  We study a theoretical model for the toxin-antitoxin (hok/sok) mechanism for
plasmid maintenance in bacteria. Toxin-antitoxin systems enforce the
maintenance of a plasmid through post-segregational killing of cells that have
lost the plasmid. Key to their function is the tight regulation of expression
of a protein toxin by an sRNA antitoxin. Here, we focus on the nonlinear nature
of the regulatory circuit dynamics of the toxin-antitoxin mechanism. The
mechanism relies on a transient increase in protein concentration rather than
on the steady state of the genetic circuit. Through a systematic analysis of
the parameter dependence of this transient increase, we confirm some known
design features of this system and identify new ones: for an efficient
toxin-antitoxin mechanism, the synthesis rate of the toxin's mRNA template
should be lower that of the sRNA antitoxin, the mRNA template should be more
stable than the sRNA antitoxin, and the mRNA-sRNA complex should be more stable
than the sRNA antitoxin. Moreover, a short half-life of the protein toxin is
also beneficial to the function of the toxin-antitoxin system. In addition, we
study a therapeutic scenario in which a competitor mRNA is introduced to
sequester the sRNA antitoxin, causing the toxic protein to be expressed.
