A theoretical model of Polycomb/Trithorax action unites stable epigenetic memory and dynamic regulation

Polycomb and Trithorax group proteins maintain stable epigenetic memory of gene expression states for some genes, but many targets show highly dynamic regulation. Here we combine experiment and theory to examine the mechanistic basis of these different modes of regulation. We present a mathematical model comprising a Polycomb/Trithorax response element (PRE/TRE) coupled to a promoter and including Drosophila developmental timing. The model accurately recapitulates published studies of PRE/TRE mediated epigenetic memory of both silencing and activation. With minimal parameter changes, the same model can also recapitulate experimental data for a different PRE/TRE that allows dynamic regulation of its target gene. The model predicts that both cell cycle length and PRE/TRE identity are critical for determining whether the system gives stable memory or dynamic regulation. Our work provides a simple unifying framework for a rich repertoire of PRE/TRE functions, and thus provides insights into  genome-wide Polycomb/Trithorax regulation.