Universal contact statistics of looped polymers resolve cohesin density and stoichiometry in vivo

Cohesin organizes mammalian chromosomes by extruding DNA loops, but whether this process involves single cohesin complexes or paired "dimers" in vivo has remained controversial. Here, we identify a universal physical signature of cohesin loop density in Hi-C contact statistics at short genomic separations. In this regime, contact statistics simplify dramatically and loops can be treated as static, enabling an analytically solvable equilibrium polymer theory for a looped chain with finite contact detection. The theory predicts a characteristic dip in the slope of the contact probability curve that depends only on two parameters: cohesin loop density and the contact capture radius determined by the experimental protocol. Applying this framework to diverse mammalian Hi-C datasets, we infer a conserved loop density of approximately six loops per megabase. Independent cohesin copy-number measurements from quantitative imaging and mass spectrometry match this value, indicating that loop extrusion is predominantly monomeric in vivo, although rare or transient higher-order assemblies cannot be excluded. More broadly, this framework integrates Hi-C, imaging, and biochemical measurements within a single physical model, providing new mechanistic insight into how motor proteins organize chromatin in vivo. Significance StatementHow many cohesin complexes are required to extrude a chromatin loop in living cells remains a central question in genome biology. We develop a polymer-physics framework that links short-range Hi-C features to the density of cohesin-mediated loops in vivo. The theory explains a characteristic contact signature that depends solely on loop density. Applying this readout across mammalian datasets, we infer [~] sixloops per megabase in interphase chromatin, implying that [~] 60 - 70% of the genome is folded within cohesin-mediated loops. Independent imaging and biochemical measurements yield comparable values, supporting a predominantly monomeric mode of loop extrusion in vivo while not excluding rare or transient dimeric events. By bridging polymer physics with genome-wide contact maps, this framework provides a quantitative route to dissect how motor proteins organize chromosomes.