Valency-driven division of labor balances chromatin compaction and structural plasticity

Chromatin folding is regulated by multivalent protein complexes and condensates, yet how the multivalent binding quantitatively controls chromatin compaction, domain organization, and cell-to-cell heterogeneity remains unresolved. Here we develop the Chromatin-associated Protein Complex Maximum Entropy Model (CPC-MEM), a data-driven, physics-based polymer framework in which Hi-C contacts are realized through an explicit, finite pool of diffusing chromatin-associated protein complexes (CPCs) with prescribed CPC-chromatin interaction valency. When fitted to Hi-C, CPC-MEM generates chromatin structural ensembles that simultaneously reproduce population-averaged contact maps and single-cell super-resolution distance statistics. We uncover a clear division of labor across valency: low-valency CPCs act as abundant linkers that compact chromatin, homogenize folding, and refine local structure, whereas high-valency CPCs form sparse co-bridging hubs that nucleate chromatin domains and increase conformational heterogeneity. Mixtures of valencies naturally produce a "hub-and-matrix" chromatin architecture that optimally balances compaction with structural plasticity. Our study provides a quantitative mechanism by which locus-specific chromatin interaction preferences, together with the valency and abundance of CPCs and condensates in the nucleus, jointly shape functional 3D genome organization.