One aim of synthetic biology is to exert systematic control over cellular behavior, either for medical purposes or to "program" microorganisms. An engineering approach to the design of biological controllers demands a quantitative understanding of the dynamics of both the system to be controlled and the controllers themselves. Here we focus on a widely used method of exerting control in bacterial cells: plasmid vectors bearing gene-promoter pairs. We study two variants of the simplest such element, an unregulated promoter constitutively expressing its gene, against the varying genomic background of four Escherichia coli cell strains. Absolute protein numbers and rates of expression vary with both cell strain and plasmid type, as does the variability of expression across the population. Total variability is most strongly coupled to the cell division process, and after cell size is scaled away, plasmid copy number regulation emerges as a significant effect. We present simple models that capture the main features of the system behavior. Our results confirm that complex interactions between plasmids and their hosts can have significant effects on both expression and variability, even in deliberately simplified systems.