Magnetic Polymer Models for Epigenetics-Driven Chromosome Folding

TL;DR

This paper models how epigenetic modifications influence chromosome folding using magnetic polymer models, revealing phase transitions and stable states that align with biological observations.

Contribution

It introduces a novel magnetic polymer model for epigenetics-driven chromosome folding, combining mean-field analysis and Brownian Dynamics simulations, including non-equilibrium effects.

Findings

First-order phase transition causes epigenetic spreading and chromosome collapse

Simulations confirm mean-field predictions of folding behavior

Non-equilibrium models reveal new stable chromatin phases

Abstract

Epigenetics is a driving force of important and ubiquitous phenomena in nature such as cell differentiation or even metamorphosis. Oppositely to its widespread role, understanding the biophysical principles that allow epigenetics to control and rewire gene regulatory networks remains an open challenge. In this work we study the effects of epigenetic modifications on the spatial folding of chromosomes -- and hence on the expression of the underlying genes -- by mapping the problem to a class of models known as magnetic polymers. In this work we show that a first-order phase transition underlies the simultaneous spreading of certain epigenetic marks and the conformational collapse of a chromosome. Further, we describe Brownian Dynamics simulations of the model in which the topology of the polymer and thermal fluctuations are fully taken into account and that confirms our mean-field predictions. Extending our models to allow for non-equilibrium terms yields new stable phases which qualitatively agrees with observations in vivo. Our results show that statistical mechanics techniques applied to models of magnetic polymers can be successfully exploited to rationalize the outcomes of experiments designed to probe the interplay between a dynamic epigenetic landscape and chromatin organization.