Effective model of protein-mediated interactions in chromatin

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 nonequilibrium 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 polymers 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. An effective description of this system can be useful in elucidating the fundamental mechanisms that govern chromatin structuring in particular and indirect interactions in general.