Bacterial persistence is a bottleneck in designing an effective antibiotic dosing strategy for complete eradication of bacterial populations. Persister cells are not antibiotic-resistant mutants; rather they exhibit a different phenotype from normal cells, namely they lower their growth rate significantly when attacked by an antibiotic, thereby experiencing much lower death rates than normal cells. Persisters usually constitute only a small fraction of a total bacterial population. Because of dormancy of persister cells, an antibiotic has reduced efficacy when used to quickly eradicate a bacterial infection. The bactericidal action of the antibiotic is compromised due to phenotypic switching of normal cells to persister cells in the presence of the antibiotic and back-switching from persister cells to normal cells when the antibiotic is eventually depleted (
Lewis 2007).
Balaban, Merrin et al. (2004) proposed a simple model to study the bacterial phenotypic switching in the presence of an antibiotic. Subsequently, several investigators (
Cogan 2007,
Fasani and Savageau 2013) have proposed more complex models incorporating toxin hypotheses, to study the emergence of persistence and phenotypic switching. Based on these models, various dosing strategies,
such as piecewise constant dosing with alternate dose/withdrawal, have been studied (
Cogan 2006,
De Leenheer and Cogan 2009,
Cogan, Brown et al. 2012) in attempts to increase the bactericidal effect of an antibiotic. Some of these strategies are difficult to implement in practice, and many rely on the fidelity of the model describing the effect of an antibiotic on bacteria eradication. In this paper, we propose a robust optimal dosing strategy, which considers the effect of model parameter uncertainty on optimal dosing. To illustrate our approach, we first use experimental data to build a dynamic mathematical model, which we use next to study the population dynamics of normal and persister cells in the presence of an antibiotic. We finally use the model to find a robustly optimal dosing strategy for bacterial disinfection.
References
Balaban, N. Q., J. Merrin, R. Chait, L. Kowalik and S. Leibler (2004). "Bacterial persistence as a phenotypic switch." Science 305(5690): 1622-1625.
Cogan, N. G. (2006). "Effects of persister formation on bacterial response to dosing." Journal of Theoretical Biology 238(3): 694-703.
Cogan, N. G. (2007). "Incorporating toxin hypothesis into a mathematical model of persister formation and dynamics." Journal of Theoretical Biology 248(2): 340-349.
Cogan, N. G., J. Brown, K. Darres and K. Petty (2012). "Optimal Control Strategies for Disinfection of Bacterial Populations with Persister and Susceptible Dynamics." Antimicrobial Agents and Chemotherapy 56(9): 4816-4826.
De Leenheer, P. and N. G. Cogan (2009). "Failure of antibiotic treatment in microbial populations." Journal of Mathematical Biology 59(4): 563-579.
Fasani, R. A. and M. A. Savageau (2013). "Molecular mechanisms of multiple toxin-antitoxin systems are coordinated to govern the persister phenotype." Proceedings of the National Academy of Sciences of the United States of America 110(27): E2528-E2537.
Lewis, K. (2007). "Persister cells, dormancy and infectious disease." Nature Reviews Microbiology 5(1): 48-56.
