resources, CG models enjoy surging popularity and are becoming increasingly equal partners to atomically detailed models. This perspective surveys the rapidly developing landscape of CG models for biomolecular systems. In particular, this review seeks to provide a balanced, coherent, and unified presentation of several distinct approaches for developing CG models, including top-down, network-based, native-centric, knowledge-based, and bottom-up modeling strategies. The review summarizes their basic philosophies, theoretical foundations, typical applications, and recent developments. Additionally, the review identifies fundamental inter-relationships among the diverse approaches and discusses outstanding challenges in the field. When carefully applied and assessed, current CG models provide highly efficient means for investigating the biological consequences of basic physicochemical principles. Moreover, rigorous bottom-up approaches hold great promise for further improving the accuracy and scope of CG models for biomolecular systems.

RNA 3D structure prediction by using a coarse-grained model and experimental data

RNAs form complex secondary and three-dimensional structures, and their biological functions highly rely on their structures and dynamics. Here we developed a general coarse-grained framework for RNA 3D structure prediction. A new, hybrid coarse-grained model that explicitly describes the electrostatics and hydrogen-bond interactions has been constructed based on experimental structural statistics. With the simulated annealing simulation protocol, several RNAs of less than 30-nt were folded to within 4.0 Å of the native structures. In addition, with limited restraints on Watson-Crick basepairing based on the data from NMR spectroscopy and small-angle X-ray scattering (SAXS) information, the current model was able to characterize the complex tertiary structures of large size RNAs, such as 5S ribosome and U2/U6 snRNA. We also demonstrated that the pseudoknot structure was better captured when the coordinating Mg(2+) cations and limited basepairing restraints were included. The accuracy of our model has been compared favorably with other RNA structure prediction methods presented in the previous study of RNA-Puzzles. Therefore the coarse-grained model presented here offers a unique approach for accurate prediction and modeling of RNA structures.

Coarse-graining entropy, forces, and structures

Coarse-grained (CG) models enable highly efficient simulations of complex processes that cannot be effectively studied with more detailed models. CG models are often parameterized using either force- or structure-motivated approaches. The present work investigates parallels between these seemingly divergent approaches by examining the relative entropy and multiscale coarse-graining (MS-CG) methods. We demonstrate that both approaches can be expressed in terms of an information function that discriminates between the ensembles generated by atomistic and CG models. While it is well known that the relative entropy approach minimizes the average of this information function, the present work demonstrates that the MS-CG method minimizes the average of its gradient squared. We generalize previous results by establishing conditions for the uniqueness of structure-based potentials and identify similarities with corresponding conditions for the uniqueness of MS-CG potentials. We analyze the mapping entropy and extend the MS-CG and generalized-Yvon-Born-Green formalisms for more complex potentials. Finally, we present numerical calculations that highlight similarities and differences between structure- and force-based approaches. We demonstrate that both methods obtain identical results, not only for a complete basis set, but also for an incomplete harmonic basis set in Cartesian coordinates. However, the two methods differ when the incomplete basis set includes higher order polynomials of Cartesian coordinates or is expressed as functions of curvilinear coordinates.

Coarse-grain model of the benzene ring with para-substituents in the molecule

A new two-site coarse-grain model of the benzene ring with substituents in the para-position is proposed for use with multiscale simulations. The model uses a modified Lennard-Jones potential and introduces an additional shifting parameter to the description of the atom-atom interactions. Furthermore, the model separates sets of parameters of Van-der-Waals interactions into inter- and intramolecular. The shifting parameter is specified separately for each pair of atom types for both inter- and intramolecular interactions. The model itself consists of two superatoms. It allows for high speed calculations, "remembers" the benzene ring orientation in multiscale simulations, and can be used together with well-known sets of "united atoms" potentials. This model was tested on p-xylene, 1-ethyl-4-methylbenzene, and 1-methyl-4-propylbenzene. Structural properties for all three substances in the full-atomic model, the "united atoms" model, and the suggested coarse-grained model are discussed. The results demonstrate that the local structure derived from the coarse-grained model is very similar to that derived from the "united atoms" model.