The physical chemistry of interphase loop extrusion

Loop extrusion constitutes a universal mechanism of genome organization, whereby structural maintenance of chromosomes (SMC) protein complexes load onto the chromatin fiber and generate DNA loops of increasingly-larger sizes until their eventual release. In mammalian interphase cells, loop extrusion is mediated by the cohesin complex, which is dynamically regulated by the interchange of multiple accessory proteins. Although these regulators bind the core cohesin complex only transiently, their disruption can dramatically alter cohesin dynamics, gene expression, chromosome morphology and contact patterns. Still, a theory of how cohesin regulators and their molecular interplay with the core complex modulate genome folding remains at large. Here we derive a model of cohesin loop extrusion from first principles, based on in vivo measurements of the abundance and dynamics of cohesin regulators. We systematically evaluate potential chemical reaction networks that describe the association of cohesin with its regulators and with the chromatin fiber. Remarkably, experimental observations are consistent with only a single biochemical reaction cycle, which results in a unique minimal model that may be fully parameterized by quantitative protein measurements. We demonstrate how distinct roles for cohesin regulators emerge simply from the structure of the reaction network, and how their dynamic exchange can regulate loop extrusion kinetics over time-scales that far exceed their own chromatin residence times. By embedding our cohesin biochemical reaction network within biophysical chromatin simulations, we evidence how variations in regulatory protein abundance can alter chromatin architecture across multiple length- and time-scales. Predictions from our model are corroborated by biophysical and biochemical assays, optical microscopy observations, and Hi-C conformation capture techniques. More broadly, our theoretical and numerical framework bridges the gap between in vitro observations of extrusion motor dynamics at the molecular scale and their structural consequences at the genome-wide level.