Influence of active loop extrusion on the statistics of triple contacts in the model of interphase chromosomes

The statistics of triple contacts between the regions of an interphase chromosome in the presence of an active loop extrusion mechanism is theoretically studied. When modeling chromatin as an ideal polymer chain with quenched disorder of random loops, an expression for the conditional probability of contact between two chain regions in the presence of an additional contact with a third region is obtained in the one-loop approximation. The analysis of the expression shows that the loop extrusion mechanism breaks scale invariance and makes an ideal chain non-Markovian and non-Gaussian, suggesting ways to extract the characteristics of loop extrusion from experimental data concerning the frequencies of multiple contacts in interphase chromosomes. In addition, the results of the work demonstrate limitations of the widespread Gaussian polymer models as regards the reproduction of some features of the conformation statistics of chromosomes.