A mathematical model clarifies the ABC Score formula used in enhancer-gene prediction

Enhancers are discrete DNA elements that regulate the expression of eukaryotic genes. They are important not only for their regulatory function, but also as loci that are frequently associated with disease traits. Despite their significance, our conceptual understanding of how enhancers work remains limited. CRISPR-interference methods have recently provided the means to systematically screen for enhancers in cell culture, from which a formula for predicting whether an enhancer regulates a gene, the Activity-by-Contact (ABC) Score, has emerged and has been widely adopted. While useful as a binary classifier, it is less effective at predicting the quantitative effect of an enhancer on gene expression. It is also unclear how the algebraic form of the ABC Score arises from the underlying molecular mechanisms and what assumptions are needed for it to hold. Here, we use the graph-theoretic linear framework, previously introduced to analyze gene regulation, to formulate the default model, a mathematical model of how multiple enhancers independently regulate a gene. We show that the algebraic form of the ABC Score arises from this model. However, the default model assumptions also imply that enhancers act additively on steady-state gene expression. This is known to be false for certain genes and we show how modifying the assumptions can accommodate this discrepancy. Overall, our approach lays a rigorous, biophysical foundation for future studies of enhancer-gene regulation.