J Am Chem Soc. 2019 Dec 17.
Biomolecular condensates are emerging as an important organizational principle within living cells. These condensed states are formed by phase separation, yet little is known about how material properties are encoded within the constituent molecules and how the specificity for being in different phases is established. Here we use analytic theory to explain the phase behavior of the cancer-related protein SPOP and its substrate DAXX. Binary mixtures of these molecules have a phase diagram that contains dilute liquid, dense liquid, and gel states. We show that these discrete phases appear due to a competition between SPOP-DAXX and DAXX-DAXX interactions. The stronger SPOP-DAXX interactions dominate at sub-stoichiometric DAXX concentrations leading to the formation of crosslinked gels. The theory shows that the driving force for gel formation is not the binding energy, but rather the entropy of distributing DAXX molecules on the binding sites. At high DAXX concentrations the SPOP-DAXX interactions saturate, which leads to the dissolution of the gel and the appearance of a liquid phase driven by weaker DAXX-DAXX interactions. This competition between interactions allows multiple dense phases to form in a narrow region of parameter space. We propose that the molecular architecture of phase-separating proteins governs the internal structure of dense phases, their material properties and their functions. Analytical theory can reveal these properties on the long length and time scales relevant to biomolecular condensates.