# Bifractal nature of chromosome contact maps

## TL;DR

This paper reveals that chromosomal contact maps from Hi-C data are bifractal, characterized by two fractal dimensions, and introduces a hierarchical model that accurately describes their multifractal spectrum and conformational changes.

## Contribution

It introduces a novel multifractal analysis revealing bifractality in Hi-C contact maps and provides an exact hierarchical model that matches experimental data.

## Key findings

- Hi-C maps are bifractal with two distinct fractal dimensions.
- The hierarchical model accurately predicts the multifractal spectrum.
- The method improves estimation of the contact probability scaling exponent.

## Abstract

Modern biological techniques such as Hi-C permit to measure probabilities that different chromosomal regions are close in space. These probabilities can be visualised as matrices called contact maps. In this paper, we introduce a multifractal analysis of chromosomal contact maps. Our analysis reveals that Hi-C maps are bifractal, i.e. complex geometrical objects characterized by two distinct fractal dimensions. To rationalize this observation, we introduce a model that describes chromosomes as a hierarchical set of nested domains and we solve it exactly. The predicted multifractal spectrum is in excellent quantitative agreement with experimental data. Moreover, we show that our theory yields to a more robust estimation of the scaling exponent of the contact probability than existing methods. By applying this method to experimental data, we detect subtle conformational changes among chromosomes during differentiation of human stem cells.