  We perform simulations of a system containing simple model proteins and a
polymer representing chromatin. We study the interplay between protein-protein
and protein-chromatin interactions, and the resulting condensates which arise
due to liquid-liquid phase separation, or a via a 'bridging-induced attraction'
mechanism. For proteins which interact multivalently, we obtain a phase diagram
which includes liquid-like droplets, droplets with absorbed polymer, and coated
polymer regimes. Of particular interest is a regime where protein droplets only
form due to interaction with the polymer; here, unlike a standard phase
separating system, droplet density rather than size varies with the overall
protein concentration. We also observe that protein dynamics within droplets
slow down as chromatin is absorbed. If the protein-protein interactions have a
strictly limited valence, fractal or gel-like condensates are instead observed.
Together this provides biologically relevant insights into the nature of
protein-chromatin condensates in living cells.
