Quantification of surface tension effects and nucleation-and-growth rates during self-assembly of biological condensates

Liquid-solid and liquid-liquid phase separation (PS) drives the formation of functional and disease-associated biological assemblies. Principles of phase equilibrium are here employed to derive a general kinetic solution that predicts the evolution of the mass and size of biological assemblies. Thermodynamically, protein PS is determined by two measurable concentration limits: the saturation concentration and the critical solubility. Due to surface tension effects, the critical solubility can be higher than the saturation concentration for small, curved nuclei. Kinetically, PS is characterized by the primary nucleation rate constant and a combined rate constant accounting for growth and secondary nucleation. It is demonstrated that the formation of a few number of large condensates is possible without active mechanisms of size control and in the absence of coalescence phenomena. Our exact analytical solution can be used to interrogate how the elementary steps of PS are affected by candidate drugs.