Physiologically-Based Pharmacokinetics And

8/11/2019 Physiologically-Based Pharmacokinetics And

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Xu, Eiseman, Egorin, and DArgenio186

model proidedin vivoestimates of endogenous HSP70 and HSP90 turnoer. In modeling pharm-acokinetics and pharmacodynamics, Bayesian inference was employed to estimate the kinetic,

physiological and molecular parameters when prior information was aailable.

KEY WORDS: geldanamycin; physiologically-based pharmacokinetics; molecular pharmaco-dynamics; intrinsic clearance; Bayesian estimation; onco-protein; heat shock protein; auto-regulation.

INTRODUCTION

17-(allylamino)-17-demethoxygeldanamycin (17AAG) is a derivative of

the benzoquinone ansamycin antibiotic geldanamycin and is currently in

phase I testing (1). Geldanamycin is a potent antiproliferative agent that

produces growth arrest in the G1 phase of most tumor cell lines (2); how-

ever, it is also associated with dose-limiting hepatotoxicity.In itroand ani-

mal studies have shown that while the antiproliferative activity and

mechanism of action of 17AAG is similar to that of geldanamycin (35), it

is considerably less hepatotoxic than its precursor (6).

Preclinical pharmacology studies of 17AAG, including metabolism

studies in mouse and human hepatic preparations, reveal several metabolites

including the active CYP3A4 product 17-(amino)-17-demethoxygeldanamy-

cin (17AG) (7). Murine pharmacokinetic studies of intravenous 17AAG

show that both 17AAG and 17AG are widely distributed to tissues, where

they are present in most tissues at substantial concentrations, with only

small amounts of each compound detected in urine (8). Compartmental and

non-compartmental analyses of plasma data reported in mice indicate linear

kinetics over a dose range of 26.67 to 40 mgkg with a total systemic clear-ance of 17AAG in the range 54 to 74 mlminkg (8).

Extensivein itrostudies indicate that the antiproliferative activity and

mechanism of action of ansamycin antibiotics, including 17AAG, correlate

with their ability to deplete oncoproteins such as p185erbB2, mutant p53 and

Raf-1 (9,10). The proto-onco-proteins p185erbB2 and Raf-1 are essential for

transmission and amplification of mitogenic signals from the cell surface to

nucleus in normal cells and both are over-expressed in certain tumor cell

lines. The specific mechanism of oncoprotein depletion by ansamycin anti-

biotics is thought to be related to their ability to disrupt the molecular

chaperone function of heat shock protein HSP90 and its homologue

GRP94, causing the degradation of their client proteins that require the

chaperones for maturation and stability (1015).

The work reported in this paper builds on the previously reported pre-

clinical pharmacology studies of 17AAG, known mechanisms of action of

ansamycin antibiotics, and current understanding of pathways involved

with the auto-regulation of heat shock proteins. The goals of the present


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Physiologically-Based PK and Molecular PD in Tumor-Bearing Mice 187

study were: (1) use data from normal mice to develop a physiologically-

based pharmacokinetic (PBPK) model of 17AAG and its primary active

metabolite 17AG; (2) use data of 17AAG and 17AG concentrations in the

tumors of nude mice bearing human breast cancer xenografts to develop a

model for the uptake and distribution of these compounds in the tumor;

(3) use measurements of p185erbB2, Raf-1 and heat shock proteins (HSP70

and HSP90) in the tumor xenografts to develop molecular pharmaco-

dynamic models relating the cellular concentrations of 17AAG and 17AG

to the targeted onco-proteins and heat shock proteins based on the known

molecular mechanisms of drug action; and (4) apply Bayesian estimation

methods that allow the combination of both informative and non-informa-

tive prior information in physiological pharmacokinetic and molecularpharmacodynamic modeling. The work culminates in a complete PBPKPD model for the investigational anticancer agent 17AAG and its metab-

olite 17AG, and provides insights into the molecular mechanism of action

of these compounds in io.

METHODS

Experimental Methods

Animal Experiments

In experiments on non-tumor-bearing mice, previously reported in (8),

48 adult female CD2F1 mice were divided into 16 time groups (one group

as vehicle control) for terminal sampling of plasma, red blood cells (RBC),

lung, brain, heart, spleen, liver, kidney and skeletal muscle at 5, 10, 15, 30,

45 min and 1, 1.5, 2, 3, 4, 6, 7, 16, 24, 48 hr following drug administration.

In a subsequent set of experiments on tumor-bearing mice, 16 NCR SCID

adult female mice (weighing 17.321.0 gm) with MDA-MB-453 humanbreast cancer xenografts in their flank were divided into 8 time groups (one

group as vehicle control ) for terminal sampling of plasma, lung, heart,

spleen, liver, kidney, and tumor at 2, 4, 7, 16, 24, 48, and 72 hr following

drug administration. In both experiments, 17AAG was injected as an intra-

venous bolus via lateral tail vein and at a dose of 40 mgkg fasted bodyweight. At each designated time point, the animals were euthanized with

carbon dioxide and venous blood was collected by cardiac puncture until

the liver became pale. Organstissues were dissected out, weighted andstored frozen until analyzed. Food was withheld until 4 hr after dosing.

In both non-tumor-bearing and tumor-bearing experiments, 17AAG was

supplied by the National Cancer Institute (8).


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Assays

Plasma and tissue concentrations of 17AAG and 17AG were deter-

mined by HPLC (see Ref. 8 for details). The concentrations of Raf-1,p185erbB2, HSP90 and HSP70 in tumor tissues were determined by western

blot analysis. The western blot band density readings were first normalized

to actin and then referenced to the average normalized reading of the con-

trols. The measurement variances for each protein were determined by giv-

ing a group of three animals control vehicle and measuring the levels of the

protein in various organs.

Blood Distribution and Protein Binding

The concentration profiles of 17AAG and 17AG in venous RBC andplasma indicated that a rapid equilibrium was achieved between the two

fractions in blood for both compounds. Accordingly, the RBC and plasma

concentrations of 17AAG and 17AG from the non-tumor experiments were

used to calculate the RBC-plasma partition coefficient (RGCRBCCplasma)for each compound: RAAGG2.47J1.23 (meanJSD, nG30) and RAGG

5.86J2.88 (nG30). The unbound fractions of 17AAG and 17AG in plasma

(fupGCplasma,free/Cplasma) were measured in a separate in itrostudy with the

following results: fup,AAGG0.063J0.015 (nG10) and fup,AGG0.081J0.042

(nG10) (8). It was found that RAAG, RAG , and fup,AAG were concentrationindependent. The unbound free fractions in blood thus can be calculated as

follows:

fuu,drugG1AHct

(1AHct)CHctRdrugfup,drug (1)

Using a hematocrit (Hct) of 0.45 yields,fub,AAGG0.0209 andfub,AGG0.0140.

Concentrations of 17AAG and 17AG in venous blood were calculated from

the plasma and RBC measurements as follows:

CVen(t)G(1AHct)Cplasma (t)CHctCRBC(t) (2)

No study of 17AAG or 17AG protein binding in the interstitial fluid

or cells was conducted. Thus concentrations of both compounds in inter-

stitial fluid and cells were taken to be homogenous. The exchange of each

compound across the vascular wall was therefore assumed to occur between

the free fraction in blood and the total in tissue.

Physiologically-Based Pharmacokinetic Modeling

Non-Tumor-Bearing Mice

The PBPK model for 17AAG and 17AG in non-tumor-bearing mice

was constructed through the following six steps: (1) fit sums of exponentials


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to the venous blood data of 17AAG and 17AG separately; (2) simul-

taneously model the distribution of 17AAG and 17AG in the lung using

the fitted venous exponential functions as input, and predict the arterial

concentration-time profile for each compound; (3) in each non-eliminating

organ, simultaneously model the distribution of 17AAG and 17AG using

the predicted arterial concentration-time profiles as input; (4) simul-

taneously model the liver distribution and metabolism (see below for

detailed description); (5) construct a whole-body model from the foregoing

results and model the distribution in the unsampled tissues (Misc.); and (6)

simulate the resulting whole-body model to predict the concentration pro-

files of 17AAG and 17AG in blood and all tissues.

In modeling the individual organs, both perfusion-limited and dif-fusion-limited models were evaluated to describe the distribution of 17AAG

or 17AG in each organ. See Appendix A for the diagrams, equations and

parameter descriptions of the two model structures for non-eliminating and

eliminating organs. The lists of fixed and estimated model parameters are

given in Tables AI and AII. Different combinations of the perfusion- and

diffusion-limited models for the distribution of 17AAG and 17AG in the

same organ were evaluated by fitting simultaneously to the measurements

of both compounds. The models of 17AAG and 17AG in the same organ

shared the same set of anatomical and physiological parameters.The liver is the only eliminating organ of significance for 17AAG and

17AG (8). No prior information is available on the intrinsic clearances of

17AAG (CLintAAG), 17AG (CLintAG) in the liver or on the fraction of

CLintAAG responsible for the formation of 17AG (fm). Furthermore, these

parameters cannot be uniquely determined via individual organ model-

based estimation using solely the measured liver concentration data. To

solve this problem of unidentifiability of hepatic parameters, the following

equation relating the systemic clearance to the intrinsic clearance of 17AAG

in the liver was derived (see Appendix B for detailed derivation):

CLsAAGGQVVfub,AAGkV,EV,AAG

Q1CkEV,V,AAGCLintAAG VEVCVVfub,AAGkV,EV,AAG(3)

where Q, VV, kV,EV,AAG , and kEV,V,AAG are parameters for liver. In deriving

this systemic-intrinsic clearances relationship constraint, a diffusion-limited

model was used for the distribution of 17AAG in the liver. The systemic

clearance of 17AAG (CLsAAG) was calculated as dose divided by the area

under the predicted arterial concentration-time profile of 17AAG. A similar

constraint derivation for the metabolite 17AG is given in Appendix C, and


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leads to the following equation for the case of a perfusion-limited model:

AUC(CArt,AG(t))GfmCLintAAGAUC(CEV,AAG(t))

CLintAGRAG(4)

The area under the arterial concentration-time curve of 17AG

(AUC(CArt,AG )) was calculated from the predicted arterial concentration

profile of 17AG. With these two additional relationship constraints, the

drug-specific kinetic parameters of liver can be uniquely estimated for the

composite liver model.

The unsampled tissues, including the carcass, were modeled as a single

tissue (labeledMisc.) arranged in parallel with the other systemic organs.

The previously selected models for each of the measured non-eliminating

organs and for the liver were included in a whole-body model with each of

the four candidate models for Misc. Weight and blood flow of Misc.

were calculated by subtracting the sum of the organ weights and blood flows

of the measured organs from the total body weight and cardiac output.

Other parameters ofMisc.were estimated for each of the four candidate

whole-body models byfitting the model prediction of venous concentration

profiles to the venous measurements of 17AAG and 17AG simultaneously.

Tumor-Bearing Mice

A whole-body model for the distribution of 17AAG and 17AG intumor-bearing mice was constructed by adding a parallel vascular bed

representing the tumor to the whole-body model developed for the non-

tumor-bearing mice. All kinetic and physiological parameters for normal

organs were fixed at the values determined from the non-tumor model, and

the anatomical parameters were replaced by those measured in the tumor

animal experiments. It was assumed in this approach that the animal physi-

ology and drug transport kinetics in tumor-bearing mice were the same as

those in non-tumor-bearing mice.

A number of different diffusion-limited models were evaluated todescribe the tumor distribution of 17AAG and 17AG, including a model

with a vascular and an extra-vascular space, and a model with an extra-

cellular and cellular space, as well as several models containing vascular,

interstitial and cellular spaces. One of the tested models is shown in Fig. 1,

with Eqs. (58) describing the drug concentration (17AAG or 17AG) in

each of the tumor spaces and the measured tissue concentration.

VVdCV

dt

GQ(CArtACV)APSV,IT(CVACIT) (5)

VITdCIT

dtGPSV,IT(CVACIT)AkIT,CCITVITCkC,ITCCVC (6)


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Fig. 1. Tumor Model. The subscripts V, IT, and C represent the vascular space,interstitial space and cellular space; PSV,IT represents the permeability surface-areaproduct of the vascular wall; kIT,Cand kC,ITare the transport rate constants acrossthe cell membrane.

VCdCC

dtGkIT,CCITVITAKC,ITCCVC (7)

CtissueGCITVITCCCVC

VITCVC(8)

After incorporating the candidate tumor models into the whole-body

model for the two compounds, the parameters of the tumor models were

estimated by fitting the model predictions to the measured tumor tissue

concentrations of 17AAG and 17AG simultaneously.

Model Validation

The organ concentrations of 17AAG and 17AG measured in the

tumor-bearing animal experiments were used in model validation. The

whole-body PBPK model with tumor was simulated to predict the organconcentrations of 17AAG and 17AG, which were then compared to the

organ concentrations measured in the tumor experiments.

Molecular Pharmacodynamic Modeling

The concentration profiles of 17AAG and 17AG in the tumor cells

predicated from the whole-body PBPK model with tumor were used to

model the action of these compounds on the tumor cell onco-proteins

(p185erbB2 and Raf-1) and heat shock proteins (HSP70 and HSP90). These

ansamycins were shown to be equally potent in depleting p185erbB2 (3), and

were assumed to also exhibit equal potency in their actions on Raf-1, HSP70

and HSP90.


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Onco-Protein Responses

The role of HSP90 in chaperoning Raf-1 is summarized in Fig. 2. After

HSP90 binds to newly synthesized Raf-1, the HSP90-Raf-1 complex is trans-ported to the cell membrane where it is available for activation by Ras.

Following activation, the HSP90-Raf-1 complex binds to unknown cyto-

skeletal elements, activates down-stream kinases and promotes tumor

growth (14). Ansamycins, including 17AAG, are thought to act by inducing

the degradation of the HSP90-Raf-1 complex at each of its three sites equ-

ally, and by inhibiting transport of the complex as shown in Fig. 2 (14).

Since the net action of ansamycins is to enhance the proteasomal degra-

dation of Raf-1 and since the cellular Raf-1 measured in our experiments is

the sum of the protein at the three sites, the simplified indirect responsemodel (16) shown in Fig. 3 and Eq. (9) were postulated to explain the

response of Raf-1 to 17AAG and 17AG. A similar model was used for the

onco-protein p185erbB2.

dO

dtGRsynAkdg,b1C Emax (AAGCAG)EC50C(AAGCAG)O (9)

Fig. 2. Molecular mechanism of Raf-1 depletion by ansamycin antibiotics (14). 1: The newlysynthesized Raf-1 protein complexes with HSP90; 2: The Raf-1-HSP90 complex in cytosol istransported to the cell membrane; 3: HSP90 remains bound to Raf-1 when Raf-1 is recruitedand activated by Ras; 4: HSP90 remains bound to Raf-1 when Raf-1 binds to unknown cyto-skeletal elements and activates downstream kinases. Ansamycins destabilize the cytosolic, Ras-associated and skeleton-associated Raf-1. The disappearances of Raf-1 from the three fractionsare equal. Raf-1 synthesis in ansamycin treated cells is elevated (approximately 3-fold) andansamycins inhibit the transportation of Raf-1-HSP90 complex.


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Fig. 3.Indirect response model for Raf-1 and erbB2.O represents the onco-proteins Raf-1 andp185erbB2 with the associated parameters unique to each onco-protein; Rsynrepresents the zero-order synthesis rate of the protein; kdg,b represents the basalfirst-order degradation rate of theprotein; (AAGCAG ) is the total concentration of 17AAG and 17AG in tumor cells.

Heat Shock Protein Responses

The molecular mechanism of heat shock protein auto-regulation and

the responses of HSP70 and HSP90 following exposure to 17AAG and

17AG are depicted in Fig. 4. The transcription of HSP genes and the

resulting synthesis of HSPs are enhanced upon exposure of cells to proteo-

toxic stress such as the presence of ansamycin antibiotics. This transcrip-

tional enhancement is due to the activation of heat shock transcription

factor 1 (HSF1), which is capable of specifically binding to the HSP genespromoter sequence and thereby enhancing the transcription of HSP genes.

While the synthesis of HSPs is up regulated by active HSF1, the transcrip-

tional activity of HSF1 is down regulated by direct binding of HSP70,

HSP90 and other co-factors (1720). We have hypothesized that this auto-

regulatory system is responsible for the heat shock response measured in

the mouse tumor xenograft model following 17AAG administration. Based

on the signaling pathway shown in Fig. 4, the feedback control model

described in Fig. 5 was constructed for which the following equations can

be written:

dHSP70P1

dtGR70syn HSF1Ak70 HSP70P1 (10)

dHSP70Pi

dtGk70 HSP70P(iA1)Ak70 HSP70Pi iG2, . . . ,n (11)

dHSP70

dt

Gk70 HSP70PnAk70dg,b

1C

E70max (AAGCAG)

EC70

50C(AAGCAG )HSP70 (12)

dHSF1

dtGFactAkdeact A(HSP70CHSP90)HSF1 (13)


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Fig. 4. The auto-regulation of HSP70 and HSP90 through HSF1a gene-transcription-mediated feedback control system. HSF1 exists in the control state as inert monomers. Uponstress (such as exposure to 17AAG and 17AG), the concentration of HSP70 is reduced. HSF1loses contact with HSP70, and trimerizes. The transcriptionally active trimers of HSF1 bindto heat-shock protein genes and lead to the production of HSP70 and HSP90 proteins. Thetranscriptional activity of HSF1 is repressed by direct binding of HSP70 and HSP90 to theHSF1 trimer, and HSF1 eventually returns to its inert monomer state.

A time-dependent transduction system (21) was adopted to model the timedelay in HSP70 gene expression (Eqs. (10), (11)). The initial values of

HSP70pi (iG1, . . . , n) were assumed to be equal and were estimated. The

initial values of HSP70 and HSF1 were set at one. The differential equations

for HSP90 follow the same format as those for HSP70 (Eqs. (10)(12)). The

activation function of HSF1, Factin Eq. (13), is depicted in detail in Fig. 5.

It is a function of HSP70 and involves several parameters including the

basal activation rate (Ract,b) and the amplification factor (A). The function

Fact increases as HSP70 decreases below its baseline value (HSP70b). When

HSP70 exceeds this baseline, the rate of activation of HSF1 reminds at its

basal level (Ract,b). The rate of de-activation of HSF1 is a function of the

HSP70 and HSP90 concentrations. The amplification factorA was assumed

to be the same for activation and deactivation.


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Fig. 5. Model diagram of HSP auto-regulation upon treatment of 17AAG and 17AG. TheHSP70 and HSP90 represent the normalized concentration of the two heat-shock proteins;Rsyn

is the basal zero-order synthesis rate and kdg,bis the basal first-order degradation rate; HSPP1HSPPn are the transit compartments representing the protein synthesis delay for HSP70 andHSP90; k70 and k90 are the transit rate constants where the total delay time Gnk (21); Factis the activation function of HSF1 transcriptional activity, in which Ract,bis the basal and zero-order activation rates, and HSP70b is the HSP70 concentration at control condition; kdeact isthe basal first-order de-activation rate of HSF1 transcriptional activity; A is the scalar rep-resenting the amplification effect of gene activation and deactivation.

Estimation Methods and Software

In the modeling steps described above, model parameters were esti-

mated using either Maximum Likelihood estimation (ML) when no prior

information was available for any of the model parameters, or Maximum a

PosterioriBayesian estimation (MAP) when prior information was available

for at least one of the model parameters. Both ML and MAP estimation

were performed using the ADAPT pharmacokineticpharmacodynamic sys-tems analysis software (22). Model selection was guided using the Akiake

information criterion (AIC) for ML estimation and generalized information

criterion (GEN-IC) for MAP estimation (see Ref. 22).

A version of MAP estimation has been used that allows estimation of

parameters for which prior information (mean and covariance) is available

as well as parameters with no prior information (i.e., parameters with non-

informative priors). For example, for a perfusion-limited organ model, prior


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information was available for organ blood flow while no prior information

was available for the 17AAG or 17AG partition coefficients. In general, if

represents the vector of all parameters to be estimated, and 1 is the

subset of parameters with known distribution p1(1) and 2 is an indepen-

dent subset of parameters with distribution p2(2), then the MAP estimate

of(MAP) is:

MAPGarg max{lnl(z 1 , 2)Clnp1 (1)Clnp2 (2)} (14)

wherez is the vector of measured data andl(z ) is the likelihood function.Ifp2(2) is non-informative, p2(2)Gconstant, then:

MAPGarg max{lnl(z 1 , 2)Clnp1 (1)} (15)

Equation (15) can be solved when the likelihood is normally distributed and

p1(1) is either normally or log-normally (used herein) distributed.

The following equation was used to model the variance of the normally

distributed output error for 17AAG, 17AG, Raf-1, p185erbB2, HSP90, and

HSP70: 2i(tj)G(interCslopeyi(tj))2. The values for inter and slope for

17AAG and 17AG are 0.136 and 0.104. For the onco-proteins, slopeG

0.167, and for the heat shock proteins, slopeG0.180, with interG0 for both

the onco-proteins and heat shock proteins.

RESULTS

Physiologically-Based Pharmacokinetic Model

Whole-Body Results

The composite whole-body model for 17AAG-17AG in tumor-bearing

mice is depicted in Fig. 6. The individual organ models for the uptake of

17AAG incorporate diffusion-limited exchange for all organs, while per-

fusion-limited models were selected to describe 17AG uptake in all organs.

Estimates of the model parameters (with the exception of liver and tumor

which are presented in the next sections) are given in Table I (physiological

parameters) and Table II (drug-specific kinetic parameters). Table II lists

the vascular-to-extra-vascular clearance (CLV,EVGkV,EVVVfub) and the

extra-vascular-to-vascular clearance (CLEV,VGkEV,VVEV) for each diffusion-

limited organ as well as Rthe partition coefficient value for each per-

fusion-limited organ. Recall that while the protein binding of 17AAG and

17AG was measured in the blood and incorporated in the model, it was

assumed that all 17AAG and 17AG in tissue are available for extra-

vascular-to-vascular transport. The predicted tissue concentrations from the

whole-body model for non-tumor-bearing mice and the measured tissue

concentrations for 17AAG and 17AG are shown in Figs. 7 and 8.


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Fig. 6. Composite whole-body model for 17AAG and 17AG intumor-bearing mice. The acronyms for the organs used in equa-tions are: LU: lung, BR: brain, HT: heart, SP: spleen, LI: liver,KI: kidney, MU: muscle, Art: arterial blood and Ven: venousblood.


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Fig. 7. Whole-body model simulation results for 17AAG.

The estimated model parameters are listed in Table III and Fig. 10 shows

the liver concentration-time profiles of 17AAG and 17AG predicted by the

estimated whole-body non-tumor mouse model.

The uptake of 17AAG in liver tissue was found to be diffusion-limited

with no significant transport from the extra-vascular space to the vascular

space (kEV,VG0). This result is supported by in itro studies of 17AAG

metabolism in mice and human hepatic preparations, in which the metabolic

activity was found to reside predominantly in microsomes with little or no

metabolism of 17AAG in liver cytosol (7). Our model suggests that upon

entering hepatocytes, 17AAG is either trapped in microsomes where it is

metabolized or secreted into bile. Interestingly, with only the difference of


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Fig. 8. Whole-body model simulation results for 17AG.

a propenyl group (CH2CHCH2) on the side chain of the ansamycin ring,

17AG produced in microsomes can be released from microsomes and trans-

ported out of hepatocytes into blood circulation. 17AG can be secreted into

bile but cannot be further metabolized (7). A perfusion-limited model was

found to adequately describe the distribution of 17AG in the liver. The

hepatic metabolism of 17AAG is complex, with metabolites, including

17AG, found in the plasma and bile of mice treated with 17AAG (7,8).However, neither the identity of the metabolites nor the metabolic or

secretory pathways have been fully characterized. By simultaneously model-ing the distribution and elimination of 17AAG and 17AG in liver, we wereable to estimate that 40% of the total intrinsic clearance of 17AAG involvesthe formation of its metabolite 17AG.


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Fig. 9. Liver model diagram of 17AAG and 17AG.

Table III.Liver Model Kinetic and Physiological ParameterEstimates

Parameter Unit 17AAG 17AG

kV,EV hr1 6132

CLV,EV mlhr 27.45 R 4.87CLint mlhr 4.93 3.34

fm 0.40 Q

a % CO 18.9VV

b % VLI 23.9

aLiterature meanJSDG16.10J2.45 (23,24).bLiterature meanJSDG31.0J7.0 (25).


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Fig. 10. Whole-body model simulation result of 17AAG and 17AG concentrations in liver.

Tumor Model

Of the five different models postulated to describe the uptake of

17AAG and 17AG in the human breast tumor xenografts, the model shown

in Fig. 1 was selected for both 17AAG and 17AG. The resulting estimates

of the vascular-interstitial permeability-surface area product (PSV,IT) as well

as the interstitial-cellular exchange rate constants (kIT,Cand kC,IT) are listed

in Table IV for both 17AAG and 17AG. Table V lists the model estimates

of tumor vascular and interstitial volumes. Because the distribution of both

17AAG and 17AG in tumor was diffusion-limited, there was no information

Table IV. Tumor Model Kinetic Parameters

Parameter Unit 17AAG 17AG

PSV,IT mlhr 0.227 0.264kIT,C hr

1 0.186 0.566kC,IT hr

1 0.062 0.057

Table V. Tumor Model Physiological Parameters

PopulationParameter Unit Estimate meanJSD

Q mlmingm tissue a 0.154J0.114a

VV % tumor volume 6.5 5.5J2.1b

VIT % tumor volume 54.3 43.4J3.5c

aQ was fixed at the mean value in the model estimation. Mean and stan-dard deviation obtained from measurements of 31 human anaplastic car-cinomas (26).

bLiterature values from Refs. 27 and 28 were pooled to generate the popu-lation mean and SD for the vascular volume.

c Mean was calculated from the interstitial volumes reported for carci-nomas in Ref. 29, and the highest CV% reported in Ref. 29 was used toobtain the SD.


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Fig. 11. Tumor model results of PK16A. Model predictions (solid lines) and measurements(symbols) of 17AAG (left) and 17AG (right) concentrations in tumor tissue (interstitial and

cellular). The dashed lines are the model predictions of the concentrations of 17AAG and17AG in tumor cells.

in the data on tumor blood flow. Tumor blood flow thus was fixed at the

population mean value and not estimated as the other physiological param-

eters. The 17AAG and 17AG tumor tissue and cell concentrations predicted

from the composite whole-body model with tumor are shown in Fig. 11

together with the tumor tissue measurements.

Model Validation

The whole-body model constructed using the data from the non-tumor

animal study was used to predict the 17AAG and 17AG concentrations

measured in the organs of the tumor-bearing mice. Figure 12 shows the

model predictions along with the measured concentrations for 17AAG in

selected tissues, while the corresponding results for 17AG are displayed in

Fig. 13.

Molecular Pharmacodynamic ModelsThe Onco-Proteins Raf-1 and p185erbB2

The model predictions and the measured values of Raf-1 and p185 erbB2

in the tumor are shown in Fig. 14. Long-term model simulation predicts

that the level of Raf-1 in tumor returns to its base value at approximately

200 hr, while p185erbB2 returns to its pre-drug value at about around 120 hr

(graphs not shown). Estimated model parameters are listed in Table VI and

compared with corresponding in itro literature values. The half-lives of

Raf-1 and p185erbB2 andEC50 of Raf-1 estimated from the model compare

favorably to the values reported from in itroexperiments. The degradation

rate of p185erbB2 was estimated to be linearly related to the concentration of

17AAG and 17AG, so no EC50on p185erbB2 depletion was estimated.


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Fig. 12. Measured and predicted concentrations of 17AAG in organs in tumor-bearing mice.

Fig. 13. Measured and predicted concentrations of 17AG in organs in tumor-bearing mice.


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Fig. 14. Onco-protein model predictions and measurements.

Table VI. Onco-Protein Models Parameter Estimates and Literature Values

Raf-1 p185erbB2

Model Literature Model LiteratureParameter Unit estimation values estimation values

t1/2a hr 22.6 11b, 17.5b 8.63 7c, 9.5d

EC50 nM 3.47 3.4e f

Rsyn norm. conc.hr 0.03 0.08 Emax 4.30 0.24

f

aHalf-life of endogenous protein turnover (t1/2Gln 2kdg,b from Fig. 3);b

In

itromeasurement reported in Ref. 14.cIn itro measurement reported in Ref. 30.dIn itromeasurement reported in Ref. 11.eThe value is derived from the in itro EC50 of geldanamycin reported in Ref. 14, given that

17AAG is three-fold more potent than geldanamycin (3) and that the concentration of 17AAGin tumor cells is 2.3 times that in whole tissue.

fFor p185erbB2, a linear model relating drug induced degradation to total drug concentrationwas used in the place of the Emaxmodel. In the table, Emax represents this scale factor.

Heat Shock ProteinsHSP70 and HSP90

The measurements and model predictions of HSP70 and HSP90 in

tumor are shown in Fig. 15. Long-term model simulation predicts that the

Fig. 15. Heat-shock protein model predictions and measurements.


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Table VII. Heat-Shock Protein Model Parameter Estimates

HSP70 HSP90

Model ModelParameter Unit estimation estimation

t1/2a hr 4.51 40.4

EC50 nM 0.90 38.7Rsyn hr

1 0.15 0.02Emax 1.64 31.9 hr 13.6 0Ract,b 0.08kdeact 0.04A 331

aHalf-life of endogenous protein turnover (t1/2Gln 2kdg,b from

Fig. 5).

level of HSP70 in tumor returns to its baseline value at approximately

200 hr, while HSP90 returns to its pre-drug value at about around 300 hr

(graphs not shown). Table VII lists the resulting estimates of the heat shock

protein model parameters. There is no report in the literature from eitherin

io or in itro studies that provide a basis for comparing the results from

our analysis.

DISCUSSION AND CONCLUSION

Distribution of 17AAG and 17AG in Individual Organs

The model and the data agree reasonably well for 17AAG and 17AG

in venous blood and all organs, except for 17AG in brain and lung. The

measured values of 17AG concentration in brain tissue fall mostly on the

edge of the lower limit of quantification, and the measurements are associ-

ated with large standard deviation. While there is no report on whether

17AG can cross the bloodbrain barrier, the data and our model suggest

there is little uptake in brain tissue. It is also likely that the measurements

of 17AG in brain included drug in the residual blood remaining in the tissue

sample. The lung 17AG data has a peak value at 5 min while the peak

concentration of 17AG in venous blood is not reached until 30 min, which

resulted in a poorfit regardless of the models tested. We could notfind any

physiological evidence to explain the lung 17AG data. However, the particu-

lar models used to describe 17AG distribution in brain and lung had little

effect on the whole-body model predictions, including those in the tumor.

The Bayesian estimates of all the physiological parameters are reason-

able given the prior means, except for muscle blood flow. The relatively

large variability in muscle concentration data, especially that of 17AG, may

contribute to this discrepancy.


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Estimation of Intrinsic Clearances and 17AAG Metabolism in the Liver

The intrinsic clearance of 17AAG (CLintAAG), the fraction ofCLintAAG

associated with the formation of 17AG (fm) and the intrinsic clearanceof 17AG CLintAG in the liver are especially relevant to understanding the

distribution, metabolism and hepatic toxicity of 17AAG. We have estab-

lished a method to uniquely estimate these parameters at the stage of indi-

vidual organ analysis in the model developing process (i.e., using only the

liver measurements and the arterial concentration profiles). The relationship

between intrinsic clearance and systemic clearance of 17AAG was derived

from a simplified whole-body model by solving the model equations in

Laplace domain assuming linear kinetics and only hepatic elimination (see

Appendix B ). We have proved that the CLintAAGCLsAAG relationshipdepends only on the liver model (work not shown), when the remaining

systemic organs are lumped into a single composite tissue. The resulting

equation relatingCLintAAGand CLsAAGwas then included in the liver model

as the additional constraint, thus allowing CLintAAG to be uniquely esti-

mated as part of the individual liver modeling procedure. An equation rela-

ting CLintAGand fm to the systemic distribution of 17AG was also derived

in a similar fashion (see Appendix C) to uniquely estimate CLintAGandfm.

The approach we developed for estimating liver clearance in PBPK

models has the following advantages: (1) it allows intrinsic clearance andits related parameters (such as fm) to be estimated without constructing the

whole-body model; (2) it makes it possible to model the unsampled tissues,

when significant drug uptake is accounted in those unsampled tissues.

Although the liver model describes the data reasonably well, there was

a consistent overprediction of 17AAG in the early time period from 0

15 min. The highest mean measured concentration of 17AAG in liver tissue

was 89 mgml at 5 min, while the model prediction at 5 min is 215 gml.A number of factors might contribute to this discrepancy. Firstly, roughly

75% of the blood entering the liver is the venous effluent from the small

intestine, stomach, pancreas, and spleen, while the model assumes no uptake

of 17AAG in the small intestine, stomach or pancreas. The uptake of

17AAG to those tissues may have a significant effect on the drugs distri-

bution. Secondly, in our investigation of different liver model structures, we

found that a model consisting of three sub-organ spaces (vascular, inter-

stitial, and cellular) did not reduce the over prediction. The systemic clear-

ance, defined by the 17AAG data of venous blood and other organs,

indicated a high-transport rate of 17AAG from blood to liver tissue, while

the liver 17AAG measurements, especially at early times, are consistent with

a lower transport rate independent of the liver model structure. This obser-

vation suggests a discrepancy between the information imbedded in liver


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measurements and that in venous and other organ measurements. It is poss-

ible that the continuous metabolism of 17AAG in liver tissue during the

time of animal and organ processing contributes to this discrepancy. And

lastly, the assumption of a constant fm may contribute to the difference

between measured and predicted 17AAG liver concentrations as well.

Tumor Xenograft Uptake of 17AAG and 17AG

One of the attractive properties of geldanamycin derivatives as

anticancer agents is their considerably longer half-lives in tumor compared

to normal organstissues. We were able to describe this property by a three-component model that includes vascular, interstitial fluid and cellular spaces

of the tumor. The model revealed that sustained concentration-time profilesof 17AAG and 17AG in tumor tissue was due to a relatively slow diffusion

across the cell membrane, while in normal organs this process was estimated

to be essentially instantaneous. The concentrations of 17AAG and 17AG in

tumor cells themselves were estimated to be both 2.3 times higher than those

in the tumor tissue (in extra-vascular space), showing the preferential uptake

of both compounds in tumor cells.

It was found from the data that although the concentration of 17AG

in blood was generally less than that of 17AAG, the concentration of 17AG

in tumor was significantly higher (1.5 to 3 fold) than that of 17AAG after2 hr following dosing. In the tumor models for 17AAG and 17AG, the per-

meability surface-area product (PS) of the vascular wall was estimated to

be similar for 17AAG (0.23 mlhr) and 17AG (0.26 mlhr), and the trans-port rate constants of the two compounds from cellular to interstitial space

(kC,IT) were also estimated to be similar (0.062 hr1 for 17AAG and

0.057 hr1 for 17AG). However, the transport rate constant of 17AG from

interstitial space to the cellular space (kIT,C) was estimated to be significantly

higher than that of 17AAG (0.57 hr1 for 17AG vs. 0.19 hr1 for 17AAG).

The model estimates suggest that the preferential uptake of 17AG over17AAG in tumor tissue is due to a more effective uptake mechanism of

17AG in the tumor cells rather than in the interstitial fluid of tumor tissue.

Pharmacodynamic Model for the Onco-Proteins

Mechanisms of Raf-1 synthesis, transport, activation, and depletion by

ansamycins have been studied extensively at the sub-cellular and molecular

level (see Fig. 2). Because the three forms of measurable Raf-1 protein were

destabilized equally by ansamycins, they were modeled as one single pool

of Raf-1 with an indirect response model. Although HSP90 plays a key role

in the regulation of Raf-1 stabilization and degradation, it was not included

in the Raf-1 model, for the following reasons: (1) HSP90 is present in the


25/35


cells in excess (12% of total proteins in the cell is HSP90), so that all the

Raf-1 molecules are chaperoned by HSP90; (2) the binding of HSP90 to

newly synthesized Raf-1 is essentially instantaneous; and (3) the degradation

of Raf-1 is assumed to be instantaneous following the disruption of the

HSP90-Raf-1 complex by 17AAG and 17AG. Although the transport and

activation pathways of p185erbB2 are different from those of Raf-1, the

action of ansamycin antibiotics on the degradation of p185erbB2 is the same

as that of Raf-1 and therefore was also described using the same indirect

response model.

In the model, the synthesis of the onco-proteins was assumed to remain

constant following drug administration. However, it was reported that the

synthesis of Raf-1 in geldanamycin treated cells was elevated approximately

3-fold (14). In addition, in herbimycin A treated SKBr3 cells (0.35 mM,

6 hr), it was reported that p185erbB2 mRNA levels were elevated by 30% and

the total protein synthesis decreased by 16% (31). Although the synthesis of

p185erbB2 protein was not measured directly, the above finding suggests the

possible induction of p185erbB2 synthesis following ansamycin treatment.

The mechanism of the synthesis inductions remains unknown, nor has there

been any quantitative analysis of the process. With limited data and infor-

mation, we were not able to model the synthesis induction. The discrepancy

between measured and model predicted p185erbB2 concentrations might be a

direct result of this inability. The data and model prediction suggest that

after a period of depletion, the fast recovery of p185erbB2 is at least partially

the result of the induced p185erbB2 synthesis.

Pharmacodynamic Model of HSP Auto-Regulation

The auto-regulation of the heat shock transcriptional response, dis-

covered in the early 1990s is an example of a self-regulatory biological pro-

cess. While the role of heat shock proteins as molecular chaperons is under

intensive study, little quantitative information is available on the dynamicsof HSP auto-regulation. For example, there have been no published reports

of the half-life of HSP70 or HSP90, thus the model-based estimates obtained

from our modeling work represent the first reported HSP70 and HSP90

turnover rates (HSP90 t1/2G40.43 hr and HSP70 t1/2G4.51 hr).

There has been considerable debate regarding the pathways responsible

for mediating the cellular stress signal in the heat shock auto-regulatory

system (19). One hypothesis states that external stress alters HSF1 directly,

while a second postulates that HSP70 serves as the intermediary between

cell stress and HSF1 activation. The model developed herein incorporates

the later hypothesis, and assumes that HSF1 activation increases linearly as

HSP70 decreases below its control value with that it remains constant as

HSP70 increases above the control value.


26/35


The time course of HSPs concentration measurements in this study is

not long enough to adequately reveal the dynamics of the processes associ-

ated with the return of HSP70 or HSP90 to their baseline values. The esti-

mated parameter values and the model prediction of HSPs recovery

reported, await confirmation by further in itro and in io studies.

Bayesian Analysis

Recent advances in PBPK modeling have further established the rel-

evance of this approach in drug development (e.g., Ref. 32). Bayesian

methods have also been applied previously in PBPK modeling within a hier-

archical population modeling framework (e.g., Refs. 33, 34). While the

MAP estimation approach used herein does not involve a mixed effectsmodeling formulation, it does provide a simple-to-use method for incorpor-

ating prior uncertainty in PBPK modeling, and can be implemented using

most nonlinear regression software.

The use of Bayesian inference in model development exposes all parts

of the model, including the model structure and the prior distribution, to

appropriate criticism. An example of how the model development in the

work reported herein benefits from the model criticism function of Bayesian

inference is as follows. One of the models considered for the tumor uptake

of 17AAG and 17AG was a 2-compartment diffusion-limited model con-sisting of an extra-cellular compartment and an intra-cellular compartment,

i.e., assuming drug exchange across the leaky tumor vascular wall is

instantaneous. This model would have been selected as the best model based

on the AIC selection criterion, if the physiological parameters were fixed at

their prior values and the kinetic parameters were estimated by maximum

likelihood estimation. However, the Bayesian analysis of this model resulted

in unrealistic physiological parameter values, suggesting that this 2-com-

partment model structure is inappropriate. Indeed, by including separate

vascular and interstitial spaces, a 3-compartment model with reasonableparameter estimates was established for tumor. The exchange of the com-

pounds across the vascular wall was determined by a permeability area-

surface product estimated at 0.23 mlhr and 0.26 mlhr for 17AAG and17AG.

SUMMARY

In the present work, we have: (1) constructed a physiologically-based

pharmacokinetic model for 17AAG and 17AG in nude mice bearing human

tumor xenografts, to characterize the disposition of 17AAG and 17AG in

normal mice organs and human breast tumor xenografts; (2) established


27/35


the modeling procedures to uniquely estimate the intrinsic clearances and

clearance related parameters in the liver at individual organ analysis level,

and to uniquely identify the model of unsampled tissues; (3) constructed

pharmacodynamic models, based on the molecular mechanism of action,

for onco-protein depletion and heat shock protein auto-regulation, with the

drug concentration-time profiles at the site of action predicted by the

pharmacokinetic model; (4) applied Bayesian inference to characterize the

kinetic and dynamic properties of the compounds, the physiological and

anatomical properties of the animal and the molecular properties of the

proteins involved in the drug response. From the modeling efforts, a number

of insights having been gained into both the kinetic and dynamic character-

istics of 17AAG and 17AG and their target molecules, and into the model-

ing procedures and techniques for PBPKPD model development.

ACKNOWLEDGMENTS

This work was supported in part by NIH grant P41-RR01861 made to the

BMSR (Biomedical Simulations Resource), and by the NCI, CM07106 and

CA099168.

APPENDIX

Appendix A. Individual Organ Models

Perfusion-Limited Model for Non-Eliminating Organs

Fig. A1. Perfusion-limited model for non-eliminating organs. VT is the totalvolume of organ T; QTis the bloodflow to the organ; CT is the concentrationof the drug in the organ; RT is the partition coefficient; CArt is the concen-tration of drug in arterial blood; CT,Ven is the venous effluent drug concen-tration (CT,VenGCTRT). In this model, the measured tissue concentration isCT.


28/35


Diffusion-Limited Model for Non-Eliminating Organs

Fig. A2. Diffusion-limited model for non-eliminating organs. CT,V and VT,Vrepresent the drug concentration and volume for the organ vascular space;CT,EV and VT,EV represent the corresponding terms for the extra-vascularspace;kV,EVand kEV,Vrepresent the drug transport rates between the vascularand extra-vascular spaces; fub is the fraction of unbound drug in the vascularspace. In this model, the measured tissue concentration is CT,EV.

Perfusion-Limited Model for Eliminating Organs

Fig. A3. Perfusion-limited model for eliminating organ. CLintT represents theintrinsic clearance of the drug.


29/35


Diffusion-Limited Model for Eliminating Organs

Fig. A4.Diffusion-limited model for eliminating organs.CLintTrepresents the intrin-sic clearance of the drug.

Table AI. Parameters Measured in Animal Studies

Measured value (meanJSD)

Parameter Units PK7 (non-tumor) PK16A (with tumor)

BW gm 16.80J0.71 19.15J1.28Tumor weight gm 0.26J0.11VLU ml 0.16J0.05 0.16J0.02VBR ml 0.39J0.05 VHT ml 0.12J0.02 0.12J0.01VSP ml 0.06J0.01 0.04J0.01VLI

a ml 0.67J0.05 0.93J0.10VKI ml 0.24J0.02 0.28J0.02

VMUb

ml 6.45 7.35VMisc

c ml 7.02 8.08

fub,AAG 0.0209fub,AG 0.0140

aMean of the values before feeding only.bThe total muscle value was calculated from literature reported muscle frac-

tional weight WfMUG0.384 (25), using the measured body weight of thestudied animals.

cVolume of the unsampled tissues was calculated as follows, with literaturereported bone fractional weight WfboneG0.107, blood fractional weightWfbloodG0.076 and bone density equals 1.3:

VMiscGBWAWiAWfblood BWAWfbone BW

1C

Wfbone BW

1.3

(istands for each measured organs).


30/35


Table AII. Parameters Estimated in Model Development

Parameter Units Priora Parameter Units Priora Parameter Units Priora

QBRb,c

% CO 3.35J

1.04 VLU,Ve

% VT 50J

11 VMisc,Vh

% VT 4.0J

1.6QHT % CO 6.72J2.66 VBR,V % VT 3.0J1.2f VT,EV,V

i % VT QSP % CO 0.42J0.32 VHT,V % VT 4.0J1.6

g Rj NIQLI % CO 16.1J2.45 VSP,V % VT 17J1.0 kV,EV

j hr1 NI

QKI % CO 11.1J0.05 VLI,V % VT 31J7.0 kEV,Vj hr

1 NIQMU % CO 18.0J8.85 VKI,V % VT 24J11 CLint

k mlhr NIQMisc

d % CO VMU,V % VT 4.0J1.4 fml NI

aMeanJSD when prior information is available; NI for non-informative prior.bLiterature values from Refs. 23 and 24 were pooled to generate the population mean and SD

for the organ blood flow QTs.cQTs can be converted to mlhr form by multiplying the values by CO (cardiac output), which

is calculated as 30.82 (ml

hr

gm BW) BW (23). QLUGCO.

dQMiscwas calculated as the difference between CO and the sum of the measured organ bloodflows.

eThe organ fractional vascular volume VT,Vs were obtained from reference (25). VT,Vs canbe converted to ml form by multiplying the values by the corresponding values ofVT fromTable AI.

fNo information was available onVBR,VSD, the highest CV% reported for the VT,Vs was thusadopted.

gNo information was available. VHT,Vwas assumed to have a mean of 0.04 (same as that ofmuscle), and the highest CV% reported for the VT,Vs was adopted to obtain its SD.

hNo information was available. Mean and SD were set to be the same as those for heart.iExtra-vascular volume for each organ was calculated as VTAVT,V.j

Estimated for both 17AAG and 17AG for each of the eight organstissues.kHepatic intrinsic clearance estimated for both 17AAG and 17AG.lFraction of 17AAG converted to 17AG in liver cells.

Parameter Categories and Parameter Values

Tables AI and AII list all the parameters for the PBPK model. The

parameters that were measured in the animal experiments are listed in Table

AI along with their values. In model development, these parameters were

fixed at their listed values. Table AII lists parameters that were estimated

as part of the model development, including parameters for which priormean and standard deviation were available, as well as parameters for which

no prior information was available (i.e., with non-informative prior).

Appendix B. Derivation of 17AAG CLintCLs Relationship in the Liver

Diffusion-Limited Model

This Appendix presents the derivation of an equation relating the sys-

temic clearance of 17AAG (CLs) to the hepatic intrinsic clearance (CLint)

with a diffusion-limited model for hepatic distribution. Consider the simpli-

fied PBPK model shown in Fig. B1, in which all the systemic organs except

the lung are lumped into a single effective tissue Other. Assuming linear


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Fig. B1. Reduced 17AAG whole-body model for intrinsic clearance deri-vation.

kinetics and the liver is the only eliminating organ, the five differential equa-

tions describing this system can be expressed in Laplace domain as follows:

sVLUCLU(s)GQCVen(s)ACLU(s)RLU (B1)

sVVCV(s)GQLICLU(s)RLU ACV(s)AkV,EVfubVVCV(s)CkEV,VVEVCEV(s) (B2)

sVEVCEV(s)GkV,EVfubCV(s)VVAkEV,VCEV(s)VEVACLintCEV(s) (B3)

sVOCO(s)GQOCLU(s)RLU ACO(s)

RM (B4)

sVVenCVen(s)ADoseGQOCO(s)

ROCQLICV(s)AQCVen(s) (B5)

Equations (B1)(B5) can be solved for (CLU

(s))RLU

. Since

CLsGDose

AUC(CArt(t))(B6)


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33/35


sVOCO,AG (s)GQOCLU,AG(s)RLU,AG ACO,AG(s)

RO,AG (C3)

sVVenCVen,AG(s)GQOCO,AG(s)

RO,AGCQLI

CAG(s)

RAGAQtotal CVen,AG(s) (C4)

Equations (C1)(C4) can be solved for (CLU,AG(s))RLU,AG. Since

AUC(CArt,AG(t))GAUCCLU,AG(t)RLU,AG Glims0CLU,AG(s)

RLU,AGG

CLU,AG (sG0)

RLU,AG(C5)

Therefore:

AUC(CArt,AG(t))GfmCLintAAGAUC(CEV,AAG(t))

CLintAGRAG(C6)

AUC(CEV,AAG(t)) can be derived from Eqs. (B2) and (B3) in the 17AAG

model for the case ofkEV,VG0, and is given as follows:

AUC(CEV,AAG(t))GQLIVVkV,EV,AAGfubCArt,AAG(t)

QLICLintAAGCVVkV,EV,AAGfubCLintAAG

(C7)

Fig. C1. Reduced 17AG whole-body model for intrinsic clearance deri-vation. All concentration and drug-specific parameters refer to AG exceptwhere noted.


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