Using computational modelling to reveal mechanisms of epigenetic Polycomb control

Abstract

The Polycomb system is essential for stable gene silencing in many organisms. This regulation is achieved in part through addition of the histone modifications H3K27me2/me3 by Polycomb Repressive Complex 2 (PRC2). These modifications are believed to be the causative epigenetic memory elements of PRC2-mediated silencing. As these marks are stored locally in the chromatin, PRC2-based memory is a cis-acting system. A key feature of stable epigenetic memory in cis is PRC2-mediated, self-reinforcing feedback from K27-methylated histones onto nearby histones in a read-write paradigm. However, it was not clear under what conditions such feedback can lead to stable memory, able, for example, to survive the perturbation of histone dilution at DNA replication. In this context, computational modelling has allowed a rigorous exploration of possible underlying memory mechanisms and has also greatly accelerated our understanding of switching between active and silenced states. Specifically, modelling has predicted that switching and memory at Polycomb loci is digital, with a locus being either active or inactive, rather than possessing intermediate, smoothly varying levels of activation. Here, we review recent advances in models of Polycomb control, focusing on models of epigenetic switching through nucleation and spreading of H3K27me2/me3. We also examine models that incorporate transcriptional feedback antagonism and those including bivalent chromatin states. With more quantitative experimental data on histone modification kinetics, as well as single-cell resolution data on transcription and protein levels for PRC2 targets, we anticipate an expanded need for modelling to help dissect increasingly interconnected and complex memory mechanisms.

Keywords: computational models; epigenetics; mathematical modelling; polycomb repressive complex 2.

Figure 1.. Memory model with opposing histone modifications.

(Top) Schematic of the A–U–M model. A given histone has an activating (A) or a silencing mark (M) or is unmodified (U). The curved arrows represent self-reinforcing interactions where M histones promote transitions towards M (red arrows) and A histones promote transitions towards A (green arrows). (Bottom) The A–U–M model generates bistable states with histones predominantly either A (ON) or M (OFF). The states are maintained through replication despite the incorporation of new unmodified U histones at DNA replication. The self-reinforcing feedbacks can add marks to neighbouring histones (short-ranged, solid arrow) or, in addition, to distant histones (long-ranged, dashed arrow), thereby rebuilding the digital state that existed prior to replication.

Figure 2.. Memory model with transcriptional antagonism.

(Left) Model with transcriptional antagonism to Polycomb silencing. H3K27me2/me3 feedback to generate more methylation (H3K27me2 feedback suppressed for clarity) and also silence expression. Transcription disrupts silencing through demethylation and nucleosome exchange. The overall module can also generate bistable gene expression states. (Middle, Right) Example model simulations showing H3K27 methylation dynamics over time. (Top) Each coloured marker shows the K27 state of an H3 histone in a system of 30 nucleosomes (60 histones) at a particular time. Red: me3; white: me1/2; orange: me0. The nucleosomes are initialised in me0 (middle) and me3 (right). (Bottom) Same simulations but showing overall H3K27me0 (orange) and H3K27me3 (red) levels. Sudden dips of H3K27me3 and rises of H3K27me0 caused by simulated DNA replication.