  The spreading and regulation of epigenetic marks on chromosomes is crucial to
establish and maintain cellular identity. Nonetheless, the dynamical mechanism
leading to the establishment and maintenance of a given, cell-line specific,
epigenetic pattern is still poorly understood. In this work we propose, and
investigate in silico, a possible experimental strategy to illuminate the
interplay between 3D chromatin structure and epigenetic dynamics. We consider a
set-up where a reconstituted chromatin fibre is stretched at its two ends
(e.g., by laser tweezers), while epigenetic enzymes (writers) and
chromatin-binding proteins (readers) are flooded into the system. We show that,
by tuning the stretching force and the binding affinity of the readers for
chromatin, the fibre undergoes a sharp transition between a stretched,
epigenetically disordered, state and a crumpled, epigenetically coherent, one.
We further investigate the case in which a knot is tied along the chromatin
fibre, and find that the knotted segment enhances local epigenetic order,
giving rise to "epigenetic solitons" which travel and diffuse along chromatin.
Our results point to an intriguing coupling between 3D chromatin topology and
epigenetic dynamics, which may be investigated via single molecule experiments.
