Coarse-grained conformational surface hopping: Methodology and transferability

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.

Statistical Mechanical Design Principles for Coarse-Grained Interactions across Different Conformational Free Energy Surfaces

Systematic bottom-up coarse-graining (CG) of molecular systems provides a means to explore different coupled length and time scales while treating the molecular-scale physics at a reduced level. However, the configuration dependence of CG interactions often results in CG models with limited applicability for exploring the parametrized configurations. We propose a statistical mechanical theory to design CG interactions across different configurations and conditions. In order to span wide ranges of conformational space, distinct classical CG free energy surfaces for characteristic configurations are identified using molecular collective variables. The coupling interaction between different CG free energy surfaces can then be systematically determined by analogy to quantum mechanical approaches describing coupled states. The present theory can accurately capture the underlying many-body potentials of mean force in the CG variables for various order parameters applied to liquids, interfaces, and in principle proteins, uncovering the complex nature underlying the coupling interaction and imparting a new protocol for the design of predictive multiscale models.

Enhancing pressure consistency and transferability of structure-based coarse-graining

Coarse-graining, which models molecules with coarse-grained (CG) beads, allows molecular dynamics simulations to be applied to systems with large length and time scales while preserving the essential molecular structure. However, CG models generally have insufficient representability and transferability. A commonly used method to resolve this problem is multi-state iterative Boltzmann inversion (MS-IBI) with pressure correction, which matches both the structural properties and pressures at different thermodynamic states between CG and all-atom (AA) simulations. Nevertheless, this method is usually effective only in a narrow pressure range. In this paper, we propose a modified CG scheme to overcome this limitation. We find that the fundamental reason for this limitation is that CG beads at close distances are ellipsoids rather than isotropically compressed spheres, as described in conventional CG models. Hence, we propose a method to compensate for such differences by slightly modifying the radial distribution functions (RDFs) derived from AA simulations and using the modified RDFs as references for pressure-corrected MS-IBI. We also propose a method to determine the initial non-bonded potential using both the target RDF and pressure. Using n-dodecane as a case study, we demonstrate that the CG model developed using our scheme reproduces the RDFs and pressures over a wide range of pressure states, including three reference low-pressure states and two test high-pressure states. The proposed scheme allows for accurate CG simulations of systems in which pressure or density varies with time and/or position.

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.

Broad chemical transferability in structure-based coarse-graining

Compared to top-down coarse-grained (CG) models, bottom-up approaches are capable of offering higher structural fidelity. This fidelity results from the tight link to a higher-resolution reference, making the CG model chemically specific. Unfortunately, chemical specificity can be at odds with compound-screening strategies, which call for transferable parametrizations. Here we present an approach to reconcile bottom-up, structure-preserving CG models with chemical transferability. We consider the bottom-up CG parametrization of 3,441 C7O2 small-molecule isomers. Our approach combines atomic representations, unsupervised learning, and a large-scale extended-ensemble force-matching parametrization. We first identify a subset of 19 representative molecules, which maximally encode the local environment of all gas-phase conformers. Reference interactions between the 19 representative molecules were obtained from both homogeneous bulk liquids and various binary mixtures. An extended-ensemble parametrization over all 703 state points leads to a CG model that is both structure-based and chemically transferable. Remarkably, the resulting force field is on average more structurally accurate than single-state-point equivalents. Averaging over the extended ensemble acts as a mean-force regularizer, smoothing out both force and structural correlations that are overly specific to a single state point. Our approach aims at transferability through a set of CG bead types that can be used to easily construct new molecules, while retaining the benefits of a structure-based parametrization.

A microcanonical approach to temperature-transferable coarse-grained models using the relative entropy

Bottom-up coarse-graining methods provide systematic tools for creating simplified models of molecular systems. However, coarse-grained (CG) models produced with such methods frequently fail to accurately reproduce all thermodynamic properties of the reference atomistic systems they seek to model and, moreover, can fail in even more significant ways when used at thermodynamic state points different from the reference conditions. These related problems of representability and transferability limit the usefulness of CG models, especially those of strongly state-dependent systems. In this work, we present a new strategy for creating temperature-transferable CG models using a single reference system and temperature. The approach is based on two complementary concepts. First, we switch to a microcanonical basis for formulating CG models, focusing on effective entropy functions rather than energy functions. This allows CG models to naturally represent information about underlying atomistic energy fluctuations, which would otherwise be lost. Such information not only reproduces energy distributions of the reference model but also successfully predicts the correct temperature dependence of the CG interactions, enabling temperature transferability. Second, we show that relative entropy minimization provides a direct and systematic approach to parameterize such classes of temperature-transferable CG models. We calibrate the approach initially using idealized model systems and then demonstrate its ability to create temperature-transferable CG models for several complex molecular liquids.

Conservative Potentials for a Lattice-Mapped Coarse-Grained Scheme

The conservative potential, arising from a coarse-grain (CG) mapping scheme for nonbonded atomistic particles, is studied. This is a bottom-up approach from first-principles that maps atomistic particles to fluid element-like subcells whose centers lie on a regular, cubic lattice. Unlike standard CG mapping schemes, the current one uses dynamic labeling which on-the-fly changes the CG labels of the particles. The subcells can also be different sizes and shapes, in principle. Equilibrium atomistic molecular dynamics trajectories for different Lennard-Jones fluids are calculated and converted to CG ones, from which CG probability distribution functions are calculated. Correlation studies show position and mass CG variables are uncoupled in a given subcell, as are different vector components of position. Furthermore, the strongest coupling occurs with neighboring cells in specific directions, and the resulting distribution is well described by a multivariate Gaussian. This implies the CG potential has a generalized quadratic form, whose derivative can be determined analytically. A microscopic rationalization is provided for the signs and relative magnitudes of different correlation coefficients, and in some cases, a connection is made with bulk properties of the fluid. We argue the generalized quadratic form should be robust to changes in the particulars of the CG scheme, as well as the nature of the atomistic intermolecular potential. Only a few potential parameters need to be calculated from the underlying atomistic system. This is significant because it indicates the transferability of this form to other, more complex systems. This transferability will be tested in future work, where mapping schemes with fuzzy boundaries will be considered.

Dynamical properties across different coarse-grained models for ionic liquids

Room-temperature ionic liquids (RTILs) stand out among molecular liquids for their rich physicochemical characteristics, including structural and dynamic heterogeneity. The significance of electrostatic interactions in RTILs results in long characteristic length- and timescales, and has motivated the development of a number of coarse-grained (CG) simulation models. In this study, we aim to better understand the connection between certain CG parameterization strategies and the dynamical properties and transferability of the resulting models. We systematically compare five CG models: a model largely parameterized from experimental thermodynamic observables; a refinement of this model to increase its structural accuracy; and three models that reproduce a given set of structural distribution functions by construction, with varying intramolecular parameterizations and reference temperatures. All five CG models display limited structural transferability over temperature, and also result in various effective dynamical speedup factors, relative to a reference atomistic model. On the other hand, the structure-based CG models tend to result in more consistent cation-anion relative diffusion than the thermodynamic-based models, for a single thermodynamic state point. By linking short- and long-timescale dynamical behaviors, we demonstrate that the varying dynamical properties of the different CG models can be largely collapsed onto a single curve, which provides evidence for a route to constructing dynamically-consistent CG models of RTILs.

Investigating the energetic and entropic components of effective potentials across a glass transition

By eliminating unnecessary details, coarse-grained (CG) models provide the necessary efficiency for simulating scales that are inaccessible to higher resolution models. However, because they average over atomic details, the effective potentials governing CG degrees of freedom necessarily incorporate significant entropic contributions, which limit their transferability and complicate the treatment of thermodynamic properties. This work employs a dual-potential approach to consider the energetic and entropic contributions to effective interaction potentials for CG models. Specifically, we consider one- and three-site CG models for ortho-terphenyl (OTP) both above and below its glass transition. We employ the multiscale coarse-graining (MS-CG) variational principle to determine interaction potentials that accurately reproduce the structural properties of an all-atom (AA) model for OTP at each state point. We employ an energy-matching variational principle to determine an energy operator that accurately reproduces the intra- and inter-molecular energy of the AA model. While the MS-CG pair potentials are almost purely repulsive, the corresponding pair energy functions feature a pronounced minima that corresponds to contacting benzene rings. These energetic functions then determine an estimate for the entropic component of the MS-CG interaction potentials. These entropic functions accurately predict the MS-CG pair potentials across a wide range of liquid state points at constant density. Moreover, the entropic functions also predict pair potentials that quite accurately model the AA pair structure below the glass transition. Thus, the dual-potential approach appears a promising approach for modeling AA energetics, as well as for predicting the temperature-dependence of CG effective potentials.