  Cells regulate fates and complex body plans using spatiotemporal signaling
cascades that alter gene expression. Enhancers, short DNA sequences (50-150
base pairs), help coordinate these cascades by attracting regulatory proteins
to enhance the transcription of distal genes by binding to promoters. In
humans, there are hundreds of thousands of enhancers dispersed across the
genome, which poses a challenging coordination task to prevent unintended gene
activation. To mitigate this problem, the genome contains additional DNA
elements, insulators, that block enhancer-promoter interactions. However, there
is an open problem with how the insulation works, especially as
enhancer-insulator pairs may be separated by millions of base pairs. Based on
recent empirical data from Hi-C experiments, this paper proposes a new
mechanism that challenges the common paradigm that rests on specific
insulator-insulator interactions. Instead, this paper introduces a stochastic
looping model where enhancers bind weakly to surrounding chromatin. After
calibrating the model to experimental data, we use simulations to study the
broad distribution of hitting times between an enhancer and a promoter when
there are blocking insulators. In some cases, there is a large difference
between average and most probable hitting times, making it difficult to assign
a typical time scale, hinting at highly defocused regulation times. We also map
our computational model onto a resetting problem that allows us to derive
several analytical results. Besides offering new insights into
enhancer-insulator interactions, our paper advances the understanding of gene
regulatory networks and causal connections between genome folding and gene
activation.
