Magnetic Polymer Models for Epigenetics-Driven Chromosome Folding

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.

to appear in PRE

References in corpus (13)

• Non-equilibrium chromosome looping via molecular slip-links
• The physics of epigenetics
• Ephemeral protein binding to DNA shapes stable nuclear bodies and chromatin domains
• Shaping Epigenetic Memory via Genomic Bookmarking
• Synergy of Topoisomerase and Structural-Maintenance-of-Chromosomes Proteins Creates a Universal Pathway to Simplify Genome Topology
• First measurement of the differential branching fraction and $CP$ asymmetry of the $B^{\pm }\to {\pi }^{\pm }{\mu }^{+}{\mu }^{-}$ decay
• A Symmetry Breaking Model for X Chromosome Inactivation
• Theory for stability and regulation of epigenetic landscapes
• Bifurcation in epigenetics: implications in development, proliferation and diseases
• Nonequilibrium Theory of Epigenomic Microphase Separation in the Cell Nucleus
• Magnetic Polymer Models for Epigenomic Organisation and Phase Separation
• Phase diagram of magnetic polymers
• Epigenetic Transitions and Knotted Solitons in Stretched Chromatin

Cited by in corpus (5)

• Nonequilibrium Theory of Epigenomic Microphase Separation in the Cell Nucleus
• Magnetic Polymer Models for Epigenomic Organisation and Phase Separation
• Rheology and Viscoelasticity of Proteins and Nucleic Acids Condensates
• Competition between local erasure and long-range spreading of a single biochemical mark leads to epigenetic bistability
• Emergence of compact-disordered phase in a polymer Potts model