The entire genome becomes mobilized following DNA damage. Understanding the mechanisms that act at the genome level requires that we embrace experimental and computational strategies to capture the behavior of the long-chain DNA polymer, which is the building block for the chromosome. Long-chain polymers exhibit constrained, sub-diffusive motion in the nucleus. Cross-linking proteins, including cohesin and condensin, have a disproportionate effect on genome organization in their ability to stabilize transient interactions. Cross-linking proteins can segregate the genome into sub-domains through polymer–polymer phase separation (PPPS) and can drive the formation of gene clusters through small changes in their binding kinetics. Principles from polymer physics provide a means to unravel the mysteries hidden in the chains of life.

Transient DNA loops occur throughout the genome due to thermal fluctuations of DNA and the function of SMC complex proteins such as condensin and cohesin. Transient crosslinking within and between chromosomes and loop extrusion by SMCs have profound effects on high-order chromatin organization and exhibit specificity in cell type, cell cycle stage, and cellular environment. SMC complexes anchor one end to DNA with the other extending some distance and retracting to form a loop. How cells regulate loop sizes and how loops distribute along chromatin are emerging questions. To understand loop size regulation, we employed bead–spring polymer chain models of chromatin and the activity of an SMC complex on chromatin. Our study shows that (1) the stiffness of the chromatin polymer chain, (2) the tensile stiffness of chromatin crosslinking complexes such as condensin, and (3) the strength of the internal or external tethering of chromatin chains cooperatively dictate the loop size distribution and compaction volume of induced chromatin domains. When strong DNA tethers are invoked, loop size distributions are tuned by condensin stiffness. When DNA tethers are released, loop size distributions are tuned by chromatin stiffness. In this three-way interaction, the presence and strength of tethering unexpectedly dictates chromatin conformation within a topological domain.

We present a novel method for identifying topological features of chromatin domains in live cells using single-particle tracking and topological data analysis (TDA). By applying TDA to particle trajectories, we can effectively detect complex spatial patterns, such as loops, that are often missed by traditional time series analysis. Using simulations of polymer bead–spring chains, we have validated the accuracy of our method and determined its limitations for detecting loops. Our approach offers a promising avenue for exploring the topological complexity of chromatin in living cells using TDA techniques.

Homology search is a means through which DNA double-strand breaks (DSBs) explore the genome for sequences that enable error-free repair, known as homologous recombination. A better understanding of this search process is fundamental to the relationship between higher-order chromosome organization and DNA damage. Here, we use an entropic bead-spring polymer chain model to simulate the spatiotemporal dynamics of the yeast genome during interphase. The chromosome is organized by transient and dynamic cross-links representing structural maintenance of chromosome (SMC) complexes. DNA damage is modeled as a break in the bead-spring chain, coupled with a removal of crosslinks from beads proximal to the break site. We show that the removal of cross-links drives the exploration of genomic space by the damaged ends, while rates and densities of intact dynamic crosslinking have only a minor role. Local depletion of SMC cross-links proximal to the break site enables the damaged segment to escape the chromosome territory and enhances its ability to explore the genome. Our study reveals a foundational principle by which DSBs can encounter distant regions of sequence homology.