  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.
