Topological weight and structural diversity of polydisperse chromatin loop networks

TL;DR

This paper introduces a method to compute the topological weights and structural diversity of polydisperse chromatin loop networks, linking network topology to transcriptional regulation and noise control.

Contribution

It develops a novel approach using resistor network analogy and combinatorial theorems to analyze the topology and diversity of chromatin loop networks with arbitrary transcription unit patterns.

Findings

Topological weights can be computed using resistor network analogy.

Structural diversity depends on transcription unit patterning.

Method provides insights into transcriptional noise regulation.

Abstract

Current biophysical models for transcriptionally active chromatin view this as a polymer with sticky sites, mimicking transcription units such as promoters and enhancers which interact via the binding of multivalent complexes of chromatin-binding proteins. It has been demonstrated that this model spontaneously leads to microphase separation, resulting in the formation of a network of loops with transcription units serving as anchors. Here, we demonstrate how to compute the topological weights of loop networks with an arbitrary 1D pattern of transcription units along the fibre (or `polydisperse' loop networks), finding an analogy with networks of electric resistors in parallel or in series. We also show how the BEST (de Bruijn, van Aardenne-Ehrenfest, Smith and Tutte) theorem in combinatorics can be used to find the combinatorial multiplicity of any class of loop networks. Our results can be used to compute the structural diversity, or Shannon entropy, of loop networks: we show that this quantity depends on the 1D patterning of transcription units along the chain, possibly providing a pathway to control transcriptional noise in eukaryotic genes.