Towards a robust algorithm to determine topological domains from colocalization data

TL;DR

This paper introduces a new algorithm to identify hierarchical topological domains in the genome from colocalization data, distinguishing between different polymer conformations based on spectral analysis.

Contribution

The paper presents a novel algorithm that analyzes modularity in colocalization matrices to reveal hierarchical chromatin domain structures, and introduces a spectrum of cluster borders for conformation identification.

Findings

The algorithm successfully detects hierarchical domain structures in simulated data.

Spectral analysis of cluster borders differentiates equilibrium and fractal polymer conformations.

The method provides an additional criterion for identifying fractal conformations.

Abstract

One of the most important tasks in understanding the complex spatial organization of the genome consists in extracting information about this spatial organization, the function and structure of chromatin topological domains from existing experimental data, in particular, from genome colocalization (Hi-C) matrices. Here we present an algorithm allowing to reveal the underlying hierarchical domain structure of a polymer conformation from analyzing the modularity of colocalization matrices. We also test this algorithm on several model polymer structures: equilibrium globules, random fractal globules and regular fractal (Peano) conformations. We define what we call a spectrum of cluster borders, and show that these spectra behave strikingly differently for equilibrium and fractal conformations, allowing us to suggest an additional criterion to identify fractal polymer conformations.