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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. 

In yeasts and higher eukaryotes, chromatin motions may be tuned to genomic functions, with transcriptional activation and the DNA damage response both leading to profound changes in chromatin dynamics. The RAD51 recombinase is a key mediator of chromatin mobility following DNA damage. As functions of RAD51 beyond DNA repair are being discovered, we asked whether RAD51 modulates chromatin dynamics in the absence of DNA damage and found that inhibition or depletion of RAD51 alters chromatin motions in undamaged cells. Inhibition of RAD51 increased nucleosome clustering. Predictions from polymer models are that chromatin clusters reduce chain mobility and, indeed, we measured reduced motion of individual chromatin loci in cells treated with a RAD51 inhibitor. This effect was conserved in mammalian cells, yeasts, and plant cells. In contrast, RAD51 depletion or inhibition increased global chromatin motions at the microscale. The results uncover a role for RAD51 in regulating local and global chromatin dynamics independently from DNA damage and highlight the importance of considering different physical scales when studying chromatin dynamics. 

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.