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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:
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
2.5 90% ACN 10% 0.1% Formic Acid in H2O
3.0 90% ACN 10% 0.1% Formic Acid in H2O
3.2 2% ACN 98% 0.1% Formic Acid in H2O
4.0 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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551
552
553
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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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