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PRC1 (Polycomb repressive complex 1) plays a significant role in cellular differentiation and development by repressing lineage-inappropriate genes. PRC1 proteins phase separate to form Polycomb condensates (bodies) that are multi-component hubs for silencing Polycomb target genes; however, the molecular principles that underpin the condensate assembly and biophysical properties remain unknown. Here, by using biochemical reconstitution, cellular imaging, and multiscale molecular simulations, we show that PRC1 condensates are assembled via a scaffold-client liquid-liquid phase separation (LLPS) model by which Chromobox 2 (CBX2) is the scaffold and other subunits of the CBX2-PRC1 complex act as clients. The clients induce a reentrant phase transition of CBX2 condensates in a concentration-dependent manner. The composition of the multi-component, heterotypic LLPS systems directs the assembly and biophysical properties of CBX2-PRC1 condensates and selectively promotes the formation of CBX4-PRC1 condensates, but specifically dissolves condensates of CBX6-, CBX7-, and CBX8-PRC1. Additionally, the composition of CBX2-PRC1 condensates controls the enrichment of CBX4-, CBX7-, and CBX8-PRC1 into condensates but the exclusion of CBX6-PRC1 from condensates. Our results show the composition- and stoichiometry-dependent scaffold-client assembly of multi-component PRC1 condensates and supply a conceptual framework underlying the molecular basis and dynamics of Polycomb condensate assembly.

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Markov state models (MSMs) have become one of the most important techniques for understanding biomolecular transitions from classical molecular dynamics (MD) simulations. MSMs provide a systematized way of accessing the long time kinetics of the system of interest from the short-time scale microscopic transitions observed in simulation trajectories. At the same time, they provide a consistent description of the equilibrium and dynamical properties of the system of interest, and they are ideally suited for comparisons against experiment. A few software packages exist for building MSMs, which have been widely adopted. Here we introduce MasterMSM, a new Python package that uses the master equation formulation of MSMs and provides a number of new algorithms for building and analyzing these models. We demonstrate some of the most distinctive features of the package, including the estimation of rates, definition of core-sets for transition based assignment of states, the estimation of committors and fluxes, and the sensitivity analysis of the emerging networks. The package is available at .