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 binding response was the sum of the binding 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. We treated MCF-7 cells with retinoic acid, TGF-beta, or both signals simultaneously over a period of 72 hours, after which we performed paired bulk RNA-seq and ATAC-seq. We performed three biological replicates (with one biological unit consisting of one 10 cm dish of cells) and within each experimental replicate we tested three different doses of retinoic acid (50, 200, and 400 nM), TGF-beta (1.25, 5, and 10 ng/ml), and both signals (50 nM + 1.25 ng/ul, 200 nM + 5 ng/ul, 400 nM + 10 ng/ul), as well as three different ethanol controls with varied starting cell densities.