Chromosome disentanglement driven via optimal compaction of loop-extruded brush structures

Eukaryote cell division features cyclical manipulation of the compaction state of chromosomes that is synchronized with their physical and topological segregation. It has been proposed that lengthwise compaction of chromatin into mitotic chromosomes via loop extrusion underlies the compaction-segregation/resolution process. We analyze this disentanglement scheme via considering the chromosome to be a succession of DNA/chromatin loops - a polymer 9brush9- where active extrusion of loops controls the brush structure. Given topoisomerase (TopoII)-catalyzed topology fluctuations, we find that inter-chromosome entanglements are minimized for a certain 9optimal9 loop size dependent on the average chromosome size in accord with experimental data, suggesting that selective pressure has pushed chromosome architecture to one with minimal entanglement. Application of the model to the interphase genome indicates that active loop extrusion can maintain a level of chromosome compaction with suppressed entanglements; the transition to the metaphase state ramps up lengthwise compaction, driving complete topological segregation. Optimized genomic loops may provide a means for evolutionary propagation of gene-expression patterns while simultaneously maintaining a disentangled genome. We also find that compact metaphase chromosomes have a densely packed core along their cylindrical axes that explains their observed mechanical stiffness. Our model proposes a unified view of structural reorganization of chromosomes through the cell cycle in good agreement with a wide range of experimental observations for varied organisms, predicts testable scaling laws including the long-known relationship between genome size and metaphase chromosome thickness, and can be generalized to the case of bacteria.