a physiologically-based pharmacokinetic model for capreomycin

7/28/2019 A Physiologically-Based Pharmacokinetic Model for Capreomycin

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Title: A Physiologically-Based Pharmacokinetic Model for Capreomycin1

Running title: A PBPK Model for Capreomycin2

Authors: B. Reisfeld*,1

, C.P. Metzler1,

, M.A. Lyons1, A.N. Mayeno

1, E.J. Brooks

2, M.A.3

DeGroote24

Key words: Mycobacterium tuberculosis, therapeutics, pharmacokinetics, computational5

modeling, pharmacodynamics, pbpk, mouse, human, anti-tuberculosis agents.6

Author affiliations:7

1Department of Chemical and Biological Engineering; Colorado State University, Fort8

Collins, CO 805239

2Department of Microbiology, Immunology, and Pathology; Colorado State University, Fort10

Collins, CO 8052311

12

13

* Brad Reisfeld; Department of Chemical and Biological Engineering; Colorado State University; 1370 Campus

Delivery; Fort Collins, CO 80523-1370; voice: 970-491-1019, fax: 970-491-7369, email:

[email protected]

current address Vertex Pharmaceuticals, Cambridge, MA

Copyright 2011, American Society for Microbiology and/or the Listed Authors/Institutions. All Rights Reserved.Antimicrob. Agents Chemother. doi:10.1128/AAC.05180-11AAC Accepts, published online ahead of print on 5 December 2011


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Abstract14

The emergence of multidrug-resistant tuberculosis (MDR-TB) has led to a renewed interest in15

the use of second-line antibiotic agents. Unfortunately, there is currently a dearth of16

information, data, and computational models that can be used to help design rational regimens17

for administration of these drugs. To help fill this knowledge gap, an exploratory18

physiologically-based pharmacokinetic (PBPK) model, supported by targeted experimental19

data, was developed to predict the absorption, distribution, metabolism, and excretion20

(ADME) of the second-line agent capreomycin, a cyclic peptide antibiotic often grouped with21

the aminoglycoside antibiotics. To account for inter-individual variability, Bayesian inference22

and Monte Carlo methods were used for model calibration, validation, and testing. Along with23

the predictive PBPK model, the first for an anti-tuberculosis agent, this study has provided24

estimates of various key pharmacokinetic parameter distributions and has supported a25

hypothesized mechanism for capreomycin transport into the kidney.26

27


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Introduction28

An estimated 500,000 cases of multi-drug resistant tuberculosis (MDR-TB) emerge each year29

with 150,000 deaths (50). MDR-TB refers to strains that are resistant to at least isoniazid and30

rifampicin. The World Health Organization (WHO) guidelines for treatment of MDR-TB31

include regimens containing Group 2 injectable agents (51). One such agent is capreomycin32

(CAP), a commonly used second line injectable drug with activity against many MDR-TB33

strains. It is generally reserved for patients who have had prior exposure to or whose34

isolates have documented resistance to kanamycin and streptomycin (51). Moreover, CAP35

has unique effectiveness against both the dormant and active forms of tuberculosis (25).36

However, the drug is nephrotoxic and ototoxic, especially in patients with renal impairment or37

in geriatric patients (26).38

CAP is a polypeptide antibiotic composed of four molecular analogs, IA, IIA, IB, and IIB. Its39

mode of action, though not fully understood, involves ribosomal inhibition of protein40

synthesis (22). Studies suggest that CAP binds to, and inhibits the function of, the 16S rRNA41

molecule of the M. tuberculosis 30S ribosomal subunit, as supported by up-regulation of a42

methyltransferase gene and the 16S rRNA processing protein gene (20). Due to similar43

nomenclature, side effects, and mode of action, CAP is often compared to, and grouped with,44

aminoglycoside antibiotics (AGAs) (19, 22, 24), despite its structural distinction.45

CAP and AGAs are nephrotoxic (26, 38), with some of the administered dose being retained46

in the epithelial cells of the kidney proximal tubules. The accumulation of AGAs is notable as47

the concentration in the kidney is much higher than that in the serum (41). In the proximal48


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tubule cells, AGAs must enter via apical membrane binding and endocytosis because the49

charged drug molecule cannot freely cross the cellular membrane. Megalin, a glycoprotein50

expressed in some specialized epithelial cells including in the renal tubule and inner ear51

epithelium, is the proposed endocytic receptor for such drugs (13, 41, 49). As noted earlier,52

CAP is known to exert both renal and ototoxicity, which supports the likelihood that megalin53

is responsible for uptake (38). As further evidence that megalin is an important factor in AGA54

uptake, a study comparing normal and genetically megalin-deficient mice was conducted by55

Schmitz et al. (48). In these studies, after exposure to gentamicin, wild-type mice had56

significant drug accumulation in the kidneys, whereas megalin-deficient mice did not.57

Despite its long history as an antibiotic, there is limited experimental information and few58

pharmacokinetic models available for the disposition of CAP. In the 1960s, Black et al.59

measured the pharmacokinetics of CAP in humans (3, 4) and derived peak serum60

concentrations and urinary excretion levels. Lee et al. (34) measured early time (up to two61

hours) serum levels of two different formulations of CAP in rats and looked at the impact of62

impurities on safety. In the present context, the most directly relevant experimental study to63

date is that of Le Conte et al. (33), who measured the concentrations of free and liposomal64

CAP in the blood, spleen, kidney, and lung of normal mice at various points (0.25, 0.5, 0.75,65

1, 2, 4, and 6 hours) after administration. Notably, the concentration of CAP and the area66

under the curve (AUC) in the kidney were found to be much higher than that in all the other67

measured tissues at all time points. These investigators did not measure concentrations at later68

time points so that peak kidney concentrations, and decays from these concentrations, were69

not noted.70


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Especially for second-line agents, where side effects and toxicity are inherent concerns, it is71

critical to develop information and models that allow the examination of drug levels in72

specific tissue types, such as the kidney. The classical data-driven pharmacokinetic model73

assumes the body to be one homogenous, well-mixed vessel. To examine chemical74

distribution in specific tissues, a more sophisticated approach is needed. Using75

physiologically-based pharmacokinetic (PBPK) modeling, the body is divided into several76

physiologically-representative compartments organs, blood, tissues with a mass-balance77

for each compartment. With this approach, dose extrapolation, different routes of dosing, and78

animal-to-animal extrapolation may all be performed by changing relevant physiological and79

biochemical properties and by including appropriate allometric scaling laws (30, 31).80

Although traditionally used for environmental toxicants, PBPK models are increasingly used81

for the prediction of ADME for various drugs (45-47), including antibiotics (9, 10, 16, 32). A82

relatively recent advance in PBPK modeling has been the incorporation of approaches for83

accounting for inter-individual variability in anatomy, physiology, biochemistry, and84

chemical exposure (1, 6, 8, 12, 36, 39). Among other things, these approaches allow a85

rigorous incorporation of uncertainties, as well as predictions of chemical ADME in86

susceptible subpopulations.87

Overall, there is a knowledge gap in data and methods for predicting the ADME of second-88

line agents for the treatment of MDR-TB, and until totally new regimens are approved,89

optimized use of second-line drugs available to clinicians is a current research priority (42).90

The present exploratory study is meant to help fill the knowledge gap by acquiring tissue91

pharmacokinetic data and developing a PBPK model for CAP disposition. Although PK/PD92


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models have been developed (23), to our knowledge, this is the first published PBPK model93

for an anti-tuberculosis drug.94

95


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Materials and Methods96

Experimental Study97

The aim of the laboratory portion of this study was to determine the tissue and blood levels of98

CAP in mice at specified time points following subcutaneous injection.99

Mice. Female, six to eight week old C57BL/6 female mice were purchased from Jackson100

Laboratories (Bar Harbor, ME) and were housed in the Painter Center at Colorado State101

University. All experiments were approved by the Institutional Animal Care and Use102

Committee. Mice were randomly assigned to three groups: low-dose (N=24), high dose103

(N=24), and control (N=4).104

Drug. Capreomycin sulfate was purchased from Sigma Chemical Co. (St Louis, MO).105

Capreomycin solution was prepared by dissolving 92.5 mg (low-dose solution) and 231 mg106

(high-dose solution) of capreomycin sulfate in 10 ml phosphate buffer saline (1X, pH 7.4)107

(Fisher Scientific, Pittsburgh, PA). The vehicle solution was 1X PBS.108

Pharmacokinetic studies. The dosing regimen was determined through a pilot study in mice109

(TB Pharmacokinetic Laboratory of National Jewish Medical and Research Center, Dr. C.110

Peloquin), in which CAP plasma levels were measured following a single dose.111

Concentrations were adjusted to span doses that match human bioequivalence measures [Cmax112

(maximum plasma concentration), t1/2 (half life)], leading to recommended dosing levels of113

100 mg/kg and 250 mg/kg for the present study. At time zero, the drug or control solution was114

administered subcutaneously to the mice. All mice received an injection of 0.2 ml of the115


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relevant solution. This corresponded to 100 mg/kg, 250 mg/kg, and 0 mg/kg capreomycin116

sulfate for mice in the low-dose, high-dose, and control groups, respectively. At each of the117

time points (0.5, 1, 2, 6, and 20 h), four mice from both the low-dose and high-dose groups118

were sacrificed via CO2 euthanasia followed by cervical dislocation. All of the mice in the119

control group were sacrificed at the 1 hr time point. Immediately following sacrifice, blood120

was collected by cardiac puncture, placed in a serum vial, put on ice for one hour after121

collection, and spun down to collect the serum; and the kidneys, lungs, spleen, and liver were122

harvested, weighed, and then flash frozen in cryovials at -80 C.123

Capreomycin analyses. Capreomycin was quantified by LC/MS/MS (vide infra). The tissues124

were prepared for analysis by adding water to give 100 mg tissue per ml, followed by125

sonication. Sonication was performed in small bursts while the tissue remained on ice in order126

to mitigate the effects of heat generated by the sonicator. In some cases, the larger organs127

were subdivided. The organs were prepared as follows in order to improve homogeneity:128

spleen (used in entirety due to the small size); kidneys (one kidney was used from each129

mouse; it was assumed that there was no preferential clearance in one kidney or the other);130

lung (portions of each lobe of the lung were removed and homogenized together); liver (after131

removal of the gallbladder, the liver was diced into small pieces, mixed, and a random sample132

of pieces was taken). Following sonication, 200 l of the tissue homogenate or 100 l of133

serum were added to a microcentrifuge tube containing 10 l of capreomycin standard or 10134

l of 50% acetonitrile. The mixtures were vortexed briefly. To the tissue homogenate, 150 l135

of methanol + 1% formic acid was added, while 300 l of methanol + 1% formic acid was136

added to the serum samples to induce protein precipitation. Each sample was then vortexed137


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for 10 minutes, followed by centrifugation for 10 minutes to remove cell debris and protein138

from the liquid portion. Supernatant was then transferred to plastic autosampler vials for139

analysis. Plastic vials were used as capreomycin exhibits binding to glass (37). HPLC was140

performed using a Waters Atlantis HILIC Silica, 5 m, 4.6 x 50 mm column with a141

Phenomenex C18 guard cartridge. Standard curves for CAP (from 500 ng/mL to 50 g/mL)in142

matrix (control serum or tissue homogenate) were generated, by adding capreomycin sulfate143

standards prepared in 50% acetonitrile: 50% H2O with 0.1% acetic acid. The PK results for144

CAP in the paper refer to capreomycin free base (the base form of the drug rather than the salt145

form; "free" does not refer to unbound drug). Lower limits of quantitation (LLOQ) for146

capreomycin in each tissue were determined to be as follows: kidney (50 ng/mg), serum (1147

ng/mg), liver (10 ng/mg), lung (10 ng/mg), spleen (10 ng/mg). Further LC-MS/MS method148

details are provided in the Appendix.149

The use of tissue homogenates is appropriate for use in the PBPK modeling approach used150

here because compartments are assumed to be well mixed and homogenous with respect to151

drug concentration. This is in contrast to studies of drug activity and efficacy, in which results152

derived from these types of samples could be misleading or erroneous (40).153

PBPK Modeling Study154

The aim of this study was to develop a PBPK model, calibrated and validated with155

experimental data, to predict the time-dependent ADME of capreomycin in mice.156

Model structure and equations. The structural model for capreomycin was based on a157

generic whole body PBPK model (28) with subsequent modifications of the kidney158


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compartment. This model comprises compartments for the lung, skin, fat, muscle, kidney,159

brain, heart, bone, liver, spleen, gut, arterial blood, venous blood, and a carcass compartment160

that contains all tissues not accounted for in other compartments. This flexible structure161

allowed the prediction of drug concentrations in tissues relevant for examinations of toxicity162

and pharmacological efficacy relevant to TB, as well as the possibility of assessing the impact163

of different dosing routes. Some of the compartments are not directly relevant to the efficacy164

and toxicity of CAP (e.g., heart and skin); however, they are included here because they165

provide additional detail for scaling to other species and are often germane to studies in which166

drug concentrations are measured in these tissues. The connection between compartments and167

pathway of blood flow is shown in Figure 1.168

Associated with each compartment is a mass balance for the drug. In all compartments, we169

assumed flow-limited mass transfer, viz., the blood entering a tissue is quickly in equilibrium170

with the tissue. The full set of governing equations for the model is given in the Appendix171

(eqn A2 eqn A13).172

Due to similarities in certain physicochemical and pharmacodynamic properties between173

AGAs and capreomycin, we assumed that the mechanisms for capreomycin ADME are174

related to those of other AGAs (52). As noted earlier, transport of AGAs is known to be175

dependent on megalin endocytosis followed by lysosomal sequestration (41, 48, 49). To176

account for the sequestration of capreomycin in the present model, we represented the kidney177

by a system comprising two linked compartments: a shallow (S) and deep (D) compartment,178

both of which were assumed to be well mixed (Figure 2). Although the correlation is not179

exact, anatomically, the deep compartment would approximate the cells along the walls of the180


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kidney tubules, while the shallow compartment would represent the remainder of the kidney181

tissue.182

The absorption for the kidney compartment was modeled using an equation describing183

saturable kinetics, as seen in the literature for similar applications (2, 14, 18). For example,184

Giuliano et al. (21) demonstrated that gentamicin and netilmicin accumulation in the kidney185

could be described using a Michaelis-Menten (saturable kinetics) equation (eqn 1), which is186

traditionally used to describe an enzyme-substrate reaction. For the present model, megalin187

corresponds to the enzyme, v0 is the renal accumulation rate, vmax is the maximum renal188

accumulation rate, [S] is the capreomycin concentration (in the shallow compartment), andKM189

is the Michaelis constant.190

][

][max0

SK

Svv

M +

= (eqn 1)191

Here, although capreomycin consists of 4 distinct molecules, this mixture was treated as a192

lumped single chemical entity in this model.193

Model parameters and accounting for variability. The following experimental inputs were194

used directly in the model: body weight of the mice, and lung, liver, kidney, and spleen195

weights. For the remaining organs, and for approximate blood flow through each organ,196

values from Brown et al. (11) and Davies and Morris (17) were used. The tissue density for197

all of the organ systems was assumed to be equal to that of water (11). With the exception of198

that for the lung, all of the tissue:blood partition coefficients were set equal to one. The199

lung:blood partition coefficient was set equal to two based on the observation that200


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aminoglycosides are transported into the lungs by endocytosis (27), augmenting the baseline201

thermodynamic partitioning. A lung:blood partition coefficient greater than one is consistent202

with the observation that aminoglycosides are eliminated more slowly from the lung than203

from the serum (15, 35). The list of model parameters used in the simulations is summarized204

in Table A3 of the Appendix.205

Owing to the unique nature of the model structure, and the lack of literature values for206

physiological transport values for capreomycin, the model parameters listed in Table 1 were207

determined using calibration simulations (vide infra).208

Solution Method. Simulations were performed in two steps. First, a series of calibration209

simulations were conducted using a Bayesian approach (7, 8, 35) to determine the unknown210

parameters for the model. This approach rests on a relationship among probability211

distributions involving unknown parameters and available data y given by Bayes theorem212

( ) ( ) ( )| |p y p y p . Here, the posterior distribution ( )|p y is obtained as the product213

of the prior distribution

( )p and the likelihood

( )|p y . The model calibration involves the214

identification of the parameters (Table 1) with those that are needed to complete the215

specification of the PBPK model (Table A3). The data y corresponds to experimentally216

obtained concentration-time profiles resulting from a known dose. The likelihood contains the217

underlying PBPK model (eqn A2 - eqn A13) calculated with the parameters . Combining the218

likelihood of the data with prior parameter distributions results in the posterior probability219

distribution for the parameters conditioned on the data. To verify the robustness of the220


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posterior estimates, several types of priors were used, including truncated-normal and uniform221

distributions.222

Following the calibration step, Monte Carlo (MC) simulations were performed, in which the223

PBPK model equation system was solved using values sampled from the parameter224

distributions found in the calibration step. In a typical MC simulation, 1000 model runs were225

conducted, each containing a set of parameters randomly sampled from the distributions226

found earlier. The result of these runs was families of time-dependent concentration profiles227

of capreomycin in each model compartment.228

All simulations were performed using GNU MCSim (5) (v. 5.2), a simulation package that is229

useful in solving statistical and differential equation systems, performing Monte Carlo230

stochastic simulations, and conducting Bayesian inference through Markov chain Monte231

Carlo (MCMC) simulations. For the MCMC simulations, chains of length 10,000 were used232

and convergence was assessed using visual inspection. All calculations were performed on a233

PC workstation with a 2.8 GHz dual core Intel Pentium processor and 8 GB of RAM running234

the Windows XP operating system.235

236


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Results237

Experimental Study238

The measured low-dose and high-dose concentrations of capreomycin in the organs of interest239

are shown in Figure 3 (a-e). For all tissues except the kidney, the peak concentration of240

capreomycin occurred at some time prior to 0.5 hours. Within the resolution of the data, the241

concentrations were found to decay exponentially over time, consistent with a first-order242

elimination process, with both low- and high-dose data following similar elimination kinetics.243

The capreomycin was eliminated relatively rapidly, with concentrations falling below the244

LLOQ in one to two hours for all tissues, besides the kidney.245

For the kidney, peak concentrations for both low- and high-doses occurred around three hours246

after administration and then decayed relatively slowly. Concentrations of capreomycin in the247

kidney were still well above the LLOQ after 20 hours. The only other study in which tissue248

concentrations for capreomycin were measured (33) focused on time points up to six hours,249

and decay in concentration from the peak value was not seen. The kidney concentrations at all250

time points are several times those in any other compartment, consistent with the transporter-251

enhanced uptake mechanism and supporting data described earlier.252

253


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Modeling Study254

Estimated Parameter Values255

Based on the calibration simulations described earlier, probability distributions of the256

unknown parameters were determined. Table 2 summarizes the means and standard257

deviations for the values in these distributions, while Figure 4 shows the distributions for each258

of these parameters. These parameters provide rough estimates for various transport259

properties for CAP that are difficult to measure directly, including the kinetics of260

accumulation in the kidney, the rate of renal clearance, and the rate of hepatic clearance.261

However, as mentioned earlier, it is difficult to compare these values to others in the literature262

because of the paucity of previous detailed pharmacokinetic and transport studies for263

capreomycin.264

265

Comparisons Between Experimental Data and Model Predictions266

The MC simulations produce a family of concentration profiles in each organ compartment267

based on the animal and organ weights and sampling the distributions of model parameters268

depicted in Figure 4. The fifth and ninety-fifth percentile curves for the low-dose MC269

simulation results, along with the corresponding experimental data, are shown in Figure 6.270

Similar comparisons for the high-dose case are shown in Figure 7.271

For the low-dose case, agreement between simulations and experiments was generally good272

for all organs, with the experimental points falling within the range of simulations in most273

cases. The largest discrepancy appears in the peak serum concentrations for capreomycin. Part274


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of this discrepancy arises because very early time data (


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Discussion297

Although a few studies have investigated the pharmacokinetics of capreomycin in blood (3, 4,298

29, 34, 43, 44), only one study to date (33) has examined tissue concentrations of299

capreomycin over time, and this study focused on relatively early-time data which do not300

capture important late clearance events, especially for the kidney. To our knowledge no PBPK301

models have been published for any anti-tuberculosis drugs. Moreover, even existing PBPK302

models for antibiotics (9, 10, 16, 32) have not included considerations of inter-individual303

variability, an important consideration in the interpretation of ADME predictions for these304

drugs. The PBPK model for capreomycin disposition in mice developed in this study begins305

to close this knowledge gap. It provides predictions that are generally in good agreement with306

results from a corresponding experimental study and, through a Bayesian model calibration,307

has provided distributions for several parameters related to capreomycin transport.308

The approach used here has important advantages relative to classical PK or population-PK309

approaches. Since classical models are not based upon the true anatomy, physiology, and310

biochemistry of the species of interest, they cannot, in general, be used to generate reliable311

predictions outside the range of doses, dose routes, and species used in the studies upon which312

they were based. Such extrapolations, which are essential in estimating the dose-response of313

chemicals, can be performed more accurately using PBPK modeling approaches.314

Despite these advantages, there are limitations to the current study. Because of the relatively315

small sample size, the model and results should be viewed as exploratory in nature. In316

addition, very early time data were not collected in this study, making characterization of the317


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peak concentration difficult and adding uncertainty to the analysis. Future studies could make318

use of optimal sampling theory to design appropriate studies to capture these events in an319

efficient manner.320

Current work is focused on improving the model, principally through the inclusion of321

additional data; the Bayesian approach used here provides for a straightforward means of322

incorporating these data as they become available. Also, we are assessing the feasibility of323

extrapolating the model to humans using appropriate physiological parameters from Brown et324

al. (11) and Davies and Morris (17) and calibrating and validating using the human325

pharmacokinetic data from Black et al. (3, 4). In addition, because of similarities between326

CAP and AGAs as described earlier, the model is being extended to AGAs. Longer-term aims327

are to use this model, along with appropriate pharmacodynamic and toxicity data, as part of a328

predictive framework to help optimize drug regimens to treat MDR-TB.329

330

331


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Acknowledgements332

The authors thank Janet Gilliland for assistance in the animal studies, Dr. Ryan Hansen for333

conducting the analytical chemistry analyses, and Dr. Daniel Gustafson for providing334

resources for pharmacokinetic analyses and for helpful comments about capreomycin335

pharmacokinetics. The authors also thank the anonymous reviewers for their valuable336

comments and suggestions to improve the quality of the paper. We gratefully acknowledge337

funding for this project from a Capacity Building Grant awarded by the Infectious Disease338

Supercluster at Colorado State University.339

340


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Appendix341

Analysis of Capreomycin IA and IB from Mouse Tissues by LC/MS/MS342

Instrument: Shimadzu LC-20AD High Performance Liquid Chromatograph system343

(Shimadzu Corporation, Kyoto, Japan). Column: Waters Atlantis HILIC Silica 5 m, 4.6 x344

50 mm (part#186002028), protected by a Phenomenex C18 Guard Cartridge (and filter frits).345

Vials: plastic. Injection Volume: 75 l. Loop: 100 l. Flow Rate: 800 l/min. Run Time: 4346

min. Column Oven: RT.347

LC Gradient Conditions:348

Time (min) % Organic Phase % Aqueous Phase

0.50 2% ACN 98% 0.1% Formic Acid in H2O





349

MS Conditions350

Instrument: MDS Sciex 3200 Q-TRAP triple quadrupole mass spectrometer (Applied351

Biosystems, Foster City, CA) with a TurboIonSpray source. MRM Positive Ion Mode.352

Scan/Dwell Time: 300 msec. Transitions Monitored:353

Capreomycin IA (669.30 507.00 amu) DP: 71.0; CE: 45; CEP: 30; CXP: 6354

Capreomycin IB (653.3 491.3 amu) DP: 55.0; CE: 48; CEP: 33.8; CXP: 4355


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Curtain (CUR) Gas: 20. Collision (CAD) Gas: 12 (High). Ion Spray Voltage: 2500. Source356

Temperature: 550C. Ion Source Gas 1: 35. Ion Source Gas 2: 30. Entrance Potential (EP):357

10. Ihe: on.358

For analysis, both transitions were integrated as one. As capreomycin IA and IB are, by far,359

the major constituents, only these two components were quantified. The weight of sulfate was360

taken into account for quantitation, and the PK results for CAP in this paper refer to361

capreomycin free base (the base form of the drug rather than the salt form).362

363

Governing Equations for PBPK Model364

Although the model structure is applicable for both intravenous and subcutaneous dose, in this365

section, we focus solely on the subcutaneous dose. Consistent with the structural model366

(Figure 1), for all organs except the lung, blood, kidney, and liver, a capreomycin mass367

balance may be written as368

( )organ organorgan

organ

d M CQ CAdt P

=

, (eqn A2)369

where Morgan is the drug mass in the organ, Qorgan is blood flow to organ, CA is the drug370

concentration in the arterial blood flow, Corgan is the drug concentration in the organ, and371

Porgan is the tissue-blood partition coefficient. Organ flows are fractions of the cardiac output,372

QC, which is allometrically-scaled to body weight (QCBW0.75

) (11, 17). The mass of drug373

in the lung,MLU, is governed by374


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( )d MLU CLU QLU CA

dt PLU

=

. (eqn A3)375

A mass balance on the venous blood, considering the drug dose, is376

( )( ) organorgans organ

organ

C d MSC d MVQ QLU CV

dt P dt

=

, (eqn A4)377

whereMSCis the mass of drug in the subcutaneous compartment, given by378

( )_

d MSC SC Decay MSC

dt= . (eqn A5)379

Here SC_Decay is the rate of drug movement from the subcutaneous compartment into the380

venous blood. On the arterial side, the governing equation takes the following form:381

( )d MA CLU QLU CA

dt PLU

=

. (eqn 6)382

Based on the conceptual model for the kidney (Figure 2), the following series of equations383

may be formulated:384

( )d MKE CLR CVKS

dt= (eqn A7)385

max( )

m

V CVKS d MKA

dt K CVKS

=

+

(eqn A8)386

( )d MKDECLRD CVKD

dt= (eqn A9)387

( ) ( ) ( ) ( )( )

d MKS d MKA d MKE d MKDE QK CA CVKS

dt dt dt dt = + (eqn A10)388

( ) ( ) ( )d MKD d MKA d MKDE

dt dt dt = (eqn A11)389


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( ) ( ) ( )d MK d MKS d MKD

dt dt dt

= + (eqn A12)390

Here,MKEis the mass of drug excreted from the kidney,MKDEis the mass of drug excreted391

from the deep compartment and returned to blood flow, MKA is the mass of drug392

accumulating in the deep compartment of the kidney, MKSis the mass of drug in the shallow393

compartment, CLR is the rate of capreomycin clearance from kidney blood flow, CLRD is the394

rate of capreomycin clearance from the deep kidney compartment, CVKSis the capreomycin395

concentration in the well-mixed blood in the kidney that is then mixed with the venous blood,396

CVKD is the capreomycin concentration in the well-mixed deep kidney compartment, and397

Vmax andKm are Michaelis-Menten parameters for accumulation.398

Finally, for the liver compartment, we have399

( )d MLQLA CA QS CVS QG CVG QL CVL CLH CVL

dt= + + , (eqn A13)400

where CVL is the concentration of drug in the liver, and CLH is the hepatic clearance rate401

(CLH= CLHCBW).402


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403

404


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Figure Captions554

Figure 1. PBPK model structure555

Figure 2. Conceptual model of the kidney556

Figure 3. Low dose and high dose pharmacokinetic data in various tissues (N=4): (a) serum,557

(b) kidney, (c) lung, (d) liver, and (e) spleen. Mean SD are shown. Scales for the abscissa558

and ordinate differ for each plot. Data points below the LLOQ are not shown. LLOQ559

(ng/mg): kidney (50.0), serum (1.0), liver (10.0), lung (10.0), spleen (10.0).560

Figure 4. Parameter distributions found in the calibration simulations for (a) Km, (b) Vmax,561

(c) CLRD, (d) CLR, (e) CLHC, (f) SC_Decay.562

Figure 5. Measured and predicted serum concentration for the low-dose group based on (a)563

using the measured peak concentration as the actual peak value, and (b) extrapolating to564

determine the peak concentration565

Figure 6. Low dose pharmacokinetic data and model predictions in various tissues: (a) serum,566

(b) kidney, (c) lung, (d) liver, and (e) spleen. The experimental data are shown with symbols,567

and the fifth and ninety-fifth percentile curves for the simulation data are shown with dashed568

lines. Data points below the LLOQ are not shown.569

Figure 7. High dose pharmacokinetic data and model predictions in various tissues: (a) serum,570

(b) kidney, (c) lung, (d) liver, and (e) spleen. The experimental data are shown with symbols,571

and the fifth and ninety-fifth percentile curves for the simulation results are shown with572

dashed lines. Data points below the LLOQ are not shown.573

574


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Tables575

576


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577

Table 1. Parameters to be determined through model calibration578

Symbol Units Description (relevant compartment)

KM ng/kg Michaelis constant in accumulation kinetics (kidney)

Vmax ng/h Michaelis-Menten maximum accumulation rate (kidney)

CLR l/h Overall renal clearance (kidney)

CLRD l/h Deep renal compartment clearance (kidney)

CLHC l h-1 kg-1 Hepatic clearance rate (liver)

SC_Decay h-1Subcutaneous dose decay rate (subcutaneous); release into

venous blood.

579


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580

Table 2. Summary statistics for the parameters estimated in the calibration simulations581

Parameter Mean SD

Km(ng/kg) 5.55 x 108 0.46 x 108

Vmax (ng/h) 1.04 x 106 0.08 x 106

CLR (kg/h) 0.012 0.001

CLRD (kg/h) 3.47 x 10-6 0.25 x 10-6

CLHC(l hr-1 kg-1) 3.97 0.27

SC_Decay (h-1) 0.902 0.164

582


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Table A3. Parameters for use in PBPK modeling583

BW fromindividualmouse data

partition coefficients

BP (blood:plasma) 1 PSK (skin:blood) 1

PLU (lung:blood) 2 PKS (shallow kidney:blood) 1

PBR (brain:blood) 1 PS (spleen:blood) 1

PF (fat:blood) 1 PG (gut:blood) 1

PH (heart:blood) 1 PL (liver:blood) 1

PM (muscle:blood) 1 PCR (carcass:blood) 1

PB (bone:blood) 1

Fractional tissue weights (17) Fractional tissue flows

(fraction of cardiac output) (17)

VLUC (lung) 0.0044 (exp) QLUC (lung) 1.0

VBRC (brain) 0.018 QBRC (brain) 0.033

VFC (fat) 0.070 QFC (fat) 0.043

VHC (heart) 0.004 QHC (heart) 0.066

VMC (muscle) 0.384 QMC (muscle) 0.159

VBC (bone) 0.107 QBC (bone) 0.110

VSKC (skin) 0.165 QSKC (skin) 0.058

VKC (kidney) 0.014 (exp) QKSC (shallow kidney) 0.091

VKSC (shallow kidney) 0.010 QSC (spleen) 0.01

VKDC (deep kidney) 0.004 QGC (GI tract) 0.13

VSpC (spleen) 0.0037 (exp) QLAC (hepatic artery) 0.02

VGC (GI) 0.042 QCRC carcass 0.28

VLC (liver) 0.05 (exp)

VVC (venous blood) 0.0327

VAC (arterial blood) 0.0163

VRCR (carcass) 1 - sum of allothers

584


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a physiologically-based pharmacokinetic model for capreomycin

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