Phase separation in sequence and space: Coupling folding landscape of chromatin with epigenetics

Chromosomal regions adopt heritable stable states resulting in bistable gene expression without changes to the underlying DNA sequence. Such epigenetic control is due to covalent modifications of histones, which are inextricably linked to chromatin structure. An associated positive feedback mechanism has also been posited wherein enzymes catalyse reactions to similarly modify nucleosomes in close proximity. Theorists have long sought analytically tractable mathematical models that capture the interplay between chromatin structure and the spread/maintenance of epigenetic marks. We propose a model wherein the polymer is modelled as a matrix of contacts between sites (nucleosomes); additionally, each site carries a binary variable denoting its epigenetic state. Following our previous work, we then treat both the addition/removal of epigenetic marks, and making/breaking of contacts in the polymer chain as a stochastic reaction network, and employ field theoretic methods to study the coupled system. We are interested in interrogating the effects of dynamical asymmetry, modulating cooperativity of polymer folding on the coupled landscape, and the formation and maintenance of spatiotemporal domains, and biological consequences thereof to processes such as gene regulation and cellular differentiation.