Animal genomes are organized into topologically associated domains (TADs). TADs are thought to contribute to gene regulation by facilitating enhancer-promoter (E-P) contacts within a TAD preventing these contacts across TAD borders. However, the absolute difference in contact frequency across TAD boundaries is usually less than two-fold, even though disruptions of TAD borders can change gene expression by ten-fold. Existing models fail to explain this hypersensitive response. Here, we propose a futile cycle model of enhancer-mediated regulation that can exhibit hypersensitivity through bistability and hysteresis. Consistent with recent experiments, this regulation does not exhibit strong correlation between enhancer-promoter contact and promoter activity, even though regulation occurs through contact. Through mathematical analysis and stochastic simulation, we show that this system can create an illusion of enhancer-promoter biochemical specificity and explain the importance of weak TAD boundaries. It also offers a mechanism to reconcile apparently contradictory results from recent global TAD disruption with local TAD boundary deletion experiments. Together, these analyses advance our understanding of cis-regulatory contacts in controlling gene expression, and suggest new experimental directions.

Animal genomes are organized into topologically associated domains (TADs), which exhibit more intra-domain than inter-domain contact. However, the absolute difference in contact is usually no more than twofold, even though disruptions to TAD boundaries can change gene expression by 8-10 fold. Existing models fail to explain this superlinear transcriptional response to changes in genomic contact. Here, we propose a futile cycle model where an enzyme stimulated by association with its products can exhibit bistability and hysteresis, allowing a small increase in enhancer-promoter contact to produce a large change in expression without obvious correlation between E-P contact and promoter activity. Through mathematical analysis and stochastic simulation, we show that this system can create an illusion of enhancer-promoter specificity and explain the importance of weak TAD boundaries. It also offers a mechanism to reconcile recent global cohesin loop disruption and TAD boundary deletion experiments. We discuss the model in the context of these recent controversial experiments. Together, these analyses advance our interpretation and understanding of cis-regulatory contacts in controlling gene expression, and suggest new experimental directions.

The genetic regulatory code is determined by more than the arrangement of transcription factor binding sites on the genome. Epigenetic regulation is known to play a key role in determining whether binding sites are accessible to transcription factors. Therefore, both cis regulatory architecture and accessibility must be considered to achieve a predictive understanding of transcriptional regulation. In the early embryo of the fruit fly Drosophila melanogaster, the transcription factor Zelda has been proposed to mediate transcriptional activation by facilitating chromatin accessibility. Zelda's role in the activation of hunchback, one of the most widely studied genes in developmental biology, provides an opportunity to uncover the quantitative interplay between the regulation of accessibility and gene expression dynamics in development. Currently, the consequences of Zelda's regulatory actions remain unclear, as does its effects on gene expression dynamics. For example, does Zelda-mediated access to DNA modulate the rate of polymerase loading at promoters or dictate the probability of promoters turning on? To reveal the molecular consequences of the regulation of chromatin accessibility on development, we use novel technologies to image real time transcriptional dynamics of a hunchback reporter in living embryos. By examining zelda mutant flies, we find that the loss of Zelda has no effect on polymerase loading rates at the promoter. Contrastingly, these mutants presented a substantial delay in transcriptional onset after mitosis. Thus, while Zelda does not affect the rate of transcriptional initiation, it does play a role in determining the proper timing of transcription. We present a theoretical Monod-Wyman-Changeux based model aimed at explaining the interplay between chromatin accessibility, transcription factor binding, and output gene expression. Our model makes experimentally testable predictions about how the number, placement, and affinity of Zelda binding sites within enhancers dictate transcriptional dynamics.

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