  The most common gene regulation mechanism is when a transcription factor
protein binds to a regulatory sequence to increase or decrease RNA
transcription. However, transcription factors face two main challenges when
searching for these sequences. First, they are vanishingly short relative to
the genome length. Second, many nearly identical sequences are scattered across
the genome, causing proteins to suspend the search. But as pointed out in a
computational study of LacI regulation in Escherichia coli, such almost-targets
may lower search times if considering DNA looping. In this paper, we explore if
this also occurs over chromosome-wide distances. To this end, we developed a
cross-scale computational framework that combines established
facilitated-diffusion models for basepair-level search and a network model
capturing chromosome-wide leaps. To make our model realistic, we used Hi-C data
sets as a proxy for 3D proximity between long-ranged DNA segments and binding
profiles for more than 100 transcription factors. Using our cross-scale model,
we found that median search times to individual targets critically depend on a
network metric combining node strength (sum of link weights) and local
dissociation rates. Also, by randomizing these rates, we found that some actual
3D target configurations stand out as considerably faster or slower than their
random counterparts. This finding hints that chromosomes' 3D structure funnels
essential transcription factors to relevant DNA regions.
