Topology Regulation during Replication of the Kinetoplast DNA

We study theoretically the replication of Kinetoplast DNA consisting of several thousands separate mini-circles found in organisms of the class Kinetoplastida. When the cell is not actively dividing these are topologically connected in a marginally linked network of rings with only one connected component. During cell division each mini-circle is removed from the network, duplicated and then re-attached, along with its progeny. We study this process under the hypothesis that there is a coupling between the topological state of the mini-circles and the expression of genetic information encoded on them, leading to the production of Topoisomerase. This model describes a self-regulating system capable of full replication that reproduces several previous experimental findings. We find that the fixed point of the system depends on a primary free parameter of the model: the ratio between the rate of removal of mini-circles from the network (R) and their (re)attachment rate (A). The final topological state is found to be that of a marginally linked network structure in which the fraction of mini-circles linked to the largest connected component approaches unity as R/A decreases. Finally we discuss how this may suggest an evolutionary trade-off between the speed of replication and the accuracy with which a fully topologically linked state is produced.