A mathematical model exhibiting the effect of DNA methylation on the stability boundary in cell-fate networks.

Cell-fate networks are traditionally studied within the framework of gene regulatory networks. This paradigm considers only interactions of genes through expressed transcription factors and does not incorporate chromatin modification processes. This paper introduces a mathematical model that seamlessly combines gene regulatory networks and DNA methylation (DNAm), with the goal of quantitatively characterizing the contribution of epigenetic regulation to gene silencing. The 'Basin of Attraction percentage' is introduced as a metric to quantify gene silencing abilities. As a case study, a computational and theoretical analysis is carried out for a model of the pluripotent stem cell circuit as well as a simplified self-activating gene model. The results confirm that the methodology quantitatively captures the key role that DNAm plays in enhancing the stability of the silenced gene state.