Loop extrusion with dynamic barriers explains genome folding for long-lived cohesin mutants*

Loop extrusion performed by molecular motors is a universal mechanism governing genome folding across various cell types and organisms. In this process, a loop extrusion complex binds to DNA, and processively enlarges DNA loops until it dissociates. In mammalian interphase cells, extrusion is performed by the cohesin complex limited by CTCF-mediated boundaries at specific genomic locations. Strong evidence for loop extrusion comes from chromosome conformation capture techniques (e.g. Hi-C), which use high-throughput sequencing to generate genome-wide contact maps. Extrusion manifests in distinct features of contact maps at intermediate scales (kb-mb), including domains with peaks at their corners. While existing polymer physics models successfully reproduce certain features of contact maps, they do not account for recent observations of CTCF binding dynamics. Motivated by these findings, we propose a model where boundary elements dynamically switch between bound and unbound states, with rates parametrized from recent biophysical data. Using this model, we investigated how the characteristics of boundary elements impact features observable in experimental genomic and imaging datasets, including ChIPseq, Hi-C, and immunofluorescence microscopy. Our analysis highlights the importance of multiple timescales. Beyond the occupancy of the boundary elements, their average binding lifetime relative to the average cohesin binding lifetime is a pivotal factor. At a fixed occupancy, the ratio of boundary lifetime to extruder lifetime greatly alters simulated ChIPseq and simulated Hi-C. Our simulations suggest that CTCF clusters may thus be crucial for reconciling experimentally-observed rapid CTCF binding dynamics. Importantly, when time spent in the bound state becomes very high, the dynamic barrier model transitions to a stalling regime, with similar behavior to models that do not account for CTCF dynamics. Collectively, our biophysical model identifies a specific range of CTCF binding and unbinding times which are consistent with experimental observations from ChIP-Seq measurements and Hi-C data. More generally, we illustrate how the integration of dynamic biophysical measurements into genomics models will sharpen our understanding of genome regulation.