Stroboscopic photoactivated single particle tracking (spaSPT) relies on stochasticlabeling to isolate the paths of individual fluorophores, and can provide information about the behavior of biological macromolecules in their native cellular environment. Existing spaSPT modalities generate large numbers of short trajectories, each representing a fragment of an individual emitter's path. When interpreting this data through the lens of diffusion models, it is essential to account for the fragmentary nature of trajectories, experimental biases arising from the imaging geometry, and our ignorance about the correct underlying diffusion model. In this thesis, we describe several methods for interpretation of spaSPT data that provide estimates about the number and characteristics of mobility states in spaSPT data while accounting for known experimental artifacts. We explore the uses and limitations of these models on simulated and experimental datasets.

In the final chapter, we apply these methods to study the competitive chromatin binding in the type II nuclear receptors (T2NRs). T2NRs are a class of ligand-activated transcription factors that require heterodimerization with a common factor, the retinoid X receptor (RXR), to bind chromatin and regulate target genes. Because all T2NRs must dimerize with a common pool of RXR, competition between individual T2NRs may limit access to the bound state. This mechanism has been proposed to underlie the oncogenic inactivation of wildtype retinoic acid receptor alpha (RARA), a prototypical T2NR, in the presence of RARA fusion proteins that occur in acute promyelocytic leukemia (APL). Such fusion proteins may compete RXR away from the wildtype RARA, impairing its ability to regulate target genes. Here, we use spaSPT to directly measure the effects of RARA fusion proteins on the chromatin binding of endogenously tagged RARA and RXR. Using the tools developed in the previous chapters, we find that RARA fusion proteins act as stronger competitors for dimerization with RXR than wildtype T2NRs, and are also seemingly exempt from a novel autoregulatory mechanism that controls the concentration of wildtype RARA. Together, these results provide new insights into the interdependence of T2NR gene regulation and the manner by which it is disrupted in disease.