Gene regulation gravitates towards either addition or multiplication when combining the effects of two signals

Signals often ultimately affect the transcription of genes, and often, two different signals can affect the transcription of the same gene. In such cases, it is natural to ask how the combined transcriptional response compares to the individual responses. Mechanistic models can predict a range of combined responses, with the most commonly applied models predicting additive or multiplicative responses, but systematic genome-wide evaluation of these predictions are not available. Here, we performed a comprehensive analysis of the transcriptional response of human MCF-7 cells to two different signals (retinoic acid and TGF-β), applied individually and in combination. We found that the combined responses exhibited a range of behaviors, but clearly favored both additive and multiplicative combined transcriptional responses. We also performed paired chromatin accessibility measurements to measure putative transcription factor occupancy at regulatory elements near these genes. We found that increases in chromatin accessibility were largely additive, meaning that the combined accessibility response was the sum of the accessibility responses to each signal individually. We found some association between super-additivity of accessibility and multiplicative or super-multiplicative combined transcriptional responses, while sub-additivity of accessibility associated with additive transcriptional responses. Our findings suggest that mechanistic models of combined transcriptional regulation must be able to reproduce a range of behaviors.