Theoretical Methods for Assessing the Density of Protein Nanodroplets

Many intrinsically disordered proteins (IDPs) are known to undergo liquid-liquid phase separation (LLPS), which is a physical process that drives the formation of biomolecular condensates and membraneless organelles in biological cells. Molecular dynamics (MD) simulations provide valuable tools to explore both the molecular mechanisms of LLPS and the physical properties of biomolecular condensates. However, a direct comparison of MD simulation results with phase diagrams obtained experimentally is normally prevented not only by the high computational costs of simulating large biomacromolecular systems on sufficient timescales but also by conceptual challenges. Specifically, there currently seems to be no standard or unambiguous method of defining and determining volumes occupied by coexisting phases at the nanoscale, with typically no more than a few hundred biomacromolecules in the simulation box. The goal of this work is to fill in this gap in the methodology. Focusing on α-synuclein as a model IDP, we test and compare three methods for determining the molecular density of protein nanodroplets, or clusters, generated in MD simulations or using other molecular modeling approaches. Two of the methods are based on approximating nanodroplets with homogeneous spheres and ellipsoids, respectively. The third method, which is expected to yield the most physically accurate results, is based on the SPACEBALL algorithm, with optimized, cluster-specific radii for volume probes. Our results contribute to the construction of accurate phase diagrams on the basis of MD simulations of IDP systems.