Different relative scalings between transient forces and thermal fluctuations tune regimes of dynamic clustering

An example system of collective behavior in the presence of active agents is the structural maintenance of chromosome (SMC) protein complexes within the nucleus that create an architecture to facilitate the organization and proper function of the genome. Of the diverse functions these SMC proteins are capable of producing, we focus on the creation of localized clusters of chromatin in the nucleolus through transient cross-links. Large-scale simulations revealed three different dynamic behaviors as a function of timescale: slow cross-linking leads to no clusters, fast cross-linking 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 cross-links, we predict these three distinct regimes of cluster behavior. Standard time averaging that takes the fluctuations of the transient cross-link force to zero predicts the existence of rigid clusters. Accounting for the interaction of both fluctuations from the cross-links 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 cross-link 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.