Incorporating toxin hypothesis into a mathematical model of persister formation and dynamics

Biofilms are well known for their extreme tolerance to antibiotics. Recent experimental evidence has indicated the existence of a small fraction of specialized persister cells may be responsible for this tolerance. Although persister cells seem to exist in planktonic bacterial populations, within a biofilm the additional protection offered by the polymeric matrix allows persister cells to evade elimination and serve as a source for re-population. Whether persister cells develop through interactions with toxin/antitoxin modules or are senescent bacteria is an open question. In this investigation we contrast results of the analysis of a mathematical model of the toxin/antitoxin hypothesis for bacteria in a chemostat with results incorporating the senescence hypothesis. We find that the persister fraction of the population as a function of washout rate provides a viable distinction between the two hypotheses. We also give simulation results that indicate that a strategy of alternating dose/withdrawal disinfection can be effective in clearing the entire persister and susceptible populations of bacteria. This strategy was considered previously in analysis of a generic model of persister formation. We find that extending the model of persister formation to include the toxin/antitoxin interactions in a chemostat does not alter the qualitative results that success of the dosing strategy depends on the withdrawal time. While this treatment is restricted to planktonic bacterial populations, it serves as a framework for including persister cells in a spatially dependent biofilm model.