Accepted_test

Human chromosomes are 2-m-long polymers compacted into a 10-μm-sized cell nucleus. To fit in this volume and function, chromosomes are believed to be folded into loops by the process of loop extrusion, wherein molecular motors gradually grow loops by reeling in the polymer chain. While loop extrusion has been seen in single-molecule experiments, loops remain elusive to direct observations in living cells. The lack of a tractable physical model limits researchers’ ability to interpret experimental data. We introduce such a model and solve it analytically. We solve it for the contact probability statistics as well as for the spatial distance statistics. Our model reproduces universally observed shapes of the contact probability for different mammalian cells. Moreover, we reveal and describe a novel topological phenomenon, the "dilution of entanglements", taking place in a crumpled chain folded into short-scale unentangled loops. The fact that our model recapitulates key features of experimental data suggests a common physical principle of chromosome organization across different scales, from several kbp up to 1-2 Mbp (million of base pairs). Thus, our theoretical framework allows us to interpret experimental data and infer parameters of chromosome folding.