Limits of Chromosome Compaction by Loop-Extruding Motors

Abstract

During mitosis, human chromosomes are linearly compacted about 1000-fold by loop-extruding motors. Recent experiments have shown that condensins extrude DNA loops but in a "one-sided" manner. This contrasts with existing models, which predict that symmetric, "two-sided" loop extrusion accounts for mitotic chromosome compaction. We explore whether one-sided extrusion, as it is currently seen in experiments, can compact chromosomes by developing a mean-field theoretical model for polymer compaction by motors that actively extrude loops and dynamically turnover. The model establishes a stringent upper bound of only about tenfold for compaction by strictly one-sided extrusion. We confirm this result with stochastic simulations. Thus, strictly one-sided extrusion as it has been observed so far cannot be the sole mechanism of chromosome compaction. However, as shown by the model, other two-sided or effectively two-sided mechanisms can achieve sufficient compaction.

Theory of chromatin organization maintained by active loop extrusion

“…We develop a model of chromatin organization regulated by active loop extrusion with three main components: i) a binding and unbinding component, ii) a one-dimensional component of loop extrusion kinetics, and iii) a three-dimensional component for the spatial organization of chromatin. The first two components are similar to previous models ( 31 , 77 ), though we focus our results on TAD formation and contact probabilities rather than chromosome compaction. Our model predicts chromatin contact probabilities, which we compare with Hi-C and ChIA-PET data targeted toward CTCF since these two experimental assays are commonly used to probe chromatin organization.…”

“…We assume that the number density of chromatin-bound cohesins during the G1 phase of the cell cycle is time independent corresponding to a steady state. For definiteness, in this paper, we describe passive cohesin binding that follows equilibrium detailed balance and does not consume energy, as in previous work ( 77 ). The free-energy change per pair of loci due to cohesin binding with two domains attached to different chromatin loci is ( Fig.…”

Theory and Simulations of condensin mediated loop extrusion in DNA

“…In this mechanism two condensin heads move away from each other extruding loops in a symmetric manner. Cooperative action of many condensins [13,14] might be necessary to account for the ∼ (1, 000 − 10, 000) fold compaction of human chromosomes [15]. In the only available theoretical study thus far [16], a plausible catalytic cycle for the condensin is coupled to loop extrusion.…”

The dynamic role of cohesin in maintaining human genome architecture

“…[5,63] Cohesin depletion has a larger impact on the stability of TADs than the lack of CTCF. [18,43,64,65] Studies of ChIP have already suggested that cohesin is also highly enriched at the chromatin site, which may also be associated with CTCF, underlying the establishment of the loop and hence regulating the gene expression at the CTCF sites. [14,66] An analysis of the Cohesin-mediated loop by Grubert et al suggests the high variability of the cohesin-mediated loop in 24 cell lines compared to the nonvariable loops enriched by CTCF at the loop boundary.…”

“…These two models refer to the cases that one site of cohesin is blocked by some barrier like CTCF, or two sites are capable of a one‐dimensional diffusion, respectively. Extensive simulation research by Banigan and Mirny [ 65 ] shows that the one‐sided LEM is insufficient to achieve 1000‐fold compaction. However, this level of compaction can be achieved if at least ∼80% of the extruders in chromatin are two‐sided.…”