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.

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 for significantly reduced overall computational cost. e.g., to better treat heterogenous systems, rare events, etc, will also provide clear benefit to the ML-CMD approach developed in this work.

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.