  The emergence of and transitions between distinct phenotypes in isogenic
cells can be attributed to the intricate interplay of epigenetic marks,
external signals, and gene regulatory elements. These elements include
chromatin remodelers, histone modifiers, transcription factors, and regulatory
RNAs. Mathematical models known as Gene Regulatory Networks (GRNs) are an
increasingly important tool to unravel the workings of such complex networks.
In such models, epigenetic factors are usually proposed to act on the chromatin
regions directly involved in the expression of relevant genes. However, it has
been well-established that these factors operate globally and compete with each
other for targets genome-wide. Therefore, a perturbation of the activity of a
regulator can redistribute epigenetic marks across the genome and modulate the
levels of competing regulators. In this paper, we propose a conceptual and
mathematical modeling framework that incorporates both local and global
competition effects between antagonistic epigenetic regulators in addition to
local transcription factors, and show the counter-intuitive consequences of
such interactions. We apply our approach to recent experimental findings on the
Epithelial-Mesenchymal Transition (EMT). We show that it can explain the
puzzling experimental data as well provide new verifiable predictions.
