Abstract
Chromosome organization mediated by structural maintenance of chromosome complexes is crucial in many organisms. Cohesin extrudes chromatin into loops that are thought to lengthen until it is obstructed by CTCF proteins. In complex cellular environments, the loop extrusion machinery may encounter other chromatin-binding proteins. How these proteins interfere with the cohesin-meditated extrusion process is largely unexplored, but recent experiments have shown that some proteins serve as physical barriers that block cohesin translocation. Other proteins containing a cohesin-interaction motif serve as chemical barriers to induce cohesin pausing through interactions with it. Here, we develop an analytically solvable approach for the loop extrusion model incorporating barriers to investigate the effect of the barrier on the passive extrusion process. To further quantify the impact of barriers, we calculate the mean looping time it takes for cohesin to translocate to form a stable loop before dissociation. Our finding reveals that the physical barrier can accelerate the loop formation, and the degree of acceleration is closely related to the impedance strength of the physical barrier. In particular, the synergy of the cohesin loading site and the physical barrier site accelerates loop formation more significantly. The proximity of the cohesin loading site to the barrier site facilitates the rapid formation of stable loops in long genomes, which implies loop extrusion and chromatin-binding proteins might shape functional genomic organization. Conversely, chemical barriers consistently impede loop formation, with increasing impedance strength of the chemical barrier leading to longer loop formation time. Our study contributes to a more comprehensive understanding of the complexity of the loop extrusion process, providing a new perspective on the potential mechanisms of gene regulation.