  Within the nucleus, structural maintenance of chromosome protein complexes,
namely condensin and cohesin, create an architecture to facilitate the
organization and proper function of the genome. Condensin, in addition to
performing loop extrusion, creates 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.
