Liquid-Liquid Phase Separation of HP Lattice Proteins: A Finite-Size Scaling Analysis

Abstract: Biomolecular condensates are dense droplets of proteins and nucleic acids inside living cells that form through a liquid-liquid phase separation (LLPS) process, in which intrinsically disordered proteins (IDPs) often play an important role. Furthermore, it has been shown that several of these IDPs can form similar droplets on their own. Understanding the forces driving the LLPS of IDPs, and how the process depends on the amino acid sequence, is a challenging task. One difficulty is that the systems amenable to computational modelling are limited in size. It is therefore important to analyse and understand how simulated properties depend on the system size. A finite-size scaling theory for droplet formation through phase separation exists. This thesis explores the usefulness of this theory in the study of biomolecular LLPS, using a minimal lattice-based hydrophobic-polar (HP) protein model. By Monte Carlo methods, computer simulations of two HP sequences of length 10 are conducted for a range of system sizes, with up to 640 chains. A finite-size scaling analysis of the simulation results reveals that only one of the two sequences undergoes LLPS. Furthermore, it is found that the temperature at which droplet formation sets in converges slowly to its value for infinite system size. Hence, finite-size scaling analysis is useful both in deciding the phase behaviour of the sequences and in determing the underlying phase diagram.