One of the principal challenges in the field of biophysics, particularly that of protein-nucleic acid interactions, is the need to analyze information from single proteins as opposed to ensembles of many molecules. Consequently, the advent of high-resolution imaging in single molecule microscopy has enabled researchers to probe the underlying processes of gene regulatory networks and other biological systems. There is, nonetheless, a tradeoff between spatial and temporal resolution, or the ability to localize a molecule in space at increasingly shorter time scales. As such, this dissertation addresses these challenges that hinder single molecule studies by:: i) developing deconvolution techniques in order to localize both immobile and dynamic molecules from their single images with improved spatial and temporal resolution,: ii) determining a protein\u27s diffusive properties with high temporal resolution, and: iii) applying our analytical methods to study model biological systems
