A Polymer Model with Epigenetic Recolouring Reveals a Pathway for the de novo Establishment and 3D Organisation of Chromatin Domains

One of the most important problems in development is how epigenetic domains can be first established, and then maintained, within cells. To address this question, we propose a framework which couples 3D chromatin folding dynamics, to a "recolouring" process modelling the writing of epigenetic marks. Because many intra-chromatin interactions are mediated by bridging proteins, we consider a "two-state" model with self-attractive interactions between two epigenetic marks which are alike (either active or inactive). This model displays a first-order-like transition between a swollen, epigenetically disordered, phase, and a compact, epigenetically coherent, chromatin globule. If the self-attraction strength exceeds a threshold, the chromatin dynamics becomes glassy, and the corresponding interaction network freezes. By modifying the epigenetic read-write process according to more biologically-inspired assumptions, our polymer model with recolouring recapitulates the ultrasensitive response of epigenetic switches to perturbations, and accounts for multi-domain conformations, strikingly similar to the topologically-associating-domains observed in eukaryotic chromosomes.