  Protein-mediated interactions are ubiquitous in the cellular environment, and
particularly in the nucleus, where they are responsible for the structuring of
chromatin. We show through molecular--dynamics simulations of a polymer
surrounded by binders that the strength of the binder-polymer interaction
separates an equilibrium from a non-equilibrium regime. In the equilibrium
regime, the system can be efficiently described by an effective model in which
the binders are traced out. Even in this case, the polymer display features
that are different from those of a standard homopolymer interacting with
two-body interactions. We then extend the effective model to deal with the case
where binders cannot be regarded as in equilibrium and a new phenomenology
appears, including local blobs in the polymer. Providing an effective
description of the system can be useful in clarifying the fundamental
mechanisms governing chromatin structuring.
