Entropic Competition between Supercoiled and Torsionally Relaxed Chromatin Fibers Drives Loop Extrusion through Pseudo-Topologically Bound Cohesin.

We propose a model for cohesin-mediated loop extrusion, where the loop extrusion is driven entropically by the energy difference between supercoiled and torsionally relaxed chromatin fibers. Different levels of negative supercoiling are controlled by varying imposed friction between the cohesin ring and the chromatin fiber. The speed of generation of negative supercoiling by RNA polymerase associated with TOP1 is kept constant and corresponds to 10 rotations per second. The model was tested by coarse-grained molecular simulations for a wide range of frictions between 2 to 200 folds of that of generic fiber and the surrounding medium. The higher friction allowed for the accumulation of higher levels of supercoiling, while the resulting extrusion rate also increased. The obtained extrusion rates for the given range of investigated frictions were between 1 and 10 kbps, but also a saturation of the rate at high frictions was observed. The calculated contact maps indicate a qualitative improvement obtained at lower levels of supercoiling. The fits of mathematical equations qualitatively reproduce the loop sizes and levels of supercoiling obtained from simulations and support the proposed mechanism of entropically driven extrusion. The cohesin ring is bound on the fibers pseudo-topologically, and the model suggests that the topological binding is not necessary.