Kinetics of chromosome condensation in the presence of topoisomerases: a phantom chain model.

We discuss the requirement of type II DNA topoisomerase in the process of mitotic chromosome condensation. Using a known model describing the collapse of homopolymers, we propose that the compaction process necessitates a change in the topological state (i.e., a self-knotting) of the chromosomal chain. We argue that the enzymes are necessary to reach the compact metaphase state in a time interval that is much smaller than the time expected in the uncatalyzed process. The folding process is such that the potential entanglement points are localized at particular regions of the chromosome known as the scaffold-associated regions. The concentration of entanglements in the metaphase chromosome is related to the average size of the radial loops. A phantom chain model for the condensation process, in which each potential entanglement point is dealt with by a topoisomerase II molecule, is proposed.