THEORETICAL MODELING OF CHROMATIN DYNAMICS

The cell nucleus is an extremely fascinating system from a physicist’s perspective. It houses the organism’s entire genome, with its intricate folding and dynamic rearrangement over multiple scales that, alongside processes such as gene regulation, DNA repair, and chromosomal segregation, provide a fertile ground for applying physical models. Within the nucleus, the genome is organized as a biopolymer made of DNA and proteins collectively known as chromatin. Chromatin plays a central role in gene regulation, genome stability, and cellular processes, yet many aspects of its physical properties and dynamics remain poorly understood. In the last 20 years, loop-extrusion of the chromatin fiber by cohesin has been identified as one of the main mechanism driving the organization and the dynamics of the genome at scales of hundreds of kilobase pairs. This thesis addresses key questions about the role of loop-extrusion in chromatin dynamics through a multidisciplinary approach combining molecular dynamics simulations, statistical mechanics and the analysis of experimental data. The first part of the thesis investigates the subdiffusive motion of chromatin loci, focusing on how cohesin-mediated loop extrusion shapes this dynamics. We demonstrate that long-range loops, rather than the act of extrusion itself, dominate the observed behavior. A critical result is the derivation of a simple relationship between the subdiffusive exponent and average loop length, independent of other system parameters. The second part explores the dynamics of chromatin contacts, analyzing experimental data from live-cell imaging and polymer simulations. We reveal a double-exponential distribution of contact residence times when cohesin is present, reflecting the interplay between thermal motion and loop extrusion. Our model quantifies this behavior and suggests potential methods to estimate cohesin stepping speeds, though experimental limitations affect precision. We also validate that 2D analysis of contact dynamics can reliably capture essential features, overcoming experimental constraints in 3D imaging. Finally, the thesis examines the residence times of intrachain contacts in ideal polymers, offering analytical and computational insights into their dependence on monomer separation. This study highlights the limitations of simple polymer models in replicating experimental findings, suggesting directions for more realistic simulations. Overall, this work provides novel insights into chromatin and polymer dynamics, contributing to a deeper theoretical understanding of genome organization and its implications for biological processes, while outlining promising directions for future research.