Theoretical modelling of liquid-liquid phase separation: from particle-based to field-based simulation.

Liquid-liquid phase separation (LLPS) has proved to be ubiquitous in living cells, forming membraneless organelles (MLOs) and dynamic condensations essential in physiological processes. However, some underlying mechanisms remain challenging to unravel experimentally, making theoretical modeling an indispensable aspect. Here we present a protocol for understanding LLPS from fundamental physics to detailed modeling procedures. The protocol involves a comprehensive physical picture on selecting suitable theoretical approaches, as well as how and what to interpret and resolve from the results. On the particle-based level, we elaborate on coarse-grained simulation procedures from building up models, identifying crucial interactions to running simulations to obtain phase diagrams and other concerned properties. We also outline field-based theories which give the system's density profile to determine phase diagrams and provide dynamic properties by studying the time evolution of density field, enabling us to characterize LLPS systems with larger time and length scales and to further include other nonequilibrium factors such as chemical reactions.