Multivalency-dependent DNA compaction in bridging-induced condensates

Structural maintenance of chromosome complexes, particularly cohesin, plays a pivotal role in bridging DNA and mediating phase separation, which is crucial for chromosome organization. Despite recent studies on bridging-induced phase separation (BIPS), questions remain about the optimal number of protein binding sites required for efficient condensate formation. In this study, we employ coarse-grained molecular dynamics simulations to investigate the organization of topologically constrained DNA systems. We specifically focus on the mesoscale coupling between DNA supercoiling and protein-mediated BIPS, a mechanism fundamental to DNA compaction in environments where torsional stress is strictly conserved. By utilizing a circular DNA model to ensure topological integrity, our study serves as a generalized biophysical representation of both naturally circular genomic elements and locally anchored or torsionally restricted chromatin domains, providing insights into the universal physical principles governing multivalent protein–DNA assemblies. We compare four valency states (bi-, tri-, tetra-, and no-patch) using three DNA lengths (800, 1200, and 1600 beads) and incrementally applied supercoiling stress. The simulations demonstrate that tri-patch systems achieve the maximum compaction efficiency and structural integrity, with proteins exhibiting the best performance when three binding sites are present. Tetra-patch systems show similar compaction but exhibit geometric frustration and increased asphericity. The study provides a quantitative framework for designing synthetic chromosome organizers and advancing applications in artificial chromosome packaging and protein condensate therapeutics.