Project Summary Background and Knowledge Gap: Unraveling life's intracellular processes at single molecule (SM) spatiotem- poral scales is critical toward monitoring therapeutic agents and developing disease diagnostics. Yet drawing insight on biomolecular events at such scales presents profound challenges to existing fluorescence imaging. Fundamentally, this arises due to the model selection problem: unavoidable (quantum, thermal, detector) noise at the SM scale means that the data cannot easily be used to resolve “models" such as the number of molecules located within a small region of space. An experimental solution toward resolving this problem earned the 2014 Chemistry Nobel prize though such solutions necessarily come at a cost. Either spatial or temporal resolution is compromised while samples are often irradiated over extended durations inducing sample photodamage. Recent Progress: Thanks to having reached the funding midpoint of both our NIGMS R01s, we developed mathematical tools allowing us to mitigate, sometimes dramatically, spatial (R01GM130745) and temporal (R01 GM134426) compromises of existing experimental solutions to model selection. Our work has resulted in 10 publications, 15 collaborations, and 18 ongoing projects. Here are just 3 projects: 1) in recent publications, we derived SM properties using 2-3 orders of magnitude fewer photons than would normally be used to obtain bulk properties from fluorescence correlation spectroscopy (FCS); 2) in accepted work, we provide a means to determine protein cluster stoichiometry (up to hundreds of subunits) eliminating the requirement to control fluorescent label properties; 3) in work about to be submitted, we track with equal accuracy and precision about an order of magnitude more labeled molecules as winners of the Nature Methods tracking competition. Overview of Future Work: We've organized our future work as extensions of both R01's, projects merging both R01's and directions beyond both. Briefly, to ext