Compaction of chromatin domains regulates target search times of proteins.

Protein molecules must efficiently locate specific DNA sequences within the densely packed chromatin of the cell nucleus. We investigate how the spatial organisation of chromatin, specifically its organisation into Topologically Associating Domains (TADs), fundamentally affects this search process. Using exact analytical theory and simulations of different models of chromatin, we show that target search within compact, highly connected chromatin domains can leverage intersegmental jumps to significantly decrease search times. Further, we establish that there exists an optimal degree of polymer compaction that minimizes the search time for proteins to find their targets. For highly folded domains, our results suggest that rather than bulk diffusion, intersegmental transfers - jumping between chromatin segments that are close together in space - drive the optimal search process. Remarkably, when we analyse 8,355 TAD structures across the human genome, we find that their natural connectivity matches with the theoretical optimum predicted by our model. The structural organisation within TADs significantly reduces protein search times far beyond what is achievable through classical facilitated diffusion. In essence, our work suggests that packaging of chromatin inside the nucleus has implications beyond spatial organisation, and is also intricately linked to the dynamics of proteins inside the nuclear environment.