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. Examples include molecular motors, crosslinked biopolymer networks, and transient antibody crosslinking of antigens to mucus protein networks. Protein action also 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. These rapidly switching forces are on timescales faster than the time to reach thermal equilibrium, thus the system is in a constant state of disequilibrium. However, we observed 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 seek an effective thermal equilibrium that captures both the average force and fluctuations induced by the stochastically switching force. I will discuss the WBK-like method for defining the effective or quasi potential and the numerical challenges in solving for it.