From a melt of rings to chromosome territories: the role of topological constraints in genome folding

Abstract

We review pro and contra of the hypothesis that generic polymer properties of topological constraints are behind many aspects of chromatin folding in eukaryotic cells. For that purpose, we review, first, recent theoretical and computational findings in polymer physics related to concentrated, topologically simple (unknotted and unlinked) chains or a system of chains. Second, we review recent experimental discoveries related to genome folding. Understanding in these fields is far from complete, but we show how looking at them in parallel sheds new light on both.

Confinement-Induced Glassy Dynamics in a Model for Chromosome Organization

“…From a biological perspective, it could be argued that the hierarchical and scale-free organization of chromosome, without knots, is beneficial for access to a target locus [11] or for the faster response to an environmental change by easing the condensationdecondensation process [12,13]. Although the origin of chromosomal territories is controversial because equilibrium polymer configurations with many loops naturally produce segregated domains as well [14,15], a major non-equilibrium effect, glassy dynamics of the genome under strong confinement, should not be overlooked from a contributing factor in chromosome folding.…”

“…Although the origin of chromosomal territories is controversial because equilibrium polymer configurations with many loops naturally produce segregated domains as well [14,15], a major non-equilibrium effect, glassy dynamics of the genome under strong confinement, should not be overlooked from a contributing factor in chromosome folding. The relaxation time of a polymer via disentanglement [16] (τ rep ∼ N 3 [12,13,17,18]) could be far longer, effectively permanent for higher organisms, than the cell cycle time (τ cell ) [12,13] for a large N . Furthermore, a substantial increase of polymer relaxation time is also expected in a strong confinement as is the case for DNA inside viral capsid [19] even when N is not too large.…”

Effect of chain stiffness on the structure of single-chain polymer nanoparticles

“…Indeed there are no really dense 'melt-like' regions in the stiff SCNPs (see bottom panels in Fig. 5) resembling the 'territories' observed in melts of rings and chromatime [32,33,36]. These would indeed involve strong folding of chain segments and consequently a large bending penalty.…”

“…These would indeed involve strong folding of chain segments and consequently a large bending penalty. The second, and more relevant, difference is that the SCNPs do not show the approximate scaling P (s) ∼ s −1 expected for crumpled globules [32,33,36,43]. The decay of P (s) at long contour distances is, for all the investigated values of k and f , compatible with power-law behaviour, P (s) ∼ s −x , but with an exponent 1.5 ≤ x ≤ 1.8 (see results for f = 0.4 as a function of k and for k = 0 as a function of f in both panels of Fig.…”

Extruding Loops to Make Loopy Globules?

“…While polymer systems with simple topology (where the word ''topology'' is used in explicit reference to the proper branch of mathematics), such as a concentrated solution of long unconcatenated loops, do exhibit peculiar fractal and physical properties, their details are sensitive to the specific features of the polymers in question (9,10). Furthermore, these systems tend to exhibit a very wide crossover, so that their asymptotic scaling may not be sufficient to understand real experiments.…”