A new pharmacodynamic approach to study antibiotic combinations against enterococci in vivo: Application to ampicillin plus ceftriaxone.

The combination of ampicillin (AMP) and ceftriaxone (CRO) is considered synergistic against Enterococcus faecalis based on in vitro tests and the rabbit endocarditis model, however, in vitro assays are limited by the use of fixed antibiotic concentrations and the rabbit model by poor bacterial growth, high variability, and the use of point dose-effect estimations, that may lead to inaccurate assessment of antibiotic combinations and hinder optimal translation. Here, we tested AMP+CRO against two strains of E. faecalis and one of E. faecium in an optimized mouse thigh infection model that yields high bacterial growth and allows to define the complete dose-response relationship. By fitting Hill's sigmoid model and estimating the parameters maximal effect (Emax) and effective dose 50 (ED50), the following interactions were defined: synergism (Emax increase ≥2 log10 CFU/g), antagonism (Emax reduction ≥1 log10 CFU/g) and potentiation (ED50 reduction ≥50% without changes in Emax). AMP monotherapy was effective against the three strains, yielding valid dose-response curves in terms of dose and the index fT>MIC. CRO monotherapy showed no effect. The combination AMP+CRO against E. faecalis led to potentiation (59-81% ED50 reduction) and not synergism (no changes in Emax). Against E. faecium, the combination was indifferent. The optimized mouse infection model allowed to obtain the complete dose-response curve of AMP+CRO and to define its interaction based on pharmacodynamic parameter changes. Integrating these results with the pharmacokinetics will allow to derive the PK/PD index bound to the activity of the combination, essential for proper translation to the clinic.

Introduction

Enterococci are the third leading cause of hospital-associated infections [1]. They display intrinsic and acquired resistance to a wide variety of antibiotics in clinical use, including newer agents used to treat vancomycin resistant enterococcus (VRE) infections. In addition, compounds considered bactericidal against other Gram-positive cocci are usually bacteriostatic against enterococci, posing a challenge for clinicians when faced with patients with severe infections [2-4] such as endocarditis and bacteremia, and often require combined therapies aiming for synergism [5-7]. One of these combinations is ampicillin (AMP) plus ceftriaxone (CRO).

The history of this dual β-lactam combination dates back to 1995 when Mainardi et al. reported an in vitro synergistic effect between amoxicillin (AMX) and cefotaxime (CTX) against several Enterococcus faecalis strains [8]. A few years later, Gavaldà et al. found in vivo synergism of AMP plus CRO against both high-level gentamicin resistant (HLGR) and aminoglycoside susceptible E. faecalis strains in the rabbit endocarditis model [9, 10]. Their findings were later confirmed in a clinical trial [11] and are the basis for the recommendation to use AMP+CRO for E. faecalis endocarditis, with the additional advantage of less nephrotoxicity compared to aminoglycoside-containing regimens [5].

Notwithstanding, the interaction of AMP and CRO is only understood partially, because most of the data have been derived from in vitro testing (checkerboard and time-kill curves) [8, 12] and animal models of endocarditis [9, 10, 13, 14] that have several limitations for PK/PD analysis and the optimal translation to humans: (i) deficient bacterial growth, (ii) low statistical power due to intrinsic high variation and, (iii) the lack of a complete dose-response curve due to the small number of doses tested [15, 16]. These limitations preclude the accurate estimation of pharmacodynamic parameters and the determination of the PK/PD index driving the efficacy of the combination, essential for proper extrapolation to the clinic [17, 18]. Additionally, the mortality rate of endocarditis has not changed during the last 30 years, suggesting that the there is room for improvement by optimizing drug combinations and dosing regimens based on the pharmacodynamics. [5, 6].

Our group developed an optimized neutropenic mouse thigh infection model of enterococci that yields bacterial growth in control animals of at least 2 log10 CFU/g in 24 h, and has allowed to estimate accurately the pharmacodynamic parameters of anti-enterococcal antibiotics in monotherapy fitting Hill’s sigmoid model to the dose-response data [19]. Our aim here was to characterize the pharmacodynamics of the AMP+CRO combination in the optimized model and to analyze the interaction with a novel approach based on the parameters derived from Hill’s equation. Partial results of this work were presented at ASM Microbe 2018 [20].

Materials and methods

Bacterial strains, antibiotics and susceptibility testing

For in vitro and in vivo studies, the strains E. faecalis ATCC 29212, E. faecium ATCC 19434 and E. faecalis ATCC 51299 (vancomycin-resistant, with VanB phenotype), were used and kept at −70°C. In vivo experiments with E. faecalis ATCC 29212 were done with Ampicillin (Ampicilina, Genfar, Colombia) and Ceftriaxone (Rocephin, Roche, Switzerland). Due to previous reports of inequivalent ampicillin generics [21], the in vivo activity of the Genfar product (AMP innovator is not available in Colombia) was compared to innovator Ampicillin-Sulbactam (Unasyn, Pfizer, Switzerland) against β-lactamase negative enterococci and found to be equivalent in efficacy and potency. Due to later Genfar generic shortage, the experiments with E. faecium ATCC 19434 and E. faecalis ATCC 51299 were done with Ampicillin-Sulbactam. The minimal inhibitory concentrations of AMP and CRO were determined by broth microdilution in duplicate and repeated independently three times following CLSI methods [22].

Time-kill curves (TKC)

Flasks containing Brain-Heart infusion (BHI) broth with AMP at 0.5, 1 and 2 times the MIC and/or CRO at a fixed concentration of 4 mg/L, were inoculated with a 6 log10 CFU/mL bacterial suspension of E. faecalis ATCC 29212 and E. faecium ATCC 19434, prepared according to CLSI method [23]. Tubes containing only broth or bacteria without antibiotics were used as sterility and growth controls, respectively. After 0, 1, 2, 4, 8 and 24 h of incubation, aliquots of each culture (0.1 mL) were obtained. The samples were washed twice with sterile saline after centrifuging at 14,000 g for 10 minutes to prevent drug carryover. The final pellet was serially diluted and spread onto BHI agar plates and incubated for 24 h at 37°C under aerobic atmosphere.

In vitro drug interaction analysis

Individual time-kill curve data were analyzed by comparing the number of bacteria remaining after 24 hours of antibiotic exposure. By definition, synergism occurred when the combination killed 2 log10 CFU/mL or more than the single most active drug. Antagonism when the combination killed at least 2 log CFU/mL less than the most active individual agent. In-between killing values indicated indifference [24].

Inoculum preparation for in vivo experiments

The optimized mouse model requires that the inoculum is prepared under anaerobic conditions and with addition of porcine mucin. The protocol is described in detail in reference [19]. Briefly, the strains were recovered by two successive streaks on brain heart infusion (BHI) agar (Becton Dickinson, Heidelberg, Germany) with 5% sheep blood, followed by incubation for 24 h at 37°C under anaerobic atmosphere (GazPak EZ; Becton Dickinson). For all strains, 3 colonies were suspended in 10 mL of thioglycolate USP broth (Oxoid, United Kingdom), serially diluted 4 times (1:10), and incubated overnight at 37°C. The most diluted tube with complete turbidity was further diluted twice (1:10) in fresh broth, and incubated approximately for 3 hours, until it reached an OD580nm corresponding to ∼8.0 log10 CFU/mL. Finally, this tube was diluted 1:10 twice and mixed 50:50 with autoclaved 10% (wt/vol) porcine stomach mucin (Sigma-Aldrich, United States), yielding a 5.7 log10 CFU/mL bacterial suspension with 5% mucin to inoculate the animals.

Mice

Murine-pathogen free (MPF) Swiss albino mice of the strain Udea:ICR(CD-2), bred at the University of Antioquia MPF vivarium were used. They were fed and watered ad libitum, housed at a maximum density of 7 animals per box within a 693 cm2 area in a One Cage System® (Lab Products, USA), and kept under controlled temperature (20°C and 25°C) and lightning conditions (12-hour day-night cycles). The personnel in charge of in vivo experiments was trained in animal care and the thigh infection model procedures (anesthesia, thigh inoculation, intraperitoneal and subcutaneous injections, euthanasia and tissue processing) by the senior researchers of the Infectious Diseases Problem Research Group (GRIPE, University of Antioquia). Animals were randomly picked and allocated to treatment or control groups (experimental units). The health condition of the mice was checked every day of the experiment and every 3 hours during the treatment phase (the last 24 hours). The following scale was used to classify the animals: 0: no signs of disease: active mouse, well groomed, alert, active; 1: mild signs of disease, as altered hair, slightly hunched posture with preserved mobility and response to stimuli; 2: moderate signs of disease, including squinted eyes, reduced mobility or reactivity, but able to reach water and food; 3: severe signs of disease, as great difficulty to reach water and food, dehydration (sunken eyes), reduced or no response to touch. If an animal reached phase 3 before the end of the experiment, it was sacrificed immediately by cervical dislocation under isoflurane anesthesia. No animal died before meeting the euthanasia criteria. The study was reviewed and approved by the University of Antioquia Animal Experimentation Ethics Committee (July 9th 2015 session) and complied with the national guidelines for biomedical research (Resolution 008430 of 1993 by the Colombian Health Minister, articles 87 to 93) and the ARRIVE guidelines (S1 File).

Optimized mouse infection model

We used our optimized murine thigh infection model for enterococci described in reference [19]. Six-week-old female mice weighing 23 to 27 g were rendered neutropenic by two intraperitoneal injections of cyclophosphamide (Endoxan; Baxter, Germany), given four days (150 mg/kg of body weight) and one day (100 mg/kg) before infection [25]. The mice were inoculated in each thigh with 100 μL of the bacterial suspension described above under isoflurane anesthesia. Treatment started 2 h post-infection and lasted 24 h (the total duration of the experiment from the first cyclophosphamide injection to the end of antibiotic treatment was 6 days). Mice were allocated in groups of two to receive monotherapy with AMP at doses from 9.4 to 2400 mg/kg/day and CRO from 3.125 to 200 mg/kg/day (5 to 6 doses per experiment). For AMP+CRO combined therapy, the complete range of AMP doses were administered in combination with one fixed dose of CRO: 3.125, 12.5, 25, 50, 100 or 200 mg/kg/day (2 mice per dose, 5 to 8 doses per experiment). The antibiotics were injected subcutaneously every 3 h (200 μL per injection). At the end of treatment, the animals were euthanized by cervical dislocation under isoflurane anesthesia, the thighs were dissected aseptically, homogenized, serially diluted, plated, and incubated overnight for bacterial quantification (limit of detection: 2 log10 CFU/g). Groups of two untreated but infected control mice were euthanized at the initiation (0 hour) and at the end of the treatment (24 hours) to assess bacterial growth. Six independent experiments were done with E. faecalis ATCC 29212 (138 mice), one with E. faecium ATCC 19434 (32 mice) and one with E. faecalis ATCC 51299 (40 mice).

In vivo data analysis

The net antibacterial effect of each antibiotic dose was calculated by subtracting the number of CFU/g in untreated controls at 24 h from the number of CFU/g remaining in treated mice. Least-squares nonlinear regression was used to fit Hill's Equation to the dose-effect data and estimate the primary parameters maximum effect (Emax, to quantify efficacy), 50% effective dose (ED50, to quantify potency), and Hill's slope (N). Additionally, the secondary parameters bacteriostatic dose (BD), 1-log10 kill dose (1LKD) and 2-log10 kill dose (2LKD) were calculated. The differences between the complete dose-response curves or the individual parameters were tested by curve-fitting analysis (CFA). Regressions was assessed by the adjusted coefficient of determination (Adj.R2) and the standard error of estimate (Sy.x) and were considered valid only if they passed the normality of residuals and homoscedasticity tests. The experiments could be analyzed separately or jointly if a single regression curve described the datasets better than individual ones, as indicated by the overall test for coincidence (extra sum-of-squares F test). All analyses were run in Prism 7.0 (GraphPad, San Diego, United States) [26, 27].

PK/PD analysis

We used a 2-compartment pharmacokinetic model of AMP in infected ICR mice estimated by nonparametric techniques in a previous study [19]. The median of the parameters were: Kel (elimination rate constant) 20.4 h-1, Vc (volume of the central compartment) 0.007 L, Kcp (transfer rate constant from the central to the peripheral compartment) 78.2 h-1, Kpc (transfer rate constant from the peripheral to the central compartment) 15.0 h-1, and Ka (absorption rate constant) 6.45 h-1 [19, 21]. AMP exposure in the monotherapy studies was calculated in terms of the time that the free drug concentration exceeded the MIC (fT>MIC) for each of the doses and strains using Monte Carlo simulation in the Pmetrics package for R, including the between-subject variability of the parameters (S1 Table) [28]. The PK/PD index was plotted against the antibacterial effect to estimate the magnitudes required for stasis (BD), 1-log10 kill (1LKD) and 2-log10 kill (2LKD). AMP protein binding was not considered because it is only 3% in mice [29].

In vivo interaction analysis

Drug interaction was analyzed taking into account the complete dose-response curve derived by a valid nonlinear regression fitting Hill’s equation. Based on the changes of the PD parameter values with the combination, four terms of interaction were used: synergism, potentiation, antagonism and indifference. Synergism was defined as an Emax increase of at least 2 log10 CFU/g, potentiation as an ED50 reduction ≥50% without significant changes in Emax, and antagonism as an Emax reduction of 1 log10 CFU/g or more in the combination compared to the single most effective drug. Changes below these thresholds, even if statistically significant, were considered indifferent. Parameter differences were assessed by Curve Fitting Analysis (CFA) (Prism 7.0).

Human AMP pharmacokinetics/pharmacodynamics simulation

To put the animal data in clinical context we simulated the human pharmacokinetics of two AMP doses with ADAPT 5 [30]: 500 mg every 6 hours (for soft tissue infections) and 2000 mg every 4 hours (for enterococcal endocarditis), both administered in 15-minute intravenous bolus, based on the population 2-compartment model published by Soto et al. [31] with the following parameters for a typical patient weighing 70 kg and with a creatinine clearance of 71 mL/min: total clearance (CLt) 10.7 L/h, volume of the central compartment (Vc) 9.97 L, distributional clearance (CLd) 4.48 L/h and volume of the peripheral compartment (Vp) 6.14 L, and estimated the percentage free time above concentrations ranging from 0.5 to 256 mg/L, with 20% protein binding.

Results

Susceptibility testing and time-kill curves

The three strains were AMP-susceptible and CRO-resistant (CRO is inactive in monotherapy against enterococci). The modal MIC values are shown in Table 1. In the time kill curves, growth at 24 h in the CRO group was almost the same as the controls as expected. The combination of AMP at concentrations of 1 mg/L and higher with CRO fixed at 4 mg/L was synergistic against E. faecalis ATCC 29212, increasing the bacterial killing 4.94 log10 CFU/mL at AMP 1 mg + CRO, and 2.62 log10 CFU/mL at AMP 2 mg/L + CRO compared with AMP alone (Fig 1 panel a). Against E. faecium ATCC 19434 the combination was indifferent: at AMP 0.5 mg/L + CRO, bacterial killing increased only 0.57 log10 CFU/mL, and at AMP 1 mg/L + CRO, only 0.22 log10 CFU/mL (Fig 1 panel b).

Table 1

Minimal inhibitory concentrations of three strains of enterococci.

Antibiotic	CLSI Reference.b	MIC (modal value in mg/L) a
		E. faecalis ATCC 29212	E. faecalis ATCC 51299 (VanB)	E. faecium ATCC 19434
Ampicillin	0.5–2	1	0.5	0.5
Ceftriaxone	NA	128*	256*	128*
Gentamicin	4–16	8	>256	8
Linezolid	1–4	2	2	8
Moxifloxacin	0.06–0.5	0.25	0.25	2
Tigecycline	0.03–0.12	0.5	0.5	0.5
Vancomycin	1–4	2	64	4
Daptomycin	1–4	2	2	4

a. Obtained from three independent duplicate assays.

b. For E. faecalis ATCC 29212 (control strain) by standard broth microdilution.

NA, not applicable

* There is no CLSI breakpoint for ceftriaxone against enterococci.

Fig 1

In vitro time-kill curves of AMP+CRO.

(a) E. faecalis ATCC 29212, (b) E. faecium ATCC 19434. Growth control (solid black line and circles), CRO 4 mg/L (gray dashed line and triangles), AMP 1xMIC (red dashed line and squares), AMP 1xMIC plus CRO 4 mg/L (solid red line and squares), AMP 2xMIC (blue dashed line and triangles) and AMP 2xMIC plus CRO 4 mg/L (solid blue line and triangles).

In vivo pharmacodynamics

The bacterial burden in the thighs of untreated mice increased in average 2.02, 2.05, and 3.42 log10 CFU/g after 24 h for E. faecalis 29212, E. faecalis 51299 and E. faecium 19434, respectively, the expected growth of enterococci in the optimized thigh model. Hill’s equation fitted well to the data, yielding valid regressions and statistically significant parameters for AMP monotherapy and all the AMP+CRO combinations (Table 2). CRO in monotherapy was tested only against E. faecalis ATCC 29212 and was completely ineffective (bacterial burden without difference to control mice, S1 Fig).

Table 2

In vivo pharmacodynamics of AMP and AMP plus CRO against enterococci.

Strain	Treatment (CRO mg/kg/day)	Parameter magnitude ± SE			Adjusted R2	Sy.x (log10 CFU/g)	P value by CFA (ED50_AMP vs. ED50_AMP+CRO) a
		Emax (log10 CFU/g)	Hill’s slope (N)	ED50 (mg/kg/day)
E. faecalis ATCC 29212	AMP	4.96 ± 0.17	2.35 ± 0.41	126.1 ± 11.1	0.93	0.53	NA
	AMP + CRO (200)	5.55 ± 0.2	1.33 ± 0.2	46.7 ± 6.17	0.97	0.33	0.0004
	AMP + CRO (50)	5.27 ± 0.19	1.59 ± 0.27	52.7 ± 5.98	0.93	0.43	<0.0001
	AMP + CRO (37.5)	4.86 ± 0.15	2.18 ± 0.44	51.6 ± 5.28	0.98	0.29	0.0002
	AMP + CRO (25)	4.78 ± 0.22	2.1± 0.60	51.9 ± 8	0.95	0.42	0.0004
	AMP + CRO (12)	4.34 ± 0.20	3.96 ± 4.6	117.8 ± 33.9	0.97	0.41	0.9105
	AMP + CRO (3.12)	4.34 ± 0.14	2.75 ± 0.66	109 ± 11	0.96	0.39	0.4747
E. faecium ATCC 19434	AMP	7.58 ± 0.29	5.82 ± 1.14	239.4 ± 8.26	0.97	0.56	NA
	AMP + CRO (200)	7.65 ± 0.31	3.81 ± 0.68	197.6 ± 10.1	0.97	0.58	0.0067
E. faecalis ATCC 51299	AMP	4.77 ± 0.30	1.1 ± 0.17	128.3 ± 25.4	0.96	0.3	NA
	AMP + CRO (100)	4.88 ± 0.23	0.88 ± 0.18	25.7 ± 4.16	0.92	0.29	0.0019
	AMP + CRO (25)	4.50 ± 0.07	1.42 ± 0.12	24.5 ± 1.26	0.98	0.14	<0.0001

Abbreviations: AMP, ampicillin; CRO, ceftriaxone; Emax, maximum effect; ED50, 50% effective dose; N, Hill’s slope; Sy.x: standard error of estimate, NA, not applicable.

a ED50 magnitudes were compared by curve fitting analysis (CFA).

All values are presented as means and standard errors.

Regarding the PK/PD analysis of AMP monotherapy, the fT>MIC necessary for bacteriostasis and killing varied according to the strain. In the case of E. faecalis 29212, the magnitude required for stasis was 28.7%, 33.3% for 1-log10 kill and 39.9% for 2-log10 kill (Fig 2 and Table 3). Against E. faecalis 51299, the BD was 35.8% and the 2LKD 67.2% (Table 3, S1 Fig). With E. faecium 19434, its higher growth required longer exposures for stasis and killing but with minimal difference between BD and 2LKD (51.1% and 52.8%, respectively) due to the steep slope of the dose-response curve (Table 3, S2 Fig). The PK/PD analysis of AMP+CRO was not done because the index linked to the efficacy of this combination has not been defined.

Fig 2

Pharmacodynamics of AMP monotherapy against E. faecalis ATCC 29212 in terms of fT>MIC.

The data are derived from three independent experiments (N = 46 mice) that were undistinguishable by curve-fitting analysis (i.e. a single curve described better the three data sets than independent ones). BD was 28.7%, 1LKD 33.3% and 2LKD 39.9% (Table 3).

Table 3

BD, 1LKD and 2LKD of AMP vs. enterococci in terms of fT>MIC.

	fT>MIC (%) *
Parameter	E. faecalis ATCC 29212	E. faecalis ATCC 51299 (VanB)	E. faecium ATCC 19434
BD	28.7 ± 1.46	35.8 ± 2.12	51.1 ± 0.86
1LKD	33.3 ± 1.25	42.9 ± 2.75	51.9 ± 0.1
2LKD	39.9 ± 1.87	67.2 ± 6.73	52.8 ± 0.13

Abbreviations: BD, bacteriostatic dose; 1LKD, dose required to kill 1-log10 CFU/g; 2LKD, dose required to kill 2-log10 CFU/g. All values are presented as means standard errors.

The dose-response curves of AMP monotherapy and all the AMP+CRO combinations against E. faecalis 29212 are shown in Fig 3. The addition of CRO at doses of 3.125 and 12.5 mg/kg/day produced no significant effect and yielded the same curve of AMP monotherapy (P = 0.1427). However, starting at 25 mg/kg/day of CRO and up to 200 mg/kg/day, AMP ED50 was reduced >50% without significant changes in Emax (Table 2). Notably, these treatment groups (AMP+CRO 25, 37.5, 50 and 200 mg/kg/day) were better described by a single regression (P = 0.1029), yielding an Emax of 5.15 ± 0.10 log10 CFU/g (P = 0.3164 vs. AMP monotherapy) and ED50 of 51.1 ± 3.42 mg/kg/day (P<0.0001 vs. AMP monotherapy, a 59% reduction), a case of potentiation (Fig 4).

Fig 3

Dose-response curves of AMP monotherapy and AMP+CRO combinations vs. E. faecalis ATCC 29212.

AMP Monotherapy (black), AMP+CRO 200 (red), AMP+CRO 50 (green), AMP+CRO 37.5 (orange), AMP+CRO 25 (blue), AMP+CRO 12.5 (gray) and AMP+CRO 3.125 (yellow). The PD parameters are presented in Table 2.

Fig 4

Dose-response curves of AMP monotherapy and combined AMP+CRO vs. E. faecalis ATCC 29212.

AMP monotherapy (black), AMP+CRO 25, 37.5, 50 and 200 mg/kg/day combined in a single regression (red). There was no difference in Emax but a significant 59% reduction in the ED50 with the combination, indicating potentiation.

Against E. faecalis 51299, AMP potency was also increased when combined with CRO at doses of 25 mg/kg/day and higher without changing efficacy (ED50_AMP 128.3 ± 25.4 vs. ED50_AMP+CRO 24.5 ± 1.26 mg/kg/day; a reduction of 81%, P = <0.0001), indicating also potentiation (Fig 5 panel a). Finally, AMP in monotherapy was highly bactericidal against E. faecium, reaching a ~5 log10 CFU/g bacterial reduction after 24 hours of treatment (Fig 5 panel b). In combination, the ED50 was significantly reduced (ED50_AMP 239.4 ± 8.24 vs. ED50_AMP+CRO 197.7 ± 10.05 mg/kg/day, P = 0.0067), but only 17%, thus it did not reach the threshold for potentiation and the interaction was indifferent.

Fig 5

In vivo dose-response curves of AMP and AMP+CRO against other strains of enterococci.

(a) E. faecalis ATCC 51299. (b) E. faecium ATCC 19434. AMP monotherapy (black), AMP+CRO 25 (blue) AMP+CRO 100 (brown) and AMP+CRO 200 (red). Parameter values are in Table 2.

The simulated PK profile of AMP is shown in S4 Fig (500 mg q6h) and S5 Fig (2000 mg q4h). With the lower dose, the total Cmax was 42 mg/L (34 mg/L free) and the Cmin 0.9 mg/L (0.7 mg/L free). With the higher dose the total Cmax and Cmin were 176 and 10 mg/L, respectively (corresponding to free concentrations of 141 and 8 mg/L). The time that the free concentration of AMP was above the MICs is displayed in S2 Table. With 500 mg q6h dose the fT>MIC was at least 39% with MICs up to 4 mg/L, with the 2000 mg q4h dose the fT>MIC was at least 37% with MICs up to 32 mg/L.

Discussion

We found that the combination of AMP and CRO is synergistic in vitro (determined by time-kill curves) against E. faecalis, as previously reported and explained by the saturation of multiple PBPs: PBPs 4 and 5 by AMP and PBPs 2 and 3 by CRO, leading to increased kill [8, 9]. In contrast, the combination was indifferent against E. faecium ATCC 19434, consistent with published data of non-uniform synergism (isolate-dependent) against this enterococcal species [32].

In vivo, using the optimized mouse thigh infection model, we were able to obtain a complete dose-response curve of AMP monotherapy, with valid parameters derived from Hill’s sigmoid model to quantify its efficacy and potency, and the magnitude of the PK/PD index that drives its activity (fT>MIC) for stasis, 1 log10 kill and 2 log10 kill (something not possible with the previous models characterized by poor growth and high variability). We also obtained valid response-curves of AMP combined with several doses of CRO, and by assessing the changes in the PD parameters it was determined that in vivo, the interaction against E. faecalis was potentiation (>50% reduction of ED50 without changes in Emax) and not synergism (increased maximal effect), in apparent discordance with the results of the rabbit endocarditis models that showed increased killing (i.e. synergism), and the clinical trials.

The key to elucidate this apparent discordance may be in the shape of the dose-response curve and the position of a specific dose in it. When there is potentiation, the monotherapy and combination curves converge at the extremes (no efficacy and maximal efficacy regions), but they separate in the middle (the combination curve moves to the left of the monotherapy one, as seen in Fig 4), then, if the ampicillin dose used is located beyond the point of maximal efficacy (plateau), the addition of ceftriaxone will sum nothing to bacterial killing and the interaction will be interpreted as indifferent. However, if the dose is in the middle to left region of the curve, ceftriaxone will increase bacterial killing by several log10 CFU/g, turning a bacteriostatic dose into a bactericidal one, and the interaction will be interpreted as synergism. Then, in studies that use a single point of the dose-response curve, the interaction is defined according to the specific effect at that point, overlooking the complete curve and potentially leading to discordant interpretations (“missing the forest for the trees”) [33].

Regarding the comparison of murine and human exposures in terms of free time above MIC, the simulation with the ampicillin dose used for human soft tissue infections (500 mg q6h) showed that for strains with MICs up to 2 mg/L, the fT>MIC is at least 61.8%, an exposure leading to maximal efficacy and without benefit from CRO addition. However, in infections with strains exhibiting higher MICs (8 mg/L), this dose is located in the left region of the curve (fT>MIC 23.4%), below the required exposure for bacteriostasis, but sensitive to CRO potentiation. Thus, the addition of ceftriaxone would turn an ineffective AMP dose into a bactericidal one and the combination may allow to treat more resistant Enterococci without increasing the penicillin dose.

On the other hand, the high dose used for the treatment of endocarditis yields fT>MIC of at least 63% for strains with MICs up to 16 mg/L (S2 Table), suggesting that for the majority of Enterococcal isolates, this dose would be located in the right region of the curve, where no potentiation occurs. However, endocarditis is a difficult-to-cure infection due to (i) poor penetration of some antibiotics into the infected vegetations; (ii) altered metabolic state of bacteria within the lesion; and (iii) absence of adequate host-defense cellular response; also, endocarditis has been shown to require a higher antibiotic exposure for cure than non-endocardial infections. In the case of β-lactams, maintaining the concentration just above the MIC is not sufficient to ensure sterilization of vegetations [34], and data from the rabbit endocarditis model indicate that successful treatment requires through levels at least ten times the minimal bactericidal concentration (MBC). Considering that the ampicillin MBC90 of E. faecalis has been reported to be >128 mg/L [35] and the fCmax with 2000 mg q4h is around 140 mg/L, this dose would be actually located in the left (ineffective) region of a hypothetical endocarditis exposure-response curve (yet to be experimentally determined), and this would explain the increased killing effect observed with the CRO combination in the rabbit model and the results of the clinical trials.

These hypotheses deserve further study, but a PK/PD index linked specifically to the effect of the combination, not only the monotherapy, is required in order to better extrapolate to other animals and humans and to design optimal treatment regimens [36]. To date that index has not been identified, but there are some insights from this and previous work: here we found that the potentiation (ED50 reduction) of AMP vs. E. faecalis ATCC 29212 began at a CRO dose of 25 mg/kg/day and did not change with increasing doses up to 200 mg/kg/day. At the 12.5 mg/kg/day it was lost and the ED50 was the same of AMP monotherapy. This quantal dose-effect relationship (all or none) suggests that there is a CRO exposure threshold for potentiation (in this case a dose between 12.5 and 25 mg/kg/day), and once it is reached, the ED50 does not change despite dose increments. As CRO at a concentration of 4 mg/L reduces the MIC of AMP two to four-fold [9], this combination may be analogous to the penicillin-β-lactamase inhibitor combinations, where the inhibitor reduces the MIC of the partner β-lactam (i.e. a potentiation effect), and the PK/PD index driving the efficacy is the free time above a threshold (fT>threshold), as described earlier for piperacillin-tazobactam [37, 38]. Also, considering that the ampicillin MIC varies continuously depending on the changing ceftriaxone concentration in vivo, a more accurate PK/PD index could be the time above the instantaneous MIC, as described by Bhagunde et al. for β-lactam-β-lactamase inhibitor combinations [39]. These ideas merit further development and will be elaborated in a separate paper.

In conclusion, this study presents the first in vivo pharmacodynamic evaluation of an anti-enterococcal drug combination with the optimized mouse thigh infection model and proposes a new method to study in vivo antibiotic interactions that relies on the estimation of the complete dose-response relationship (in contrast to other methods that use point dose-effect or concentration-effect measurements) and defines the type of interaction according to the changes in the PD parameters Emax (synergism or antagonism) or ED50 (potentiation). With the new method we showed that the AMP+CRO combination, considered synergistic against E. faecalis in in vitro studies and the rabbit endocarditis model, is really a case of potentiation in the murine thigh infection model, and the actual antibacterial effect will depend on the dose location in the exposure-response curve. This is also the first step for determining the PK/PD index linked to the combination effect, an essential requirement to translate the results to humans and to allow the optimization of dosing regimens. The method will be now tested with other old and new anti-enterococcal combinations.

In vivo pharmacodynamics of CRO monotherapy vs. E. faecalis ATCC 29212.

CRO monotherapy was completely ineffective against E. faecalis in doses up to 200 mg/kg/day. Regression line is shown dotted because Hill’s sigmoid model did not fit to the data.

(DOCX)

Click here for additional data file.

In vivo pharmacodynamics of AMP monotherapy vs. E. faecalis ATCC 51299.

The parameters BD, 1LKD and 2LKD are shown in Table 3 of the paper.

(DOCX)

Click here for additional data file.

In vivo pharmacodynamics of AMP monotherapy vs. E. faecium ATCC 19434.

The parameters BD, 1LKD and 2LKD are shown in Table 3 of the paper.

(DOCX)

Click here for additional data file.

Simulated PK profile of intravenous AMP 500 mg every 6 hours.

PK profile in a typical patient weighing 70 kg and with a creatinine clearance of 71 mL/min. The total serum concentration of AMP along 24 hours is displayed (protein binding is 20%).

(DOCX)

Click here for additional data file.

Simulated PK profile of intravenous AMP 2000 mg every 4 hours.

PK profile in a typical patient weighing 70 kg and with a creatinine clearance of 71 mL/min. The total serum concentration of AMP along 24 hours is displayed (protein binding is 20%).

(DOCX)

Click here for additional data file.

fT>MIC of AMP doses used against enterococci in mice.

(DOCX)

Click here for additional data file.

% fT>MIC of AMP doses used against enterococci in humans.

(DOCX)

Click here for additional data file.

ARRIVE guidelines checklist.

(PDF)

Click here for additional data file.

In vivo raw data.

(XLSX)

Click here for additional data file.

21 Sep 2020

PONE-D-20-19379

A new pharmacodynamic approach to study antibiotic combinations against Enterococci in vivo: application to Ampicillin plus Ceftriaxone

PLOS ONE

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Reviewer #1: interesting pkpd study of combination therapy for Enterococcus. The authors applied proven pkpd concepts and the study is well done. My only comment to the authors is that I agree that it is clear that combination effect is most pronounced in the middle of the exposure curve, and perhaps not surprisingly as they note that at the extremes of exposures, the addition of a second agent is unlikely a priori to make too much of a difference. so with that in mind, it begs a clear question here of where on the ampicillin exposure curve are the mice relative to human exposures, so that one can put this all in clinical context. For example, are the ampicillin exposures, given it is given IV at high doses and frequent administration, already maxing out at T>MIC >50%, and if so then this model does not explain why ceftriaxone may be helpful as when ampicillin exposures are >50% you max out the effect.

The only other comment I have is that another factor that is not taken into account in these studies is time. These are 24 h studies, you can only have so much antibacterial effect in 24h of time, and thus you might see potentiating or synergistic activities outside this 24h window. Many studies have shown that when you compare short and longer duration studies, you have a very similar ED50 but significantly change the Emax and slope as you get much deeper kill with longer duration. This is a good example that it does significantly depend where on the exposure curve you are located when translating over the animal model hill curves to clinical medicine (and again why elucidating where on the curve the human exposures are for ceftriazone and ampicillin would be expected is important to place this study into context).

Reviewer #2: This study reveals very interesting antibiotic combinations against Enterococci in vivo for medical field. The manuscript is well written and the material and methods are sounds. I suggest the authors to use the latest version of CLSI.

**********

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3 Nov 2020

Reviewer #1: interesting pkpd study of combination therapy for Enterococcus. The authors applied proven pkpd concepts and the study is well done. My only comment to the authors is that I agree that it is clear that combination effect is most pronounced in the middle of the exposure curve, and perhaps not surprisingly as they note that at the extremes of exposures, the addition of a second agent is unlikely a priori to make too much of a difference. so with that in mind, it begs a clear question here of where on the ampicillin exposure curve are the mice relative to human exposures, so that one can put this all in clinical context. For example, are the ampicillin exposures, given it is given IV at high doses and frequent administration, already maxing out at T>MIC >50%, and if so then this model does not explain why ceftriaxone may be helpful as when ampicillin exposures are >50% you max out the effect.

We agree with the reviewer that it is necessary to determine where in the ampicillin exposure curve are the mice relative to humans to be able to put the results in clinical context. For this end, we simulated the human pharmacokinetics of two doses of ampicillin, one for soft-tissue infections (500 mg every 6 hours) and one for endocarditis (2000 mg every 4 hours), using the population model published by Soto et al. (Clinical Pharmacol 2014; 77(3):509-21). This model was developed for ampicillin-sulbactam, but it is useful because sulbactam does alter ampicillin pharmacokinetics. New sections of Human AMP PK/PD simulations were added to Methods (lines 197-205 of the revised version), Results (lines 279-285), and Supporting information (Table S2, Figures S4 and S5).

After obtaining the PK profile we estimated the AMP fT>MIC for a range of minimal inhibitory concentrations from 0.5 to 256 mg/L (new S2 Table) to be able to compare murine and human exposures. With the lower dose, we found that for strains with MIC up to 2 mg/L (the majority of isolates: 94% of 13,858 reported in EUCAST international MIC distribution, https://mic.eucast.org) the fT>MIC is at least 61.8%, an exposure leading to maximal efficacy and therefore without benefit from CRO combination. Notwithstanding, for more resistant strains (MIC up to 8 mg/L), this dose is located in middle to left region of the curve, where the addition of CRO would turn an ineffective dose into a bactericidal one, without increasing the amount of ampicillin.

With the higher dose, the simulation showed that the fT>MIC was �63% for strains with MICs up to 16 mg/L, suggesting that this dose is located in the right region of the curve, reaching maximal efficacy and not sensitive to CRO potentiation. However, endocarditis is a difficult to treat infection due to factors like poor penetration of some antibiotics into the vegetations and altered metabolic bacterial state, and even a fT>MIC of 100% is not sufficient to achieve cure (see below Carbon C. 1993). Then, another PK/PD index is required, but unfortunately it has not been determined yet. Notwithstanding, the data from the rabbit endocarditis model suggest that for �-lactams, plasma concentration needs to be all the time above 10 times the minimal bactericidal concentration (MBC). Due to the high MBC of ampicillin among Enterococci (>128 mg/L), even the maximal ampicillin dose (12 g/day) will fail to reach those concentrations, indicating that this dose is actually located in the left region of the curve (yet to be determined experimentally), where CRO potentiation would be feasible (a hypothesis worth testing). Two new paragraphs were included in the Discussion (lines 313-334) with two additional supporting references:

• Carbon C. Experimental endocarditis: a review of its relevance to human endocarditis. J Antimicrob Chemother. 1993;31

• Pericas JM, Garcia-de-la-Maria C, Brunet M, Armero Y, Garcia-Gonzalez J, Casals G, et al. Early in vitro development of daptomycin non-susceptibility in high-level aminoglycoside-resistant Enterococcus faecalis predicts the efficacy of the combination of high-dose daptomycin plus ampicillin in an in vivo model of experimental endocarditis. J Antimicrob Chemother. 2017;72.

The only other comment I have is that another factor that is not taken into account in these studies is time. These are 24 h studies, you can only have so much antibacterial effect in 24h of time, and thus you might see potentiating or synergistic activities outside this 24h window. Many studies have shown that when you compare short and longer duration studies, you have a very similar ED50 but significantly change the Emax and slope as you get much deeper kill with longer duration. This is a good example that it does significantly depend where on the exposure curve you are located when translating over the animal model hill curves to clinical medicine (and again why elucidating where on the curve the human exposures are for ceftriaxone and ampicillin would be expected is important to place this study into context).

We agree that a longer treatment may lead to higher bactericidal effect. With the highest doses tested in combination, the mean bacterial count after 24 hours was around 3 log10 CFU/g, indicating that there is room for an additional 1 log10 kill (the model’s limit of detection is 2 log10 CFU/g). However, even with this increased killing, the combination would not reach the 2 log10 CFU/g threshold necessary for synergism and still be considered potentiation. Further studies in other models would be required to expand the understanding of the in vivo exposure-response relationship, specially the impact of treatment duration.

Additionally, we chose the standard murine thigh infection model with 24 hours treatment (see Zak and Sande (Ed.). Handbook of animal models of infection, chapter 15, Academic Press 1999), because it has been thoroughly validated and the PK/PD indices derived from it have been shown to accurately predict findings in humans (see Ambrose PG et al. Pharmacokinetics-Pharmacodynamics of antimicrobial therapy: it’s just not for mice anymore. Clinical Infectious Diseases 2007; 44(1):79-86).

Reviewer #2: This study reveals very interesting antibiotic combinations against Enterococci in vivo for medical field. The manuscript is well written and the material and methods are sounds. I suggest the authors to use the latest version of CLSI.

Thank you for the observation. The latest version of CLSI (2020) was used and the reference was updated: Performance standards for antimicrobial susceptibility testing. 30th edition. CLSI supplement M100.: Wayne, PA: Clinical and Laboratory Standards Institute; 2020.

Submitted filename: Response to reviewers.docx

Click here for additional data file.

20 Nov 2020

A new pharmacodynamic approach to study antibiotic combinations against Enterococci in vivo: application to Ampicillin plus Ceftriaxone

PONE-D-20-19379R1

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Reviewer #2: Yes: Jiabin Li

25 Nov 2020

PONE-D-20-19379R1

A new pharmacodynamic approach to study antibiotic combinations against Enterococci in vivo: application to Ampicillin plus Ceftriaxone

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