A universal polymer signature in Hi-C resolves cohesin loop density and supports monomeric extrusion

The genome is folded by molecular motors, yet how many motors are required to generate a single chromatin loop has remained unknown. In vertebrates, cohesin extrudes loops along interphase chromosomes, but the linear density of these loops-and therefore the stoichiometry of extrusion-has not been directly measurable in living cells. A fundamental challenge is that Hi-C contact maps, the primary experimental probe of genome organization, are shaped not only by chromatin folding but also by the physics and biochemistry of contact detection itself. Here, we develop an analytical polymer theory of short-scale chromosome folding that explicitly incorporates the steps of Hi-C detection protocol. The theory predicts a characteristic dip in the logarithmic derivative of the contact probability, arising from the interplay between cohesin-mediated looping and contact capture. This dip is a universal feature of Hi-C data and provides a direct, protocol-aware readout of loop density. Applying the theory to human and mouse datasets reveals a conserved density of approximately six loops per megabase. Independent measurements of chromatin-bound cohesin quantitatively match this value, providing strong evidence that loop extrusion in vivo is predominantly mediated by single cohesin motors.