Abstract
The chromatin, a complex of DNA and proteins, serves as the substrate of genetic information in eukaryotic cells. Its three-dimensional organization plays a fundamental role in gene regulation. However, the multi-scale physical properties and mechanisms underlying this organization, beyond nucleosome formation, remain poorly understood. In this thesis, we tackle this issue using concepts from polymer physics and statistical physics. Our objectives are twofold: to extract the multi-scale polymeric properties of chromatin from recent experimental data (super-resolution microscopy, m-FISH) and to understand the coupling between polymer dynamics and the epigenetic landscape. To achieve this, we studied a magnetic polymer model that assigns an epigenetic expression or repression state to each polymer segment, while analyzing phase transitions and interactions.Our work, based on the analysis of probability density functions of chromatin segment distances, reveals the coexistence of two distinct polymeric phases: a dense, space-filling fractal phase and a more diluted, confined phase, generated by loop extrusion by proteins such as cohesin or by droplet formation through phase separation. Drawing on these experimental data, we demonstrated the influence of this latter phase on the frequency of segment interactions and proposed a method to predict the location of these loops at the single-cell level. These results were modeled using a heterogeneous random walk, characterized by non-Markovian properties due to the confined phase.By applying the hypothesis of two coexisting regimes to high-resolution data from the adult Drosophila brain, we studied the interactions between transcriptional regulatory elements. We developed a method to estimate the enrichment of contacts between promoters and enhancers according to the transcriptional state in cellular tissues. Our results emphasize the crucial role of topologically associating domains (TADs) in modulating these contacts and, consequently, gene expression.Finally, through Monte Carlo simulations, we numerically explored the coupling between the three-dimensional organization of chromatin and its epigenetic landscape using a magnetic polymer model. By analogy, this model establishes a dynamic coupling between a freely fluctuating polymer in 3D space and the internal properties of the monomers through associated spin orientations. This approach allowed us to characterize the phase transitions of the model in both the presence and absence of an external field, thus providing a theoretical framework to model the influence of epigenetic factors on the 3D organization of chromatin.