Loop statistics and fountain geometry reveal effective two-sided cohesin extrusion and crowding-induced arm desynchronization

Cohesin-driven loop extrusion shapes chromosome organization, yet what determines loop lengths and coordination between the extruding arms in vivo remains unclear. Broad extrusion "fountains" in Hi-C maps point to arm desynchronization, whose physical origin is unknown. Here we develop a kinetic theory of extrusion through transient chromatin roadblocks and neighbouring cohesins. Roadblock abundance, lifetime and partial permeability, together with cohesin crowding, combine into an effective obstacle density that renormalizes processivity and sets the mean loop length. Full loop-length distributions reveal extrusion symmetry: one-sided extrusion remains exponential, whereas effectively two-sided extrusion can generate a finite-length peak. ChIA-PET and MNase HiChIP data match the two-sided predictions, disfavouring purely one-sided extrusion. Cohesin crowding further desynchronizes the arms while leaving a residual correlation approaching {rho}=1/4. Fountain anisotropy across three vertebrates yields correlations near this value, consistent with local cohesin crowding as a sufficient mechanism for fountain formation. Fits further reveal 30-100-kb cohesin-loading regions and, in Danio rerio, a loading width comparable to the extent of enhancer enrichment, motivating a model in which an enhancer-rich loading platform acts as a collective barrier sustaining outward extrusion toward surrounding promoters. Our framework shows how cohesin and roadblock kinetics jointly determine loop statistics, shape chromosome-contact patterns, and may facilitate enhancer-promoter search.