Coarse-Graining with Equivariant Neural Networks: A Path Toward Accurate and Data-Efficient Models.

Machine learning has recently entered into the mainstream of coarse-grained (CG) molecular modeling and simulation. While a variety of methods for incorporating deep learning into these models exist, many of them involve training neural networks to act directly as the CG force field. This has several benefits of which the most significant is accuracy. Neural networks can inherently incorporate multibody effects during the calculation of CG forces, and a well-trained neural network force field outperforms pairwise basis sets generated from essentially any methodology. However, this comes at a significant cost. First, these models are typically slower than pairwise force fields, even when accounting for specialized hardware, which accelerates the training and integration of such networks. The second and the focus of this paper is the need for a considerable amount of data to train such force fields. It is common to use 10s of microseconds of molecular dynamics data to train a single CG model, which approaches the point of eliminating the CG model's usefulness in the first place. As we investigate in this work, this "data-hunger" trap from neural networks for predicting molecular energies and forces can be remediated in part by incorporating equivariant convolutional operations. We demonstrate that, for CG water, networks that incorporate equivariant convolutional operations can produce functional models using data sets as small as a single frame of reference data, while networks without these operations cannot.

OpenMSCG: A Software Tool for Bottom-Up Coarse-Graining.

The "bottom-up" approach to coarse-graining, for building accurate and efficient computational models to simulate large-scale and complex phenomena and processes, is an important approach in computational chemistry, biophysics, and materials science. As one example, the Multiscale Coarse-Graining (MS-CG) approach to developing CG models can be rigorously derived using statistical mechanics applied to fine-grained, i.e., all-atom simulation data for a given system. Under a number of circumstances, a systematic procedure, such as MS-CG modeling, is particularly valuable. Here, we present the development of the OpenMSCG software, a modularized open-source software that provides a collection of successful and widely applied bottom-up CG methods, including Boltzmann Inversion (BI), Force-Matching (FM), Ultra-Coarse-Graining (UCG), Relative Entropy Minimization (REM), Essential Dynamics Coarse-Graining (EDCG), and Heterogeneous Elastic Network Modeling (HeteroENM). OpenMSCG is a high-performance and comprehensive toolset that can be used to derive CG models from large-scale fine-grained simulation data in file formats from common molecular dynamics (MD) software packages, such as GROMACS, LAMMPS, and NAMD. OpenMSCG is modularized in the Python programming framework, which allows users to create and customize modeling "recipes" for reproducible results, thus greatly improving the reliability, reproducibility, and sharing of bottom-up CG models and their applications.

Utilizing Machine Learning to Greatly Expand the Range and Accuracy of Bottom-Up Coarse-Grained Models through Virtual Particles.

Coarse-grained (CG) models parametrized using atomistic reference data, i.e., "bottom up" CG models, have proven useful in the study of biomolecules and other soft matter. However, the construction of highly accurate, low resolution CG models of biomolecules remains challenging. We demonstrate in this work how virtual particles, CG sites with no atomistic correspondence, can be incorporated into CG models within the context of relative entropy minimization (REM) as latent variables. The methodology presented, variational derivative relative entropy minimization (VD-REM), enables optimization of virtual particle interactions through a gradient descent algorithm aided by machine learning. We apply this methodology to the challenging case of a solvent-free CG model of a 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) lipid bilayer and demonstrate that introduction of virtual particles captures solvent-mediated behavior and higher-order correlations which REM alone cannot capture in a more standard CG model based only on the mapping of collections of atoms to the CG sites.

Centroid Molecular Dynamics Can Be Greatly Accelerated through Neural Network Learned Centroid Forces Derived from Path Integral Molecular Dynamics.

For nearly the past 30 years, centroid molecular dynamics (CMD) has proven to be a viable classical-like phase space formulation for the calculation of quantum dynamical properties. However, calculation of the centroid effective force remains a significant computational cost and limits the ability of CMD to be an efficient approach to study condensed phase quantum dynamics. In this paper, we introduce a neural network-based methodology for first learning the centroid effective force from path integral molecular dynamics data, which is subsequently used as an effective force field to evolve the centroids directly with the CMD algorithm. This method, called machine-learned centroid molecular dynamics (ML-CMD), is faster and far less costly than both standard "on the fly" CMD and ring polymer molecular dynamics (RPMD). The training aspect of ML-CMD is also straightforwardly implemented utilizing the DeepMD software kit. ML-CMD is then applied to two model systems to illustrate the approach: liquid para-hydrogen and water. The results show comparable accuracy to both CMD and RPMD in the estimation of quantum dynamical properties, including the self-diffusion constant and velocity time correlation function, but with significantly reduced overall computational cost.

MRP.py: A Parametrizer of Post-Translationally Modified Residues.

MRP.py is a Python-based parametrization program for covalently modified amino acid residues for molecular dynamics simulations. Charge derivation is performed via an RESP charge fit, and force constants are obtained through rewriting of either protein or GAFF database parameters. This allows for the description of interfacial interactions between the modifed residue and protein. MRP.py is capable of working with a variety of protein databases. MRP.py's highly general and systematic method of obtaining parameters allows the user to circumvent the process of parametrizing the modified residue-protein interface. Two examples, a covalently bound inhibitor and covalent adduct consisting of modified residues, are provided in the Supporting Information.