Chromatin Structure and Dynamics : Insights from a Spectral Study of Critical Interacting Polymers

Overview & Synopsis

The primary objective of this thesis is to conduct a comprehensive examination of polymer models to establish reference results that enhance the analysis of experimental chromatin data. This research delves into both equilibrium and dynamic aspects, addressing fundamental questions about polymer behavior in biological systems. In the first part of the thesis, the focus is on equilibrium properties, providing a theoretical framework for the study of sequential FISH data. This includes introducing essential concepts of equilibrium polymer physics, such as Gaussian chains. It also explores the concept of Rouse modes in a new perspective, connecting it to signal analysis techniques. Computer simulations of self-interacting polymers are performed and analyzed, leading to the development of a spectral-based order parameter that characterizes polymer folding states, up to the establishment of a precise phase diagram for the coil-globule phase transition. The spectral approach is finally applied to sequential FISH data with two distinct results. Firstly, it detects a spectral signature indicating critical polymer behavior, thus validating the usefulness of simple polymer models in chromatin analysis. Secondly, thanks to the implementation of a specific data analysis pipeline, it reveals previously unidentified loops in the same data, offering new insights into the study of the fine chromatin organization. The second part of the thesis shifts attention to dynamical aspects of the coil-globule phase transition. This part begins by introducing stochastic dynamics and polymer dynamics concepts, including the Langevin equation and the (dynamical) Rouse model. Extensive Langevin dynamics simulations of self-interacting polymers are presented, along with an interacting Rouse model that accounts for the coil-globule phase transition and excluded volume effects. The introduction of topological constraints in simulations highlights the robustness of Rouse dynamics, which are only significantly altered in dense globule phases. In the final chapter, the acquired knowledge is applied to explain seemingly paradoxical data from a recent study of Drosophila chromatin dynamics, where again we find indications toward the pertinence of a polymer model at criticality, this time in describing chromosome dynamics. Overall, this thesis provides a valuable foundation for understanding polymer behavior in biological systems and offers insights into interpreting experimental chromatin data.