Testing the optimality properties of a dual antibiotic treatment in a two-locus, two-allele model

Abstract

Mathematically speaking, it is self-evident that the optimal control of complex, dynamical systems with many interacting components cannot be achieved with 'non-responsive' control strategies that are constant through time. Although there are notable exceptions, this is usually how we design treatments with antimicrobial drugs when we give the same dose and the same antibiotic combination each day. Here, we use a frequency-and densitydependent pharmacogenetics mathematical model based on a standard, two-locus, two-allele representation of how bacteria resist antibiotics to probe the question of whether optimal antibiotic treatments might, in fact, be constant through time. The model describes the ecological and evolutionary dynamics of different sub-populations of the bacterium Escherichia coli that compete for a single limiting resource in a two-drug environment. We use in vitro evolutionary experiments to calibrate and test the model and show that antibiotic environments can support dynamically changing and heterogeneous population structures. We then demonstrate, theoretically and empirically, that the best treatment strategies should adapt through time and constant strategies are not optimal.

Hotspot Dosages of Most Rapid Antibiotic Resistance Evolution

“…To quantify rates of adaptation (ROA), we applied a rate of change measure to population densities and growth rates. 12 Three versions of this measure (Methods) concur that adaptation to erythromycin has a non-linear, non-monotone dependence on dose, consistent with prior theory, 10 and populations adapted fastest when exposed to near-MIC dosages (30 and 35 µg / ml , Figure 2A); the latter figure reveals our first inverted-U. eTB108 behaves analogously (Figure 2) with a strong correlation between ROA in population density (Figure 2A) and ROA of population mean GFP per optical density (Figure 2B; Deming regression R 2 ≈ 0.84, p « 0.05, Figure S2), so increases in AcrB expression correlate with population density.…”

“…This is consistent with both ours and prior theory 3 which predict the peak of the inverted U could be found in principle at an arbitrary dose. Moreover, the theory of competitive release between sensitive and resistant subpopulations can explain 10 the non-monotone dose responses we observe: the MRA occurs at the dose where susceptible sub-populations are suppressed, so they ‘release’ the maximum amount of extracelullar nutrients to resistant sub-populations at those dosages that do not suppress the growth of the latter. These theories indicate our findings are not specific to erythromycin and, indeed, prior E.coli data [19, Figure S13] shows an analogous dosing hotspot for the antibiotic doxycycline.…”

“…A more sophisticated density and frequency-dependent population genetics model 10 tuned to erythromycin efflux makes a prediction we can seek in data: redolent of the Eagle Effect, 11 in drug-adapted dose responses, where population density is regressed against antibiotic dose following each treatment, do not remain monotone as they increase in density to form a ‘bump’ at the MRA hotspot. That model predicts short-term theoretical dose-responses follow standard antibiotic sensitivity assays whereby the addition of more drug reduces bacterial density, 10 but repeated antibiotic treatments could modify the dose response such that it appears non-monotone at a hotspot due to selection for subpopulations with amplified pump operons in their genomes.…”

Conditionally Redundant Bacteriocin Targeting byPseudomonas syringae

“…With the widely recognized breakdown in antibiotic-mediated control of human and agricultural pathogens 29–31 , resulting from the selection for and dissemination of antibiotic-resistance genes, there has been a push to both rethink how antibiotics are used, as well as the adoption of new control methods. To this end, researchers have explored several potentially intersecting approaches, none of which have yet been widely adopted, including: applying evolutionary principles to use antibiotics in temporal combinations to slow the emergence of resistance 32–34 , using antibiotic combinations that result in ‘collateral sensitivity’ 35 , combining antibiotics with bacteriophages (phage-therapy) in a synergistic combination 36 , and utilizing bacteriocins (including combinations thereof) as narrow-spectrum antibacterials 21,23 . Inherent in all of these approaches is the recognition that, regardless of the selective agent, there are always paths to the evolution of resistance.…”

Optimising Antibiotic Usage to Treat Bacterial Infections

“…Mathematical modelling is increasingly being used to investigate optimal treatment regimens for antibiotic therapy1314151617. However, these studies either omit pharmacodynamic data, by assuming that the antibiotic induced death rate is constant; or only analyse a very limited number of alternative treatment regimens.…”