Toxin-antitoxin systems are ubiquitous and have been implicated in persistence, the multidrug tolerance of bacteria, biofilms, and, by extension, most chronic infections. However, their purpose, apparent redundancy, and coordination remain topics of debate. Our model relates molecular mechanisms to population dynamics for a large class of toxin-antitoxin systems and suggests answers to several of the open questions. The generic architecture of toxin-antitoxin systems provides the potential for bistability, and even when the systems do not exhibit bistability alone, they can be coupled to create a strongly bistable, hysteretic switch between normal and toxic states. Stochastic fluctuations can spontaneously switch the system to the toxic state, creating a heterogeneous population of growing and nongrowing cells, or persisters, that exist under normal conditions, rather than as an induced response. Multiple toxin-antitoxin systems can be cooperatively marshaled for greater effect, with the dilution determined by growth rate serving as the coordinating signal. The model predicts and elucidates experimental results that show a characteristic correlation between persister frequency and the number of toxin-antitoxin systems.