In any biological system with memory, the state of the system depends on its history. Epigenetic memory maintains gene expression states through cell generations without a change in DNA sequence and in the absence of initiating signals. It is immensely powerful in biological systems - it adds long-term stability to gene expression states and increases the robustness of gene regulatory networks. The Polycomb group (PcG) and Trithorax group (TrxG) proteins can confer long-term, mitotically heritable memory by sustaining silent and active gene expression states, respectively. Several recent studies have advanced our understanding of the molecular mechanisms of this epigenetic memory during DNA replication and mitosis.

Epigenetic memory mediated by Polycomb group (PcG) proteins must be maintained during cell division, but must also be flexible to allow cell fate transitions. Here we quantify dynamic chromatin-binding properties of PH::GFP and PC::GFP in living Drosophila in two cell types that undergo defined differentiation and mitosis events. Quantitative fluorescence recovery after photobleaching (FRAP) analysis demonstrates that PcG binding has a higher plasticity in stem cells than in more determined cells and identifies a fraction of PcG proteins that binds mitotic chromatin with up to 300-fold longer residence times than in interphase. Mathematical modeling examines which parameters best distinguish stem cells from differentiated cells. We identify phosphorylation of histone H3 at Ser 28 as a potential mechanism governing the extent and rate of mitotic PC dissociation in different lineages. We propose that regulation of the kinetic properties of PcG-chromatin binding is an essential factor in the choice between stability and flexibility in the establishment of cell identities.

The Polycomb (PcG) and Trithorax (TrxG) group proteins work antagonistically on several hundred developmentally important target genes, giving stable mitotic memory, but also allowing flexibility of gene expression states. How this is achieved in quantitative terms is poorly understood. Here, we present a quantitative kinetic analysis in living Drosophila of the PcG proteins Enhancer of Zeste, (E(Z)), Pleiohomeotic (PHO) and Polycomb (PC) and the TrxG protein absent, small or homeotic discs 1 (ASH1). Fluorescence recovery after photobleaching and fluorescence correlation spectroscopy reveal highly dynamic chromatin binding behaviour for all proteins, with exchange occurring within seconds. We show that although the PcG proteins substantially dissociate from mitotic chromatin, ASH1 remains robustly associated with chromatin throughout mitosis. Finally, we show that chromatin binding by ASH1 and PC switches from an antagonistic relationship in interphase, to a cooperative one during mitosis. These results provide quantitative insights into PcG and TrxG chromatin-binding dynamics and have implications for our understanding of the molecular nature of epigenetic memory.

How fast? How strong? How many? So what? Why do numbers matter in biology? Chromatin binding proteins are forever in motion, exchanging rapidly between bound and free pools. How do regulatory systems whose components are in constant flux ensure stability and flexibility? This review explores the application of quantitative and mathematical approaches to mechanisms of epigenetic regulation. We discuss methods for measuring kinetic parameters and protein quantities in living cells, and explore the insights that have been gained by quantifying and modelling dynamics of chromatin binding proteins.