Magnetic Polymer Models for Epigenomic Spreading and Chromatin Organization

In this thesis we present a detailed investigation of the interplay between 3D organization of the chromatin and epigenomic spreading in Eukaryotic nuclei, via polymer physics models. We begin with a review of the biology behind epigenetic processes, and of some basic physical models that have been proposed to describe them. We also examine the model presented in [1], and study in details its equilibrium and non-equilibrium dynamics via extensive molecular dynamic simulations. At equilibrium we confirm the existence of a first-order phase transition between a swollen and epigenetically disordered phase, and a compact ordered one. At non-equilibrium we prove the existence of two novel phases [2] where the polymer is organized in a compact-disordered or swollen-ordered fashion. We extend the model by inserting “genomic bookmarking” [2], that is transcription factors permanently bound to the DNA and which enhance the positive feedback loop in the epigenetic machinerie. We also develop a more realistic, biologically inspired, model which successfully reproduces the distribution of epigenetic marks in a Drosophila chromosome. We next discuss the model proposed in [1] and its relation with magnetic polymer models on a lattice [3]. We find a Landau-Ginzburg-like expression for the free-energy of a dense magnetic polymer in the mean-field approximation. The new free-energy, and ad hoc Montecarlo simulations, confirm the presence of a first-order phase transition between a swollen-disordered phase and a compact-ordered one at equilibrium. We also study the non-equilibrium kinetic of the mean-field model by employing a set of opportunely modified “Model A” equations. At last, we develop a phenomenological mean-field model for a melt of chromatin fibers in a closed system akin to the Eukaryotic nuclei [4]. The phenomenological free-energy will depend on a conserved density field and a non-conserved magnetisation field. The equilibrium phases will be hence investigated analytically via a common-tangent construction construction, and include both uniform and demixed phases undergoing phase separation. The dynamics of the equilibrium phases is then studied via a set of “Model C” equations in order to estimate the critical coarsening exponents. Finally, we insert in the kinetic equations some non-equilibrium terms akin to a first-order reaction which arrest the phase separation.