Theory of chromosome structural dynamics by processive loop extrusion

The processivity of Structural Maintenance of Chromosome complexes defines the characteristic run length and lifetime of loop extrusion events, which set up the large-scale architecture of chromosomes. We introduce an active, non-Markovian mechanistic model that explicitly incorporates motor processivity to provide a statistical mechanical treatment that identifies the nontrivial effects induced by the processive character of such active motors. At low activity, in interphase, processive loop extrusion generates effective cooperative multibody interactions, which lead to the so-called "chromatin jets." Upon increasing activity, symmetry breaking occurs, as seen in the characteristic, cylindrically anisotropic mitotic chromosome organization. The strength of the motor processivity determines whether the symmetry breaking transition leads to crystalline ordering or to liquid-crystalline architectures for the mitotic chromosome.