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.