Aminoglycoside Concentrations Required for Synergy with Carbapenems Against

Aminoglycoside Concentrations Required for Synergy with Carbapenems against

Pseudomonas aeruginosa Determined via Downloaded from Mechanistic Studies and Modeling

Rajbharan Yadav,a Jürgen B. Bulitta,c Elena K. Schneider,a Beom Soo Shin,d Tony Velkov,a Roger L. Nation,a Cornelia B. Landersdorfera,b,e Drug Delivery, Disposition and Dynamics, Monash Institute of Pharmaceutical Sciences, Monash University, Parkville, Victoria, Australiaa; Centre for Medicine Use and Safety, Faculty of Pharmacy and Pharmaceutical Sciences, Monash University, Parkville, Victoria, Australiab; Center for Pharmacometrics and Systems http://aac.asm.org/ Pharmacology, College of Pharmacy, University of Florida, Orlando, Florida, USAc; School of Pharmacy, Sungkyunkwan University, Suwon, Gyeonggi-do, South Koread; School of Pharmacy and Pharmaceutical Sciences, University at Buffalo, State University of New York, Buffalo, New York, USAe

ABSTRACT This study aimed to systematically identify the aminoglycoside concentrations required for synergy with a carbapenem and characterize the permeabilizing effect Received 5 April 2017 Returned for of aminoglycosides on the outer membrane of Pseudomonas aeruginosa. Monotherapies modification 2 July 2017 Accepted 4 September 2017 and combinations of four aminoglycosides and three carbapenems were studied for ac- Accepted manuscript posted online 11 on August 13, 2018 by MONASH UNIVERSITY tivity against P. aeruginosa strain AH298-GFP in 48-h static-concentration time-kill studies September 2017 (SCTK) (inoculum: 107.6 CFU/ml). The outer membrane-permeabilizing effect of tobramy- Citation Yadav R, Bulitta JB, Schneider EK, Shin cin alone and in combination with imipenem was characterized via electron microscopy, BS, Velkov T, Nation RL, Landersdorfer CB. 2017. Aminoglycoside concentrations required for confocal imaging, and the nitrocefin assay. A mechanism-based model (MBM) was de- synergy with carbapenems against veloped to simultaneously describe the time course of bacterial killing and preven- Pseudomonas aeruginosa determined via tion of regrowth by imipenem combined with each of the four aminoglycosides. No- mechanistic studies and modeling. Antimicrob Agents Chemother 61:e00722-17. https://doi tably, 0.25 mg/liter of tobramycin, which was inactive in monotherapy, achieved .org/10.1128/AAC.00722-17. Ն synergy (i.e., 2-log10 more killing than the most active monotherapy at 24 h) com- Copyright © 2017 American Society for bined with imipenem. Electron micrographs, confocal image analyses, and the nitro- Microbiology. All Rights Reserved. cefin uptake data showed distinct outer membrane damage by tobramycin, which Address correspondence to Jürgen B. Bulitta, [email protected]fl.edu, or Cornelia B. Landersdorfer, was more extensive for the combination with imipenem. The MBM indicated that [email protected]. aminoglycosides enhanced the imipenem target site concentration up to 4.27-fold. Tobramycin was the most potent aminoglycoside to permeabilize the outer membrane; tobramycin (0.216 mg/liter), gentamicin (0.739 mg/liter), amikacin (1.70 mg/liter), or streptomycin (5.19 mg/liter) was required for half-maximal permeabilization. In summary, our SCTK, mechanistic studies and MBM indicated that tobramycin was highly synergistic and displayed the maximum outer membrane disruption potential among the tested aminoglycosides. These findings support the optimization of highly promising antibiotic combination dosage regimens for critically ill patients.

KEYWORDS tobramycin, imipenem, synergy, outer membrane, mathematical modeling

ultidrug-resistant (MDR) Pseudomonas aeruginosa has emerged as a major threat Mto hospitalized patients worldwide and causes infections associated with a high degree of morbidity and mortality (1, 2) in patients of all ages. This situation creates severe challenges to physicians treating such patients due to the shortage of new and efﬁcacious antibiotics (2, 3). Synergistic combinations of available antibiotics offer a promising and tangible option to combat MDR P. aeruginosa. Carbapenems are potent ␤-lactam antibiotics that have been used as a ﬁrst-line treatment in monotherapy against susceptible P. aeruginosa isolates in nosocomial

December 2017 Volume 61 Issue 12 e00722-17 Antimicrobial Agents and Chemotherapy aac.asm.org 1 Yadav et al. Antimicrobial Agents and Chemotherapy infections; however, an extensive rise in emergence of resistance over the last decades has diminished the clinical utility of carbapenem monotherapy (4–6). Aminoglycosides in monotherapy have demonstrated substantial bacterial load reduction, but this was followed by rapid and extensive emergence of resistance and ultimately treatment failure (7, 8). In the past, in vitro and in vivo studies on carbapenem-aminoglycoside combinations demonstrated synergy (9–13). The outer bacterial membrane of P. aeruginosa is a formidable barrier for the target site penetration of many antibiotics (14–16). The primary mechanism of action of aminoglycosides (i.e., interference with protein synthesis within the bacterial cell) is well known and characterized (17). However, the disruptive effect of aminoglycosides Downloaded from on the outer membrane of Gram-negative bacteria is less recognized (18–21). Kadu- rugamuwa et al. (22, 23) reported that albumin-conjugated aminoglycosides can Ͼ cause 3-log10 killing of P. aeruginosa before entering into the cytosol and thus without interfering with protein synthesis. Therefore, we hypothesized that disruption of the outer membrane by an aminoglycoside enhances the periplasmic target site penetration of carbapenems and thereby contributes to synergistic bacterial killing. To the best of our knowledge, the http://aac.asm.org/ minimum concentrations of different aminoglycosides required for synergistic killing of P. aeruginosa in combination with carbapenems have not been previously identiﬁed. Furthermore, the permeabilizing effect of several aminoglycosides on the outer bacterial membrane in combination with different carbapenems has not been characterized via mechanistic experimental studies and mechanism-based mathematical models (MBM). This study primarily aimed to systematically identify the minimum concentration of four aminoglycosides required to achieve synergy with each of three carbapenems on August 13, 2018 by MONASH UNIVERSITY against P. aeruginosa. Second, we sought to characterize the outer membrane- permeabilizing effect of tobramycin alone and in combination with a carbapenem using scanning and transmission electron microscopy, confocal imaging, and the nitroceﬁn assay. Finally, we simultaneously determined the extent and time course of synergistic bacterial killing and resistance prevention by the studied aminoglycoside- carbapenem combinations via MBM.

RESULTS P. aeruginosa AH298-GFP was susceptible to meropenem and doripenem (MIC: 1 mg/liter), and to imipenem with an MIC of 4 mg/liter (i.e., the highest MIC deemed susceptible by the EUCAST). This strain was susceptible to tobramycin (MIC: 0.25 mg/liter), gentamicin (0.50 mg/liter), and amikacin (2.0 mg/liter) but resistant to streptomycin (MIC: 16 mg/liter see Table S1 in the supplemental material). The log10 mutation frequencies on 3ϫ-MIC agar plates were below Ϫ7.6 for all antibiotics except doripenem (Ϫ5.30) and streptomycin (Ϫ5.58). Imipenem was the most active carbapenem in monotherapy, with bacterial killing of

2.09 to 2.47 log10 for concentrations of 2 to 16 mg/liter at 6 h (Table 1). Early bacterial killing (i.e., at 6 h) by meropenem and doripenem was less than that by imipenem; however, at 24 h, 1 mg/liter of meropenem provided slightly better killing than imipenem at 4 mg/liter. Notably, while tobramycin at 0.25 mg/liter was inactive in monotherapy, it achieved synergy at 24 h with imipenem at 2 or 4 mg/liter and meropenem at 1 mg/liter (Table 1). Tobramycin at 0.25 mg/liter in combination with doripenem at 1 to 4 mg/liter was beneﬁcial (killing at6hof2.98 to 3.11 log10) compared to monotherapies but was not synergistic at 24 h. Tobramycin at 1 mg/liter combined with imipenem (2 to 16 mg/liter), meropenem (1 to 4 mg/liter), or doripenem (4 mg/liter) prevented regrowth at 48 h (Table 1). Based on the results of our ﬁrst set of static concentration time-kill experiments (SCTK) (Table 1), we performed the second set of SCTK with imipenem at 4 mg/liter (i.e., close to the average unbound steady-state plasma concentrations in patients) alone and in combination with each of four aminoglycosides. These studies sought to identify the minimum aminoglycoside concentrations which yield synergy at 24 h. As little as

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TABLE 1 Log10 change in viable counts compared to those at 0 h for AH298-GFP in the ﬁrst set of static concentration time-kill studies at an initial inoculum of ϳ107.6 CFU/mla

Log10 change in viable counts from that at 0 h for AH298-GFP at: Drug(s) 6h 24h 48h None (growth control) 1.96 2.50 2.76 IPM (1 mg/liter) 1.00 1.82 2.75 IPM (2 mg/liter) Ϫ2.09 1.75 2.73 IPM (4 mg/liter) Ϫ2.37 1.64 2.80 IPM (8 mg/liter) Ϫ2.44 Ϫ1.98 2.54

IPM (16 mg/liter) Ϫ2.47 Ϫ3.62 Ϫ4.31 Downloaded from TOB (0.25 mg/liter) 1.44 1.87 2.72 TOB (0.5 mg/liter) Ϫ2.21 1.53 2.62 TOB (1 mg/liter) Ϫ2.43 0.06 2.42 IPM (1 mg/liter) ϩ TOB (0.25 mg/liter) Ϫ2.18 2.05 2.73 IPM (1 mg/liter) ϩ TOB (0.5 mg/liter) Ϫ2.31 Ϫ1.41 2.66 IPM (1 mg/liter) ϩ TOB (1 mg/liter) Ϫ3.71 Ϫ2.34 1.78 IPM (2 mg/liter) ϩ TOB (0.25 mg/liter) Ϫ3.23 Ϫ1.02 1.97 IPM (2 mg/liter) ϩ TOB (0.5 mg/liter) Ϫ3.53 Ϫ3.00 Ϫ1.26 IPM (2 mg/liter) ϩ TOB (1 mg/liter) Ϫ3.98 Ϫ3.26 Ϫ2.17 http://aac.asm.org/ IPM (4 mg/liter) ϩ TOB (0.25 mg/liter) Ϫ3.10 Ϫ3.59 2.44 IPM (4 mg/liter) ϩ TOB (0.5 mg/liter) Ϫ3.20 Ϫ3.77 Ϫ4.26 IPM (4 mg/liter) ϩ TOB (1 mg/liter) Ϫ4.26 Ϫ4.70 Ϫ4.77 IPM (8 mg/liter) ϩ TOB (0.25 mg/liter) Ϫ4.29 Ϫ4.20 Ϫ4.70 IPM (8 mg/liter) ϩ TOB (0.5mg/liter) Ϫ4.11 Ϫ3.97 Ϫ4.72 IPM (8 mg/liter) ϩ TOB (1 mg/liter) Ϫ4.20 Ϫ4.70 Ϫ5.45 IPM (16 mg/liter) ϩ TOB (0.25 mg/liter) Ϫ3.97 Ϫ3.97 Ϫ4.00 IPM (16 mg/liter) ϩ TOB (0.5mg/liter) Ϫ4.36 Ϫ4.33 Ϫ5.23 IPM (16 mg/liter) ϩ TOB (1 mg/liter) Ϫ4.26 Ϫ6.23 Ϫ7.23

None (growth control) 0.95 1.43 2.08 on August 13, 2018 by MONASH UNIVERSITY MEM (1 mg/liter) Ϫ0.20 Ϫ1.01 1.35 MEM (2 mg/liter) Ϫ0.39 Ϫ2.65 0.20 MEM (4 mg/liter) Ϫ1.35 Ϫ2.75 Ϫ0.69 TOB (0.25 mg/liter) 0.58 1.47 2.13 TOB (1 mg/liter) Ϫ3.87 Ϫ1.27 1.48 MEM (1 mg/liter) ϩ TOB (0.25 mg/liter) Ϫ2.88 Ϫ3.05 Ϫ0.40 MEM (1 mg/liter) ϩ TOB (1 mg/liter) Ϫ4.12 Ϫ3.87 Ϫ3.42 MEM (2 mg/liter) ϩ TOB (0.25 mg/liter) Ϫ3.05 Ϫ3.29 Ϫ1.67 MEM (2 mg/liter) ϩ TOB (1 mg/liter) Ϫ3.94 Ϫ4.07 Ϫ4.73 MEM (4 mg/liter) ϩ TOB (0.25 mg/liter) Ϫ3.42 Ϫ4.37 Ϫ3.40 MEM (4 mg/liter) ϩ TOB (1 mg/liter) Ϫ4.01 Ϫ4.38 Ϫ5.16 None (growth control) 1.25 1.89 2.01 DOR (1 mg/liter) 0.18 0.79 1.17 DOR (2 mg/liter) 0.19 Ϫ0.65 1.14 DOR (4 mg/liter) Ϫ0.97 Ϫ1.80 1.18 TOB (0.25 mg/liter) 0.55 1.44 1.66 TOB (1 mg/liter) Ϫ3.81 Ϫ0.01 1.41 DOR (1 mg/liter ϩ TOB (0.25 mg/liter) Ϫ2.98 0.55 1.45 DOR (1 mg/liter ϩ TOB (1 mg/liter) Ϫ3.77 Ϫ3.06 0.91 DOR (2 mg/liter ϩ TOB (0.25 mg/liter) Ϫ3.09 Ϫ1.56 1.19 DOR (2 mg/liter ϩ TOB (1 mg/liter) Ϫ4.39 Ϫ2.69 0.19 DOR (4 mg/liter ϩ TOB (0.25 mg/liter) Ϫ3.11 Ϫ1.74 1.19 DOR (4 mg/liter ϩ TOB (1 mg/liter) Ϫ4.50 Ϫ2.95 Ϫ1.34 a Ͼ Cells shaded in dark gray represent 2 log10 more bacterial killing than the most active monotherapy (i.e., meeting the empirical deﬁnition of synergy), and cells shaded in light gray represent 1.0 to 2.0 log10 more killing than the most active monotherapy. IPM, imipenem; TOB, tobramycin; MEM, meropenem; DOR, doripenem.

0.25 mg/liter of tobramycin demonstrated synergy with imipenem 4 mg/liter at 24 h, followed by extensive regrowth at 48 h (Fig. 1A). Gentamicin at 0.5 mg/liter, amikacin at 1 mg/liter, or streptomycin at 16 mg/liter was required to yield synergy at 24 h in combination with 4 mg/liter of imipenem; between 24 and 48 h, extensive regrowth occurred (Fig. 1B, C, and D). These results on combinations with 4 mg/liter of imipenem indicated that tobramycin was synergistic at lower concentrations than those of gentamicin, followed by amikacin and, ﬁnally, streptomycin.

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FIG 1 Observed (symbols) and individual MBM-ﬁtted (lines) viable count proﬁles for imipenem combined with each of four aminoglycosides (tobramycin, gentamicin, amikacin, and streptomycin) against AH298- GFP. The left-hand graphs in each of the panels (A to D) show growth controls and aminoglycoside monotherapies. The right-hand graphs in each of the panels show aminoglycosides in combination with imipenem at 4 mg/liter. Observed viable counts below the limit of counting (i.e., below 1.0 log10 CFU/ml) were plotted as 0. IPM, imipenem; TOB, tobramycin; GEN, gentamicin; AMK, amikacin; STR, streptomycin.

Emergence of resistance during antibiotic treatment was defined as viable counts of resistant bacteria above those of the growth control line (broken black horizontal line in Fig. 2) at 48 h. All monotherapies (except tobramycin at 16 and 32 mg/liter) displayed extensive emergence of resistance quantified on antibiotic-containing agar plates (3ϫ MIC) (Fig. 2). Imipenem at 4 mg/liter in combination with 0.5 to 32 mg/liter of tobramycin, 8 mg/liter of gentamicin, 8 mg/liter of amikacin, or 64 mg/liter of streptomycin demonstrated suppression of resistance to both imipenem and the respective aminoglycoside (Fig. 2). Imipenem at 4 mg/liter in combination with even 1ϫ MIC of tobramycin (0.25 mg/liter) or gentamicin (0.5 mg/liter) was sufficient to suppress the amplification of imipenem resistance (Fig. 2A and B).

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FIG 2 Subpopulations resistant to imipenem and aminoglycosides (tobramycin, gentamicin, amikacin, and streptomycin) on 3ϫ-MIC agar plates at 48 h for control and treatment arms. The left-hand graphs for each of the panels (A to D) represent the bacterial counts on imipenem-containing agar plates and the right-hand graphs represent the counts on aminoglycoside-containing agar plates. All monotherapies (except tobramycin at 16 and 32 mg/liter) resulted in ampliﬁ- cation of resistant subpopulations. Resistance suppression to both imipenem and aminoglycosides at 48 h was achieved by imipenem at 4 mg/liter in combination with Ն2ϫ MIC (0.5 mg/liter) of tobramycin, 16ϫ MIC (8 mg/liter) of gentamicin, or 4ϫ MIC (8 mg/liter and 64 mg/liter) of amikacin and streptomycin. The lowest (purple symbols) and highest (green symbols) concentrations of each aminoglycoside are highlighted in each panel.

Our third set of SCTK contained the superior (tobramycin), intermediate (amikacin), and least synergistic (streptomycin) aminoglycosides in combination with meropenem. These SCTK evaluated whether the ranking of the outer membrane effect of aminoglycosides differed between carbapenems. These SCTK revealed that tobramycin was synergistic also with meropenem, as only 0.25 mg/liter tobramycin was required to achieve synergy with 1 mg/liter of meropenem (2.10 log10 more killing than the best active monotherapy at 24 h), followed by regrowth at 48 h (see Fig. S1A). Amikacin at

1 mg/liter in combination with meropenem at 1 mg/liter yielded synergy (2.11 log10 more killing than the best active monotherapy at 24 h), followed by extensive regrowth (Fig. S1B). Streptomycin at 16 mg/liter achieved synergy with 1 mg/liter of meropenem

(2.73 log10 more killing than the best active monotherapy at 24 h) and prevented regrowth at 48 h (Fig. S1C). All monotherapies (except tobramycin at 4 and 16 mg/liter) resulted in ampliﬁcation of resistant subpopulations that grew on 3ϫ-MIC drug plates. Meropenem at 1 mg/liter in combination with Ն2ϫ MIC of tobramycin or amikacin and 4ϫ MIC of streptomycin demonstrated suppression of resistance to both meropenem and the aminoglycosides (Fig. S2).

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FIG 3 Scanning (A) and transmission (B) electron microscopy images of the AH298-GFP strain treated with imipenem and tobramycin alone and in combinations for 2 h. Thin arrows indicate outer membrane blebbing and numerous protrusions, while thick arrows show dents on the outer bacterial membrane.

Dotted thick arrows indicate drastic disruptions with extensive loss of intracellular material and absence on August 13, 2018 by MONASH UNIVERSITY of the outer membrane.

Electron microscopy. Scanning electron microscopy (SEM) and transmission electron microscopy (TEM) imaging of AH298-GFP cells treated with imipenem and tobramycin alone and in combination for 2 h demonstrated extensive ultrastructural changes (Fig. 3). The bacterial cell surfaces in the untreated growth control were smooth, uniform, and intact (Fig. 3A). Imipenem treatment resulted in a relatively smooth cell surface and induced the formation of a spheroid cell shape, as expected due to inactivation of penicillin-binding proteins (PBPs) (Fig. 3). Tobramycin alone created several peripheral outer membrane blebs and protrusions. Imipenem plus tobramycin combinations demonstrated extensive ultrastructural damage that was evidenced by dents, blebs, leakage, and numerous pits and protrusions (Fig. 3A). TEM analysis confirmed the SEM findings, as monotherapies and even more so combination treatments showed severe ultrastructural damage, cell disintegration with leakage of intracellular materials, and even the near-complete absence of a bacterial cell membrane (Fig. 3B). Confocal imaging. Confocal microscopy provided further evidence of outer membrane damage by tobramycin in monotherapy and combination with imipenem (Fig. 4). Our quantitative analysis for strain AH298-GFP (expressing green fluorescent protein [GFP]) demonstrated that tobramycin at 16 and 32 mg/liter reduced the cytosolic GFP signal by 71% Ϯ 5.7% and 82% Ϯ 9.0% relative to the growth control. For the combinations of tobramycin with 4 mg/liter of imipenem, the GFP signal was reduced even more (by 84% Ϯ 6.4% and 90% Ϯ 9.6% [Fig. 4]). Nitrocefin assay. We assessed the extent of nitrocefin hydrolysis under imipenem, tobramycin, and combination treatment to further assess the permeability of the outer membrane for nitrocefin. The nitrocefin assay showed a slightly higher absorbance for 16 and 32 mg/liter of tobramycin than for the control (Fig. 5). Nitrocefin hydrolysis was considerably more extensive for all three imipenem-tobramycin combinations (Fig. 5). The AmpC ␤-lactamase-related hydrolysis of nitrocefin was considerably higher (P value ϭ 0.0058; unpaired t test) for 0.25 mg/liter of tobramycin combined with imipenem at 4 mg/liter than for the monotherapies.

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FIG 4 (A) Confocal microscopy images of cytosolic GFP signals from AH298-GFP treated with imipenem and tobramycin alone and in combinations for 2 h. (B) GFP signal as the percentage of untreated growth control following drug treatment (data are averages Ϯ SD).

Mechanism-based modeling. Our MBM required three preexisting bacterial populations (i.e., 6 compartments) to adequately describe the time course of bacterial killing and resistance of AH298-GFP (Fig. 6). This MBM simultaneously described the effects of all five monotherapies and the combinations of imipenem with each of the four aminoglycosides. The model yielded unbiased and precise curve fits (Fig. 6; see also Fig. S3). The coefficient of correlation was 0.989 for the observed versus individual

fitted log10 viable counts. It is very difficult to obtain experimental data on the two states for a given population. Model performance for competing models incorporating only two populations (i.e., 4 compartments) was clearly inferior based on the significantly poorer (233.61 points; P Ͻ 0.0001) objective function (Ϫ1ϫ log likelihood in S-ADAPT) and population fit plots. Subpopulation synergy alone was not sufficient to describe the time course of bacterial killing and regrowth following combination treatments. Informed by the mechanistic experimental data, inclusion of outer membrane disruption by the aminoglycosides (i.e., mechanistic synergy) was essential to simultaneously describe all viable count data (Fig. 1; see also Fig. S3). In the model (Fig. 6), disruption of the outer membrane by the aminoglycoside was assumed to enhance the target site penetration

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FIG 5 Outer membrane-permeabilizing activity of imipenem and tobramycin alone and in combinations against AH298-GFP measured by the nitroceﬁn uptake assay. Data are presented as the averages Ϯ SD of four independent measurements taken at 30 min. http://aac.asm.org/ of the carbapenem. This mechanistic synergy was expressed as a decrease in the

KC50,IPM (the imipenem concentration causing 50% of the maximum killing rate constant [Kmax]; see Table 2) of all three bacterial populations (Fig. S4A). A decrease in

KC50,IPM in the MBM is equivalent to an increase of the imipenem target site concentration. Implementing mechanistic synergy for all three populations improved the ﬁnal model performance signiﬁcantly (Ϫ1ϫ log likelihood improvement by 44; P Ͻ 0.0001, likelihood ratio test). on August 13, 2018 by MONASH UNIVERSITY To illustrate the maximum achievable synergy, we calculated the fold increase in the carbapenem target site concentrations at aminoglycoside concentrations similar to the

FIG 6 Structure of the mechanism-based model for bacterial growth and killing by imipenem plus an aminoglycoside. The IPMS/AGSS population was susceptible to both imipenem and the four aminoglycosides. The other two populations, i.e., IPMR/AGSI (imipenem resistant and aminoglycoside intermediate) and IPMI/AGSR (imipenem intermediate and aminoglycoside resistant), are not shown. A life cycle growth model (58, 60) was utilized to describe the underlying biology of bacterial replication via two states for each of the three populations. The maximum killing rate constant (Kmax) and the associated antibiotic concentration (KC50) causing 50% of Kmax are explained in Table 2. The permeabilizing effect of aminoglycosides on the outer bacterial membrane (i.e., the aminoglycoside enhancing the target site penetration of imipenem) was applied to all combinations. The outer membrane effect parameters

(Imax,OM,AGS and IC50,OM,AGS) are explained in Table 2.

December 2017 Volume 61 Issue 12 e00722-17 aac.asm.org 8 Aminoglycoside Concentrations and Mechanism of Synergy Antimicrobial Agents and Chemotherapy unbound peak concentrations. For all three bacterial populations, the imipenem target site concentration increased 3.50- to 4.27-fold in the presence of 64 mg/liter of streptomycin, 64 mg/liter of amikacin, 32 mg/liter of gentamicin, and 32 mg/liter of tobramycin compared to that in the absence of an aminoglycoside (Fig. S4A). To describe the outer membrane permeabilization in the model, the fold increase in target site concentrations was expressed as a fold decrease in KC50,IPM (Fig. S4A). Tobramycin was found to be highly potent with respect to the outer membrane- permeabilizing effect, as the model-estimated IC50,OM,AGS (i.e., aminoglycoside concentration causing 50% of Imax,OM,AGS; see Table 2) was considerably lower for tobramycin

(0.216 mg/liter) than for gentamicin (0.739 mg/liter; 3.42-fold difference relative to Downloaded from tobramycin), amikacin (1.70 mg/liter; 7.87-fold difference relative to tobramycin), and streptomycin (5.19 mg/liter; 24.02-fold difference relative to streptomycin [Fig. S4B]). Overall, these results suggested that the outer membrane-permeabilizing effect was achieved at the lowest concentrations for tobramycin, followed by gentamicin, amikacin, and, ultimately, streptomycin.

DISCUSSION http://aac.asm.org/ This is the first study to systematically identify the minimum concentrations of four aminoglycosides that yield synergy in combination with carbapenems and to characterize the permeabilizing effect of aminoglycosides on the outer membrane of P. aeruginosa via qualitative and quantitative approaches including MBM. We selected four aminoglycosides that differ in their outer membrane binding affinities (19). Our SCTK for the combinations of imipenem 4 at mg/liter with each of four aminoglycosides demonstrated that tobramycin was synergistic at the lowest concentrations (i.e., only 0.25 mg/liter was required for synergy at 24 h [Fig. 1A]); this synergy on August 13, 2018 by MONASH UNIVERSITY was achieved at (slightly) higher concentrations for gentamicin (0.5 mg/liter [Fig. 1B]), amikacin (1 mg/liter [Fig. 1C]), and, finally, streptomycin (16 mg/liter [Fig. 1D]). Resis- tance to both imipenem and tobramycin was suppressed at 48 h by 4 mg/liter of imipenem combined with Ն2ϫ MIC (0.5 mg/liter) of tobramycin, 16ϫ MIC (8 mg/liter) of gentamicin, or 4ϫ MIC (8 mg/liter or 64 mg/liter) of amikacin or streptomycin (Fig. ϫ Ϫ 2). The log10 mutation frequency quantified at 1.75 MIC of imipenem was 4.70, Ϫ which was similar to the model-estimated log10 mutation frequency ( 3.72) for the intermediate population from drug-free-plate data of SCTK. Aminoglycosides bind to the negatively charged lipopolysaccharides in the outer membrane of Gram-negative bacteria and can thus disrupt the outer membrane structure (22, 23). This occurs before they penetrate into the cytosol and exert their intracellular effect on protein synthesis (17). The permeabilizing effect likely enhances the periplasmic target site penetration of other antibiotics (e.g., carbapenems) used in combination with an aminoglycoside. To evaluate this synergy mechanism, we assessed imipenem and tobramycin (i.e., the aminoglycoside with the highest outer membrane binding affinity) alone and in combination via three experimental approaches in P. aeruginosa. The SEM and TEM micrographs showed outer membrane damage to P. aeruginosa cells by tobramycin in monotherapy after2hofexposure; this ultrastructural damage was even more pronounced for the combinations (Fig. 3). The changes to the outer membrane of P. aeruginosa caused by tobramycin monotherapy (Fig. 3A) were in agreement with similar effects reported for gentamicin (22). While the cell surface following exposure to imipenem monotherapies was smooth and intact (Fig. 3 and 4), imipenem induced the formation of a spheroid cell shape as expected. These changes in morphology are likely due to the high affinity of imipenem toward penicillin-binding proteins (especially PBP2) (24–26). The more extensive outer membrane damage for the combination than for monotherapies suggested that imipenem caused additional bacterial damage after2hofdrug exposure. The confocal imaging analysis demonstrated an extensive decrease in the cytosolic GFP from the bacterial cells for tobramycin monotherapy and its combinations (Fig. 4). The loss of GFP was slightly more extensive for the combinations

December 2017 Volume 61 Issue 12 e00722-17 aac.asm.org 9 Yadav et al. Antimicrobial Agents and Chemotherapy than for tobramycin monotherapies. In agreement with the SEM and TEM micrographs, these results provided additional evidence of more pronounced outer membrane damage by tobramycin-containing treatments. Further supporting the SEM, TEM, and cytosolic GFP studies, the extent of nitrocefin uptake was greater under treatment at high tobramycin concentrations, especially for the imipenem-tobramycin combinations (Fig. 5), than with the control and imipenem monotherapy. When the outer membrane is permeabilized by an aminoglycoside, nitrocefin can penetrate more rapidly into the periplasm, where it is hydrolyzed; this leads to more extensive nitrocefin hydrolysis and thus an increased absorbance (27).

Nitrocefin uptake was significantly increased (P ϭ 0.0058) for tobramycin at 0.25 Downloaded from mg/liter combined with 4 mg/liter of imipenem relative to that with monotherapy with imipenem at 4 mg/liter. Thus, enhanced target site penetration and hydrolysis of nitrocefin occurred at a low tobramycin concentration (0.25 mg/liter), in agreement with the synergy results from SCTK (Fig. 1A; Table 1). This nitrocefin assay may be particularly sensitive to enhanced target site penetration of both nitrocefin and imipenem. In the presence of tobramycin, the higher periplasmic imipenem concentrations likely lead to inactivation of penicillin-binding protein 4, which is known to http://aac.asm.org/ extensively and rapidly upregulate the inducible AmpC ␤-lactamase in P. aeruginosa (28). This mechanism may have contributed to the more extensive nitrocefin uptake for the combinations relative to those for the monotherapies (Fig. 5). Future studies are needed to further investigate these mechanistic details and the time course of outer membrane permeabilization and AmpC induction. Our MBM characterized the time course of synergistic bacterial killing and prevention of regrowth well for imipenem plus four aminoglycosides and parameter estimates were precise (Fig. 6; Table 2; see also Fig. S3). A model with only one Kmax for the on August 13, 2018 by MONASH UNIVERSITY aminoglycosides across all three bacterial populations resulted in a significantly (6.20 points) poorer objective function (Ϫ1ϫ log likelihood in S-ADAPT) and inferior population fits compared to those with the model with three Kmax values. It is important to note that killing is a function of the Kmax,KC50, and the aminoglycoside concentration. The bacterial killing function that defines the extent of killing of each population [i.e., ϫ ϩ Kmax CAGS/(CAGS KC50,AGS)] is incorporated in equation 2 (see Materials and Methods). The function that describes bacterial killing of each population by all four aminoglycosides has been simulated using Berkeley Madonna. This was performed with the respective Kmax and KC50 values for each of the three populations across a range of relevant concentrations. Simulations indicated that, notwithstanding the lower Kmax value for the intermediate than for the other two populations, bacterial killing was less extensive for the resistant and intermediate populations than for the susceptible population (Fig. S5). The same relative magnitude of killing, i.e., susceptible Ͼ intermediate Ͼ resistant, was observed across all four aminoglycosides. This clearly indicates the importance of considering the respective values for not only Kmax but also KC50 for each of the three populations. In the MBM, the aminoglycosides permeabilized the outer membrane and thus significantly (P Ͻ 0.001) enhanced the target site penetration of imipenem (Fig. S4), as informed by the mechanistic studies (Fig. 3, 4, and 5). The permeabilizing effect by aminoglycosides was expressed as a substantial decrease in KC50 of imipenem

(KC50,IPM) for all three bacterial populations. We calculated the impact of this synergy mechanism in the presence of the highest clinically achievable unbound aminoglycoside peak concentrations (Fig. S4A). Notably, tobramycin was estimated to permeabilize the outer membrane at the lowest aminoglycoside concentrations, followed by gentamicin, amikacin, and, ﬁnally, streptomycin (Fig. S4B). This is reﬂected by the aminoglycoside concentrations required to half-maximally permeabilize the outer membrane (IC50,OM,AGS [Table 2]) and is in agreement with the SCTK results (Fig. 1). Thus, our results suggest that extensive synergistic bacterial killing and resistance suppression can be achieved at clinically relevant concentrations of tobramycin, gentamicin, and amikacin (Fig. 1 and 2; see also Fig. S1) due to the aminoglycoside permeabilizing the outer membrane in susceptible

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TABLE 2 Population mean parameter estimates for the imipenem-aminoglycoside (i.e., tobramycin, gentamicin, amikacin and streptomycin) combination model against AH298-GFP Parameter (unit)a Abbreviation Population mean value (SE[%])

Initial inoculum (log10 CFU/ml) LogCFU0 7.53 (1.7) Maximum population size (log10 CFU/ml) Log CFUmax 9.21 (1.0) Ϫ1 Replication rate constant (h ) k21 50 (ﬁxed)

Mean generation time (min) S S Ϫ1 IPM /AGS k12,SS 52.9 (3.8) R I Ϫ1 IPM /AGS k12,RI 215 (13.8) I R Ϫ1 IPM /AGS k12,IR 52.9 (3.8) Downloaded from

Log10 mutation frequencies Ϫ IPM LogMUT,IPM 3.72 (4.2) Ϫ AGS LogMUT,AGS 8.22 (1.1)

Killing by IPM Ϫ1 Maximum killing rate constant (h ) Kmax,IPM 4.66 (14.7)

Imipenem concn causing 50% of Kmax,IPM (mg/liter) S S IPM /AGS KC50,SS,IPM 2.81 (12.3) http://aac.asm.org/ R/ I IPM AGS KC50,RI,IPM 105 (18.3) I R IPM /AGS KC50,IR,IPM 83.5 (7.7)

Maximum killing rate constants (hϪ1) S S IPM /AGS Kmax,SS,AGS 14.1 (7.9) R I IPM /AGS Kmax,RI,AGS 5.78 (23.7) I R IPM /AGS Kmax,IR,AGS 14.1 (7.9)

AGS concn causing 50% of Kmax,AGS (mg/liter) TOB GEN AMK STR on August 13, 2018 by MONASH UNIVERSITY S S IPM /AGS KC50,SS,AGS 4.05 (18.5) 6.01 (20.0) 7.98 (19.3) 84.8 (11.9) R I IPM /AGS KC50,RI,AGS 34.4 (11.2) 41.8 (11.5) 119 (8.5) 699 (10.4) I R IPM /AGS KC50,IR,AGS 178 (11.4) 195 (8.0) 372 (7.1) 2740 (4.2)

Permeabilization of the outer membrane by AGS b Maximum fractional decrease of KC50,IPM by AGS Imax,OM,AGS 0.773 (0.536 to 0.803) via outer membrane disruption

AGS concn causing 50% of Imax,OM,AGS (mg/liter) IC50,OM,AGS TOB GEN AMK STR 0.216 (20.9) 0.739 (16.6) 1.70 (17.2) 5.19 (18.6)

SD of residual error on log10 scale SDCFU 0.486 (4.0) aAGS, aminoglycoside; IPM, imipenem; TOB, tobramycin; GEN, gentamicin; AMK, amikacin; STR, streptomycin. b 95% conﬁdence interval for Imax,OM,AGS.

P. aeruginosa. These results provide a mechanistic explanation for the synergy that we previously found for carbapenem-aminoglycoside combinations against P. aeruginosa isolates highly resistant to both antibiotics (13). Our findings are in agreement with a study by Loh et al. (19) on the correlation between the aminoglycoside MICs and their binding affinity to the outer membrane of P. aeruginosa. This study demonstrated the highest outer membrane affinity for tobramycin compared to eight other evaluated aminoglycosides. In particular, our MBM model and estimated IC50,OM,AGS provide a quantitative framework that allows us to predict the impact of this synergy mechanism in the context of clinically relevant carbapenem-aminoglycoside dosage regimens (Fig. S4B). Several prior studies have shown carbapenem and aminoglycoside synergy against P. aeruginosa; however, limited or no information was provided on the characterization of the synergistic potential of aminoglycosides, type of synergy, and suppression of resistance via a mechanistic and MBM-based approach (29–33). The combination of meropenem plus an aminoglycoside in the hollow-fiber infection model and in murine pneumonia and septicemia models achieved synergistic bacterial killing, suppression of resistance, or both (10, 12, 34). Few studies have assessed the outer membrane disruption of Gram-negative bacteria by aminoglycosides (18–22). These studies used either 1-N-phenylnaphthylamine (18, 19) or SEM and TEM to characterize the

December 2017 Volume 61 Issue 12 e00722-17 aac.asm.org 11 Yadav et al. Antimicrobial Agents and Chemotherapy effect of aminoglycosides on the outer bacterial membrane in monotherapy (22). However, none of these studies identified the minimum aminoglycoside concentrations required for synergy. In addition, no study characterized the outer membrane-permeabilizing effect of various aminoglycosides in monotherapy and combination with a carbapenem via SCTK, electron micrographs, confocal images, nitrocefin uptake assay, and MBM. In conclusion, tobramycin was the most synergistic and streptomycin the least synergistic aminoglycoside in combination with a carbapenem against P. aeruginosa. Our MBM adequately characterized the synergistic bacterial killing and resistance prevention by all combinations. The synergy mechanism proposed by MBM (i.e., the Downloaded from aminoglycosides permeabilizing the outer bacterial membrane) was confirmed by electron micrographs of ultrastructural damage, loss of cytosolic GFP, and nitrocefin uptake results. The aminoglycoside concentration required to half-maximally permeabilize the outer membrane was lowest for tobramycin (0.216 mg/liter), followed by gentamicin (0.739 mg/liter), amikacin (1.70 mg/liter), and streptomycin (5.19 mg/liter). This is the first study that identified the minimum synergistic concentrations of four aminoglycosides in combinations with a carbapenem and character- http://aac.asm.org/ ized the outer membrane-permeabilizing effect of aminoglycosides at clinically relevant concentrations by a combination of experimental and modeling approaches.

MATERIALS AND METHODS Bacterial strain, antibiotics, and susceptibility testing. P. aeruginosa strain AH298-GFP (containing the AmpC ␤-lactamase), which contains a chromosomal gene for green ﬂuorescent protein (GFP) and expresses GFP under the control of the growth rate-dependent rrnBp1 promoter as described previously

(35). All susceptibility testing and static concentration time-kill experiments (SCTK) were performed in on August 13, 2018 by MONASH UNIVERSITY cation-adjusted Mueller-Hinton II broth (CAMHB; BBL, BD, Sparks, MD). Viable counting was conducted on cation-adjusted Mueller-Hinton II agar (CAMHA; Medium Preparation Unit, The University of Melbourne). Stock solutions of imipenem (Merck Sharp & Dohme Pty., NSW, Australia), meropenem (Fresenius Kabi, NSW, Australia), doripenem (AK Scientific, Inc., Union City, CA), tobramycin (AK Scientific, Inc.), gentamicin (AK Scientific, Inc.), amikacin (Sigma-Aldrich, St. Louis, MO), and streptomycin (AK Scientific, Inc.) were prepared in sterile distilled water and filter sterilized with a Millex-GV 0.22-␮m polyvinylidene difluoride (PVDF) syringe filter (Merck Millipore Ltd., Cork, Ireland). The MICs were determined in triplicate according to Clinical and Laboratory Standards Institute (CLSI) guidelines (36). European Committee on Antimicrobial Susceptibility Testing (EUCAST) breakpoints were used to define resistance (37). Static concentration time-kill experiments. All SCTK were performed over 48 h using an initial inoculum of ϳ107.6 CFU/ml against AH298-GFP as described previously (13, 38–40). In keeping with other ϳ 7.6 in vitro studies, we targeted an inoculum of 10 log10 CFU/ml to mirror bacterial densities in severe infections in patients (41–43). This permitted characterization of the mechanism of synergistic effect of an aminoglycoside in combination with a carbapenem at a relatively high bacterial density. In the first set of SCTK, we studied three carbapenems (imipenem [1 to 16 mg/liter], meropenem [1 to 4 mg/liter], and doripenem [1 to 4 mg/liter]) and tobramycin (0.25 to 1 mg/liter) in monotherapy and combinations. The second set of SCTK assessed imipenem (4 mg/liter) and four different aminoglycosides (tobramycin [0.25 to 32 mg/liter], gentamicin [0.25 to 8 mg/liter], amikacin [0.25 to 8 mg/liter], and streptomycin [0.5 to 64 mg/liter]) in monotherapy and combinations. The final set of SCTK was conducted using meropenem (1 mg/liter) with tobramycin (0.25 to 16 mg/liter), amikacin (0.5 to 8 mg/liter), or streptomycin (2 to 64 mg/liter) in monotherapy and combinations. The antibiotic concentrations studied included the range of clinically achievable unbound concentrations of carbapenems and aminoglycosides following standard dosing in patients, i.e., the maximum achievable concentrations, average steady-state concentrations, and trough concentrations (40, 44–50). We also examined relatively low concentrations of aminoglycosides, which did not have a bacterial killing effect in monotherapy, to quantify their potential beneficial and synergistic effects in combination with a carbapenem, the latter due to the effect of the aminoglycosides on the bacterial outer membrane. Serial broth samples were taken within 5 to 10 min before dosing (i.e., at 0 h) and at 1, 3, 6, 24, 29, and 48 h. At 24 h, bacterial suspensions were centrifuged, the supernatants carefully removed, and bacteria resuspended in fresh, prewarmed broth with the targeted antibiotic concentration(s). For imipenem and tobramycin combinations, bacterial samples were collected at three additional time points (9, 12, and 16 h). As previously described, at 6 and 30 h an amount corresponding to 50% of the original dose was supplemented for imipenem, 30% of the original dose for meropenem, and 30% for doripenem, to further offset the thermal degradation of carbapenems based on our stability data (40, 51, 52). All bacterial samples were washed twice in sterile saline to remove antibiotic carryover. Viable counts were determined by manual plating of 100 ␮l of an undiluted or appropriately diluted suspension in saline (1:10-fold) onto CAMHA plates (38–40, 53). Aliquots of the undiluted or diluted sample were plated on agar plates supplemented with a carbapenem or an aminoglycoside at 3ϫ MIC to quantify the

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resistant subpopulations. The less susceptible or resistant imipenem subpopulations at baseline (0 h) were also quantified on agar plates containing 7 mg/liter (1.75ϫ MIC) of imipenem. Electron microscopy. To characterize the outer membrane damage to bacterial cells, scanning electron microscopy (SEM) and transmission electron microscopy (TEM) were performed as described previously (54, 55). Briefly, one colony of AH298-GFP was used to prepare an overnight culture, from which 20-ml log-phase cultures (at ϳ108 CFU/ml) in CAMHB were obtained. The bacterial cultures were treated for 2 h with the targeted concentrations of imipenem (4 mg/liter) and tobramycin (16 mg/liter and 32 mg/liter) alone and in combinations and incubated at 37°C, followed by centrifugation at 3,220 ϫ g for 10 min. Bacterial cells were fixed, washed, and imaged as described previously (54, 55). Confocal imaging. Confocal imaging was performed to quantify the signal from cytosolic GFP; as described previously (55, 56), damage to the outer membrane can cause an extensive loss of GFP and thus decreased fluorescence intensity from cytosolic GFP. In brief, bacterial cells were grown on chamber Downloaded from slides and treated for 2 h with monotherapies and combinations of imipenem (4 mg/liter) and tobramycin (16 mg/liter and 32 mg/liter) at 37°C. An LSM780 confocal microscope (Zeiss) equipped with a 63ϫ oil objective was used to assess the cell morphology; excitation/emission filters used were 475 and 520 to 560 nm (55). Fiji ImageJ software was used for quantitative data analysis. The percentage of GFP signal was calculated as treated cells/untreated control cells ϫ 100. The studied imipenem and tobramycin concentrations included clinically achievable unbound plasma concentrations at steady state (46, 48). Nitrocefin assay. We studied the ␤-lactamase-related hydrolysis of nitrocefin in the presence or absence of antibiotic(s) to further assess the permeability of the outer membrane (27, 55). Nitrocefin is a chromogenic cephalosporin and a substrate of periplasmic ␤-lactamases (such as AmpC in P. aeruginosa). As the rate of hydrolysis of nitrocefin by the AmpC ␤-lactamase is high (57), disruption of the outer http://aac.asm.org/ membrane by an aminoglycoside is expected to enhance the target site penetration and thus the hydrolysis of nitrocefin. Briefly, one colony of AH298-GFP was used to prepare an overnight culture in CAMHB from which 10 ml of log-phase bacterial suspension (ϳ108 CFU/ml) was obtained. The pellet was collected by centrifugation at 3,220 ϫ g for 10 min and was washed twice in phosphate-buffered saline

(PBS; pH 7.2) and resuspended in PBS to an optical density at 600 nm (OD600) of 0.50. A total volume of 200 ␮l of reaction mixture in each well of a 96-well plate was comprised of 100 ␮l of bacterial suspension, 50 ␮l of antibiotic solution (imipenem at 4 mg/liter and tobramycin at 0.25 mg/liter, 16 mg/liter, or 32 mg/liter, alone and in combinations), 46 ␮l of PBS, and 4 ␮l of 2 mM nitrocefin solution. The absorbance (492 nm) was measured at room temperature. The presented data are the averages of four independent on August 13, 2018 by MONASH UNIVERSITY measurements Ϯ standard deviations (SD) at 30 min. Mechanism-based modeling of monotherapies and combinations. An MBM was developed to characterize the time course of bacterial killing and resistance and assess the potential type of synergy for imipenem in combination with each of four aminoglycosides (13, 40, 58, 59). Viable counts of the total population from all five antibiotics in monotherapy or combinations were modeled simultaneously. Life cycle growth model. The MBM model incorporated a life cycle growth model that defined the underlying biology of bacterial replication for each population, as described previously (58, 60)(Fig. 6). Imipenem and aminoglycoside combination model. The proposed model for the combinations of imipenem and the respective aminoglycoside comprised three preexisting populations, including a double-susceptible (SS), imipenem-resistant and aminoglycoside-intermediate (RI), and imipenem- intermediate and aminoglycoside-resistant (IR) population (Fig. 6). Each of these populations was described by the two states (i.e., compartments) of the life cycle growth model (Fig. 6). Thus, the composite model contained six compartments. The total concentration of all viable bacteria (CFUall) was determined as follows (each CFUNNx term indicates the concentration of viable bacteria for population NN in state x):

ϭ ϩ ϩ ϩ ϩ ϩ CFUall CFUSS1 CFUSS2 CFURI1 CFURI2 CFUIR1 CFUIR2 (1) The rates of bacterial killing by each antibiotic alone or in combination were higher than the maximal bacterial growth rate. Therefore, the antibacterial effects were described via direct killing processes. The time course of bacterial growth, killing, and, where applicable, regrowth during treatment with imipenem and each of four aminoglycosides alone and in combination were ﬁtted simultaneously. The differential equation for the concentration of bacteria belonging to the double-susceptible population S S (IPM /AGS ) in state 1 (CFUSS1) contained killing by both imipenem and the aminoglycoside (initial conditions described below) is as follows: d͑CFU ͒ SS1 ϭ 2 ϫ PLAT ϫ k ϫ CFU Ϫ k ϫ CFU dt 21 SS2 12,SS SS1 K ϫ C K ϫ C Ϫ max,IPM IPM ϩ max,SS,AGS AGS ϫ ͩ ϩ ϫ ϩ ͪ CFUSS1 (2) CIPM ͑OM_effect KC50,SS,IPM͒ CAGS KC50,SS,AGS where CIPM is the imipenem concentration and CAGS the aminoglycoside (i.e., tobramycin, gentamicin, Ϫ amikacin, or streptomycin) concentration in broth. The plateau factor (PLAT) is deﬁned as 1 [CFUall/ ϩ (CFUall CFUmax)], with CFUmax being the maximum population size. The factor 2 represents doubling of bacteria during replication (58). The maximum killing rate constants (Kmax) and the associated antibiotic concentrations (KC50) causing 50% of Kmax are illustrated in Fig. 6 and Table 2. The permeabilizing effect of the aminoglycosides on the outer membrane (OM_effect; i.e., a synergy term) is described in equation 4 (see below). We assumed that killing by imipenem and the aminoglycosides affected both states 1 and 2 and thus included the same killing terms for both states. This resulted in the following differential equation for state 2 of the double-susceptible population (CFUSS2):

December 2017 Volume 61 Issue 12 e00722-17 aac.asm.org 13 Yadav et al. Antimicrobial Agents and Chemotherapy

d͑CFU ͒ SS2 ϭϪk ϫ CFU ϩ k ϫ CFU dt 21 SS2 12,SS SS1 K ϫ C K ϫ C Ϫ max,IPM IPM ϩ max,SS,AGS AGS ϫ ͩ ϩ ϫ ϩ ͪ CFUSS2 (3) CIPM ͑OM_effect KC50,SS,IPM͒ CAGS KC50,SS,AGS The differential equations for the other two populations (i.e., IPMR/AGSI and IPMI/AGSR) consisted of the same structure as for CFUSS1 and CFUSS2 but used different parameters for KC50,IPM, k12, Kmax,AGS, and

KC50,AGS as described previously (39, 40). Mechanism-based modeling of synergy. We evaluated subpopulation synergy (i.e., antibiotic A killing the bacteria resistant to antibiotic B and vice versa) and mechanistic synergy (i.e., antibiotic A enhancing the killing by antibiotic B against one or multiple bacterial populations) (39). Mechanistic synergy was employed by assuming that the aminoglycosides could enhance the target site penetration Downloaded from of imipenem due to their permeabilizing effect on the outer bacterial membrane (22, 23, 61), as assessed in our mechanistic experimental studies. This outer membrane effect was applied in the model via the term OM_effect (13) (parameters explained in Table 2): I ϫ C ϭ Ϫ max,OM,AGS AGS OM_effect 1 ͩ ϩ ͪ (4) CAGS IC50,OM,AGS

Initial conditions. The size of the total inoculum (logCFU0) and the log10 mutation frequencies for the intermediate (LogMUT,IPM) and resistant (LogMUT,AGS) subpopulations were estimated parameters from drug-free-plate data of SCTK studies (40, 58)(Fig. 6).

Observation model. An additive residual error model on a log10 scale was employed to fit the viable http://aac.asm.org/ count data of the total population. For observations below 100 CFU/ml (equivalent to fewer than 10 colonies per plate), a previously developed residual error model was utilized to fit the number of colonies per plate (38). Observed viable counts below the limit of counting (i.e., 1 log10 CFU/ml, equivalent to one colony per agar plate) were plotted as 0 and modeled as 0 colonies per agar plate. Estimation. All parameters were simultaneously estimated via an importance sampling algorithm (S-ADAPT setting: pmethod ϭ 4) in the parallelized S-ADAPT software (version 1.57) (62) facilitated by the SADAPT-TRAN tool (63, 64). The between-curve variability of the parameters was fixed to a final, small coefficient of variation (38). Competing models were evaluated by the biological plausibility of the parameter estimates, the objective function (Ϫ1ϫ log likelihood in S-ADAPT), standard diagnostic plots, and visual predictive checks, as described previously (65–68). on August 13, 2018 by MONASH UNIVERSITY

SUPPLEMENTAL MATERIAL Supplemental material for this article may be found at https://doi.org/10.1128/AAC .00722-17. SUPPLEMENTAL FILE 1, PDF ﬁle, 0.7 MB.

ACKNOWLEDGMENTS We thank Philip S. Stewart and Søren Molin for providing the GFP-labeled P. aeruginosa strain used in this study. We thank Bartolome Moya for a critical review of the manuscript. This work was partly supported by Australian National Health and Medical Re- search Council (NHMRC) project grants (APP1045105 to J.B.B., R.L.N., T.V., and C.B.L., APP1101553 to C.B.L., J.B.B., and R.L.N., and APP1062040 to C.B.L. and J.B.B.). R.Y. is thankful to the Australia Government and Monash Institute of Graduate Research for providing a Monash Graduate Scholarship and Monash International Postgraduate Research Scholarship. C.B.L. is the recipient of an NHMRC Career Development Fellow- ship (APP1062509). We declare no conﬂict of interest.

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