An important question in the context of the 3D organization of chromosomes is the mechanism of formation of large loops between distant base pairs. Recent experiments suggest that the formation of loops might be mediated by Loop Extrusion Factor proteins like cohesin. Experiments on cohesin have shown that cohesins walk diffusively on the DNA, and that nucleosomes act as obstacles to the diffusion, lowering the permeability and hence reducing the effective diffusion constant. An estimation of the times required to form the loops of typical sizes seen in Hi-C experiments using these low effective diffusion constants leads to times that are unphysically large. The puzzle then is the following, how does a cohesin molecule diffusing on the DNA backbone achieve speeds necessary to form the large loops seen in experiments? We propose a simple answer to this puzzle, and show that while at low densities, nucleosomes act as barriers to cohesin diffusion, beyond a certain concentration, they can reduce loop formation times due to a subtle interplay between the nucleosome size and the mean linker length. This effect is further enhanced on considering stochastic binding kinetics of nucleosomes on the DNA backbone, and leads to predictions of lower loop formation times than might be expected from a naive obstacle picture of nucleosomes. 2 structure inside the nucleus remains an important open question [16, 40, 41, 62]. An 3 ubiquitous structural motif, as observed through 14, 25, 47] and other 4 experiments [34, 36, 50] are the formation of large loops, ranging from kilobases to 5 megabases. These loops play both a structural as well as functional roles, bringing 6 together regions of the DNA that are widely spaced along the backbone [1, 9, 35]. In 7 recent years, much work has been done in trying to understand the mechanism of 8 formation of these large loops. There is now a significant body of experimental 9 observations that implicate a class of proteins called the Structural maintenance of 10 chromosome (SMC) protein complexes -such as cohesin and condensin in the formation 11 and maintenance of these large chromosomal loops [19, 20, 28, 33, 54, 55, 58, 59, 64]. 12 Structural maintenance of chromosome (SMC) protein complexes are known to play 13 a major role in chromosome segregation in interphase and mitosis . Both cohesin and 14 condensin consists of SMC subunits and share structural similarities. SMC subunits 15 1/15 (SMC1, SMC3 in cohesin and SMC2, SMC4 in condensin) fold back on themselves to 16 form approximately a 50nm long arm. These two arms are then connected at one end 17 by a hinge domain and other two ends which have ATPase activity are connected by a 18 kleisin subunit (RAD21 in cohesin and condensin-associated protein H2 [CAPH2] in 19condensin)to form a ring like structure of the whole complex [5, 21, 26, 27, 42, 43, 48].
20This ring like structure has been hypothesized to form a topological association with the 21 DNA backbone [38, 46]. In particular, experiments on cohesin have shown that such 22 topol...