Information-theoretic tools for parametrized coarse-graining of non-equilibrium extended systems

Maximum Entropy Theory of Multiscale Coarse-Graining via Matching Thermodynamic Forces: Application to a Molecular Crystal (TATB)

The MSCG/FM (multiscale coarse-graining via force-matching) approach is an efficient supervised machine learning method to develop microscopically informed coarse-grained (CG) models. We present a theory based on the principle of maximum entropy (PME) enveloping the existing MSCG/FM approaches. This theory views the MSCG/FM method as a special case of matching the thermodynamic forces from the extended ensemble described by the set of thermodynamic (relevant) system coordinates. This set may include CG coordinates, the stress tensor, applied external fields, and so forth, and may be characterized by nonequilibrium conditions. Following the presentation of the theory, we discuss the consistent matching of both bonded and nonbonded interactions. The proposed PME formulation is used as a starting point to extend the MSCG/FM method to the constant strain ensemble, which together with the explicit matching of the bonded forces is better suited for coarse-graining anisotropic media at a submolecular resolution. The theory is demonstrated by performing the fine coarse-graining of crystalline 1,3,5-triamino-2,4,6-trinitrobenzene (TATB), a well-known insensitive molecular energetic material, which exhibits highly anisotropic mechanical properties.

Mapping the configurational landscape and aggregation phase behavior of the tau protein fragment PHF6

The PHF6 (Val-Gln-Ile-Val-Tyr-Lys) motif, found in all isoforms of the microtubule-associated protein tau, forms an integral part of ordered cores of amyloid fibrils formed in tauopathies and is thought to play a fundamental role in tau aggregation. Because PHF6 as an isolated hexapeptide assembles into ordered fibrils on its own, it is investigated as a minimal model for insight into the initial stages of aggregation of larger tau fragments. Even for this small peptide, however, the large length and time scales associated with fibrillization pose challenges for simulation studies of its dynamic assembly, equilibrium configurational landscape, and phase behavior. Here, we develop an accurate, bottom-up coarse-grained model of PHF6 for large-scale simulations of its aggregation, which we use to uncover molecular interactions and thermodynamic driving forces governing its assembly. The model, not trained on any explicit information about fibrillar structure, predicts coexistence of formed fibrils with monomers in solution, and we calculate a putative equilibrium phase diagram in concentration-temperature space. We also characterize the configurational and free energetic landscape of PHF6 oligomers. Importantly, we demonstrate with a model of heparin that this widely studied cofactor enhances the aggregation propensity of PHF6 by ordering monomers during nucleation and remaining associated with growing fibrils, consistent with experimentally characterized heparin-tau interactions. Overall, this effort provides detailed molecular insight into PHF6 aggregation thermodynamics and pathways and, furthermore, demonstrates the potential of modern multiscale modeling techniques to produce predictive models of amyloidogenic peptides simultaneously capturing sequence-specific effects and emergent aggregate structures.

Simulating Polymerization by Boltzmann Inversion Force Field Approach and Dynamical Nonequilibrium Reactive Molecular Dynamics

The radical polymerization process of acrylate compounds is, nowadays, numerically investigated using classical force fields and reactive molecular dynamics, with the aim to probe the gel-point transition as a function of the initial radical concentration. In the present paper, the gel-point transition of the 1,6-hexanediol dimethacrylate (HDDMA) is investigated by a coarser force field which grants a reduction in the computational costs, thereby allowing the simulation of larger system sizes and smaller radical concentrations. Hence, the polymerization is investigated using reactive classical molecular dynamics combined with a dynamical approach of the nonequilibrium molecular dynamics (D-NEMD). The network structures in the polymerization process are probed by cluster analysis tools, and the results are critically compared with the similar all-atom system, showing a good agreement.

Recent Progress towards Chemically-Specific Coarse-Grained Simulation Models with Consistent Dynamical Properties

Coarse-grained (CG) models can provide computationally efficient and conceptually simple characterizations of soft matter systems. While generic models probe the underlying physics governing an entire family of free-energy landscapes, bottom-up CG models are systematically constructed from a higher-resolution model to retain a high level of chemical specificity. The removal of degrees of freedom from the system modifies the relationship between the relative time scales of distinct dynamical processes through both a loss of friction and a “smoothing” of the free-energy landscape. While these effects typically result in faster dynamics, decreasing the computational expense of the model, they also obscure the connection to the true dynamics of the system. The lack of consistent dynamics is a serious limitation for CG models, which not only prevents quantitatively accurate predictions of dynamical observables but can also lead to qualitatively incorrect descriptions of the characteristic dynamical processes. With many methods available for optimizing the structural and thermodynamic properties of chemically-specific CG models, recent years have seen a stark increase in investigations addressing the accurate description of dynamical properties generated from CG simulations. In this review, we present an overview of these efforts, ranging from bottom-up parameterizations of generalized Langevin equations to refinements of the CG force field based on a Markov state modeling framework. We aim to make connections between seemingly disparate approaches, while laying out some of the major challenges as well as potential directions for future efforts.

Theory of wavelet-based coarse-graining hierarchies for molecular dynamics

We present a multiresolution approach to compressing the degrees of freedom and potentials associated with molecular dynamics, such as the bond potentials. The approach suggests a systematic way to accelerate large-scale molecular simulations with more than two levels of coarse graining, particularly applications of polymeric materials. In particular, we derive explicit models for (arbitrarily large) linear (homo)polymers and iterative methods to compute large-scale wavelet decompositions from fragment solutions. This approach does not require explicit preparation of atomistic-to-coarse-grained mappings, but instead uses the theory of diffusion wavelets for graph Laplacians to develop system-specific mappings. Our methodology leads to a hierarchy of system-specific coarse-grained degrees of freedom that provides a conceptually clear and mathematically rigorous framework for modeling chemical systems at relevant model scales. The approach is capable of automatically generating as many coarse-grained model scales as necessary, that is, to go beyond the two scales in conventional coarse-grained strategies; furthermore, the wavelet-based coarse-grained models explicitly link time and length scales. Furthermore, a straightforward method for the reintroduction of omitted degrees of freedom is presented, which plays a major role in maintaining model fidelity in long-time simulations and in capturing emergent behaviors.

Big-deep-smart data in imaging for guiding materials design

Harnessing big data, deep data, and smart data from state-of-the-art imaging might accelerate the design and realization of advanced functional materials. Here we discuss new opportunities in materials design enabled by the availability of big data in imaging and data analytics approaches, including their limitations, in material systems of practical interest. We specifically focus on how these tools might help realize new discoveries in a timely manner. Such methodologies are particularly appropriate to explore in light of continued improvements in atomistic imaging, modelling and data analytics methods.

Construction of dissipative particle dynamics models for complex fluids via the Mori-Zwanzig formulation

We present a bottom-up coarse-graining procedure to construct mesoscopic force fields directly from microscopic dynamics. By grouping many bonded atoms in the molecular dynamics (MD) system into a single cluster, we compute both the conservative and non-conservative interactions between neighboring clusters. In particular, we perform MD simulations of polymer melts to provide microscopic trajectories for evaluating coarse-grained (CG) interactions. Subsequently, dissipative particle dynamics (DPD) is considered as the effective dynamics resulting from the Mori-Zwanzig (MZ) projection of the underlying atomistic dynamics. The forces between finite-size clusters have, in general, both radial and transverse components and hence we employ four different DPD models to account differently for such interactions. Quantitative comparisons between these DPD models indicate that the DPD models with MZ-guided force fields yield much better static and dynamics properties, which are consistent with the underlying MD system, compared to standard DPD with empirical formulae. When the rotational motion of the particle is properly taken into account, the entire velocity autocorrelation function of the MD system as well as the pair correlation function can be accurately reproduced by the MD-informed DPD model. Since this coarse-graining procedure is performed on an unconstrained MD system, our framework is general and can be used in other soft matter systems in which the clusters can be faithfully defined as CG particles.