Fig. 3: A hierarchy of interaction strengths between PCH, nucleoli and protein(s) with dual affinities for both PCH and nucleoli recapitulates +rDNA and −rDNA in vivo organization.
a, Schematic of the spatial organization of three immiscible phases using nucleoplasm (N), PCH (H) and the nucleolus (No) as an example. The balance of the interfacial tensions (γij) between each pair of phases (γH–N, γNo–N and γH–No) determines their equilibrium configuration. The spreading coefficient, Si (top right), is determined from these interfacial tensions. Phases with higher interfacial tension relative to the nucleoplasm form the inner layers, whereas those with lower interfacial tension form outwards to minimize the total surface free energy. PCH organizes around the nucleolus in vivo, implying γNo–N > γH–N. Thus, the possible combinations of Si predict the configuration of the three phases, ranging from complete engulfing to partial engulfing to no engulfing. This framework motivated the development of our coarse-grained model for PCH–nucleolar organization. b, Coarse-grained modelling of PCH–nucleolar assembly with four minimal components: PCH (H) as a self-interacting polymer, rDNA (rD) as polymeric block embedded in PCH, Fib (F) representative of a self-associating nucleolar protein and a self-associating protein X with dual affinity to Fib and PCH representing those enriched in the PCH void in −rDNA nuclei. c,d, The matrices indicate the pairwise interaction strengths, \({\epsilon }_{{ij}}\) (blue gradient, units: \({k}_{{\rm{B}}}T\)), where i and j can represent F, rD, H or X. The indicated affinity hierarchies result in simulated outcomes that recapitulate the in vivo organization in +rDNA (c) and −rDNA (d). Snapshots of the corresponding simulation results are shown below each interaction matrix. e, Distance \(({d}_{{\rm{H}}{\rm{F}}})\) between the centres of mass of PCH and Fib clusters in +rDNA and −rDNA simulations. In the presence of rDNA, the distance between PCH and Fib is small, corresponding to the simulation snapshot in c (purple profile). In the absence of rDNA–Fib interactions, PCH and Fib are farther apart (no engulfing), corresponding to the simulation snapshot in d (green profile).
