Fig 1.
Drug interaction network for P. aeruginosa.
(A) Schematic representation, adapted from [17], of the principle underlying the drug proportion parameter θ (line of equal dose; dashed lines), which is subsequently used to determine drug interactions, in comparison to different shapes of isobolograms (solid lines), as observed in synergistic (in red; top panel) or antagonistic (in blue; bottom panel) interactions. (B) Schematic illustration of the different interaction types as a function of the drug proportion parameter θ, ranging from synergism to antagonism. Drugs are combined in 9 different proportions (n = 9 for each combination), with each drug alone set to inhibit 75% of growth (S1 Fig). After a fixed time (12 h), bacterial growth is measured, and a quadratic model is used to fit the observed data. The α test [17] was used to determine significance of synergism or antagonism (S1 Table). (C) The α parameter was inferred from measured data to reconstruct a drug interaction network including 52 different antibiotic combinations. Combinations were formed from 12 different drugs, here represented as the nodes of the network, spanning 5 different antibiotic classes (see outer ring). The drug interaction profile is shown through the links (lines) formed between the nodes, and its strength is highlighted by the thickness of the lines and color. Red, black, and blue lines correspond to synergistic, additive, or antagonistic interactions, respectively (see also S3 Fig). The data for this panel are provided in S3 Data. AZL, azlocillin; CAR, carbenicillin; CEF, cefsulodin; CEZ, ceftazidime; CIP, ciprofloxacin; DOR, doripenem; GEN, gentamicin; IC75, concentration inhibiting 75% of bacterial growth; IMI, imipenem; PIT, piperacillin + tazobactam; STR, streptomycin; TIC, ticarcillin; TOB, tobramycin.
Table 1.
List of antibiotics used in this study.
Fig 2.
Collateral sensitivity network.
The FCRs among 8 of the 12 drugs used in this study were obtained from our previous work [30]. FCR ranges from 0 to 1, such that 0 indicates that all populations (12–20 populations per combination) were sensitive to the corresponding other drug, thus having complete reciprocal sensitivity, whereas 1 highlights that none of the populations with resistance to one of the antibiotics in a pair suffered exacerbated sensitivity against the other. For the graphical illustration, we divided the combinations into 4 groups: complete collateral sensitivity (FCR ≤ 0.25; dark purple lines), partial collateral sensitivity (0.25 < FCR ≤ 0.5; light dashed pink lines), partial cross-resistance (0.5 < FCR < 0.75; light green dashed lines), and complete cross-resistance (FCR ≥ 0.75; dark green lines). CAR, carbenicillin; CEF, cefsulodin; CIP, ciprofloxacin; DOR, doripenem; FCR, frequency of collateral resistances; GEN, gentamicin; IMI, imipenem; PIT, piperacillin + tazobactam; STR, streptomycin.
Fig 3.
Experimental design and inference of adaptation rates.
(A) Schematic representation of the evolution experiment with antibiotic combinations. Thirty-eight combinations were serially transferred every 12 h (season) into fresh medium containing antibiotics mixed in 5 different proportions (n = 8 per proportion and drug combination). An uninhibited control was also included, replicated 4 times, resulting in a total of 44 populations per combination and 1,672 for all combinations. Single-drug treatments of any drug A and B aimed at inhibiting 75% of growth relative to a drug-free environment (i.e., IC75). (B) An example of the quantitative growth measures obtained for a particular combination (CIP plus GEN) and the various drug proportions. Each panel shows 1 out of 5 seasons of growth (measured with OD as a proxy ± SD) over a 12-h period. Vertical grey lines denote the time window from which the slope was calculated to infer the growth rate r of each evolving population during exponential growth. All the drug proportions considered are highlighted in different colors (yellow to red), as well as the no-drug control (black). (C) Six exemplary populations from the CIP plus GEN combination experiments illustrating the change in growth rate r over 10 seasons of growth for each of the drug proportions. The rate of adaptation was calculated following previous work [16], and as indicated on the left of panel C, tadapt is defined as the time required to reach half of the change in growth rate, Δr. The data for this figure are provided in S4 Data. CFU, colony-forming unit; CIP, ciprofloxacin; GEN, gentamicin; OD, optical density; IC75, concentration inhibiting 75% of bacterial growth.
Fig 4.
(A) ACE network built from the rates of adaptation of surviving populations in the combination environment. The color and thickness of the lines (links) formed between the drugs (nodes) reflect the quantiles within which the inferred adaptation rates are found relative to the entire distribution: orange thick lines denote the combinations with the slowest adaptation rates (one of the aims of treatment efficacy), and grey thin lines highlight those with fast adaptation. (B) ACE network on the number of extinction events observed in the combination treatments. Thickness and color of the links represent the number of extinct populations, ranging from 0 (grey) to 8 (dark orange). Adaptation rates and extinction frequencies are inferred from the growth characteristics provided in S4 Data. ACE, antibiotic combination efficacy; AZL, azlocillin; CAR, carbenicillin; CEF, cefsulodin; CEZ, ceftazidime; CIP, ciprofloxacin; DOR, doripenem; GEN, gentamicin; IMI, imipenem; PIT, piperacillin + tazobactam; STR, streptomycin; TIC, ticarcillin; TOB, tobramycin.
Fig 5.
BN analysis of antibiotic resistance evolution under combination therapy.
(A) BN obtained from a constraint-based interleaved incremental association algorithm including 4 different random variables: drug interaction types, FCR, proportion of extinctions, and rate of adaptation. (B) Based on the BN, we calculated the conditional probabilities of rate of adaptation for different types of collateral effects (top panel) and extinction frequencies for different antibiotic interaction characteristics (bottom panel). The Bayesian analysis is based on data for drug interaction characteristics (S2 Data), collateral effects [30], and extinction frequencies, and adaptation rates are inferred from growth characteristics during experimental evolution (S4 Data). Adap., rate of adaptation; BN, Bayesian network; Ext., proportion of extinctions; FCR, frequency of collateral resistances; Int., drug interaction types.
Fig 6.
Weighted ACE networks and their Bayesian analysis.
We assessed to what extent adaptation to one of the drugs of a pair determined the overall rate of adaptation to the combination treatment. The stronger component drug of each pair was identified as the one with lower adaptation rates in monotherapy. We subsequently standardized the adaptation rates towards the combination by those towards either (A) the stronger or (B) the weaker component drug, resulting in 2 weighted ACE networks. Orange thick lines indicate slower adaptation, while grey thin bands denote fast adaptation. (C) Results of the BN analysis on the original network versus the 2 standardized networks. The relationship between drug interaction type and extinction frequency was stable across all analyses, while the dependence of adaptation rate on evolved collateral effects disappeared when adaptation rates were standardized by the stronger component. Adaptation rates are inferred from the data on growth characteristics during experimental evolution, provided in S4 Data. ACE, antibiotic combination efficacy; AZL, azlocillin; BN, Bayesian network; CAR, carbenicillin; CEF, cefsulodin; CEZ, ceftazidime; CIP, ciprofloxacin; DOR, doripenem; GEN, gentamicin; IMI, imipenem; PIT, piperacillin + tazobactam; STR, streptomycin; TIC, ticarcillin; TOB, tobramycin.
Fig 7.
Influence of the initial inhibition level on adaptation rate and population extinction.
In a separate round of evolution experiments, we evaluated the consequences of the initial inhibition levels in synergistic and antagonistic combinations. The experiment was performed following the protocol of the main evolution experiment (Fig 3A), with the exception that the starting doses of the combinations were fixed at different levels of inhibition for the combinations. (A) Inferred rates of adaptation as a function of initial inhibitory levels. We determined initial inhibition by measuring in the first season of the evolution experiment the AUC of growth over time (measured as OD as a proxy) for each replicate population and then standardized it against the average AUC of the no-drug control (x-axis, AUCi). The rate of adaptation (y-axis) was inferred as for the main evolution experiment (Fig 3). (B) Extinction was significantly more often observed in synergistic rather than antagonistic combinations, even at the same level of inhibition (results for logistic regression analysis in S4 Table). Adaptation rates and extinction frequencies are inferred from growth characteristics during experimental evolution, provided in S5 Data. AUC, area under the curve; AUCi, area under the curve of relative inhibition of growth; CAR, carbenicillin; CIP, ciprofloxacin; GEN, gentamicin; OD, optical density; PIT, piperacillin + tazobactam; STR, streptomycin; TOB, tobramycin.