abstract: The interaction of proteins with chromatin regulates many cellular functions. Most DNA binding proteins interact both non-specifically and transiently with many chromatin sites, as well as specifically and more stably with cognate binding sites. These interactions and chromatin structure are important in governing protein dynamics. These questions can be addressed theoretically using diffusion models. I will show how that the dynamics of proteins is determined by the 3d organization of chromatin in the nucleus. The time to find a chromatin target depends on chromatin organization around it, which determines the local association and disassociation rates. Hence, the problem of facilitated search by a protein can be mapped to a continuous-time Markov chain. I the second half of the talk I will discuss how protein dynamics can be analyzed to reveal new features of chromatin and protein organization (In collaboration with Anders Hansen & Xavier Darzacq, UC Berkeley). CTCF, a zinc-finger DNA binding protein, functions as a master regulator of 3D genome organization by regulating chromatin looping. Using single-particle tracking (SPT) of endogenously Halo-tagged CTCF in live mammalian cells we discovered that CTCF exhibits a highly unusual, anomalous motion. CTCF proteins generally exist in either a chromatin-associated (bound) or diffusing state (free). We developed a computational framework to study specifically the diffusing subpopulation and found CTCF behavior to be highly anisotropic. Surprisingly, this anisotropy was localized to “domains”, suggesting transient trapping of CTCF in these domains. We found that certain mutations changed the characteristic of CTCF dynamics, allowing it to perform isotropic, Brownian-like motion. Micro-C analysis revealed the importance of these domains in maintaining chromatin loops. In summary, I will present our unpublished discovery of a novel mechanism of nuclear diffusion and a surprising link to CTCF-mediated nuclear organization.