The field of synthetic biology has significantly grown over the past decade. Some of the major goals include creating simple gene circuits in order to elucidate complex biological network behaviors and creating new regulation and functionalities in cell. These gene networks allow us to study dynamics of intracellular gene and protein regulation, as they are essential in maintaining homeostasis and cell survival in response to changing or stressful environments. Single cell analytic techniques enable us to study dynamic gene expression of individual cells, which can sometimes be masked by population statistics. First, we developed a microfluidic chemostat for the long-term culturing and imaging of three well characterized strains of cyanobacteria and microalgae. Although microfluidic technology has been applied to culture and monitoring a diverse range of bacterial and eukaryotic species, cyanobacteria and eukaryotic microalgae present several challenges that have made them difficult to culture in a microfluidic setting. Second, we investigated the native ClpXP protease in Escherichia coli, and the correlation between proteins targeted for ClpXP degradation as a result of queueing (competition for a common enzyme). We compared the results to computational model predictions and generated evidence to support the hypothesis that E. coli can adapt the production of ClpXP in response to the number of mistranslated or tagged proteins targeted for ClpXP degradation in the cellular environment. Third, we expressed ClpXP from E. coli in Saccharomyces cerevisiae, and further investigated its properties in an non-native system using flow cytometry. We engineered a ``probe'' that can detect when the processing capacity of ClpXP is saturated in S. cerevisiae. Together, these studies illustrated how synthetic biology and single-cell analytic techniques could help study fundamental cellular processes.