Theoretical and computational methods of protein liquid-liquid phase separation

Liquid-liquid phase separation (LLPS) of proteins is an emerging field in the research of biophysics. Many intrinsically disordered proteins (IDPs) are known to have the ability to assemble via LLPS and to organize into protein-rich and dilute phases both in vivo and in vitro. Such a kind of phase separation of proteins plays an important role in a wide range of cellular processes, such as the formation of membraneless organelles (MLOs), signaling transduction, intracellular organization, chromatin organization, etc. In recent years, there appeared a great number of theoretical analysis, computational simulation and experimental research focusing on the physical principles of LLPS. In this article, the theoretical and computational simulation methods for the LLPS are briefly reviewed. To elucidate the physical principle of LLPS and to understand the phase behaviors of the proteins, biophysicists have introduced the concepts and theories from statistical mechanics and polymer sciences. Flory-Huggins theory and its extensions, such as mean-field model, random phase approximation (RPA) and field theory simulations, can conduce to understanding the phase diagram of the LLPS. To reveal the hidden principles in the sequence-dependent phase behaviors of different biomolecular condensates, different simulation methods including lattice models, off-lattice coarse-grained models, and all-atom simulations are introduced to perform computer simulations. By reducing the conformational space of the proteins, lattice models can capture the key points in LLPS and simplify the computations. In the off-lattice models, a polypeptide can be coarse-grained as connected particles representing repeated short peptide fragments. All-atom simulations can describe the structure of proteins at a higher resolution but consume higher computation-power. Multi-scale simulation may provide the key to understanding LLPS at both high computational efficiency and high accuracy. With these methods, we can elucidate the sequence-dependent phase behaviors of proteins at different resolutions. To sum up, it is necessary to choose the appropriate method to model LLPS processes according to the interactions within the molecules and the specific phase behaviors of the system. The simulations of LLPS can facilitate the comprehensive understanding of the key features which regulate the membraneless compartmentalization in cell biology and shed light on the design of artificial cells and the control of neurodegeneration.