Using multicanonical Monte Carlo simulations to investigate the effect of polymer sequence on interfacial surface tension in a phase-separated system

Abstract

MLOs, droplets of proteins and/or nucleic acids which form by liquid-liquid phase separation (LLPS), have been the subject of substantial interest since their discovery. Given their inherent ability to respond dynamically to the needs of the cell, considerable work has gone into investigating the factors which regulate and promote their assembly and disassembly. Surface tension is a fundamental physical property of all phase-separated liquids, and its magnitude has ramifications for their characteristics; study of surface tension may therefore yield mechanistic insights into the behavior of MLOs. Of particular interest is the effect of protein sequence on surface tension in phase-separated systems. The last few years have been a ‘golden age’ for investigation of the relationship between polymer sequence and phase separation, although the bulk of this research focuses on nonspecific intermolecular interactions, including electrostatics and -stacking. Moreover, little attention has been paid to the specific role of sequence, if any, in determining surface tension. This may be explained by the absence of any straightforward method of measuring interfacial surface tension in vitro. However, in silico simulations of phase separation have been successfully used to extrapolate surface tension in model systems for more than three decades. We propose a novel computational technique to measure the variance of surface tension with polymer sequence using histogram reweighting of on-lattice multicanonical Monte Carlo simulations with finite-size scaling. We represent sequence variation using a coarse-grained model of multi-domain polymers containing two motifs capable of both nonspecific intermolecular and specific, saturating intramolecular interactions, and extrapolate surface tension values from successive simulations of their phase separation at decreasing temperature. We find that surface tension and polymer sequence are related, and that polymers with larger domain sizes have lower surface tension values and phase separate more readily. We posit that this may be due to their limited conformational entropy and inability to readily self-bond. Our findings suggest that sequence relevance to surface tension and phase separation extends beyond nonspecific interactions, such as electrostatics and -stacking, to include the readiness of polymers to specifically self-bond. This is an encouraging result, but further investigation using other simulation techniques or, where possible, in vitro approaches, is warranted.