Extended Data Fig. 7. The force-dependent step size of cohesin loop extrusion does not solely explain the observed force dependence of CTCF blocking loop extrusion.
a, Magnetic tweezers setup to observe individual loop extrusion steps by human cohesin, depending on the applied force, based on48. The change in bead height Δz corresponds to steps by cohesin. b, Example magnet tweezer trace showing stepwise changes in bead height in the presence of cohesin, NIPBL-MAU2 and ATP. Line denotes steps fitted using the step-finding algorithm. c, Step sizes in nanometres as measured by Magnetic Tweezer experiments, for various applied forces ranging from 0.1 pN to 1 pN. The horizontal line is the median; boxes extend to the quartiles and the whiskers show the range of the data (median-1.5* interquartile range (IQR); median+1.5*IQR). N = 100, 128, 168, 116, 148, 338, 270 from left to right from 2 independent experiments. d, Step sizes versus force from (c), but converted to base pairs. The median, quartiles and data range are shown as described in (c). e, Simulation setup: starting from a randomly chosen binding position along DNA, cohesin takes steps along DNA, which are sampled from the measured step size distribution. An ‘encounter’ is considered if cohesin comes within 50 bp of CTCF. Under the lenient assumption that the CTCF N-terminus is unstructured and may be approximated by a freely jointed chain, its radius of gyration RG is estimated using the NK = 268 amino acids from the N-terminus to zinc finger 126, with a contour length of lK ~0.4 nm per amino acid66, resulting in RG = NklK2/6 ~7 nm67. This distance corresponds to roughly 20 bp, given the contour length of a basepair of 0.3 nm. A threshold of 50 bp was thus conservatively chosen because the CTCF N-terminus may be as long as 14 nm but is likely more compact due to folding of the CTCF N-terminus. The simulations thus likely represent an upper limit of the encounter probability. f, Simulated encounter probability of cohesin and CTCF (mean ± 95% binomial confidence interval; N = 500 independent simulations). Note that the encounter probability does not exceed ~40%, even at the smallest step size distribution (measured at 1 pN). In contrast, the blocking probability of N-terminal encounters of cohesin and CTCF increases from 0 to 100% within 0-0.14 pN (Fig. 2g). Force-dependent step sizes of cohesin can thus not solely explain the observed N-terminal blocking probability. We therefore suspect that DNA tension increases the blocking efficacy of CTCF by other mechanisms, such as by reducing not only cohesin’s step size but also the frequency with which it takes steps, thus providing more time for CTCF and cohesin to bind to each other; or by reducing thermal fluctuations of DNA49, which could reduce the space that CTCF has to explore to find cohesin. It is also conceivable that cohesin’s ‘motor’ activity can overcome the low 1 µM binding affinity of CTCF-cohesin interactions26 more easily at low DNA tension than at high tensions, which are close to the stalling force of loop extrusion, and at which cohesin has to generate higher forces to extrude DNA. Finally, DNA tension could also change cohesin’s responsiveness to CTCF by influencing how cohesin performs loop extrusion68.