  In this paper, we propose a thermodynamic mechanism for the formation of
transcriptional foci via the joint agglomeration of DNA-looping proteins and
protein-binding domains on DNA: The competition between the gain in protein-DNA
binding free energy and the entropy loss due to DNA looping is argued to result
in an effective attraction between loops. A mean-field approximation can be
described analytically via a mapping to a restricted random-graph ensemble
having local degree constraints and global constraints on the number of
connected components. It shows the emergence of protein clusters containing a
finite fraction of all looping proteins. If the entropy loss due to a single
DNA loop is high enough, this transition is found to be of first order.

Subcellular Processes;Soft Condensed Matter;Statistical Mechanics;Biological Physics;Genomics