Short-scale analytical theory shows cohesin actively extrudes loops as a single motor
Dmitry Starkov (Skoltech, Moscow)
Cohesin-dependent loop extrusion is a key active mechanism of DNA organization, yet it remains unclear whether chromatin loops in living cells are generated primarily by individual cohesin motors or by higher-order structures. To fill this major gap, we build an analytical, protocol-aware polymer-physics model that extracts a missing parameter – the linear density of loops – directly from Hi-C data. We focus on short genomic distances, where contact statistics simplify and chromatin can be described as an ideal polymer folded by quenched disorder of cohesin-mediated loops. In this regime, the Hi-C signal is governed by the interplay between loop-induced polymer compaction and a finite-resolution contact-detection process, which can be described by an effective Gaussian detection kernel. This results in a perturbative expression for the contact probability of a looped chain under a finite contact-detection radius. Our theory recapitulates a characteristic dip in the logarithmic derivative of the contact probability that is broadly observed in experiments. By fitting this minimal model to a diverse range of mammalian Hi-C datasets, we infer approximately six loops per megabase. Independent imaging and mass spectrometry measurements of cohesin density are consistent with our inferred loop density, supporting the monomeric mode of cohesin-mediated DNA loop extrusion.