A Fast Method for Computing Chemical Potentials and Phase Equilibria of Macromolecular Mixtures

Abstract

Chemical potential is a fundamental property for determining thermodynamic equilibria involving exchanges of molecules, such as between two phases of molecular systems. Previously we developed the FMAP method for calculating excess chemical potentials according to Widom insertion [1, 2]. Intermolecular interaction energies were expressed as correlation times and evaluated via fast Fourier transform. Here we extend this method to calculate phase equilibria. Chemical potentials are calculated by FMAP at a wide range of molecular densities and the boundary between low- and high-density phases is identified by the Maxwell equal-area rule. When benchmarked on a Lennard-Jones fluid, our method produces an accurate phase diagram at 10% of the computational cost of the present best method. Importantly, the gain in computational speed increases dramatically as the molecules become more complex, potentially reaching many orders of magnitude in speedup for atomistically represented proteins [2]. Our method thus opens the door to accurate determination of phase equilibria for macromolecular mixtures. Of particular interest are protein-protein mixtures and protein-RNA mixtures that involve poly-valent interactions. These mixtures are known to undergo a liquid-liquid phase separation, both in vitro and in vivo. Our phase calculations for these systems will lead to much need physical understanding of the liquid-liquid phase separation and how it is used for many biological functions. 1. Qin, S., Zhou, H. X. J. Chem. Theory Comput. 2013, 9, 4633−4643. 2. Qin, S., Zhou, H. X. J. Chem. Theory Comput. 2014, 10, 2824-2835.