  The phase-separation occurring in a system of mutually interacting proteins
that can bind on specific sites of a chromatin fiber is here investigated. This
is achieved by means of extensive Molecular Dynamics simulations of a simple
polymer model which includes regulatory proteins as interacting spherical
particles. Our interest is particularly focused on the role played by
phase-separation in the formation of molecule aggregates that can join distant
regulatory elements, such as gene promoters and enhancers, along the DNA. We
find that the overall equilibrium state of the system resulting from the mutual
interplay between binding molecules and chromatin can lead, under suitable
conditions that depend on molecules concentration, molecule-molecule and
molecule-DNA interactions, to the formation of phase-separated molecular
clusters allowing robust contacts between regulatory sites. Vice-versa, the
presence of regulatory sites can promote the phase-separation process.
Different dynamical regimes can generate the enhancer-promoter contact, either
by cluster nucleation at binding sites or by bulk spontaneous formation of the
mediating cluster to which binding sites are successively attracted. The
possibility that such processes can explain experimental live-cell imaging data
measuring distances between regulatory sites during time is also discussed.
