A Permeability-Limited Physiologically Based Pharmacokinetic (PBPK

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A Permeability-limited Physiologically Based Pharmacokinetic (PBPK) Model for Perfluorooctanoic Acid (PFOA) in Male Rats Weixiao Cheng, and Carla Ng Environ. Sci. Technol., Just Accepted Manuscript • DOI: 10.1021/acs.est.7b02602 • Publication Date (Web): 31 Jul 2017 Downloaded from http://pubs.acs.org on August 3, 2017

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Environmental Science & Technology

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A Permeability-limited Physiologically Based Pharmacokinetic (PBPK)

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Model for Perfluorooctanoic acid (PFOA) in Male Rats

3

Weixiao Cheng and Carla A. Ng*

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Department of Civil and Environmental Engineering, University of Pittsburgh, Pittsburgh,

5

Pennsylvania 15261, USA

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* Address correspondence to: Carla A. Ng, Department of Civil & Environmental Engineering,

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University of Pittsburgh, 3700’Hara St, Pittsburgh, PA 15261. Tel.: 412-383-4075. Fax: 412-

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624-0135. E-mail: [email protected]

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ACS Paragon Plus Environment


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ABSTRACT: Physiologically based pharmacokinetic (PBPK) modeling is a powerful in silico

10

tool that can be used to simulate the toxicokinetics and tissue distribution of xenobiotic

11

substances, such as perfluorooctanoic acid (PFOA) in organisms. However, most existing PBPK

12

models have been based on the flow-limited assumption and largely rely on in vivo data for

13

parameterization. In this study, we propose a permeability-limited PBPK model to estimate the

14

toxicokinetics and tissue distribution of PFOA in male rats. Our model considers the cellular

15

uptake and efflux of PFOA via both passive diffusion and transport facilitated by various

16

membrane transporters, association with serum albumin in circulatory and extracellular spaces,

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and association with intracellular proteins in liver and kidney. Model performance is assessed

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using seven experimental datasets extracted from three different studies. Comparing model

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prediction with these experimental data, our model successfully predicts the toxicokinetics and

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tissue distribution of PFOA in rats following exposure via both IV and oral routes. More

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importantly, rather than requiring in vivo data fitting, all PFOA-related parameters were obtained

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from in vitro assays. Our model thus provides an effective framework to test in vitro-in vivo

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extrapolation and holds great promise for predicting toxicokinetics of per- and polyfluorinated

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alkyl substances in humans.

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1. INTRODUCTION

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Perfluorooctanoic acid (PFOA) is one of the most important perfluoroalkyl substances that has

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been widely used in industrial and consumer products since 19501. The strong carbon-fluorine

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bonds in PFOA make it very resistant to metabolic and environmental degradation, which,

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coupled with its widespread use, results in its worldwide presence2-4. Although production of

31

PFOA has been eliminated by many manufacturers5, worldwide human exposure to PFOA

32

continues6-9.

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PFOA toxicokinetics have been studied extensively in mammals, and results show that the

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substance is well absorbed orally and not metabolized10-12. It is primarily accumulated in plasma,

35

liver, and kidney, with lowest levels in adipose and muscle10, 13-17. In addition, PFOA can be

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eliminated through urine and feces, with urine being the major route. It has been reported that

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renal elimination rates are both species- and sex-dependent18. In humans, the half-life of PFOA

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in blood is estimated to be about 3.5 years with no significant gender difference19. However, the

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clearance of PFOA in rats is considerably sex-dependent, with reported half-lives ranging from

40

hours to several days in female and male rats, respectively20, 21.

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Two principal underlying molecular mechanisms have been identified to explain observed PFOA

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toxicokinetics: protein binding and cell membrane transport. Studies revealed that PFOA is

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strongly bound to serum albumin as well as cytosolic fatty acid binding proteins (FABPs)22-25,

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which are pervasive in different tissues such as liver and kidney. Therefore, binding to different

45

proteins is an important determinant for high accumulation in blood, liver, and kidney. For

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membrane transport, both passive diffusion and protein-facilitated transport play important roles

47

in cellular uptake of PFOA26-29. A number of transporters (named using all capital letters to

48

denote human transporters, or by one capital followed by lowercase letters for animal 3 / 30



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transporters30), such as organic anion transporters (OATs/Oats) and organic anion transporting

50

polypeptides (OATPs/Oatps) have been identified that are responsible for renal tubular excretion

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and reabsorption of PFOA in humans and rats27-29.

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Due to its persistence and bioaccumulation, the potential human health risks of PFOA have

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received intense attention from environmental scientists and regulatory agencies5. As

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toxicokinetics data are particularly scarce for humans, in silico tools, such as physiologically

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based pharmacokinetic (PBPK) models, are becoming a promising alternative to inform risk

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assessment of chemicals like PFOA31. By appropriate specification of species- and chemical-

57

specific parameters, PBPK models can be employed to simulate absorption, distribution,

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metabolism, and excretion (ADME) of compounds in animals and humans, providing a useful

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tool to understand and extrapolate pharmacokinetics across different species and dosing

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scenarios32.

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A number of PBPK models have been developed to simulate the toxicokinetics and distribution

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of PFOA in humans, rats, and monkeys33-39. However, all these models were based on the flow-

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limited assumption, which means that the substance uptake rate to the tissue compartment is

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limited by the blood flow rate, not by cell membrane permeability32. Flow limited kinetics

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commonly occur for small and lipophilic molecules (molecular weight < 300 Da)32. But for large

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and charged molecules like PFOA (molecular weight = 414.09 Da40 and pKa < 1, meaning >99%

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ionized at environmentally relevant pH30), permeability across the cell membrane becomes the

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limiting process. Therefore, a model that takes this into account may provide more insight into

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realistic behavior32. In addition, existing models use in vivo test data to fit parameters, and thus

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the predictive power of these models largely depends on the in vivo data used (in these studies, a

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range from 14 of 30 to 88 of 105 total parameters were obtained by fitting33-39). Although the 4 / 30


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flow-limited assumption performs well for animals with sufficient in vivo data for fitting

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parameters, when applied to humans, the flow-limited model does not work well. Take Fabrega

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et al.39 for example: in that study, most perfluoroalkyl substances (PFASs), including PFOA,

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were under-predicted substantially in human liver. The authors ascribed this to the high

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uncertainty caused by the limited in vivo data they relied on for model parameterization. Beyond

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the need for more reliable models in the absence of in vivo data for humans, there is increasing

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motivation to reduce in vivo experiments in animal studies. The National Research Council’s

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2007 report, Toxicity Testing in the 21st Century, proposes a shift from in vivo animal studies to

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in vitro assays and sophisticated modeling approaches41. Such a shift means in vitro and in silico

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approaches must become better developed and independent of in vivo data41, 42. A PBPK model

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that could reasonably predict tissue distribution without need of in vivo data would therefore be

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of great benefit for human toxicology and risk assessment. To develop such a mechanistic model,

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a better and more reliable understanding of the organism of interest and the specific molecular

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mechanisms that drive PFOA toxicokinetics is required.

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To the best of our knowledge, the PBPK model developed by Ng and Hungerbühler43 is the only

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one that explicitly considers membrane permeability, active transport, and protein binding. It was

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successfully used to evaluate bioconcentration of perfluorinated alkyl acids in fish. However, due

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to limited fish-specific protein data, the protein binding and active transport processes were

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parameterized utilizing existing data from studies for humans and rats43. Despite the overall good

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prediction results, given the physiological difference between mammals and fish, further

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development of this model warrants implementation in a mammalian system with better

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availability of data for parameterization.

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In this study, we have substantially modified the original fish model and applied it to estimate 5 / 30



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the plasma toxicokinetics and tissue distribution of PFOA in male rats, for which most protein-

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related parameters were available. We then evaluated whether the predicted results are consistent

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with measured experimental data from 3 separate studies10, 14, 15, where different PFOA dose

98

levels and administration routes were used (providing a total of seven data sets) for male rats.

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Like the original model, our model is also a permeability-limited model including both protein

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binding and active transport. Moreover, rather than requiring fitting to experimental data, all

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PFOA-related parameters were obtained from in vitro studies, and then used to predict in vivo

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ADME (i.e., in vitro-in vivo extrapolation, an alternative approach to traditional animal testing42).

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Key improvements were also made to the original model. Enterohepatic circulation of PFOA is

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now included, given the observation that it may contribute to PFOA accumulation in liver and

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blood44. A gut compartment, bile and feces flows, and a “rest of body” compartment for those

106

tissues not explicitly modeled, were also added. Moreover, additional protein interactions, such

107

as active PFOA uptake into hepatocytes mediated by Na+/taurocholate cotransporting

108

polypeptide (Ntcp) and renal efflux by organic solute transporter (Ost) were considered, in order

109

to reflect recent observations for male rats45. Finally, the method used for deriving active

110

transport rates and the sensitivity analysis were improved, as described in sections 2.3.2 and 2.5.

111

Our model predicts the concentration of PFOA in different rat tissues as a function of time,

112

following either intravenous (IV) or oral dosing, and provides a flexible framework to test in

113

vitro-in vivo extrapolation.

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2. MATERIALS AND METHODS

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2.1 Rat Model Structure.

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The model includes 7 tissues: blood, kidney, liver, gut, muscle, adipose and the rest of the body 6 / 30


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(Figure 1). Since this is a permeability-limited model, the consideration of tissue

118

subcompartments is required. Except for blood, each tissue contains both a vascular space and

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tissue space, the latter of which can be further divided into two subcompartments: interstitial

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fluid and tissue. To characterize absorption and elimination processes of PFOA, gut lumen, renal

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filtrate and bile compartments were newly incorporated.

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The blood compartment functions as systemic circulation, connecting each tissue compartment.

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In blood, PFOA binds to serum albumin based on the equilibrium association constant, KAlb a .

124

Interstitial fluids of other compartments also contain albumin to which PFOA could bind46, 47.

125

Enterohepatic circulation may play a role in the distribution of PFOA in liver44 and thus was

126

considered in our model. Due to scarcity of data, we only included two transporters that could be

127

associated with the cycling of PFOA in liver: Oatp1a1 and Ntcp, both of which are located at the

128

basolateral membrane of hepatocytes48. Oatp1a1 has been demonstrated to transport PFOA27,

129

while for Ntcp only interactions with perfluorooctane sulfonate (PFOS) were reported45. Given

130

the structural similarity between PFOA and PFOS, we assume that Ntcp could also transport

131

PFOA. Once in the hepatocyte, PFOA can bind to liver-type fatty acid binding protein (L-FABP),

132

while the free fraction is available for excretion into the bile duct via passive diffusion. Biliary

133

PFOA is then circulated to gut lumen, where reabsorption of PFOA from the intestine back to

134

systemic circulation can occur, as well as elimination of PFOA through defecation.

135

The kidney is another major elimination tissue, involving glomerular filtration, tubular secretion,

136

and reabsorption processes. The free fraction of PFOA can transport from blood into filtrate

137

through both glomerular filtration and renal tubular secretion. The latter process is mainly

138

mediated via organic anion transporters (Oat1 and Oat3) located at the basolateral membrane of

139

proximal tubular cells18. PFOA is actively reabsorbed by Oatp1a1 from filtrate back to the tissue 7 / 30



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compartment18, where PFOA can bind to two different proteins, L-FABP and α2µ-globulin

141

(traditionally but erroneously called kidney fatty acid binding protein49), both of which are

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present in rat kidney tissue50, 51. The free fraction of PFOA in kidney tissue might be excreted

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into blood through organic solute transporters (Ostα/β). Based on the observation of lower

144

kidney:blood PFOA concentration in male rats compared to female rats, it is hypothesized that

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male rats have more effective efflux transporters on the renal basolateral membrane excreting

146

intracellular PFOA back to blood29; Ostα/β and Mrp6 are proposed to be promising candidates

147

for PFOA efflux18. Given available kinetic data for Ostα/β, it was included in our model.

148

Finally, muscle and adipose were selected for comparison to other tissues, since they typically

149

have the lowest levels of PFOA10,

150

compartment, “rest of body”.

151

2.2 Experimental Data.

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Several studies have reported toxicokinetics and tissue distribution of PFOA in male rats for both

153

oral and IV dosing10, 14, 15. In order to compare different administration routes, data on single oral

154

and IV doses of 1 mg PFOA/kg body weight (BW) were chosen for our model evaluation10, 14.

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Moreover, data from a single oral dose of 0.1 mg PFOA/kg BW and IV dose of 0.041 mg

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PFOA/kg BW were used to verify model performance at low doses10, 15. This is of particular

157

toxicological relevance since the general population is exposed to low levels of PFOA, with

158

estimated daily intakes in the range of 1 to 130 ng PFOA/kg BW52. A total of seven experimental

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datasets collected from three different studies were used and are briefly described below.

160

We extracted four datasets from the Kemper study10. The first two datasets are toxicokinetic data

161

for male rats administered by two routes: oral and IV dose. Specifically, four male Sprague-

15

. All remaining tissues were lumped into a single

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Dawley (SD) rats were dosed 1 mg PFOA/kg BW through oral or IV administration, respectively,

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then blood samples were collected at different times and analyzed. A third experiment measuring

164

terminal tissue distribution was chosen for comparison to predicted PFOA levels in each organ.

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In this experiment, 1 mg 14C-FPOA/kg BW was administered orally to four male SD rats. After

166

28 days, tissue samples were collected for analysis. Finally, the fourth dataset is a toxicokinetic

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experiment with an oral dose of 0.1 mg PFOA/kg BW, where the PFOA concentration in blood

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of four male SD rats, collected at different timepoints, was analyzed.

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From a second study, conducted by Kim et al.14, two datasets were extracted wherein 1 mg

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PFOA/kg BW oral and IV dose, respectively, were administrated to 5 male and 5 female SD rats.

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Blood samples were collected and analyzed at different time points. At the end, tissue samples

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including liver, kidney, heart, lung, and spleen were collected for analysis.

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To further assess our model, we selected another dataset from a third study15 where four male

174

Wistar rats were intravenously dosed with the low dose of 0.041 mg [1-14C]PFOA/kg BW.

175

PFOA concentrations in blood collected at different time points and tissues, including liver,

176

kidney, intestine, testis, spleen, fat, heart, lung, brain, stomach, and carcass, analyzed after 2

177

hours, were available.

178

For all three studies (seven datasets in all), data were taken directly from tables if available or

179

extracted from plots using WebPlotDigitizer53.

180

2.3 Model Parameterization.

181

All parameters used in our model were rat-specific, except capillary surface area, albumin

182

concentrations in interstitial fluid compartments, and the transport kinetics of Ostα/β. The first

183

two parameters were estimated from other mammalian studies46, 47, 54, and Ostα/β kinetics were 9 / 30



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based on an uptake study in human cells45. All these parameters are explained in detail below.

185

2.3.1 Rat Physiology.

186

Physiological parameters were obtained from the literature. The average body weight of rats in

187

each experimental dataset was used for model simulation. Fractional tissue volume, blood flow

188

rate, interstitial fluid and blood volumes, and capillary surface area for each compartment are

189

summarized in Supporting Information (SI) Table S1. Other parameters, including volume of

190

bile, renal filtrate, and gut content, as well as urinary, biliary, and fecal flow rates are also

191

indicated. Detailed information on derivation of physiological parameters is provided in Table

192

S1.

193

2.3.2 Protein-related Parameters.

194

Protein Concentrations. Table S2 indicates the concentrations of albumin, two specific

195

intracellular proteins (L-FABP and α2µ-globulin), and total protein in different compartments.

196

Total protein content is used to calculate tissue-specific uptake kinetics into cells, as explained in

197

SI section S2-1. Plasma albumin concentration was obtained from the study of Davies and

198

Morris55. For interstitial fluid compartments, the albumin concentrations related to serum levels

199

were available from other mammalian studies46, 47, and the same fluid:plasma albumin ratios for

200

liver, muscle and adipose were used in our rat model. Kidney and gut were assumed to have

201

similar interstitial albumin levels as liver, while the “rest of body” was assumed to be the same

202

as muscle. We assumed no albumin is present in tissue intracellular compartments.

203

Finally, for the two intracellular proteins considered, L-FABP is dominant in liver cytosol56 but

204

also present in kidney cells50; while α2µ-globulin is a male-specific protein predominant in rat

205

kidney cytosol51. The concentrations of these two proteins are indicated in Table S2. 10 / 30


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Protein Interaction. Two forms of protein interaction were considered in our model: protein

207

binding and active transport.

208

For protein binding, the equilibrium association constants (Ka) for PFOA binding to albumin, L-

209

FABP, and α2µ-globulin were available from the literature22,

210

estimate the Ka for PFOA binding to rat serum albumin to be 3.1 × 103 M-1. It is worth noting

211

that this value is much smaller than Ka for human serum albumin24, 57. Since this is, to the best of

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our knowledge, the only available value for rats, its uncertainty was considered in our model

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sensitivity analysis. The interaction of L-FABP with PFCAs of different chain length has been

214

measured using fluorescence displacement and isothermal titration calorimetry techniques, and it

215

was shown that three binding sites exist for L-FABP interacting with PFOA: a single high-

216

affinity binding site and two additional low-affinity binding sites23. We assume these three

217

binding events are independent of one another. The interaction between α2µ-globulin and PFOA

218

was also determined and indicates a relatively weak binding affinity of about 2 mM49. However,

219

given the high concentration of α2µ-globulin in kidney51, we took this protein into consideration

220

when building our model.

221

Utilizing Ka, the individual rate constants for PFOA association and dissociation from each

222

protein (bon and boff) were derived in the same manner as in the original fish model43, as

223

described in SI Section S2-2.

224

For active transport, uptake kinetics of five organic anion transport proteins including Oat1, Oat3,

225

Oatp1a1, Ostα/β, and Ntcp (Table S4) were used for parameterization of active transport of

226

PFOA. Similar to the original model, the uptake kinetics of Oat1, Oat3, and Oatp1a1 transporters

227

were obtained from the Weaver et al. study27. Based on another study where uptake rates of

228

PFOS for rat Ntcp and human Ostα/β were available45, we assumed that rat Ntcp has the same 11 / 30


23, 49

(Table S3). Han et al.22


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kinetics for transporting PFOA as PFOS and that kinetics of rat Ostα/β transporting PFOA is the

230

same as human Ostα/β transporting PFOS. Finally, all uptake or efflux proteins were assumed to

231

be unidirectional. These in vitro to in vivo extrapolations are further described in SI Section S3-3

232

and Table S6.

233

2.4 Mass Balance Equations.

234

Our model is based on permeability-limited equations that consider three or four

235

subcompartments for each tissue. Based on the original model43, the effective membrane

236

permeabilities for each tissue were obtained from a PFOA cellular uptake study27, as summarized

237

in Table S5. Each compartment is described by mass balance equations that are established

238

according to PFOA-protein interactions and exchange between connected compartments.

239

For an individual tissue i (i = A, G, K, L, M, and R, for adipose, gut, kidney, liver, muscle, and

240

rest of body, respectively), the mass of free and bound PFOA in each subcompartment j (j = F

241

and T, for fluid and tissue subcompartment, respectively) is determined. In blood compartment

242

(B), which is in contact with and can be considered a subcompartment of each tissue:

243

244

= ∑ b M − ∑ b M + b M − b M

+ b M − b M

(1)

245

246

In interstitial fluid subcompartment iF:

247

!"

248

= b M − b M

(2)

# # # = b M − b M + b# M − b # M + b# $% M − b$% M

+ b M − b M

(3)

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249

!"

250

In tissue subcompartment iT (i = A, M, and R):

251

!&

252

!&

253

For tissues (i = K, L, and G) containing additional compartments, namely filtrate, bile, or gut

254

lumen (GL), the mass balance equations in tissue subcompartment iT and corresponding

255

additional compartments are:

256

'&

# # # = b# M − b M

(6)

(# (# (# (# −b(# M + b (# M + b(# $% M − b M

258

'&

259

"!)*+*

261

(# (# (# = b(# M − b M

263

.&

264

!)

265

0&

266

0.

(8)

, -

M

(9)

/ /# / /# /# = b/ /# M − b/# / M + b/ /# M − b/# M $% M + b

262

(7)

(# = b M − b M + b(# M − b (# M

− b (# M − $%

.&

(5)

( (# ( (# ( (# (# = b( (# M − b(# ( M + b( (# M $% M − b$% M + b

257

260

(4)

# # # # # # # = b # M − b# M + b # $% M − b$% M + b M − b M

= b M − b M

/# /# /# +b/# M − b M

(10)

/# /# /# = b/# M − b M

(11)

/# = b/# M − b /# M −

, -

M

(12)

1 1# 1/ 1# = b1 1# M − b1# 1 M + b1/ 1# M − b1# 1/ M

1# 1/ = b1# 1/ M − b1/ 1# M +

, -

M −

,$2 -1/

1# M

13 / 30


(13)

(14)


Page 14 of 34

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M ijfree represents unbound PFOA in ij subcompartment, which can freely transport between

268

ij compartments, while M bound refers to PFOA bound to albumin, L-FABP or α2µ-globulin.

269

Parameters bij-ik and bij-jk active are first-order rate constants for passive diffusion and active transport

270

between subcompartments ij and ik (j ≠ k), respectively. Q and V are the flow rate and volume of

271

a compartment, respectively. The protein-binding rate constant in subcompartment ij is bijon and

272

the dissociation rate constant is bijoff. All rate constants for transport among compartments are

273

explained in detail in SI Section S3.

274

2.5 Sensitivity and Uncertainty Analysis.

275

There were 72 independent parameters used in our model to predict the toxicokinetics and tissue

276

distribution of PFOA in rats, and no parameters were fit to match the data. We conducted a

277

Monte Carlo uncertainty analysis to characterize the propagation of uncertainty to predicted

278

PFOA concentration profiles in three key tissues: blood, liver, and kidney. For each of the 10000

279

iterations, parameters were sampled from uniform, normal or lognormal distributions (see SI

280

Section S4 and Table S7). Correlation analysis was then conducted between sampled parameters

281

and predicted PFOA concentrations to quantify the sensitivity of the model to each input

282

parameter.

283

2.6 Software and Model Code.

284

The PBPK model considered in this study was programmed in MATLAB (MATLAB R2016a),

285

and the code is available in SI section S6.

286

3. RESULTS

287

3.1 Plasma Toxicokinetics.

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We first compare the toxicokinetics of PFOA predicted by our model to six datasets extracted

289

from three different studies where different administration routes and dose levels were

290

available10, 14, 15 (Figure 2). In order to compare between predicted concentrations and these data,

291

we ran the model using the BWs and doses given in each experimental study. Since the

292

information on BW was not given by Kim et al14., we assumed these rats were the same average

293

BW as in Kemper10, given that both studies used SD rats as test species.

294

As indicated in Figure 2, all experimental datasets fall within the 95% confidence interval of the

295

predicted concentrations of PFOA in plasma, and the geometric means of simulated results (solid

296

lines) indicate similar time course behaviors observed in each experiment. In addition, based on

297

the geometric means of predicted results, the toxicokinetic parameters, including the maximum

298

plasma concentration of PFOA (Cmax), the time required to reach the peak concentration (Tmax),

299

the half-life (T1/2), and the clearance of PFOA (CL), were calculated and compared with the

300

Kemper study10, as shown in Table S8. Compared to the mean of Cmax in the Kemper study, the

301

model-predicted results after 0.1 mg PFOA/kg BW and 1 mg PFOA/kg BW oral dose are

302

underestimated by a factor of 1.9 and 3, respectively, but the predicted Tmax fall well within the

303

range of the experimental values for both dose scenarios. Furthermore, the T1/2 (6.80, 6.93, and

304

6.93 days for 0.1 mg PFOA/kg BW oral dose, 1 mg PFOA/kg BW oral dose, and 1 mg PFOA/kg

305

BW IV dose, respectively) predicted by our model are in very good agreement with the reported

306

mean values (8.41, 5.76, and 7.73 days for 0.1 mg PFOA/kg BW oral dose, 1 mg PFOA/kg BW

307

oral dose, and 1 mg PFOA/kg BW IV dose, respectively) under three different dose scenarios.

308

This suggests that the T1/2 is independent of dose scenarios. Finally, all predictions of the

309

clearance of PFOA are overestimated by about a factor of 3.

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Table 1. Correlation coefficients between parameters and predicted PFOA levels in blood, liver, and kidney. Parametersa

Bloodb

Liverb

Kidneyb

-

0.13

0.11

Blood volume (VB)

0.18

-

-

Plasma volume (Vplasma)

-0.16

-

-

Glomerular filtration rate (QGFR)

-0.26

-0.25

-

Urine flow rate (Qurine)

-0.28

-0.25

-0.36

Capillary surface area of kidney (AK)

0.27

0.26

-

-

-

0.16

Effective permeability for blood (PeffB)

0.24

0.23

-0.17

Effective permeability for liver (PeffL)

0.10

-0.34

0.11

-

-

-0.17

Steady-state cell-water concentration ratio for kidney (CRssK)

0.25

0.24

0.38

Albumin concentration in blood (CAlbB)

0.29

-

-

Albumin concentration in kidney fluid (CAlbKF)

-

-

0.13

L-FABP concentration in liver tissue (CLFABPLT)

-

0.33

-0.10

L-FABP concentration in kidney tissue (CLFABPKT)

-

-

0.12

Association constant of L-FABP binding site 1 (KLFABP1)

-

0.22

-

Association constant of albumin (Ka)

0.35

-

0.15

Renal clearance rate constant (bclear)

-0.16

-0.16

-

Renal reabsorption rate constant (breab)

0.26

0.26

0.39

Renal efflux rate constant (befflux)

0.17

0.16

-

Absorption rate constant of hepatocyte (babs)

-0.11

0.33

-0.12

Dose

Enlargement factor of apical membrane of proximal tubule (n)

Effective permeability for kidney (PeffK)

a

Only parameters with correlation coefficients ≥ 0.1 and P values < 0.05 are indicated here. The results for other

parameters can be found in Figures S1-S3. b

Coefficient values are the average of three simulation results for different doses and administration routes (1 mg/kg oral

dose, 1 mg/kg IV dose and 0.1 mg/kg oral dose). Sensitivities were similar for the three scenarios.

16 / 30


Page 17 of 34


311

In comparison with the experimental results of the Kim et al. study14, our model performs best

312

for the 1 mg PFOA/kg BW IV dose scenario, with all experimental data close to the predicted

313

geometric mean. However, for 1 mg PFOA/kg BW oral dose, the elimination rate is

314

underestimated by our model by about a factor of 3. It is worth noting that even under the same

315

dose scenarios, the PFOA toxicokinetics vary substantially among different studies (Figure 2, 1

316

mg PFOA/kg BW IV and oral dose), reflecting both natural biological variation and differences

317

in experimental procedures (e.g., sampling and analysis methods).

318

The last experimental dataset is from Kudo et al.15, where the PFOA concentration profile only

319

up to 5 hours after dosing was observed. Our model was also able to capture the behavior of

320

PFOA in plasma for this short-term experiment, including during the distribution phase, which is

321

considered to be the first 2 hours in the Kudo et al. study.

322

3.2 Tissue Distribution

323

We next evaluate our model performance in predicting the tissue distribution of PFOA through

324

comparison with four datasets extracted from the three studies10, 14, 15 (Figure 3 and Figures S4-

325

S6). As indicated in Figure 3, all measured PFOA concentrations in each tissue fall well within

326

or overlap with the model-predicted ranges, except the hepatic PFOA concentration from the

327

Kudo et al. study15, which is 4.5 times higher than the predicted result. It is worth noting that the

328

four experimental datasets were sampled at different time points, namely: dataset A at 28 days

329

following dosing, dataset B and C at 12 days following dosing, and dataset D at 2 hours after

330

dosing. Due to propagating uncertainty in the model, variability in predicted results increases

331

with time.

332

With respect to distribution patterns, our model prediction (liver > kidney > blood > gut > 17 / 30



Page 18 of 34

333

muscle ≈ adipose) is similar to that measured by Kemper (liver > kidney ≈ blood > gut > muscle >

334

adipose). In the Kim et al. study14, PFOA concentrations were available for blood, kidney, and

335

liver, and the comparison between these data and model predictions indicates the same

336

distribution pattern: liver > kidney > blood. Finally, the model under-predicts the PFOA

337

concentration in the short-term dosing simulation compared with measured data in Kudo et al.15.

338

In this case alone, predicted PFOA concentrations in liver are lower than in blood.

339

A further comparison was conducted between the geometric mean of predicted results and the

340

mean of measured data for each tissue in each study. In the blood compartment, predicted values

341

are well within a factor of 1.5 of measured concentrations for both high and low IV dose (Figure

342

3, C and D). For the oral study, even though both were at the same dose level of 1 mg PFOA/kg

343

BW, our predicted results are either underestimated or overestimated by a factor of 4.7 or 3.5,

344

respectively, which may reflect the biological or experimental variability. In the liver, our model

345

generally under-predicts the results by a factor ranging from 1.6 to 4.5 for the four different dose

346

scenarios. Similarly, in the kidney compartment, PFOA concentrations are generally under-

347

predicted within a factor ranging from 1.2 to 2.7 for all dose scenarios except Kudo et al15., for

348

which the prediction is overestimated by a factor of 2.5. For the gut compartment, data were

349

available from the Kemper10 and Kudo et al.15 studies, and our model underestimates or

350

overestimates by a factor of 3.1 or 1.4, respectively. In adipose, the predicted geometric mean

351

falls within the range of measured values in the Kemper study10, and for Kudo et al.15, the

352

prediction is overestimated by only a factor of 1.7. Finally, only one dataset from Kemper10 was

353

available for comparison with the muscle compartment, and the PFOA concentration is under-

354

predicted by our model, but within a factor of 4.

355

3.3 Uncertainty and Sensitivity Analysis 18 / 30


Page 19 of 34


356

In order to explore the effect of parameter uncertainties on model performance, Monte Carlo

357

uncertainty and sensitivity analysis was conducted for all 72 independent model parameters (SI

358

Section S4). As shown in Figures S1-S3 and Table 1, the most important parameters are related

359

to protein binding (i.e., the concentration of albumin and L-FABP in corresponding

360

compartments and the equilibrium association constants for binding to PFOA) and active

361

transport (i.e., renal clearance rate constant, renal reabsorption rate constant, renal efflux rate

362

constant, and absorption rate constants for hepatocytes). Second most important are parameters

363

relevant to passive diffusion, including the effective membrane permeability (Peff) for blood,

364

liver, and kidney, the steady-state cell-water concentration ratio for kidney (CRssK) describing

365

the back-diffusion from kidney tissue to filtrate43 and the surface area for exchange between

366

blood and kidney (AK, Table 1). Finally, some physiological parameters such as blood and

367

plasma volume, glomerular filtration rate and urine flow rate also have a significant effect on

368

predictions of tissue-specific PFOA concentrations.

369

4. DISCUSSION

370

In this study, we developed a permeability-limited PBPK model that explicitly considers PFOA-

371

protein interactions for toxicokinetics and distribution of PFOA in male rats. A total of seven

372

datasets from three different studies were used to evaluate model performance, and all the

373

experimental data fall within or overlap the prediction ranges, except PFOA concentration in the

374

liver from the Kudo et al.15 study. It is possible, given that the Kudo et al. tissue distributions

375

were sampled after only two hours, that the distribution from blood to liver in our model is

376

slower than in vivo. This prediction was the only one in which PFOA concentration was higher

377

in blood than in liver, in contrast with both the other experimental results and the other model

378

predictions. Such a lag time could be caused by our parameterization of liver blood flow, surface 19 / 30



Page 20 of 34

379

area for exchange blood-liver exchange, or passive diffusion. It is also worth noting that in the

380

Kudo et al. study the subcellular distribution of PFOA in the liver 2 hours after IV administration

381

showed that only 3% of the PFOA was detected in the cytosolic fraction, with most found in the

382

membrane fraction. It is hypothesized that PFOA might bind to some membrane components

383

such as proteins or lipids58. However, given the limited information available on membrane

384

binding, our model did not consider these interactions, which could cause the failure to capture

385

PFOA localization on hepatic membranes. Our model did successfully predict the hepatic

386

distribution of PFOA at time points of 12 and 28 days.

387

In comparisons with all three experimental studies, our model was able to predict plasma

388

toxicokinetics and tissue distribution of PFOA well within a factor of 5. Considering natural

389

biological variation and experimental differences among studies, the agreement is remarkable. In

390

the blood compartment, PFOA concentrations were generally under-predicted in comparison

391

with the Kemper study10 (Figure 2). In addition to natural biological variation, the reason for this

392

under-prediction could also be attributed to the equilibrium association constant (Ka) for binding

393

to albumin, which is the most influential parameter for the prediction in the blood. As described

394

in the Methods section 2.3.2, only one study22 was available for the Ka of rats, and the value (3.1

395

× 103 M-1) is much smaller compared with the Ka of human serum albumin in other studies (e.g.,

396

1 × 104 M-1 and 3.12 × 104 M-1). If we assume the Ka used in our model is a lower bound, then

397

the predictions would fit better with the experimental data. However, more studies are needed to

398

measure Ka for PFOA in rats before making this assumption.

399

Similarly, in each tissue compartment, our model generally under-predicts PFOA levels to a

400

small extent in comparison with all three studies except Kudo et al. (Figure 3 D). Currently, there

401

are two cytosolic proteins included in our model: L-FABP (in the liver and kidney) and α2µ20 / 30


Page 21 of 34


402

globulin (only in the kidney). However, other FABPs, which could also bind to PFOA, were not

403

considered due to the lack of protein-binding data. For example, the heart-type FABP (H-FABP),

404

which is ubiquitous in many tissues including liver, kidney, gut, and heart in the rat59, is reported

405

to have a higher fatty acid binding affinity than L-FABP60. Given the similarity of perfluorinated

406

alkyl acids to fatty acids within organisms, H-FABP may also have a higher PFOA binding

407

affinity, and the lack of H-FABP binding may explain the underestimation of PFOA levels in

408

kidney, liver, and gut compartments. In addition, it is possible that another sensitive parameter,

409

the albumin concentration in the interstitial fluid subcompartment of each tissue, was under-

410

predicted since this parameter was derived based on other mammalian studies.

411

This work is the first permeability-limited PBPK model that explicitly considers PFOA-protein

412

interactions for rats. Compared to the original fish model43, prediction accuracy is further

413

improved by incorporation of rat-specific parameters and inclusion of new tissues and proteins.

414

The good agreement between the simulation results and experimental data illustrate our model’s

415

ability to predict the toxicokinetics and tissue distribution of PFOA in rats. Our model also

416

provided several new insights on processes that drive the tissue distribution of PFOA compared

417

with previous flow-limited models. We demonstrate that L-FABP, Oatp1al and Ntcp transporters

418

play key roles for PFOA accumulation in rat liver; in kidney tissue, the efflux of PFOA back to

419

the blood by Ostα/β is also important.

420

This model includes a Monte Carlo-based uncertainty and sensitivity analyses that could be used

421

in future to address population polymorphism. Each parameter is sampled from a pre-defined

422

distribution to account for biological variation and uncertainty. A generalized model that can be

423

applied to a population (not just an individual) could therefore be easily derived by defining the

424

distributions for protein- or physiology-related parameters in a way that captures observed 21 / 30



Page 22 of 34

425

polymorphisms. Because our model is mechanistic, the influence of such polymorphisms on

426

tissue distribution, whole-body half-lives, and accumulation potentials could thus be directly

427

probed in a way that is not accessible to a model whose parameters are fit to in vivo data. Our

428

model makes these relationships explicit, thus providing an effective framework to conduct in

429

vitro-in vivo extrapolation. The in vitro-in vivo extrapolations used in our model also represent a

430

promising avenue to reduce the use of whole animals in toxicology and risk assessment, and a

431

potential solution to the challenges caused by limited human in vivo data.

432

Extrapolation to Humans. To extrapolate our model approach to humans, human physiology and

433

PFOA-protein interaction parameters are needed. All physiological parameters including

434

compartmental volume, blood and fluid flow rates, and capillary surface area for each tissue can

435

be obtained from the literature (the surface areas for some tissues in humans can be estimated

436

from other mammals)54, 55, 61, 62. The concentrations and the equilibrium association constants of

437

serum albumin and liver-type fatty acid binding protein (L-FABP) are also available46, 47, 50, 55, 63.

438

However, some protein binding parameters, such as binding characteristics of H-FABP, are still

439

missing. Importantly, more data on transporter kinetics are required to extrapolate the transport

440

rate constants of PFOA to different tissues. In vitro kinetic studies have indicated that OAT1,

441

OAT3, OAT4, and urate transporter 1 (URAT1) play key roles in human renal secretion and

442

reabsorption of PFOA29. However, kinetic data for other transporters such as OSTα/β, breast

443

cancer resistance protein (BCRP), and multidrug resistance-associated proteins (MRP2, MRP4,

444

and MRP6) are currently not available18. It is important for future studies to investigate whether

445

these transporters are involved in PFAS transport in humans.

446

Model Limitations. Some limitations that might affect the model performance need to be

447

addressed. First, many new parameters are incorporated into our model, and some are based on a 22 / 30


Page 23 of 34


448

single study (e.g., Ka for binding to proteins) or extrapolated from in vitro studies (e.g., effective

449

permeabilities and active transport rate constants), indicating that their uncertainties are very

450

high. Furthermore, some protein binding parameters such as H-FABP were not included in our

451

model due to limited data. Finally, female rats were not considered in our model due to lack of

452

data to account for the substantial gender differences in PFOA elimination in male and female

453

rats. Especially little information is available about the kinetics of some Mrps (e.g., Mrp364),

454

which are female-dominant and might play an important role in faster PFOA efflux in female

455

rats. Most of these parameters are protein-related and play important roles in predicting PFOA

456

toxicokinetics, based on our sensitivity analysis.

457

To overcome these limitations, we first call for more in vitro data on protein interactions for

458

PFOA and other PFAS. The measurement of equilibrium association constants for binding to H-

459

FABP and the transport kinetics of Mrps are urgently required, as these parameters have the

460

potential to substantially affect toxicokinetics. Further measurements of Ka for PFOA binding to

461

albumin and L-FABP are also needed, since these parameters were each obtained from a single

462

in vitro study. If more data were available, the associated uncertainties would decrease. From the

463

model perspective, statistical tools like Bayesian analysis and Markov chain Monte Carlo

464

simulations can be applied to reduce the uncertainty of parameters65 and molecular modeling

465

tools can provide suggestions for promising protein targets for further research.

466

However, it should be noted that these are in a way one-time costs for a given organism and class

467

of chemicals. It is our vision that, once sufficiently parameterized, this type of model can become

468

a flexible and generalizable predictive tool that can be applied to a variety of simulations in a

469

way that is not possible with a model trained on experimental data. The sensitivity analysis we

470

include here can serve, as we further develop such general PBPK models, to give us an idea of 23 / 30



471

when “enough is enough” as relates to the importance of specifying each physiological and

472

protein interaction parameter. The ability of our current model, uncertainties notwithstanding, to

473

successfully simulate a variety of experiments and dosing scenarios provides a first

474

demonstration of the power of this approach.

475

476

ASSOCIATED CONTENT

477

Supporting Information

478

Details on model parameterization and sensitivity analysis are available in the Supporting

479

Information (SI). This material is available free of charge via the Internet at http://pubs.acs.org/.

480

481

AUTHOR INFORMATION

482

Corresponding Author

483

*Address: 3700 O’Hara St, Pittsburgh, PA 15261 USA. Tel: 412-383-4075; Fax: 412-624-0135;

484

E-mail: [email protected].

485

Notes

486

The authors declare no competing financial interest.

24 / 30


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Page 25 of 34


487

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MODEL Environmental ScienceTISSUE & Technology Vascular Space Q in Albumin

Page 31 of 34

Interstitial Fluid

Transporters

Intracellular Space

In

sil

ic

o

Albumin

α2μ-globulin

L-FABP

MODEL ASSESSMENT In vi vo


Q out

LIVER(L) Bile

Environmental ScienceGUT(G) & Technology Q Bile Gut Lumen Q Feces

GT

LT

GF

LF

Q BL

LB

Page 32 of 34

Q BG

GB

Q Hepatic artery

LEGEND Passive diffusion Active transport

BLOOD(B)

Q Cardiac input

Q Cardiac output

Blood flow Bile, feces or urine outflow

MUSCLE(M)

Q BM

Q BG

Q BM

MB

L-FABP

MF

α2μ-globulin

MT

Albumin Oat1

ADIPOSE(A)

Q BA

Q BA

AB

Oat3

AF

Oatp1a1

AT

Ntcp Ostα/β

REST OF BODY(R)

Q BR

Q BR

RB RF RT

KIDNEY(K)

Q BK

KB

Q BK - Q GFR

KF KT

Q Urine

ACS Paragon Plus Environment Q Filtrate

GFR

Page 33 of 34

a

c


b

d



a

b

c


Page 34 of 34

d

A Permeability-Limited Physiologically Based Pharmacokinetic (PBPK

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