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

Eukaryote cell division features a chromosome compaction-decompaction cycle 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 "brush"-where active extrusion of loops controls the brush structure. Given type-II DNA topoisomerase (Topo II)-catalyzed topology fluctuations, we find that interchromosome entanglements are minimized for a certain "optimal" loop that scales with the chromosome size. The optimal loop organization is in accord with experimental data across species, suggesting an important structural role of genomic loops in maintaining a less entangled genome. 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 requires higher lengthwise compaction and drives 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 connects chromosome structural reorganization to topological resolution through the cell cycle and highlights a mechanism of directing Topo II-mediated strand passage via loop extrusion-driven lengthwise compaction.