A thermodynamic model for agglomeration of DNA-looping proteins

TL;DR

This paper introduces a thermodynamic model explaining how DNA-looping proteins form transcriptional foci through a balance of binding energy and entropy loss, leading to protein clustering.

Contribution

It presents a novel thermodynamic mechanism and a mean-field analytical approach for understanding DNA-protein cluster formation.

Findings

Protein clusters can contain a finite fraction of looping proteins.

Transition to clustering can be first order if entropy loss is high.

Analytical mapping to a restricted random-graph ensemble.

Abstract

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.