Semimechanistic pharmacokinetic/pharmacodynamic model for assessment of activity of antibacterial agents from time-kill curve experiments

In vitro pharmacokinetic/pharmacodynamic models in anti-infective drug development: focus on TB

For rapid anti-tuberculosis (TB) drug development in vitro pharmacokinetic/pharmacodynamic (PK/PD) models are useful in evaluating the direct interaction between the drug and the bacteria, thereby guiding the selection of candidate compounds and the optimization of their dosing regimens. Utilizing in vivo drug-clearance profiles from animal and/or human studies and simulating them in an in vitro PK/PD model allows the in-depth characterization of antibiotic activity of new and existing antibacterials by generating time–kill data. These data capture the dynamic interplay between mycobacterial growth and changing drug concentration as encountered during prolonged drug therapy. This review focuses on important PK/PD parameters relevant to anti-TB drug development, provides an overview of in vitro PK/PD models used to evaluate the efficacy of agents against mycobacteria and discusses the related mathematical modeling approaches of time–kill data. Overall, it provides an introduction to in vitro PK/PD models and their application as critical tools in evaluating anti-TB drugs.

SCYX-7158, an orally-active benzoxaborole for the treatment of stage 2 human African trypanosomiasis

Background

Human African trypanosomiasis (HAT) is an important public health problem in sub-Saharan Africa, affecting hundreds of thousands of individuals. An urgent need exists for the discovery and development of new, safe, and effective drugs to treat HAT, as existing therapies suffer from poor safety profiles, difficult treatment regimens, limited effectiveness, and a high cost of goods. We have discovered and optimized a novel class of small-molecule boron-containing compounds, benzoxaboroles, to identify SCYX-7158 as an effective, safe and orally active treatment for HAT.

Methodology/Principal Findings

A drug discovery project employing integrated biological screening, medicinal chemistry and pharmacokinetic characterization identified SCYX-7158 as an optimized analog, as it is active in vitro against relevant strains of Trypanosoma brucei, including T. b. rhodesiense and T. b. gambiense, is efficacious in both stage 1 and stage 2 murine HAT models and has physicochemical and in vitro absorption, distribution, metabolism, elimination and toxicology (ADMET) properties consistent with the compound being orally available, metabolically stable and CNS permeable. In a murine stage 2 study, SCYX-7158 is effective orally at doses as low as 12.5 mg/kg (QD×7 days). In vivo pharmacokinetic characterization of SCYX-7158 demonstrates that the compound is highly bioavailable in rodents and non-human primates, has low intravenous plasma clearance and has a 24-h elimination half-life and a volume of distribution that indicate good tissue distribution. Most importantly, in rodents brain exposure of SCYX-7158 is high, with C_max >10 µg/mL and AUC_{0–24 hr} >100 µg*h/mL following a 25 mg/kg oral dose. Furthermore, SCYX-7158 readily distributes into cerebrospinal fluid to achieve therapeutically relevant concentrations in this compartment.

Conclusions/Significance

The biological and pharmacokinetic properties of SCYX-7158 suggest that this compound will be efficacious and safe to treat stage 2 HAT. SCYX-7158 has been selected to enter preclinical studies, with expected progression to phase 1 clinical trials in 2011.

Human African trypanosomiasis (HAT) is caused by infection with the parasite Trypanosoma brucei and is an important public health problem in sub-Saharan Africa. New, safe, and effective drugs are urgently needed to treat HAT, particularly stage 2 disease where the parasite infects the brain. Existing therapies for HAT have poor safety profiles, difficult treatment regimens, limited effectiveness, and a high cost of goods. Through an integrated drug discovery project, we have discovered and optimized a novel class of boron-containing small molecules, benzoxaboroles, to deliver SCYX-7158, an orally active preclinical drug candidate. SCYX-7158 cured mice infected with T. brucei, both in the blood and in the brain. Extensive pharmacokinetic characterization of SCYX-7158 in rodents and non-human primates supports the potential of this drug candidate for progression to IND-enabling studies in advance of clinical trials for stage 2 HAT.

Pharmacokinetics/pharmacodynamics of colistin and imipenem on mucoid and nonmucoid Pseudomonas aeruginosa biofilms

The time course of activity of colistin and imipenem against mucoid and nonmucoid Pseudomonas aeruginosa growing in a biofilm showed that compared with those for planktonic bacteria, the kinetics of colistin and imipenem retained the concentration- and time-dependent killing, respectively, but higher doses of antibiotics and longer dosing periods were required for biofilm eradication. Biofilms of mucoid P. aeruginosa were more difficult to eradicate than nonmucoid biofilms.

Predicting in vitro antibacterial efficacy across experimental designs with a semimechanistic pharmacokinetic-pharmacodynamic model

We have previously described a general semimechanistic pharmacokinetic-pharmacodynamic (PKPD) model that successfully characterized the time course of antibacterial effects seen in bacterial cultures when exposed to static concentrations of five antibacterial agents of different classes. In this PKPD model, the total bacterial population was divided into two subpopulations, one growing drug-susceptible population and one resting drug-insensitive population. The drug effect was included as an increase in the killing rate of the drug-susceptible bacteria with a maximum-effect (E(max)) model. The aim of the present study was to evaluate the ability of this PKPD model to describe and predict data from in vitro experiments with dynamic concentration-time profiles. Dynamic time-kill curve experiments were performed by using an in vitro kinetic system, where cultures of Streptococcus pyogenes were exposed to benzylpenicillin, cefuroxime, erythromycin, moxifloxacin, or vancomycin using different starting concentrations (2 and 16 times the MIC) and elimination conditions (human half-life, reduced half-life, and constant concentrations). The PKPD model was applied, and the observations for the static as well as dynamic experiments were compared to model predictions based on parameter estimation using (i) static data, (ii) dynamic data, and (iii) combined static and dynamic data. Differences in experimental settings between static and dynamic experiments did not affect the growth kinetics of the bacteria significantly. With parameter reestimation, the structure of our previously proposed PKPD model could well characterize the bacterial growth and killing kinetics when exposed to dynamic concentrations with different elimination rates of all five investigated antibiotics. Furthermore, the model with parameter estimates based on data from only the static time-kill curve experiments could predict the majority of the time-kill curves from the dynamic experiments reasonably well. Adding data from dynamic experiments in the estimation improved the model fit for cefuroxime and vancomycin, indicating some differences in sensitivity to experimental conditions among the antibiotics studied.

Mathematical modeling to characterize the inoculum effect

Killing by beta-lactams is well known to be reduced against a dense bacterial population, commonly known as the inoculum effect. However, the underlying mechanism of this phenomenon is not well understood. We proposed a semi-mechanistic mathematical model to account for the reduced in vitro killing observed. Time-kill studies were performed with 4 baseline inocula (ranging from approximately 1 × 10(5) to 1 × 10(8) CFU/ml) of Escherichia coli ATCC 25922 (MIC, 2 mg/liter). Constant but escalating piperacillin concentrations used ranged from 0.25× to 256× MIC. Serial samples were taken over 24 h to quantify viable bacterial burden, and all the killing profiles were mathematically modeled. The inoculum effect was attributed to a reduction of effective drug concentration available for bacterial killing, which was expressed as a function of the baseline inoculum. Biomasses associated with different inocula were examined using a colorimetric method. Despite identical drug-pathogen combinations, the baseline inoculum had a significant impact on bacterial killing. Our proposed mathematical model was unbiased and reasonable in capturing all 28 killing profiles collectively (r(2) = 0.88). Biomass was found to be significantly more after 24 h with a baseline inoculum of 1 × 10(8) CFU/ml, compared to one where the initial inoculum was 1 × 10(5) CFU/ml (P = 0.002). Our results corroborated previous observations that in vitro killing by piperacillin was significantly reduced against a dense bacterial inoculum. This phenomenon can be reasonably captured by our proposed mathematical model, and it may improve prediction of bacterial response to various drug exposures in future investigations.

Discovery of novel orally bioavailable oxaborole 6-carboxamides that demonstrate cure in a murine model of late-stage central nervous system african trypanosomiasis

We report the discovery of novel boron-containing molecules, exemplified by N-(1-hydroxy-1,3-dihydrobenzo[c][1,2]oxaborol-6-yl)-2-trifluoromethylbenzamide (AN3520) and 4-fluoro-N-(1-hydroxy-1,3-dihydrobenzo[c][1,2]oxaborol-6-yl)-2-trifluoromethylbenzamide (SCYX-6759), as potent compounds against Trypanosoma brucei in vitro, including the two subspecies responsible for human disease T. b. rhodesiense and T. b. gambiense. These oxaborole carboxamides cured stage 1 (hemolymphatic) trypanosomiasis infection in mice when administered orally at 2.5 to 10 mg/kg of body weight for 4 consecutive days. In stage 2 disease (central nervous system [CNS] involvement), mice infected with T. b. brucei were cured when AN3520 or SCYX-6759 were administered intraperitoneally or orally (50 mg/kg) twice daily for 7 days. Oxaborole-treated animals did not exhibit gross signs of compound-related acute or subchronic toxicity. Metabolism and pharmacokinetic studies in several species, including nonhuman primates, demonstrate that both SCYX-6759 and AN3520 are low-clearance compounds. Both compounds were well absorbed following oral dosing in multiple species and also demonstrated the ability to cross the blood-brain barrier with no evidence of interaction with the P-glycoprotein transporter. Overall, SCYX-6759 demonstrated superior pharmacokinetics, and this was reflected in better efficacy against stage 2 disease in the mouse model. On the whole, oxaboroles demonstrate potent activity against all T. brucei subspecies, excellent physicochemical profiles, in vitro metabolic stability, a low potential for CYP450 inhibition, a lack of active efflux by the P-glycoprotein transporter, and high permeability. These properties strongly suggest that these novel chemical entities are suitable leads for the development of new and effective orally administered treatments for human African trypanosomiasis.

Pharmacokinetic/pharmacodynamic modeling and simulation to determine effective dosage regimens for doripenem

The aim of this study was to obtain information on effective dosage regimens of doripenem by a modeling and simulation approach based on pharmacokinetic (PK)/pharmacodynamic (PD) theory. The PK/PD model we have already developed was modified to explain in vitro bactericidal kinetics of doripenem for several Pseudomonas aeruginosa strains. Time-course profiles of bacterial counts in patients infected with P. aeruginosa were simulated for typical clinical dosage regimens in Japan considering the variability of PK and the patients' backgrounds by a Monte Carlo simulation. Moreover, time-course profiles of probability achieving the criterion (log(CFU/mL) < 0) were predicted for the evaluation of antibacterial efficacy by renal function. The in vitro bacterial profiles at various dosage regimens could be well explained by the PK/PD model. The simulations suggested the dependence of antibacterial efficacy on the frequency of administration, indicating time-dependent antibacterial activity. It was also suggested that 500 mg t.i.d. showed significant bacterial reduction in patients for any degree of renal function and any severities in 2 weeks after the start of treatment. Our approach to simulate time-course profiles of bacterial counts should be useful for determining and examining effective dosage regimens, including the treatment period, in drug development.

Class-dependent relevance of tissue distribution in the interpretation of anti-infective pharmacokinetic/pharmacodynamic indices

The pharmacokinetic/pharmacodynamic (PK/PD) indices useful for predicting antimicrobial clinical efficacy are well established. The most common indices include the time free drug concentration in plasma is above the minimum inhibitory concentration (MIC) (fT(>MIC)) expressed as a percent of the dosing interval, the ratio of maximum concentration to MIC (C(max)/MIC), and the ratio of the area under the 24-h concentration-time curve to MIC (AUC(0-24)/MIC). A single PK/PD index may correlate well with an entire antimicrobial class. For example, the beta-lactams correlate well with the fT(>MIC). However, other classes may be more complex and a single index cannot be generalised to the class, e.g. the macrolides. The rationale behind which PK/PD index best correlates with efficacy depends on several factors, including the mechanism of action, the microbial kill kinetics, the degree of protein binding and the degree of tissue distribution. Studies have traditionally emphasised the first two factors, whilst the significance of protein binding and tissue distribution is increasingly appreciated. In fact, the latter two factors may partially elucidate why the magnitude of reported target indices are not always as expected. For example, tigecycline and telithromycin are clinically efficacious with average serum concentrations below their MICs over a 24-h period. Therefore, to understand more fully the PK/PD relationship of antibiotics and to better predict the clinical efficacy of antibiotic dosing regimens, assessment of free drug concentrations at the site of action is warranted.

Semimechanistic pharmacokinetic-pharmacodynamic model with adaptation development for time-kill experiments of ciprofloxacin against Pseudomonas aeruginosa

The objective of this study was to implement a semimechanistic pharmacokinetic-pharmacodynamic (PK-PD) model to describe the effects of ciprofloxacin against Pseudomonas aeruginosa in vitro. Time-kill curves were generated with an initial inoculum close to 5 x 10(6)CFU/ml of P. aeruginosa PAO1 and constant ciprofloxacin concentrations between 0.12 and 4.0 microg/ml (corresponding to 0.5x and 16x MIC). To support the model, phenotypic experiments were conducted with the PAO7H mutant strain, which overexpresses the MexEF OprN efflux pump and phenyl arginine beta-naphthylamide (PAbetaN), a known efflux inhibitor of main Mex multidrug efflux systems. A population approach was used for parameter estimation. At subinhibitory ciprofloxacin concentrations (0.12 and 0.25 microg/ml), an initial CFU decay followed by regrowth was observed, attesting to rapid emergence of bacteria with increased but moderate resistance (8-fold increase of MIC). This phenomenon was mainly due to an overexpression of the Mex protein efflux pumps, as shown by a 16-fold diminution of the MIC in the presence of PAbetaN in these strains with low-level resistance. A PK-PD model with adaptation development was successfully used to describe these data. However, additional experiments are required to validate the robustness of this model after longer exposure periods and multiple dosing regimens, as well as in vivo.

Antifungal activity of alpha-mangostin against Candida albicans

This study was conducted to examine the activity of alpha-mangostin against Candida albicans, the most important microorganism implicated in oral candidiasis. Its activity was compared to Clotrimazole and Nystatin. Results showed that alpha-mangostin was effective against C. albicans, the minimum inhibitory concentration (MIC) and minimum fungicidal concentration (MFC) were 1,000 and 2,000 microg/ml, respectively. The C. albicans killing activity of alpha-mangostin was more effective than Clotrimazole and Nystatin. The cytotoxicity of alpha-mangostin was determined and it was found that alpha-mangostin at 4,000 microg/ml was not toxic to human gingival fibroblast for 480 min. The strong antifungal activity and low toxicity of alpha-mangostin make it a promising agent for treatment of oral candidiasis.

In vitro pharmacodynamic models to determine the effect of antibacterial drugs

In vitro pharmacodynamic (PD) models are used to obtain useful quantitative information on the effect of either single drugs or drug combinations against bacteria. This review provides an overview of in vitro PD models and their experimental implementation. Models are categorized on the basis of whether the drug concentration remains constant or changes and whether there is a loss of bacteria from the system. Further subdifferentiation is based on whether bacterial loss involves dilution of the medium or is associated with dialysis or diffusion. For comprehension of the underlying principles, experimental settings are simplified and schematically illustrated, including the simulations of various in vivo routes of administration. The different model types are categorized and their (dis)advantages discussed. The application of in vitro models to special organs, infections and pathogens is comprehensively presented. Finally, the relevance and perspectives of in vitro investigations in drug discovery and clinical research are elucidated and discussed.

Pharmacokinetic-pharmacodynamic modeling of the in vitro activities of oxazolidinone antimicrobial agents against methicillin-resistant Staphylococcus aureus

Linezolid is the first FDA-approved oxazolidinone with activity against clinically important gram-positive pathogens, including methicillin (meticillin)-resistant Staphylococcus aureus (MRSA). RWJ-416457 is a new oxazolidinone with an antimicrobial spectrum similar to that of linezolid. The goal of the present study was to develop a general pharmacokinetic (PK)-pharmacodynamic (PD) model that allows the characterization and comparison of the in vitro activities of oxazolidinones, determined in time-kill curve experiments, against MRSA. The in vitro activities of RWJ-416457 and the first-in-class representative, linezolid, against MRSA OC2878 were determined in static and dynamic time-kill curve experiments over a wide range of concentrations: 0.125 to 8 microg/ml (MIC, 0.5 microg/ml) and 0.25 to 16 microg/ml (MIC, 1 microg/ml), respectively. After correction for drug degradation during the time-kill curve experiments, a two-subpopulation model was simultaneously fitted to all data in the NONMEM VI program. The robustness of the model and the precision of the parameter estimates were evaluated by internal model validation by nonparametric bootstrap analysis. A two-subpopulation model, consisting of a self-replicating, oxazolidinone-susceptible and a persistent, oxazolidinone-insusceptible pool of bacteria was appropriate for the characterization of the time-kill curve data. The PK-PD model identified was capable of accounting for saturation in growth, delays in the onsets of growth and drug-induced killing, as well as naturally occurring bacterial death. The simultaneous fit of the proposed indirect-response, maximum-effect model to the data resulted in concentrations that produced a half-maximum killing effect that were significantly (P < 0.05) lower for RWJ-416457 (0.41 microg/ml) than for linezolid (1.39 microg/ml). In combination with the appropriate PK data, the susceptibility-based two-subpopulation model identified may provide valuable guidance for the selection of oxazolidinone doses or dose regimens for use in clinical studies.

A simple in vitro PK/PD model system to determine time-kill curves of drugs against Mycobacteria

In vivo tuberculosis is exposed to continually changing drug concentrations for which static minimum inhibitory concentration (MIC) testing may be a poor surrogate. While in vitro approaches to determine time-kill curves for antibiotics have been widely applied in assessing antimicrobial activity against fast growing microorganisms, their availability and application for slow-growing microorganisms including Mycobacterium tuberculosis has so far been scarce. Thus, we developed a novel simple in vitro pharmacokinetic/pharmacodynamic (PK/PD) model for establishing time-kill curves and applied it for evaluating the antimicrobial activity of different dosing regimens of isoniazid (INH) against Mycobacterium bovis BCG as a surrogate for virulent M. tuberculosis. In the in vitro model M. bovis BCG was exposed to INH concentration-time profiles as usually encountered during multiple dose therapy with 25, 100 and 300mg/day in humans who are fast or slow INH metabolizers. Bacterial killing was followed over time by determining viable counts and the resulting time-kill data was analyzed using a semi-mechanistic PK/PD model with an adaptive IC(50) function to describe the emergence of insensitive populations of bacteria over the course of treatment. In agreement with previous studies, the time-kill data suggest that AUC(0-24)/MIC is the PK/PD index that is the most explanatory of the antimicrobial effect of INH. The presented in vitro PK/PD model and associated modeling approach were able to characterize the time-kill kinetics of INH in M. bovis BCG, and may in general serve as a potentially valuable, low cost tool for the assessment of antibacterial activity in slow-growing organisms in drug development and applied pharmacotherapy.

Pharmacokinetics and pharmacodynamics of antimicrobial drugs

BACKGROUND

Antimicrobial drugs exhibit different characteristics in their correlation between antimicrobial drug concentrations and effects on microorganisms. These correlations have been studied using different approaches including in vitro analyses with constant and fluctuating concentrations and in vivo analyses involving animals and humans. Mathematical analysis includes correlation of pharmacokinetic-pharmacodynamic (PK-PD) indices to an outcome parameter. Further insight can be gained by mechanism-based modelling of antimicrobial drug effects.

METHODS AND RESULTS

This review aims to provide an overview on the various approaches used to analyse antimicrobial pharmacodynamics, to discuss the limitations of these approaches, to indicate recent developments and to summarise the current knowledge on PK-PD target values as derived from human studies.

CONCLUSION

It is expected that PK-PD analysis of antimicrobial drug effects will lead to a more efficient and possibly also less toxic antimicrobial drug therapy.

Effect of protein binding on the pharmacological activity of highly bound antibiotics

During antibiotic drug development, media are frequently spiked with either serum/plasma or protein supplements to evaluate the effect of protein binding. Usually, previously reported serum or plasma protein binding values are applied in the analysis. The aim of this study was to evaluate this approach by experimentally measuring free, unbound concentrations for antibiotics with reportedly high protein binding and their corresponding antimicrobial activities in media containing commonly used protein supplements. Free, unbound ceftriaxone and ertapenem concentrations were determined in bacterial growth medium with and without bovine/human serum albumin, as well as adult bovine serum and human plasma using in vitro microdialysis. The corresponding antimicrobial activity was determined in MIC and time-kill curve experiments using Escherichia coli ATCC 25922 and Streptococcus pneumoniae ATCC 6303 as test strains. A semimechanistic maximum effect model was simultaneously fitted to the data and respective EC(50) (concentration at half-maximum effect) values compared. Protein binding differed significantly for ceftriaxone (P < 0.05) between human plasma (76.8 +/- 11.0%) and commercially available bovine (20.2 +/- 8.3%) or human serum albumin (56.9 +/- 16.6%). Similar results were obtained for ertapenem (human plasma, 73.8 +/- 11.6%; bovine serum albumin, 12.4 +/- 4.8%; human serum albumin, 17.8 +/- 11.5%). The MICs and EC(50)s of both strains were significantly increased (P < 0.05) for ceftriaxone when comparing human and bovine serum albumin, whereas the EC(50)s were not significantly different for ertapenem. Free, unbound antibiotic concentrations differed substantially between plasma and protein supplements and correlated well with antimicrobial efficacy. Therefore, free, active concentrations should be measured in the test system instead of correcting for literature protein binding values.

Mechanism-based pharmacokinetic-pharmacodynamic models of in vitro fungistatic and fungicidal effects against Candida albicans

Mechanism-based pharmacokinetic-pharmacodynamic (PK-PD) models describing the fungistatic activity of fluconazole and the fungicidal activity of caspofungin were developed using dynamic in vitro models. Antifungal-drug pharmacokinetics was simulated in vitro, assuming a one-compartment model with an elimination half-life of 3 h and using a wide (1 to 10,000) range of initial concentrations. The number of CFUs over time was determined for up to 31 h and used for PK-PD modeling. A model incorporating first-order natural growth and natural death, plus a maximum number of viable Candida cells, was used to characterize Candida growth in the absence of a drug. Fluconazole was considered to inhibit Candida growth and caspofungin to stimulate Candida death according to an Emax pharmacodynamic model. The data were analyzed with Nonmem, using a population approach. A good fit of the data was obtained with satisfactory estimates of PK-PD parameters, especially with drug concentrations producing 50% of the maximal effect: 50% inhibitory concentrations for fluconazole growth inhibition and 50% effective concentrations for caspofungin death stimulation. In conclusion, mechanistic PK-PD models were successfully developed to describe, respectively, the fungistatic and fungicidal activities of fluconazole and caspofungin in vitro. These models provide much better information on the drug effects over time than the traditional PK-PD index based on MICs. However, they need to be further characterized.

Mechanism-based pharmacokinetic–pharmacodynamic modeling of antimicrobial drug effects

Mathematical modeling of drug effects maximizes the information gained from an experiment, provides further insight into the mechanisms of drug effects, and allows for simulations in order to design studies or even to derive clinical treatment strategies. We reviewed modeling of antimicrobial drug effects and show that most of the published mathematical models can be derived from one common mechanism-based PK-PD model premised on cell growth and cell killing processes. The general sigmoid Emax model applies to cell killing and the various parameters can be related to common pharmacodynamics, which enabled us to synthesize and compare the different parameter estimates for a total of 24 antimicrobial drugs from published literature. Furthermore, the common model allows the parameters of these models to be related to the MIC and to a common set of PK-PD indices. Theoretically, a high Hill coefficient and a low maximum kill rate indicate so-called time-dependent antimicrobial effects, whereas a low Hill coefficient and a high maximum kill rate indicate so-called concentration-dependent effects, as illustrated in the garenoxacin and meropenem examples. Finally, a new equation predicting the time to microorganism eradication after repeated drug doses was derived that is based on the area under the kill-rate curve.