An accurate model for macroscale disordered assemblies of biological macromolecules such as those formed in so-called membraneless organelles would greatly assist in studying their structure, function, and dynamics. Recent evidence has suggested that liquid–liquid phase separation (LLPS) underlies the formation of membraneless organelles. While the general mechanism of exchange of macromolecule/water for macromolecule/macromolecule interactions is known to be the driving force for LLPS, the specific interactions involved are not well understood. One way that protein–water and protein–protein interactions have been understood historically is via hydrophobicity scales. However, these scales are typically optimized for describing these relative interactions in certain cases, such as protein folding or insertion of proteins into membranes. To better describe the relative interactions of proteins that undergo LLPS, we have developed a new, data-driven hydrophobicity scale. To determine the new scale, we used coarse-grained molecular dynamics simulations using the hydrophobicity scale coarse-grained model, which relates the interactions between amino acids to their hydrophobicity. Hydrophobicity values were determined via the force-balance method on a library of proteins that includes unfolded, intrinsically disordered, and phase-separating proteins (PSP). The resulting hydrophobicity scale can better predict whether a given protein will undergo LLPS at physiological conditions by using coarse-grained molecular dynamics simulations than existing hydrophobicity scales. This new scale confirms the importance of π–π interactions between amino acids as important drivers of LLPS. This new hydrophobicity scale provides a convenient and compact description of protein–protein interactions for proteins that undergo LLPS and could be used to develop new models to describe interactions between PSP and other components, such as nucleic acids.

Order parameters (i.e., collective variables) are often used to describe the behavior of systems as they capture different features of the free energy surface. Yet, most coarse-grained (CG) models only employ two- or three-body non-bonded interactions between the CG particles. In situations where these interactions are insufficient for the CG model to reproduce the structural distributions of the underlying fine-grained (FG) model, additional interactions must be included. In this paper, we introduce an approach to expand the basis sets available in the multiscale coarse-graining (MS-CG) methodology by including order parameters. Then, we investigate the ability of an additive local order parameter (e.g., density) and an additive global order parameter (i.e., distance from a hard wall) to improve the description of CG models in interfacial systems. Specifically, we study methanol liquid-vapor coexistence, acetonitrile liquid-vapor coexistence, and acetonitrile liquid confined by hard-wall plates, all using single site CG models. We find that the use of order parameters dramatically improves the reproduction of structural properties of interfacial CG systems relative to the FG reference as compared with pairwise CG interactions alone.

To extract meaningful data from molecular simulations, it is necessary to incorporate new experimental observations as they become available. Recently, a new method was developed for incorporating experimental observations into molecular simulations, called experiment directed simulation (EDS), which utilizes a maximum entropy argument to bias an existing model to agree with experimental observations while changing the original model by a minimal amount. However, there is no discussion in the literature of whether or not the minimal bias systematically and generally improves the model by creating agreement with the experiment. In this work, we show that the relative entropy of the biased system with respect to an ideal target is always reduced by the application of a minimal bias, such as the one utilized by EDS. Using all-atom simulations that have been biased with EDS, one can then easily and rapidly improve a bottom-up multiscale coarse-grained (MS-CG) model without the need for a time-consuming reparametrization of the underlying atomistic force field. Furthermore, the improvement given by the many-body interactions introduced by the EDS bias can be maintained after being projected down to effective twobody MS-CG interactions. The result of this analysis is a new paradigm in coarse-grained modeling and simulation in which the "bottom-up" and "top-down" approaches are combined within a single, rigorous formalism based on statistical mechanics. The utility of building the resulting EDS-MS-CG models is demonstrated on two molecular systems: liquid methanol and ethylene carbonate.