Different relative scalings between transient forces and thermal fluctuations tune regimes of chromatin organization

Within the nucleus, structural maintenance of chromosome (SMC) protein complexes, namely condensin and cohesin, create an architecture to facilitate the organization and proper function of the genome.These SMC proteins are capable of creating localized clusters of chromatin in the nucleolus through transient crosslinks. Large-scale simulations revealed three different dynamic behaviors as a function of timescale: slow crosslinking leads to no clusters, fast crosslinking produces rigid slowly changing clusters, while intermediate timescales produce flexible clusters that mediate gene interaction. By mathematically analyzing different relative scalings of the two sources of stochasticity, thermal fluctuations and the force induced by the transient crosslinks, we predict these three distinct regimes of cluster behavior.Standard time-averaging that takes the fluctuations of the transient crosslink force to zero predicts the existence of rigid clusters. Accounting for the interaction of both fluctuations from the crosslinks and thermal noise with an effective energy landscape predicts the timescale-dependent lifetimes of flexible clusters. No clusters are predicted when the fluctuations of the transient crosslink force are taken to be large relative to thermal fluctuations. This mathematical perturbation analysis illuminates the importance of accounting for stochasticity in local incoherent transient forces to predict emergent complex biological behavior. The system is modeled by a general overdamped Langevin system with a driving force that switches according to a continuous-time Markov chain process. Though the system is always out of equilibrium and thus, does not obey a potential function, deriving a quasipotential can extend the field of energy landscape analysis to understand the stability and transitions of the system. In the flexible clustering regime, bead mixing is timescale-dependent. As the crosslinking rate increases, so too does the height of the effective energy barrier, indicating that the clusters are increasingly stable. In an effort to push this analysis to higher dimensions while circumventing the curse of dimensionality, machine learning methods are implemented to learn the quasipotential.