Project Abstract Biomolecular condensates are emerging as central to cellular functions in a wide variety of con- texts. These condensates often have liquid properties and are assembled from multivalent, polymer-like molecules. Together, these observations suggest a disordered network of interactions stabilizing the condensate. Liquid systems are inherently disordered, which would seem to preclude the level of order necessary for structure-function properties to emerge. However, preliminary results have shown that, hidden within the liquid disorder, is a hierarchy of molecular assemblies that give structure to the uid. Furthermore, this structure within the contacts stabilizing the liquid confers crucial functional features to the condensates. This means that in order to understand how these condensates function, it is necessary to identify structure in disordered systems. This poses a challenge to the eld of structural biology because this hierarchical structure cannot be resolved by workhorse techniques like X-ray, NMR, and cryo-EM. The proposed research will establish methods to identify and characterize structure within liquid condensates. These methods are based on theoretical modeling using an iterative re nement procedure analogous to structure determination by NMR. This will be done in two systems that are each featured in a speci c aim. The rst system is a model system for phase separation that removes com- plications with identifying and quantifying interaction sites. In determining the microscopic structure of this \sticker and spacer" binding system, which is thought to be a common motif in liquid conden- sates, this aim will establish basic principles of how molecular structure can dictate spatial organization on lengthscales ranging from the recruitment molecular clients to organelle segregation/colocalization. The second aim will develop the structural modeling techniques on the nucleolus. This nuclear organelle serves as the assembly site for ribosomes. The proposed research will use in vitro phase separation data to understand the primary molecular interactions within the granular component (GC) where rRNAs and protein assemble into ribosomal subunits. The interactions in the GC are primarily electrostatic, which is di erent than the sticker and spacer motif that is the focus of Aim 1. Next, these interactions will be used to build a kinetic theory of ribosome subunit assembly. This model will establish how the molecular structure of GC components facilitates ribosome assembly. The theories for generated in both aims will be analytic, meaning that they will allow for a thorough exploration of parameter space and can be readily applied to other systems.