Kinetic signature of cooperativity in the irreversible collapse of a polymer

We investigate the kinetics of a polymer collapse due to the formation of irreversible crosslinks between its monomers. Using the contact probability $P(s)$ as a scale-dependent order parameter depending on the chemical distance $s$, our simulations show the emergence of a cooperative pearling instability. Namely, the polymer undergoes a sharp conformational transition to a set of absorbing states characterized by a length scale $\xi$ corresponding to the mean pearl size. This length and the transition time depend on the polymer equilibrium dynamics and the crosslinking rate. We confirm experimentally this transition using a DNA conformation capture experiment in yeast.