Modeling slow-processing of toxin messenger RNAs in type-I Toxin-Antitoxin systems: post-segregational killing and noise filtering.

In type-I toxin-antitoxin (TA) systems, the action of growth-inhibiting toxin proteins
 is counteracted by the antitoxin small RNAs (sRNAs) that prevent the translation of toxin
 messenger RNAs (mRNAs). When a TA module is encoded on a plasmid, the short lifetime
 of antitoxin sRNA compared to toxin mRNAs mediates post-segregational killing (PSK) that
 contribute the plasmid maintenance, while some of the chromosomal encoded TA loci have been
 reported to contribute to persister formation in response to a specific upstream signal. Some of
 the well studied type-I TA systems such as hok/sok are known to have a rather complex regulatory
 mechanism. Transcribed full-length toxin mRNAs fold such that the ribosome binding site is not
 accessible and hence cannot be translated. The mRNAs are slowly processed by RNases, and the
 truncated mRNAs can be either translated or bound by antitoxin sRNA to be quickly degraded.
 We analyze the role of this extra processing by a mathematical model. We first consider the PSK
 scenario, and demonstrate that the extra processing compatibly ensures the high toxin expression
 upon complete plasmid loss, without inducing toxin expression upon acquisition of a plasmid or
 decrease of plasmid number to a non-zero number. We further show that the extra processing
 help filtering the transcription noise, avoiding random activation of toxins in transcriptionally
 regulated TA systems as seen in chromosomal ones. The present model highlights impacts of the
 slow processing reaction, offering insights on why the slow processing reactions are commonly
 identified in multiple type-I TA systems.