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 description can be solved analytically via a mapping to a restricted random-graph ensemble  . 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.
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.
R
description can be solved
approximation can be described
A
having local degree constraints and global constraints on the number of connected components