In Pursuit of the Triple Crown: Mechanism-Based Pharmacodynamic Modeling for the Optimization of 3-Drug Combinations against KPC-Producing Klebsiella pneumoniae

Abstract

Objectives

Optimal combination therapy for Klebsiella pneumoniae carbapenemase (KPC)-producing K. pneumoniae (KPC-Kp) is unknown. The present study sought to characterize the pharmacodynamics (PD) of polymyxin B (PMB), meropenem (MEM), and rifampin (RIF) alone and in combination using a hollow fiber infection model (HFIM) coupled with mechanism-based modeling (MBM).

Methods

A 10-day HFIM was utilized to simulate human pharmacokinetics (PK) of various PMB, MEM, and RIF dosing regimens against a clinical KPC-Kp isolate, with total and resistant subpopulations quantified to capture PD response. A MBM was developed to characterize bacterial subpopulations and synergy between agents. Simulations using the MBM and published population PK models were employed to forecast the bacterial time-course and the extent of its variability in infected patients for 3-drug regimens.

Results

In the HFIM, a PMB single-dose (‘burst’) regimen of 5.53 mg/kg combined with MEM 8 g using a 3-hour prolonged infusion every 8 h and RIF 600 mg every 24 h resulted in bacterial counts below the quantitative limit within 24 h and remained undetectable throughout the 10-day experiment. The final MBM consisted of two bacterial subpopulations of differing PMB and MEM joint susceptibility and the ability to form a non-replicating, tolerant subpopulation. Synergistic interactions between PMB, MEM, and RIF were well-quantified, with the MBM providing adequate capture of the observed data.

Conclusions

An in vitro-in silico approach answers questions related to PD optimization as well as overall feasibility of combination therapy against KPC-Kp, offering crucial insights in the absence of clinical trials.

Introduction

The rise of multidrug-resistant bacteria is one of humanity’s greatest existential threats [1, 2]. Klebsiella pneumoniae carbapenemase (KPC)-producing K. pneumoniae (KPC-Kp) are a particularly troubling microorganism, maintaining pathogenicity and virulence while eroding the utility of most broad-spectrum antimicrobials [3]. As a result, KPC-Kp infections are associated with an average mortality rate of 41% [4], and maintain the ability to disseminate resistance mechanisms to other Gram-negative organisms [3].

In the search for effective therapies, revival of historic antimicrobial agents and repurposing of others has been met with mixed results [5]. While new options to combat KPC-Kp have emerged [6], polymyxins continue to be the most-prescribed agents [7]. However, numerous in vitro and clinical reports of the low barrier to polymyxin resistance in addition to dose-limiting toxicities have led to the consensus recommendation of combination therapy for KPC-Kp [8]. Such polymyxin-based combinations frequently employ a carbapenem [6, 8], though optimal dosing regimens are unknown, as is the potential for additional benefit with inclusion of a third agent. To this end, the rifamycins are an intriguing option, maintaining a unique mechanism of action and demonstrating synergistic activity in vitro [9]. With robust clinical trial evidence lacking, pharmacodynamic modeling and simulation affords the opportunity to explore therapeutic options using a translational approach, bridging experiments conducted at the bench to inferences made at the bedside [10, 11].

The objectives of the present study were to evaluate the pharmacodynamics (PD) of high-dose meropenem (MEM) regimens alone and in combination with polymyxin B (PMB) and/or rifampin (RIF) against KPC-Kp using the hollow fiber infection model (HFIM); develop a mechanism-based model (MBM) describing the independent and interactive PD of PMB, MEM, and RIF; and to forecast bacterial killing under various clinical scenarios using model-based simulations.

Methods

Bacterial Isolate

An ST258 KPC-producing K. pneumoniae isolate, KPC-Kp 9A, was used in all experiments. This organism was isolated from the blood of a 50 year-old woman who received salvage chemotherapy for refractory acute lymphoblastic leukemia, who subsequently developed septic shock and succumbed to the infection within 24 h. The isolate harbored the beta-lactamase genes bla_KPC-2, bla_SHV-11, and bla_TEM-1, in addition to a premature stop codon in OmpK35 (with OmpK36 remaining wild-type). MIC testing by broth microdilution was performed per CLSI specifications [12], with values for PMB, MEM, and RIF provided in Table 1.

Table 1.

Simulated pharmacokinetics of agents employed in hollow fiber experiments

Agent	MIC (mg/L)	Dosing Regimen	fCmax (mg/L)	t1/2 (h)a	%fT>MIC	%fT>4xMIC	fAUC24 (mg·h/L)
PMB	0.5	5.53 mg/kg single-dose	6.0	8	---	---	61, 7.8b
		3.33 mg/kg loading dose, followed by 1.43 mg/kg every 12 h	2.4		---	---	35.9
MEM	16	2 g every 8 h (3-h infusion)	49	2.5	88	0	706
		4 g every 8 h (3-h infusion)	98		100	39	1411
		8 g every 8 h (3-h infusion)	196		100	85	2823
RIF	64	600 mg every 24 h	3.5	2.5	---	---	14

fC_max, free-drug maximum concentration; t_1/2, half-life; %fT_>MIC, percentage of time free-drug concentrations remain above the MIC for each 24-hour period; %fT_>4xMIC, percentage of time free-drug concentrations remain above 4 times the MIC for each 24-hour period; fAUC₂₄, free-drug area under the concentration-time curve for each 24-hour period

^aDerived from [14] (PMB), [15] (MEM), and [15] (RIF)

^bfAUC_0–24 = 61 mg·h/L, fAUC_24–48 = 7.8 mg·h/L, negligible PMB exposure thereafter

Hollow Fiber Infection Model Experiments

A 10-day in vitro HFIM was used to define the PD activities of PMB, MEM, and RIF alone and in 2- and 3-drug combinations against KPC-Kp 9A, as described previously [9]. PMB and RIF were purchased from Sigma-Aldrich (St. Louis, MO) and MEM was purchased from AK Scientific, Inc. (Union City, CA). HFIM experiments were conducted against a starting inoculum of ~10⁸ CFU/mL over 240 h with bacterial aliquots obtained after 0, 1,2, 3, 4, 6, 24, 26, 28, 30, 48, 50, 52, 54, 72, 74, 76, 78, 96, 144, 192, and 240 h to perform viable bacterial colony counting. Population analysis profiles (PAPs) were used to detect antibiotic-resistant subpopulations using bacterial aliquots obtained after 0, 24, 48, 72, 96, 144, 192, and 240 h of antibiotic exposure in the HFIM. PAPs were performed using Mueller-Hinton agar plates containing varying concentrations of PMB (0.5, 1, 4, and 10 mg/L) or MEM (4, 16, and 64 mg/L) and incubated for 48 h before counting colonies [13]. Plates containing PMB were made fresh prior to each HFIM experiment and plates containing MEM were prepared every 48 h during the experiment; all PAP plates were stored at 4 °C prior to use. Select colonies grown on meropenem PAP plates were confirmed to have meropenem MICs exceeding the plate’s drug concentration, thus supporting the ability of this approach to accurately quantify meropenem-resistant subpopulations. To confirm Pertinent antibiotic regimens used in the HFIM experiments simulated the human pharmacokinetics (PK) of PMB [14], MEM [15], and RIF [15], and are provided in Table 1.

Mechanism-Based Pharmacodynamic Modeling

The HFIM data were modeled in a stepwise fashion using the Monte Carlo Parametric Expectation-Maximization algorithm (PMETHOD = 4) in S-ADAPT (version 1.57), with pre-/post-processing facilitated by S-ADAPT TRAN [17, 18]. Single-drug regimens were initially fit to discern appropriate bacterial characteristics, killing functions, and parameter estimates. Dual-therapy regimens were then introduced to explore synergistic interactions, culminating in the addition of the triple-drug combination. Bacterial growth was parameterized via a two-state lifecycle model assuming transition between vegetative and replicative states [19]. Differing growth rates were explored for differing bacterial subpopulations to account for fitness costs of less-susceptible populations. Hypothetical signal molecules representing communication between bacterial cells were invoked to describe an inoculum effect wherein high bacterial densities slow the rate of replication, thereby mitigating beta-lactam-induced killing [19]. Antimicrobial effects were parameterized using sigmoidal E_max models except in the case of direct PMB killing, where effect was governed by a second-order process [20]. PD interactions between agents were characterized using both subpopulation and mechanistic synergy, where the former describes killing of a subpopulation resistant to one agent but susceptible to another and the latter acknowledges the capacity for an agent to enhance the killing effect of another [21]; in the case of mechanistic synergy, sigmoidal E_max models were utilized. Additional details regarding MBM components are provided in the Supplementary Materials. The final MBM was selected based on a combination of diagnostic plots, objective function value, and biologic plausibility of the parameter estimates.

Model-Based Simulations

Using the final MBM, clinical trial simulations were performed to predict typical microbiologic outcomes in patients receiving PMB-MEM-RIF 3-drug combinations. Published population PK models [14, 15 Table 1, 22] were leveraged to produce free-drug exposures for a population of 500 infected patients receiving the same dosing regimens as those studied in the HFIM, thereby accounting for inter-patient variability in PK. These exposures were simultaneously linked to the developed MBM for prediction of the time-course of bacterial killing over 10 days for each simulated patient. To account for differences in protein binding between patients, a log-normal 20% coefficient of variation (CV) was applied to the unbound fractions utilized for each drug (PMB – 0.42 [14]; MEM – 0.98 [15]; RIF – 0.20 [16]). For each population PK model, covariate values assumed the population mean. All simulations were conducted using the RxODE package in R (version 3.6.1) [23].

Results

Hollow Fiber Infection Model Experiments

Data from the HFIM that included MEM doses at 2 g every 8 h as a 3-h infusion have been published previously, as have corresponding PK validations [9]; experiments including MEM dosed as 4 g or 8 g every 8 h as a 3-h infusion represent new data, with all HFIM arms included in the MBM. Observed HFIM data are shown in Figure 1, with PAPs data provided as Figure 2. Monotherapies of MEM 4 g and 8 g caused bacterial reductions of ~0.5 and ~2.0 log₁₀ CFU/mL within the first 3 h, respectively, though like the 2 g regimen, regrowth was observed by 24 h. PAPs did not display appreciable MEM resistance proliferation despite regrowth. In two-drug combinations with a PMB ‘burst’ regimen (single dose of 5.53 mg/kg), MEM dosed at 4 g caused a maximum bacterial reduction of ~2.7 log₁₀ CFU/mL at 4 h but again regrew within 24 h, with amplification of polymyxin resistance based on PAPs data. When the PMB ‘burst’ regimen was paired with an 8 g MEM dose, bacterial counts were repressed to between ~2 and ~4 log₁₀ CFU/mL throughout the 240-h experiment. The triple-drug combination of a PMB ‘burst’, MEM 2 g every 8 h as a 3-h infusion, and 600 mg RIF every 24 h achieved >5 log₁₀ CFU/mL reductions within the first 6 h, with bacterial counts remaining around 3 log₁₀ CFU/mL throughout the remainder of the experiment. In contrast, no viable bacteria were detected after 24 h following the 3-drug combination with an enhanced MEM dose of 8 g.

Figure 1.

Observed (circles) and model-fitted (lines) viable total bacterial counts for 1-, 2-, and 3-drug regimens employed in the hollow fiber infection model

Figure 2.

Population analysis profiles of high-dose meropenem-containing regimens studied within the hollow fiber infection model

Mechanism-Based Pharmacodynamic Modeling

The developed MBM incorporating the killing and regrowth of bacteria following exposure to PMB, MEM, and RIF as 1-, 2-, or 3-drug regimens adequately described the observed data (Figure 1). The final model consisted of two viable bacterial subpopulations (dually PMB- and MEM-susceptible [PMB_S-MEM_S] and dually PMB- and MEM-resistant [PMB_R-MEM_R]) in addition to a non-replicating tolerant subpopulation linked to the PMB_R-MEM_R subpopulation. The direct killing effects of PMB were parameterized as different second-order rate constants for the viable subpopulations, whereas differing maximal killing rates and EC₅₀ values were employed for MEM effects. PMB displayed mechanistic synergy, lowering MEM EC₅₀ values by a maximum of 56.5%, with an EC₅₀ for the synergy estimated as a PMB concentration of 2.52 mg/L. While RIF appeared to exert no direct antimicrobial effect, the observed HFIM data suggested its combination with PMB and MEM provided synergistic benefit, particularly in terms of driving bacterial eradication. This was accounted for in the model via concentration-dependent RIF inhibition of the rate constant for bacterial transition to a tolerant subpopulation. A schematic representation of the MBM is provided as Figure 3, with corresponding parameter definitions, estimates, and standard errors provided in Table 2. Model diagnostics are included as Supplementary Figures S1 and S2.

Figure 3. Mechanism-based model schematic summarizing key elements of the parameterization.

S, susceptible; R, resistant; RIF_inh, rifampin-mediated inhibitory effect; PMB_syn, polymyxin B-mediated synergistic effect; INH_{kill, sigmol}, inhibitory inoculum effect due to hypothetical signaling molecules

Note: parameter definitions and estimates are provided in Table 2, with additional information provided as Supplementary Material.

Table 2.

Parameter definitions and estimates

Parameter	Symbol	Units	Value	SE%
Parameters Governing Bacterial Growth
Mean growth time of susceptible sub-population	MGTS	min	117	5.66
Mean growth time of resistant sub-population	MGTR	min	79.8	2.91
Log starting inoculum	LogCFU0	log10(cfu/mL)	8.28	1.25
Maximum population	LogCFUmax	log10(cfu/mL)	10.6	0.605
Mutation frequency of resistant sub-population	LogMFR	-	−4.97	1.42
Log rate of tolerant cell formation	Logktol	log10(1/h)	−2.36	15.1
Log rate of tolerant cell reversion	Logkrev	log10(1/h)	−1.85	8.46
Parameters Governing Meropenem Killing Effect
Max first-order killing effect for MEMS	Smax,S	1/h	31.1	8.18
Max first-order killing effect for MEMR	Smax,R	1/h	1.52	20.0
Meropenem concentration for 50% of Smax,S	SC50,S	mg/L	46.4	11.0
Meropenem concentration for 50% of Smax,R	SC50,R	mg/L	75.4	3.16
Shape parameter for meropenem killing	Hillm	-	2.32	11.0
Max inhibition of MEM killing by signal molecules	SIGmax	%	97.4	3.74
Log signal molecule concentration for 50% of SIGmax	LogSIG50	-	5.26	1.57
Parameters Governing Polymyxin B Killing Effect
Second-order killing effect for PMBS	kkill,S	L/mg/h	70.1	4.44
Second-order killing effect for PMBR	kkill,R	L/mg/h	2.13	14.1
Parameters Governing Rifampin Inhibition Effect
Maximum inhibition of tolerant cell formation	GRmax,RIF	%	97.9	3.61
Rifampin concentration for 50% of max inhibition	GR50	mg/L	0.129	16.3
Shape parameter for rifampin effect	Hillgr	-	3.09	15.5
Parameters Governing Increased Meropenem Permeability by Polymyxin B
Maximum decrease in meropenem SC50	SYNmax	%	56.5	45.8
Polymyxin B concentration for 50% of SYNmax	SYN50	mg/L	2.52	-
Shape parameter for polymyxin B effect on synergy	Hillsyn	-	0.0444	22.9
Residual Variance
Additive residual variance on log10 scale	σ	log10(cfu/mL)	0.578	4.32

Note: Additional information regarding the parameterization is provided as Supplementary Material

Model-Based Simulations

Results of model-based simulations depicting anticipated PD responses in patients for each of the MEM doses employed in 3-drug combinations using PMB as a single-dose ‘burst’, as well as an interpolated 3-drug combination using 4 g MEM are provided in Figure 3. Predicted bacterial killing was similar across the three MEM dosing regimens throughout much of the first 24 h, suggesting rapid initial killing with a subsequent decrease in killing rate for all 3 regimens as the predominant susceptible subpopulation was eliminated, consistent with the rapid bactericidal activity of PMB. The typical (population mean) predictions suggest that the triple-drug combination using 2 g MEM would yield substantial regrowth within 48 h (Figure 3A), whereas using 4 g MEM will delay such regrowth to day 6–7 of therapy, albeit with substantial variability, with the 80% prediction interval ranging from complete eradication to complete regrowth (Figure 3B). Notably, employing 8 g MEM predicts bacterial counts to remain suppressed (<2 log₁₀ CFU/mL) throughout the 10-day period (Figure 3C).

Discussion

Amidst a rising tide of antimicrobial resistance, determination of viable therapeutic options is desperately needed. The present study leveraged state of the art in vitro experimentation and in silico modeling and simulation to quantify the ability of PMB, MEM, and RIF combinations to combat a KPC-Kp clinical isolate. Here it was found that a PMB ‘burst’ regimen, consisting of a single 5.53 mg/kg dose, combined with high-dose MEM (8 g provided as a 3-h prolonged infusion every 8 h) and RIF 600 mg every 24 h is capable of eradicating this highly resistant organism. The developed MBM sufficiently captured the observed data from the HFIM experiments, and exemplifies the difficulty in producing clinically achievable exposures of PMB and MEM necessary to treat high-burden KPC-Kp infections.

This is the first known attempt at mathematically modeling the PD of 3-drug combinations against Gram-negative bacteria. The results of the 1- and 2-drug regimens are in line with prior HFIM reports, albeit with different organisms [24, 25]. Rapid regrowth of PMB-resistant subpopulations has been observed following extensive initial killing of both Acinetobacter baumannii [24] and Escherichia coli [25], which may be attributed to a change in the ionic character of the outer membrane and/or a loss of LPS. The synergistic effect of PMB-MEM combination has also been noted [24], with the hypothesis that PMB permeabilizes the bacterial outer membrane, inducing the uptake of coadministered antimicrobials. The addition of RIF to a combination of PMB and MEM has previously demonstrated enhanced activity in a one-compartment in vitro model against two KPC-Kp isolates, though no mathematical modeling was performed [26].

Unexpectedly, a bacteriostatic phenotype was observed between 2–5 log₁₀ CFU/mL in the HFIM experiments, leading to the incorporation in the MBM of tolerant bacterial cells arising from the PMB_R-MEM_R subpopulation that could neither replicate nor be killed. As the experimental data suggested that RIF-containing 3-drug regimens were not subject to this dormancy, a RIF-mediated inhibition of the formation of tolerant cells was introduced. Bacterial persisters have been proposed in the literature as a subpopulation of slow-growing or dormant cells that can transiently withstand antimicrobial exposure while otherwise maintaining drug susceptibility upon drug withdrawal, representing a unique entity from resistant cells [27]. Coupled with previous reports of tolerance when KPC-Kp was exposed to carbapenem monotherapy [28], the present study provides a potential mechanistic interpretation of tolerant cell formation and prevention, though these results should be considered hypothesis-generating and warrant additional study.

Stochastic simulations leveraging the developed MBM combined with published population PK indicate an average response that nearly eradicates KPC-Kp when a PMB ‘burst’ is combined with MEM 8 g as a 3 h prolonged infusion and RIF 600 mg. With regimens containing a MEM dosing regimen of 4g as a 3 h prolonged infusion, the corresponding 80% prediction interval infers extreme variability in the extent of bacterial regrowth, emphasizing the inherent difficulty of simultaneously achieving each agent’s optimal exposure given the extent of PK variability in infected patients. As the treating clinician must balance population-level knowledge within the context of their individual patient, this signals the necessity of therapeutic drug management to ensure preclinically and clinically derived PK-PD targets are achieved. Indeed, such practice is advocated in international guidelines for PMB [8], is increasingly recommended yet underutilized for β-lactams [29], and has been shown feasible for RIF [30]. If drug concentration measurements are not available, the developed MBM may still serve as a tool for simulating overall probability of a given bacterial endpoint with a desired PMB, MEM, and/or RIF dosing regimen. Importantly, modeling of the entire bacterial time-course affords predictions of antimicrobial efficacy irrespective of an MIC, allowing great flexibility in application based on the preferred clinical effect. However, direct clinical translation must be cautioned given the high doses of PMB and MEM employed here, which may result in unacceptably high toxicity rates and require additional testing.

There are several limitations to the present analyses. First is the use of a single bacterial isolate. However, isolate KPC-Kp 9A belongs to genetic sequence type ST258 and harbors bla_KPC-2, and is thus characteristic of the most prevalent KPC-Kp and of that responsible for pandemic expansion of the organism [31]. Second, it is acknowledged that the HFIM system is devoid of an immune system component, which is expected to exert an intrinsic bacterial killing effect, though it must be noted that the patient from whom the isolate was derived was immunocompromised. Third, a single RIF dosing regimen of 600 mg every 24 h was employed, and while this is the most commonly utilized regimen in the clinic, emerging evidence correlates higher doses with greater antimicrobial effect [32]. Given the present results, future experimentation with higher and varied RIF doses appears warranted. Finally, a single starting inoculum of ~8 log₁₀ CFU/mL was used, likely handicapping antimicrobial efficacy. Combined with an OmpK35 deletion creating a higher barrier to bacterial eradication, these facets coalesce to engender a “worst case” scenario and thus a conservative estimate of each regimen’s clinical adequacy.

In conclusion, KPC-Kp was highly resilient to 3-drug combinations involving PMB, MEM, and RIF. The MBM characterized direct bacterial killing effects and synergy between agents against phenotypically distinct subpopulations, suggesting that resistance suppression was possible, though at dosing regimens beyond those likely to be palatable. In the absence of clinical trials, this integrated approach holds great promise for discovering PD-optimized antimicrobial combination therapy and inferring its feasibility, providing crucial insights for an increasingly drug-resistant world.

Figure 4.

Simulated bacterial time-course for triple-drug combinations using the mechanism-based pharmacodynamic model and pharmacokinetic parameters derived from infected patients. Solid lines represent typical (population mean) predictions; shaded regions represent 80% prediction intervals.