  Many experiments show that protein condensates formed by liquid-liquid phase
separation exhibit aging rheological properties. Quantitatively, recent
experiments by Jawerth et al. (Science 370, 1317, 2020) show that protein
condensates behave as aging Maxwell fluids with an increasing relaxation time
as the condensates age. Despite the universality of this aging phenomenon, a
theoretical understanding of this aging behavior is lacking. In this work, we
propose a mesoscopic model of protein condensates in which a phase transition
from aging phase to non-aging phase occurs as the control parameter changes,
such as temperature. The model predicts that protein condensates behave as
viscoelastic Maxwell fluids at all ages, with the macroscopic viscosity
increasing over time. The model also predicts that protein condensates are
non-Newtonian fluids under a constant shear rate with the shear stress
increasing over time. Our model successfully explains multiple existing
experimental observations and also makes general predictions that are
experimentally testable.
