Effective thermal equilibrium induced by crosslinking proteins in polymer chromosome model

Biological systems under the influence of microscale active agents such as proteins are frequently modeled using switching forces as the agents shift between different states, pushing the system out of equilibirium. For example, protein action plays a crucial role in the organization of the DNA inside the cell nucleus, modeled by a bead-spring polymer, in the form of stochastic crosslinking. Despite these rapidly switching forces causing a constant state of disequilibrium, we observed in numerical simulations long-lived stable condensed clusters of beads consistent with experimental results, with the stochastic switching rate acting like an effective temperature. Rapid switching produced low-temperature-like stable clusters, slow switching produced high-temperature-like amorphic arrangements, and intermediate switching times allowed for dynamic clusters with beads exchanging between clusters. To explain the mechanism behind this emergent clustering behavior, we derive an effective thermal equilibrium that captures both the average force and fluctuations induced by the stochastically switching force, accurately predicting the mean transition time between stable configurations.