Condensation dynamics of sticky and anchored flexible biopolymers

Cells regulate gene expression in part by forming DNA-protein condensates in the nucleus. While existing theories describe the equilibrium size and stability of such condensates, their dynamics remain less understood. Here, we use coarse-grained 3D Brownian-dynamics simulations to study how long, end-anchored biopolymers condense over time due to transient crosslinking. By tracking how clusters nucleate, merge, and disappear, we identify two dominant dynamical pathways, ripening and merging, that govern the progression from an uncompacted chain to a single condensate. We show how microscopic kinetic parameters, protein density, and mechanical constraints shape these pathways. Using insights from the simulations, we construct a minimal mechanistic free-energy model that captures the observed scaling behavior. Together, these results clarify the dynamical determinants of DNA and chromatin reorganization on timescales relevant to gene regulation.