Cohesin distribution encodes chromatin 3D organization via conserved-current loop extrusion

Inhomogeneous patterns of enhanced DNA-DNA contacts at mesoscale of the genome are a generic feature of chromatin spatial organization. These features, termed topologically associating domains (TADs), have led to the loop extrusion factor (LEF) model, where TADs arise from loop extrusion by cohesin complexes. Currently, our ability to model TADs relies on the observation that in vertebrate the TAD boundaries are correlated with DNA sequence that binds CTCF, which therefore is inferred to block loop extrusion. However, although TADs feature prominently in their Hi-C maps, non-vertebrate organisms either do not express CTCF or show few TAD boundaries that correlate with CTCF sites. In all of these organisms, the counterpart of CTCF remains unknown, frustrating the comparisons between Hi-C data and simulation. To extend the LEF model across the tree of life, we propose the conserved-current loop extrusion (CCLE) model that interprets loop-extruding cohesin as a nearly-conserved probability current. By solely utilizing the cohesin ChIP-seq data, the CCLE model allows us to derive a position-dependent loop extrusion velocity and to simulate dynamic steady-state loop configurations. To demonstrate its utility across the tree of life, we apply the CCLE model to the Hi-C maps of S. pombe, S. cerevisiae, M. musculus, D. melanogaster, and C. elegans. In all cases, the model accurately predicts the TAD-scale Hi-C maps, suggesting that loop extrusion by cohesin is a highly-conserved mechanism underlying TADs.