Theory and Simulations of condensin mediated loop extrusion in DNA

Abstract

The condensation of several mega base pair human chromosomes in a small cell volume is a spectacular phenomenon in biology. This process, involving the formation of loops in chromosomes, is facilitated by ATP consuming motors (condensin and cohesin), that interact with chromatin segments thereby actively extruding loops. Motivated by real time videos of loop extrusion (LE), we created an analytically solvable model, which yields the LE velocity as a function of external load acting on condensin. The theory fits the experimental data quantitatively, and suggests that condensin must undergo a large conformational change, triggered by ATP binding and hydrolysis, that brings distant parts of the motor to proximity. Simulations using a simple model confirm that a transition between an open and closed states is necessary for LE. Changes in the orientation of the motor domain are transmitted over ∼ 50 nm, connecting the motor head and the hinge, thus providing a plausible mechanism for LE. The theory and simulations are applicable to loop extrusion in other structural maintenance complexes.How chromosomes are structurally organized in the tight cellular space is a long standing problem in biology. Remarkably, these information carrying polymers in humans containing more than 100 million base pairs, depending on the chromosome number, are densely packed (apparently with negligible knots) in the 5 − 10 µm cell nucleus [1,2]. In order to accomplish this herculean feat nature has evolved a family of SMCs (Structural Maintenance of Chromosomes) complexes [3,4] (bacterial SMC, cohesin, and condensin) to facilitate large scale compaction of chromosomes in all living systems. Compaction is thought to occur by active generation of a large array of loops, which are envisioned to form by extrusion of the genomic material [5,6] driven by ATPconsuming motors. The SMC complexes have been identified as a major component of the loop extrusion (LE) process [3,4].Of interest here is condensin, which has motor activity as it translocates on DNA [7], resulting in active extrusion loops in an ATP-dependent manner [8]. We first provide a brief description of the architecture of condensin (drawn schematically in Fig.1) because the theory is based on this picture. Condensin is a ring shaped dimeric motor to which a pair of SMC proteins (Smc2 and Smc4) are attached. Smc2 and Smc4, which have coiled coil (CC) structures, are connected at the hinge domain. The ATP binding domains are in the motor heads [4,9]. The CCs have kinks roughly in the middle of the CCs [9]. The relative flexibility in the elbow region (located near the kinks) could be the key to the conformational transitions in the CC that are powered by ATP binding and hydrolysis [4,10]. At present, there is no direct experimental evidence that this is so.Previous studies using simulations [6,11,12], which build on the pioneering insights by Nasmyth [5], suggested that multiple condensins concertedly translocate * dave.thirumalai@gmail.com along the chromosome extruding loops of increas...

Structure-function relationships of SMC protein complexes for DNA loop extrusion

“…Interestingly, real-time imaging using the EQ mutant, which blocks the ATP hydrolysis of SMC proteins, showed the O-to-B shape transition, suggesting that the B-shape is induced by ATP binding to the head domains. This result is also supported by the recent Cryo-EM studies of human cohesin and yeast cohesin complexes showing that the hinge domain is engaged with the heads and HAWK (Collier et al, 2020;Higashi et al, 2020;Takaki et al, 2021).…”

“…Moreover, recent in vivo studies of cohesin support that the hinge can be in close proximity with the head domain. Furthermore, the force-dependent step sizes observed by magnetic tweezers fits a simulation based on the scrunching model (Ryu et al, 2020b;Takaki et al, 2021). A recent study suggested a Brownian ratchet model in which the conformational changes between the O-and B-shapes are induced by thermal fluctuations due to the flexible SMC arms (Hwang and Karplus, 2019).…”

Modeling of DNA binding to the condensin hinge domain using molecular dynamics simulations guided by atomic force microscopy

“…Recent single-molecule experiments revealed that the budding yeast condensin is a molecular motor [6] that extrudes a DNA loop [7,8]. However, the detailed molecular mechanism of DNA-loop extrusion by condensin and other members of the SMC protein family remains unclear [8][9][10] and has been an ambitious target of computational modeling studies [11][12][13].…”