A physiologically based pharmacokinetic (PBPK) model to characterize and predict the disposition of monoclonal antibody CC49 and its single chain Fv constructs

International Immunopharmacology (2008) 8, 401–413

w w w. e l s e v i e r. c o m / l o c a t e / i n t i m p

A physiologically based pharmacokinetic (PBPK) model to characterize and predict the disposition of monoclonal antibody CC49 and its single chain Fv constructs Jasmine P. Davda a , Maneesh Jain b , Surinder K. Batra b , Peter R. Gwilt a , Dennis H. Robinson a,⁎ a

Department of Pharmaceutical Sciences, College of Pharmacy, University of Nebraska Medical Center, 986025 Nebraska Medical Center, Omaha, NE 68198-6025, United States b Department of Biochemistry and Molecular Biology, University of Nebraska Medical Center, 985870 Nebraska Medical Center, Omaha, NE 68198-5870, United States Received 6 September 2007; received in revised form 29 October 2007; accepted 30 October 2007

KEYWORDS Antibody pharmacokinetics; PBPK modeling; Tumor radioimmunotherapy; scFvs; IgG; FcRn

Abstract Optimization of the use of monoclonal antibodies (MAbs) as diagnostic tools and therapeutic agents in the treatment of cancer is aided by quantitative characterization of the transport and tissue disposition of these agents in whole animals. This characterization may be effectively achieved by the application of physiologically based pharmacokinetic (PBPK) models. The purpose of this study was to develop a PBPK model to characterize the biodistribution of the pancarcinoma MAb CC49 IgG in normal and neoplastic tissues of nude mice, and to further apply the model to predict the disposition of multivalent single chain Fv (scFv) constructs in mice. Since MAbs are macromolecules, their transport is membrane-limited and a two-pore formalism is employed to describe their extravasation. The influence of binding of IgG to the protective neonatal Fc receptor (FcRn) on its disposition is also accounted for in the model. The model successfully described 131I-CC49 IgG concentrations in blood, tumor and various organs/tissues in mice. Sensitivity analysis revealed the rate of transcapillary transport to be a critical determinant of antibody penetration and localization in the tumor. The applicability of the model was tested by predicting the disposition of di- and tetravalent scFv constructs of CC49 in mice. The model gave reasonably good predictions of the disposition of the scFv constructs. Since the model employs physiological parameters, it can be used to scale-up mouse biodistribution data to predict antibody distribution in humans. Therefore, the clinical utility of the model was

⁎ Corresponding author. Department of Pharmaceutical Sciences, College of Pharmacy, University of Nebraska Medical Center, 986025 Nebraska Medical Center, Omaha, NE 68198-6025, United States. Tel.: +1 402 559 5422; fax: +1 402 559 9543. E-mail address: [email protected] (D.H. Robinson). 1567-5769/$ - see front matter. Published by Elsevier B.V. doi:10.1016/j.intimp.2007.10.023

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J.P. Davda et al. tested with data for 131I-CC49 obtained in patients, by scaling up murine parameter values according to known empirical relationships. The model gave satisfactory predictions of CC49 disposition and tumor uptake in man. Published by Elsevier B.V.

1. Introduction Monoclonal antibodies (MAbs) are currently used as both diagnostic and therapeutic agents in the treatment of cancer. The success of MAbs in the treatment of solid tumors depends on their selective localization in the target tissue. Administration of radiolabeled MAbs to mice permits measurement of the antibody uptake and distribution in individual tissues. When these data are incorporated into a physiologically based pharmacokinetic (PBPK) model, a detailed, quantitative assessment of the tissue MAb uptake and disposition in the body can be obtained using computer simulation. MAbs, like other macromolecules, exhibit distinctly different disposition features compared with those of conventional small-molecule drugs. One such characteristic is their long biological half life. This results from a combination of several factors such as poor vascular permeability, protection against catabolism through binding to the FcRn receptor, and limited renal elimination [1]. The prolonged persistence of MAbs in the circulation may result in significant toxic effects in normal tissues such as bone marrow with only limited quantities delivered to the tumor [2]. Furthermore, as a result of their large size, intact MAbs demonstrate poor diffusion out of the vasculature and into a tumor mass [3]. In an effort to reduce their size and to circumvent some of the problems associated with the use of intact MAbs, immunoglobulins (IgGs) have been engineered to retain only the domains involved with antigen binding and/or mediating the effector functions of the MAb [4]. One such engineering strategy is the use of single-chain antibody fragments (scFvs) comprised of only the variable regions of the heavy and light chains of IgG, covalently connected by a flexible peptide linker [5,6]. Such fragments exhibit greater systemic clearances than intact IgG [7] and have yielded improvements in radioimmunodiagnosis and radioimmunotherapy by offering shorter imaging times and correspondingly rapid tumor penetration resulting in increased tumorto-background concentration ratios [8]. Since many of the therapeutically relevant tumor-associated antigens are glycolipids or glycoproteins with highly repetitive structures, MAbs with multiple valencies represent an enormous gain in the functional affinity due to multiple interactions within a single antigen–antibody complex [6]. Accordingly, in animal models, divalent scFvs exhibit a marked improvement in tumor targeting compared with monovalent species such as scFv and Fab because of their higher avidity and slower clearance properties rendered by their larger size [9]. To further improve their in vitro and in vivo performance, the valency of scFv has been increased by designing trivalent and tetravalent scFvs [10,11]. Unlike the empirical pharmacokinetic models that describe drug concentration–time profiles in the blood using one, two or three lumped compartments, physiologically based pharmacokinetic (PBPK) models describe drug disposition using a more realistic physiological compartmental system. PBPK

models have the potential for interspecies scaling [12], predicting pharmacokinetics of therapeutic agents prior to in vivo studies [13], and characterizing the physiological or biochemical basis for altered pharmacokinetics and associated toxicity [14,15]. Although PBPK modeling has found significant application in cancer chemotherapy, its use in the characterization and prediction of the disposition of MAbs in cancer immunotherapy has been limited. A PBPK model could aid in understanding the factors that determine antibody distribution in the body, and in identifying functions that are responsible for efficient tumor localization of the MAb, leading to an overall improvement in antibody-based diagnosis and therapy. Further, PBPK modeling provides an attractive approach to predict drug disposition profiles in man based upon the physicochemical properties of the drug and the species-specific biochemical or physiological characteristics [16]. This has a great potential for assessing the suitability of a new neoplastic agent for a tumor in a particular tissue. The purpose of the present study was to develop a PBPK model to characterize the biodistribution of the 131I-labeled murine MAb CC49 IgG. CC49 is among the most extensively studied MAbs for cancer therapy and reacts against tumorassociated antigen TAG-72 which is expressed by a majority of mucinous adenocarcinomas [5]. Further, we have applied the PBPK model to simulate the pharmacokinetics and biodistribution of di- and tetravalent scFv constructs of CC49 in mice. Finally, the clinical utility of the model was tested with data obtained from a clinical study of 131I-CC49 administered intravenously to patients with colorectal cancer [17].

2. Methods 2.1. Biodistribution studies in mice Female athymic mice (nu/nu, 4–6 weeks old) bearing LS-174T human colon carcinoma xenografts were used to study the biodistribution of radiolabeled CC49 IgG and scFvs [6]. LS-174T cells were implanted s.c. (4 × 106) and the mice were used 8 days (tumor volume, ∼ 200– 300 mm3) after the injection of cells. Dual-label biodistribution studies were performed after a simultaneous i.v. injection via the tail vein of 125I-sc(Fv)2 (5 μCi) and 131I-[sc(Fv)2]2 (2.5 μCi) or 125I-[sc(Fv)2]2 (5 μCi) and 131I-CC49 IgG (2.5 μCi). Animals (n = 6) were sacrificed at designated times (0.5, 1, 4, 6, 16, 24, and 48 h post-injection) and the tumor, blood and major organs were removed, weighed, and counted in a gamma scintillation counter. The percentage of injected dose per gram (%ID/g) was determined in each organ or tissue using the following equation: kID=g ¼

Tissue cpm 100  Injected cpm Tissue weightðgÞ

2.2. Development of the PBPK model The MAb disposition characteristics included in the development of the PBPK model were: (1) blood circulation through the organs and tissues; (2) transport of antibody across the capillary wall (according

PBPK model for MAb CC49 and scFv constructs to the two-pore model); (3) return of antibody from the interstitial space to the circulation via lymph; (4) specific binding of the antibody to tumor-associated antigen; (5) binding of the antibody to the FcRn receptor in liver, skin and muscle endothelium; (6) catabolic clearance of the antibody; and (7) elimination of catabolic products by urine. The organs and tissues included in this model were blood, heart, lung, liver, spleen, kidney, and tumor (Fig. 1). In addition, a residual carcass compartment was included to account for the remainder of the injected MAb. The organ compartments are connected by the respective blood flows as shown in Fig. 1. The disposition of large protein molecules such as MAbs is described using ‘dispersion’ tissue models. Accordingly, each tissue/organ compartment was further divided into two subcompartments, vascular space and interstitial space, where MAb from the interstitial space is drained by the lymph before being returned to the systemic circulation (Fig. 2a).

2.3. Two-pore model A two-pore model was used to mathematically describe the transport of the MAb across the capillary wall in each organ (Fig. 2b). According to this model, both fluid and large molecules are transported across blood vessel walls through large pores (∼ 250 Å) while fluid and very small molecules pass through small pores (∼ 45 Å) [18,19]. Even under ‘isogravimetric’ conditions, i.e., when net fluid flow is zero, the filtration of large molecules through the large pores is counterbalanced by an osmotic absorption of mainly

403 protein-free fluid through the small pores. This recirculation of fluid, defined by the term Jiso, causes a continuous net flux of macromolecules across the membrane [18]. Accordingly, the transport of IgG molecules across the blood vessels in each organ is given by the flux term Jorg (moles/h) which is defined by the following equation [20]:
 Ci;org PeL Jorg ¼ JL;org ð1  rL ÞCv;org þ PSL;org Cv;org  PeL  1 R e org
 Ci;org PeS þ JS;org ð1  rS ÞCv;org þ PSS;org Cv;org  Rorg ePeS  1

ð1Þ

The transport of macromolecules, such as proteins and MAbs, across blood vessels as well as through the interstitial fluid, is determined by both passive diffusion and convection [19]. Diffusion across the capillary wall is described by the permeability-surface area product PS (ml/h), while convection is described by the fluid flow rates (JL and JS; ml/h) across the large and small pores (Eq. (1)). Cv,org and Ci,org (M) are the MAb concentrations in the vascular and interstitial space, respectively. The term R represents the equilibrium distribution ratio (partition coefficient) of the MAb between the tissue and plasma. The osmotic reflection coefficient (σ) is a measure of the fraction of MAb molecules that does not pass through the pores of the blood vessel wall and is determined by the difference in hydrostatic and osmotic pressures [21]. The reflection coefficient varies from 0 for a freely permeable solute to 1 for an impermeable solute. The diffusive term in Eq. (1) is multiplied by a term involving the Péclet number (Pe), the ratio of convective to diffusive transport across the vascular membrane [20]. The rates of fluid flow through large and small pores (JL,org and JS,org) across the blood vessel wall in each organ are defined by: JL;org ¼ Jiso;org þ aL Lorg JS;org ¼ Jiso;org þ aS Lorg

ð2Þ

where Jiso is the isogravimetric fluid recirculation rate and L is the lymph flow rate through the organ. αL and αS are the fractions of hydraulic conductivity accounted for by each set of pores.

2.4. FcRn binding An intracellular subcompartment was included to account for binding of IgG to the FcRn receptor that has been shown to protect IgG from catabolism and plays an important role in determining IgG half-life [22]. In adult mice, the FcRn receptor is known to be expressed in endothelial cells of the skin, muscle, liver, adipose tissue [23] as well as in hepatocytes [24]. Internalization of MAbs from the blood or interstitial fluid into cells occurs via pinocytosis, primarily by fluid-phase endocytosis [25]. Intracellular IgG may be bound by the FcRn within the acidic environment of the endosome (Fig. 2a). FcRn-bound IgG is protected from intracellular degradation and returned to the plasma while unbound intracellular IgG undergoes lysosomal degradation (kcat in Fig. 2a). The catabolic products are cleared from the organ compartment and returned to the central blood compartment (rate of clearance is given by CLorg in Figs. 1 and 2a). In all other tissue compartments except the liver and carcass (containing the skin and muscle endothelium) where FcRn is expressed, the MAb enters the tissue and, due to lack of binding to FcRn, proceeds to catabolism.

Figure 1 Schematic diagram of the whole body PBPK model for CC49 IgG. Solid arrows indicate blood flow and dashed grey arrows indicate return of catabolites from organs to the central blood compartment (or excretion in urine for kidney). Q = blood flow; CL = catabolite clearance; U = urinary excretion rate constant; subscripts B, LU, T, H, LI, SP, RB, and K indicate blood, lung, tumor, heart, liver, spleen, carcass, and kidney, respectively.

2.5. Model parameters The physiological parameters used in the model include blood flow rate, transcapillary fluid filtration rate, lymph flow rate, permeability-surface area product, rate of catabolism, binding to the FcRn receptor, and the vascular, interstitial, and total volumes for each organ in addition to the maximum tumor-associated antigen

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Figure 2 Each tissue/organ is divided into two subcompartments; vascular and interstitial space (a). Free MAb is drained from the interstitial space by lymph before being returned to the systemic circulation. IgG is internalized by the cell (kint), binds to the FcRn receptor in the endosome, and FcRn-bound IgG is recycled to the circulation (krec). Unbound IgG is subject to lysosomal degradation (kcat). Catabolites (Cm) formed are cleared from the organ compartment (CLorg) and returned to the central blood compartment. MAb flux across the capillary wall is described by the two-pore model (b). The capillary has two types of pores, large and small, through which MAbs can pass by convection or diffusion. Fluid recirculation occurs at the rate Jiso. C = MAb concentration; Q = blood flow; L = lymph flow; J = MAb flux across the capillary wall; subscripts b, i, v, org, S, and L indicate blood, interstitial, vascular, organ, small pore, and large pore, respectively.

concentration and the urinary excretion rate. Organ volumes, including volumes of the vascular and interstitial spaces [20], and blood flow rates [26] for mice were obtained from the literature and are listed in Table 1. The value for the maximum antigen

Table 1 Model parameters obtained or calculated from the literature Vascular Interstitial Total Partition Organ/ Blood volume coefficient tissue flow rate volume volume V (ml) b R c Q (ml/h) a Vv (ml) b Vi (ml) b Blood 480 Lung 480 Heart 16.8 Kidney 48 Liver 66 Spleen 3 Tumor 6 Carcass 340.2 a b c

1.407 0.019 0.007 0.030 0.100 0.010 0.021 1.675

0.000 0.057 0.019 0.101 0.250 0.020 0.114 3.565

From Davies and Morris [26]. From Baxter et al. [20]. Calculated as described in Methods.

1.407 0.191 0.133 0.298 0.951 0.100 0.300 16.75

1.000 0.298 0.143 0.339 0.263 0.200 0.380 0.213

concentration was also obtained from the literature [27]. For the present simulations, it was assumed that the antigen was not found in the blood or in any other tissues except the tumor. Transcapillary fluid filtration rates (Jiso), lymph flow rates (L), rates of catabolic degradation (kcat), and rates of clearance of catabolic products (CL) for all organs, in addition to the urinary excretion rate constant (U), were estimated by curve fitting (described below). The parameters for FcRn-mediated IgG recycling viz. kint and krec were fitted to the liver data and the values thus obtained were used for both the liver and the residual carcass compartment. Parameters estimated by curve fitting are listed in Table 2. Antibody-dependent parameters are listed in Table 3 and were obtained as follows. The permeability-surface area product (PS) was obtained by scaling the value for albumin by the diffusion coefficient in normal tissue [18]. The PS product was assumed to be ten-fold higher in the liver and spleen due to their known higher vascular permeabilities [28]. PS values for the large and small pores in the tumor compartment were treated as adjustable parameters since human tumor xenografts have been reported to exhibit varied vascular permeabilities [29]. The osmotic reflection coefficients (σ for large and small pores) were calculated from the antibody size and pore size using the methods described by Taylor and Granger [30]. The binding affinities for IgG were taken to be zero in all organs except the tumor, where forward and reverse binding rates determined in vitro were used as baseline values [6]. In the absence

PBPK model for MAb CC49 and scFv constructs Table 2

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Model parameters estimated by curve fitting

Organ/tissue

Lymph flow rate L (ml/h)

Fluid recirculation rate Jiso (ml/h)

Rate constant for catabolism kcat (h− 1)

Catabolite clearance rate CL (ml/h)

Rate constant for excretion of catabolites U (h− 1)

Lung Heart Kidney Liver Spleen Tumor Carcass

1.1 × 10− 1 2.0 × 10− 1 7.6 × 10− 1 1.5 × 10− 1 5.8 × 10− 2 2.7 × 10− 4 5.4 × 10− 1

1.4 × 10− 1 3.0 × 10− 1 2.3 × 10− 1 7.1 × 10− 1 4.7 × 10− 1 4.7 × 10− 2 7.5 × 10− 1

3.4 × 10− 2 2.6 × 10− 2 1.0 × 10− 3 8.2 × 10− 9 9.4 × 10− 4 5.3 × 10− 4 4.4 × 10− 6

2.5 × 10− 2 1.1 × 10− 2 – 4.7 × 10− 2 7.8 × 10− 3 7.4 × 10− 4 4.0 × 10− 3

– – 2.36 × 10− 1 – – – –

Rate constants for FcRn-mediated IgG recycling a kint (h− 1) 9.26 × 10− 6 a

krec (h− 1) 0.26

Estimated by fitting the liver data; the values obtained were used for both the liver and the carcass compartment.

of experimental data, the partition coefficient (R) for each tissue was calculated using the following tissue composition-based equation obtained from the literature [31]: Rorg ¼

Vfi;org fuB  Vfi;B fuorg

ð3Þ

where Vfi is the fractional volume of the interstitial space and fu is the unbound fraction in the organ (org) and blood (B), respectively. Since it is assumed that no non-specific binding of the MAb occurs, fuB fuorg ¼ 1, and the equation is reduced to: Rorg ¼ Vfi;org



Parameter values that were not available experimentally or in the literature were estimated by first fitting the blood concentration– time data for IgG to a bi-exponential function (Eq. (3)) using WinNonlin® (version 3.2, Pharsight Corporation, Mountain View, CA). CðtÞ ¼ A1 e−k1 t þ A2 e−k2 t

ð4Þ

where λ1 and λ2 are the rate constants, and A1 and A2 are the intercepts for each exponential segment of the blood concentration– time curve. This equation, describing the blood concentration–time profile, served as a forcing function [20]. It was held constant in the PBPK model and used as the input function to fit the MAb concentra-

a

Relative sensitivity coefficient ¼

dC=dP C=P

ð5Þ

i.e., the percentage change in the MAb concentration (C) divided by the percentage change in the parameter value (P).

2.8. Application of the PBPK model to predict the disposition of CC49 scFvs in mice Once satisfactory fits of the PBPK model to the CC49 IgG biodistribution data were established, the physiological parameters, either obtained from the literature or estimated by curve fitting,

Antibody-dependent parameters for IgG and scFv constructs of CC49

MAb species

IgG [sc(Fv)2]2 sc(Fv)2

2.7. Sensitivity analyses To determine the effect of the unknown parameters on the model solution, sensitivity analysis was performed for the parameters in the tumor tissue. The value of each parameter was increased by 0.1%, the model simulations were repeated, and the new tumor MAb concentrations noted. The relative sensitivity coefficients for significant parameters were calculated using the following equation:

 sinceVfi;B ¼ 1 :

2.6. Parameter estimation by curve fitting

Table 3

tions for each organ or tissue individually to obtain values for the unknown organ-specific parameters. Subsequently, new MAb blood concentrations were calculated from the model and the simulations for each organ were repeated using the model generated values of blood concentrations instead of the bi-exponential fit. The unknown parameters were varied to obtain the minimal weighted least squares fit of the model to the blood concentration–time data (Table 2).

Size (kDa)

150 120 60

Tumor antigen concentration a

Osmotic reflection coefficients b

Specific binding rate constants c

Bmax (M)

σL

kfag (M− 1h− 1)

−7

5.62 × 10 2.81 × 10− 7 5.62 × 10− 7

0.10 0.09 0.07

σS 0.74 0.67 0.58

8

7.92 × 10 3.26 × 108 1.02 × 105

Permeability-surface area products d (ml/h/g)

krag (h− 1)

PSL

PSS

7.45 3.21 3.21

1.596 × 10− 4 4.79 × 10− 4 1.45 × 10− 3

4.68 × 10− 4 1.40 × 10− 3 1.80 × 10− 2

From Chung et al. [27]. Calculated using the methods described by Taylor and Granger [30]. c From Goel et al. [6]. d Based on albumin data [18], scaled by diffusion coefficient in normal tissue. Values for liver and spleen were assumed to be ten-fold higher than in other organs, and values for tumor were obtained by curve fitting. b

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Table 4

Parameters used for human model simulation

Vascular Interstitial Total Organ/tissue Blood volume flow rate volume volume V (ml) a Q (ml/h) a Vv (ml) b Vi (ml) b Blood Lung Heart Kidney Liver Spleen Tumor Carcass a b c

33.6 × 104 33.6 × 104 14.4 × 103 74.4 × 103 87.0 × 103 46.2 × 102 0.61 × 102 15.6 × 104

5200.0 66.5 24.5 105.0 350.0 35.0 1.4 5862.0

– 199.5 66.5 353.5 875.0 70.0 10.0 12477.5

5200.0 999.0 300.0 284.0 1809.0 173.4 20.0 61215.0

Lymph Fluid recirculation Permeability-surface area product flow rate rate PSS (ml/h/g) c PSL (ml/h/g) c L (ml/h/g) b Jiso (ml/h/g) b – 5.5 × 10− 3 1.0 × 10− 2 3.8 × 10− 2 7.5 × 10− 3 2.9 × 10− 3 1.35 × 10− 5 2.7 × 10− 2

– 1.4 × 10− 1 3.0 × 10− 1 2.3 × 10− 1 7.1 × 10− 1 4.7 × 10− 1 4.7 × 10− 2 7.5 × 10− 1

– 2.075 × 10− 5 2.075 × 10− 5 2.075 × 10− 5 2.075 × 10− 4 2.075 × 10− 4 1.634 × 10− 4 2.075 × 10− 5

– 6.084 × 10− 5 6.084 × 10− 5 6.084 × 10− 5 6.084 × 10− 4 6.084 × 10− 4 5.954 × 10− 4 6.084 × 10− 5

From Davies and Morris [26]. Scaled up from murine values proportional to body weight [32]. Scaled up from murine values proportional to (body weight)3/4 [32].

were held constant and the model was further employed to predict the disposition characteristics of the divalent and tetravalent scFv constructs of CC49. The osmotic reflection coefficients (σ) and permeability-surface area product (PS) values, which are dependent on the size of the molecule, were calculated for each of the two constructs [18,30]. As in the case of the IgG model, the specific forward and reverse binding rates (kfag and krag , respectively) for sc(Fv)2 and [sc(Fv)2]2 obtained in vitro were used as baseline values [6]. The antibody-dependent parameters calculated for the two fragments are listed in Table 3. The value for the maximum tumor antigen concentration (Bmax) for [sc(Fv)2]2 was half that used for sc(Fv)2 due to the double valency of the tetramer. The rate constants for catabolic degradation (kcat) and clearance of catabolites from each organ (CL), in addition to the urinary excretion rates (U), were estimated by curve fitting the experimental biodistribution data for the scFv constructs [6]. In addition, for the scFv simulations, the rate constant for recycling of FcRn-bound MAb (krec) to the central blood compartment was set to zero since the

constructs lack the constant domain (Fc region) and therefore do not bind to the FcRn receptor.

2.9. Application of the PBPK model to predict the disposition of CC49 IgG in humans Since the PBPK model uses physiological parameters including organ volumes, blood flow rates, and vascular permeabilities, it allows the use of scale-up techniques to predict antibody distribution in humans. For human simulations, plasma flow rates and organ volumes were obtained from the literature for a standard 70 kg man [26] with a 20 g solid tumor. Vascular (Vv) and interstitial (Vi) volumes for each organ, along with lymph flow rates (L) and fluid recirculation rates (Jiso) were scaled to human body weight from murine values (Table 4). Permeability-surface area products (PS), rate constants for catabolism (kcat) and clearance of catabolites from each organ (CL), and the urine excretion rate (U) were scaled according to (body weight)3/4 [32]. As in the case of the scFvs, the FcRn binding affinity was set to zero during

Figure 3 Model simulations and experimental data for distribution of 131I-CC49 IgG in blood, tumor, and various organs of athymic mice. The solid line in each panel represents the concentration–time profile of the antibody predicted by the PBPK model while the closed circles represent actual biodistribution data (mean ± SD of 6 mice). Concentration of the MAb is expressed as percent injected dose per gram of tissue.

PBPK model for MAb CC49 and scFv constructs Table 5

Sensitivity analyses for CC49 IgG in tumor tissue of mice

Parameter Maximum sensitivity Time (h) a

407

Q

L

0.018 0

−0.118⁎ 48

Jiso

V

0.276 35.5

− 0.994⁎ 0

σL 0.005 0

σS 0.761 7.5

R 0.576 48

PSL

PSS

0 48

−0.458 48

a

Bmax

Kd

0 48

0.007 6

Negative values indicate that MAb concentration decreases when the parameter value increases.

scale-up since CC49 is a murine MAb and does not bind to human FcRn [33]. Antibody-dependent parameters such as binding rate constants (kfag , krag ) and reflection coefficients (σ) were assumed to be the same for mice and humans. The MAb blood concentration–time profile was simulated and pharmacokinetic parameters were compared with those obtained from a clinical study of i.v. administered 131I-labeled CC49 in 16 patients with colorectal cancer [17].

2.10. Model simulation Mass balance equations used in the model are presented in the Appendix. Simulation of the resulting PBPK model was performed using the commercial software package Berkeley Madonna® applying Rosenbrock's method for stiff equations [34].

2.11. Pharmacokinetic analyses Experimentally observed and model predicted blood concentration– time curves were evaluated by compartmental analysis using WinNonlin®. The pharmacokinetic parameters were calculated from standard equations. The area under the blood concentration– time curve (AUC) was calculated using the trapezoidal rule.

3. Results 3.1. Comparison of model simulations with experimental 131 I-CC49 IgG data It is clear from Fig. 3 that the PBPK model used in this study adequately describes the 131I-CC49 IgG blood and tissue concentra-

tion–time curves in mice. This lends credence to the validity of the proposed mathematical model, and suggests that the model includes all the significant processes involved in determining the disposition characteristics of IgG. To provide satisfactory fits for 131I-CC49 IgG tissue concentrations, it was only necessary to optimize the transcapillary fluid recirculation rate (Jiso) and lymph flow rate (L) in each organ. The values of these parameters, along with those of other unknown parameters obtained by curve fitting, are listed in Table 2. In addition, PS values were optimized for the tumor due to the known variability in vascular permeabilities of human xenografts [29]. As expected, a higher uptake was seen in the tumor as compared to the normal organs as a result of specific binding of the MAb to the tumor-associated antigen. Thus, the resulting simulated concentrations for 131I-CC49 IgG in tumor at 24 and 48 h were 32.2 and 34.9%ID/g, respectively (Fig. 3) whereas actual experimental values were 28.4 ± 1.7 and 34.3 ± 2.4%ID/g, respectively [6].

3.2. Sensitivity analyses The maximum values of the sensitivity coefficients for the various parameters, and the corresponding times, obtained by sensitivity analysis for tumor tissue in mice are given in Table 5. Negative values indicate a decrease in antibody concentration with an increase in the parameter value. Values of zero or near zero indicate that the model is insensitive to the parameter. The results show that the model was sensitive to changes in tumor volume, fluid recirculation rate, lymph flow rate, small pore vascular permeability, and partition coefficient. However, small

Figure 4 Model simulations and experimental data for distribution of 125I-CC49 [sc(Fv)2]2 in blood, tumor, and various organs of athymic mice. The solid line in each panel represents the concentration–time profile of the tetravalent scFv construct predicted by the PBPK model while the closed circles represent actual biodistribution data (mean ± SD of 6 mice). Concentration of the scFv is expressed as percent injected dose per gram of tissue.

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Figure 5 Model simulations and experimental data for distribution of 125I-CC49 sc(Fv)2 in blood, tumor, and various organs of athymic mice. The solid line in each panel represents the concentration–time profile of the divalent scFv construct predicted by the PBPK model while the closed circles represent actual biodistribution data (mean ± SD of 6 mice). Concentration of the scFv is expressed as percent injected dose per gram of tissue.

changes (0.1% of initial value) in blood flow rate, tumor antigen concentration, and antibody–antigen affinity had a minimal effect on the tumor MAb concentration.

3.3. Application of the model to predict the disposition of CC49 scFvs in mice The predictive applicability of the model was tested by simulating the biodistribution of tetravalent ([sc(Fv)2]2) and divalent (sc(Fv)2) constructs of CC49 in mice. Physiological parameters in the model were maintained constant while values dependent on the size of the antibody fragment were altered. The model simulations obtained for the [sc(Fv)2]2 and sc(Fv)2 constructs are shown as solid lines in Figs. 4 and 5, respectively. In both cases, the model predicted the pharmacokinetics in blood and biodistribution in the remaining 6 organs and tissues (experimental data represented by closed circles) reasonably well. Consistent with experimental data and also with the sizedependence of elimination, the model predicted a shorter elimination half-life (3.60 h) for sc(Fv)2 compared with [sc(Fv)2]2 (4.64 h). Further, consistent with the experimental data, the model predicted a higher maximum tumor uptake (16.8% ID/g) for the tetravalent scFv compared with the divalent scFv (8.9%ID/g).

Table 6

Table 6 shows a comparison of the pharmacokinetic parameters obtained for the experimentally observed and model predicted IgG and scFv blood concentration–time curves. The pharmacokinetic parameters calculated for the model simulated data were in good agreement with those obtained for the experimental data, indicating that the blood concentration–time data were well-captured by the PBPK model. The tumor-to-blood AUC ratios obtained for IgG, divalent and tetravalent scFvs were 0.72, 4.13 and 5.28, respectively.

3.5. Application of the model to predict pharmacokinetics of CC49 IgG in humans The mouse PBPK model was used to predict the pharmacokinetics of 131I-CC49 in humans. The CC49 disposition parameters for mice were scaled to those of humans using recognized empirical relationships. The values of these scaled pharmacokinetic parameters obtained from simulated data were in reasonable agreement with those reported in a clinical study of intravenously administered 131I-CC49 in colorectal cancer patients (Table 7). The PBPK model predicted an elimination half-life of 57.5 h for 131I-CC49 in humans that

Comparison of blood pharmacokinetics (experimental data vs. model simulation) for IgG and scFv constructs

MAb species

IgG [sc(Fv)2]2 sc(Fv)2

3.4. Pharmacokinetic analyses

T1/2 (h)

AUC (%ID/g⁎h)

CL (g/h)

Tumor AUC (%ID/g⁎h)

Observed

Predicted

Observed

Predicted

Observed

Predicted

Observed

Predicted

1272.2 105.3 61.8

1682.3 113.4 71.3

72.2 5.08 3.70

69.4 4.64 3.60

0.057 0.95 1.62

0.067 0.88 1.48

1192.6 596.8 289.9

1212.1 598.5 294.5

PBPK model for MAb CC49 and scFv constructs Table 7

Comparison of 131I-CC49 pharmacokinetics and tumor uptake in humans from clinical data and model simulation Elimination half-life (h)

Clinical data PBPK model a

409

a

44.9 ± 10.6 52.5

Volume of distribution (L/kg) Central compartment

Steady state

0.053 ± 0.008 0.075

0.073 ± 0.009 0.117

Systemic clearance (ml/min)

Tumor uptake (%ID/g)

1.7 ± 0.6 2.2

0.00023–0.0024 0.0012

From Gallinger et al. [17].

compared well with the value (44.9 ± 10.6 h) obtained in patients. In addition, the model predicted a low value for the steady-state volume of distribution (0.197 L/kg) and low clearance (2.7 ml/min) reflecting the slow extravasation and limited renal filtration of the macromolecule.

4. Discussion In this study, a PBPK model was developed to describe the distribution of MAb CC49 IgG in blood and various normal and neoplastic tissues of athymic mice. Experimental data on the IgG concentrations in tumor and various normal tissues and organs following i.v. injection were analyzed using the 131I-CC49 blood concentration–time data as a forcing function to obtain quantitative estimates for various organ-specific model parameters. This approach follows the extensive PBPK analyses of specific and non-specific MAb disposition by Jain and coworkers [20,32,35]. While the twopore theory of macromolecule extravasation used by Baxter et al. [20] in their PBPK model forms the central basis of the present model, there are several key differences between the two models. In contrast to previously reported PBPK models for MAbs [20,36], the present model incorporates the effect of binding to the protective FcRn receptor on IgG disposition [22]. Further, the present model also includes terms to describe the catabolic clearance of IgG in the tissues, return of the catabolite(s) to blood, and their subsequent elimination from the body by the kidneys. Thus, the present model describes the disposition of both intact IgG and its catabolite(s). The results indicate excellent qualitative agreement between the simulated and experimental data. The initial concentrations of the IgG in the liver and spleen were found to be higher than in the other organs, consistent with their known higher vascular permeabilities [28] and also with their function as part of the mononuclear phagocytic system. Ten-fold higher values for PS were used in the model simulations for these organs. The binding affinity of CC49 IgG obtained by best fit of the model to the tumor data was 13.5 × 109 M− 1, which compares favorably with the literature value of 16.2 × 109 M− 1 [38,39]. An underlying assumption in the development of this model was that the concentration of IgG is uniform throughout the tumor tissue. This might not be true for large bulky tumors where the elevated interstitial pressure at the tumor center is known to contribute to heterogeneous distribution of macromolecules through the tumor mass [40]. However, since the tumors in the present study were small (200–300 mm3) in volume, it is reasonable to assume that these pressure distributions were fairly uniform [41]. Like other substances, MAbs may be eliminated by excretion or via catabolism. However, owing to the large molecular size, little intact IgG is filtered by the kidney, and

the vast majority of IgG is eliminated by catabolism [25]. Therefore, in contrast to the model proposed by Baxter et al. [20] that utilizes urinary excretion of intact IgG as the sole route of MAb elimination, the present model incorporates terms to describe the catabolic clearance of IgG from all the tissues, return of the catabolic products to the central blood pool, and subsequent excretion of these catabolites through the kidneys. Sensitivity analysis for the IgG indicated that the isogravimetric fluid recirculation rate (Jiso) was an important determinant of antibody accumulation in the tumor. The tumor accumulation of IgG was found to be inversely related to lymph flow rate, i.e. tumor MAb concentration increased with a decrease in the rate of lymph flow. This is consistent with the well-known enhanced permeability and retention (EPR) effect whereby impaired lymphatic drainage from the tumor leads to an increased retention of macromolecules within the tumor [42]. Antibody uptake in the tumor was also inversely related to the small pore permeability-surface area product. This was especially apparent at later time points. Since diffusion is the chief transport process that occurs through the small pores [20], lower permeability would prevent diffusion of the IgG molecules from the interstitial space back into the vascular space, thus resulting in prolonged retention of the MAb within the tumor. However, the smaller molecular size of the scFv constructs allows for diffusion back into the circulation through the small pores, resulting in higher initial uptake but subsequently poor localization at later time points compared to IgG (Figs. 4 and 5). Importantly, the tumor MAb concentration was not sensitive to small changes in tumor antigen concentration or in antigen–antibody binding affinity. This suggests that the rate of transcapillary transport rather than binding kinetics was the critical determinant of the extent of antibody penetration and the accumulation in the tumor for this high affinity binding IgG. However, the effect of the binding affinity on tumor concentrations could be quite significant in systems that are not transport-limited [20]. The model was applied to predict the pharmacokinetics and biodistribution of divalent (∼ 60 kDa) and tetravalent (∼ 120 kDa) scFv constructs of CC49 by modifying only the antibody-dependent parameters. In both cases, the model predicted concentration–time profiles for all the organs were in good agreement with those observed experimentally. Consistent with the experimental data and sizedependence of elimination, the model predicted a faster elimination half-life for sc(Fv)2 than for [sc(Fv)2]2. Further, the absence of binding of the fragments to the protective receptor FcRn also contributed to their faster elimination from the blood as compared to the IgG. In addition, the scFv constructs demonstrated higher tumor-to-blood AUC ratios, indicating improved tumor radiolocalization

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compared with IgG. In this regard, the tetramer demonstrated the best tumor targeting properties amongst the three molecular species with a tumor-to-blood AUC ratio of 5.28 compared with 4.13 and 0.72 for the dimer and IgG, respectively. The clinical utility of the model was tested with data obtained from a clinical study of 131I-CC49 administered intravenously to 16 patients with colorectal cancer [17]. The model was able to predict the pharmacokinetics of the antibody in humans with reasonable accuracy (Table 7). The differences between the pharmacokinetic parameter values obtained from the simulated antibody blood concentrations and the clinical trial were within acceptable limits of patient variability and structural limitations of the model. The maximum tumor uptake of 131I-CC49 predicted by the model was 0.0012%ID/g which is in very good agreement with the range of 0.00023–0.0024%ID/g observed in patients [17]. The model in its present form does not take into account the effect of antigen shed into the systemic circulation on the disposition of the MAb. Experimental data on antigen distribution within the tumor and the kinetics of antigen shedding are not currently available. The accuracy of the model could be improved by incorporating these factors when relevant data are available. Furthermore, tumor physiology is known to be highly variable. The use of microscopic models to describe the spatial heterogeneity in the distribution of the antibody within the tumor could also be useful. Since the model describes the distribution of the MAb in various normal organs and tissues, it could provide useful information regarding the potential uptake of the antibody in tumors located in different tissues in the body. In addition, the model may also be used to study the biodistribution of different combinations of radionuclides and antibody fragments in an effort to establish the most effective approach to achieve the optimal therapeutic ratio for cancer treatment. Finally, the PBPK model could potentially be applied to predict the pharmacokinetics and tumor uptake of MAbs and MAb constructs in humans based on preclinical observations.

Acknowledgements The study reported in this manuscript was supported, in part, by a grant from the National Institutes of Health (P50 CA72712) and the U.S. Department of Energy (DE-FG02-95ER62024) and a fellowship from the UNMC Graduate Program.

Appendix 1. Mass balance equations For blood: For IgG VB

dCB ¼ ðQ LU  LLU ÞCv;LU þ LLU Ci;LU þ LLI Ci;LI þ LSP Ci;SP dt þ LK Ci;K þ LT Ci;T þ LH Ci;H þ LRB Ci;RB  ðQ LI þ LSP þ QK þ Q T þ Q H þ Q RB ÞCB For catabolite pool in blood

VB

dCm;B ¼ CLT Cm;T þ CLLI Cm;LI þ CLSP Cm;SP þ CLH Cm;H dt þ CLRB Cm;RB þ CLLU Cm;LU  Q K CM;K MAb concentration in blood is given by:

CTOT;B ¼ CB þ Cm;B For lung: For vascular space Vv;LU

5. Conclusions

dCv;LU ¼ ðQ LI  LLI ÞCv;LI þ ðQ K  LK ÞCv;K þ ðQ T  LT ÞCv;T dt þ ðQ H  LH ÞCv;H þ ðQ RB  LRB ÞCv;RB  ðQ LU  LLU ÞCv;LU  kcat;LU Cv;LU Vv;LU  JL;LU ð1
 rL ÞCv;LU  Ci;LU PeL;LU  PSL;LU Cv;LU  RLU ePes;LU  1  JS;LU ð1
 rS ÞCv;LU  Ci;LU PeS;LU  PSS;LU Cv;LU  RLU ePes;LU  1

For interstitial space 131

The biodistribution of intravenously administered I-CC49 IgG in mice was mathematically described using a PBPK model. The model captured the experimental concentration–time curves for blood and various tissues and organs reasonably well. The model also provided helpful insights into the factors affecting MAb uptake and accumulation in the tumor. The rate of transcapillary transport was found to be the key determinant of the rate and extent of tumor CC49 MAb accretion. The applicability of the PBPK model developed for CC49 IgG was tested by predicting the pharmacokinetics and biodistribution of 125I-labeled divalent and tetravalent scFv constructs of CC49 in mice. The model gave reasonably good predictions of the pharmacokinetics and tumor uptake of the fragments. The tetravalent fragment was found to possess better tumor targeting properties than the divalent fragment. The PBPK model also allows for the scale-up of antibody biodistribution from mouse to man.

Vi;LU

dCi;LU ¼ JL;LU ð1  rL ÞCv;LU dt
þ PSL;LU Cv;LU 

 Ci;LU PeL;LU RLU ePes;LU  1

þ JS;LU ð1
 rS ÞCv;LU  Ci;LU PeS;LU  LLU Ci;LU þ PSS;LU Cv;LU  RLU ePes;LU  1 For catabolites Vv;LU

dCm;LU ¼ kcat;LU Cv;LU Vv;LU  CLLU Cm;LU dt

MAb concentration in the lung is given by: 

CTOT;LU

 Cv;LU þ Cm;LU Vv;LU þ Ci;LU Vi;LU ¼ VLU

PBPK model for MAb CC49 and scFv constructs For liver: For vascular space

For tumor: For vascular space

dCv;LI ¼ ðQ SP  LSP ÞCv;SP þ ðQ LI  QSP þ LSP ÞCB dt þ kree Cend;LI Vv;LI  kint Cv;Li V
v;LI  ðQ LI   LLI ÞCv;LI Ci;LI PeL;LI  JL;LI ð1  rL ÞCv;LI  PSL;LI Cv;LI − Pes;LI  1 R e LI
 Ci;LI PeS;LI  JS;LI ð1  rS ÞCv;LI  PSS;LI Cv;LI  RLI ePes;LI  1

Vv;LI

For interstitial space


Vi;Li



dCi;LI Ci;LI PeL;LI ¼ JL;LI ð1  rL ÞCv;LI þ PSL;LI Cv;LI  Pes;LI  1 dt R e LI
 Ci;LI PeS;LI þ JS;LI ð1  rS ÞCv;LI þ PSS;LI Cv;LI  RLI ePes;LI  1  LLI Ci;LI

For endosomal space Vv;LI

411

dCend;LI ¼ kint Cv;LI Vv;LI  krec Cend;LI Vv;LI  kcat;LI Cend;LI Vv;LI dt

Vv;T

For free antibody concentration in the interstitial space ! f dCi;T Cfi;T PeL;T ¼ JL;T ð1  rL ÞCv;T þ PSL;T Cv;T  Vi;T Pe dt RT e s;T  1 ! Cfi;T PeS;T þ JS;T ð1  rS ÞCv;T þ PSS;T Cv;T − RT ePes;T  1    kfag Cfi;T Bmax  Cbi;ag Vi;T þ krag Cbi;ag Vi;T  LT Cfi;T For bound antibody concentration in the interstitial space Vi;T

For catabolites Vv;LI

dCm;LI ¼ kcat;LI Cv;LI Vv;LI  CLLI Cm;LI dt

MAb concentration in the liver is given by:   Cv;LI þ Cend;LI þ Cm;LI Vv;LI þ Ci;LI Vi;LI CTOT;LI ¼ VLI For spleen: For vascular space Vv;SP

dCv;SP ¼ QSP CB  ðQSP  LSP ÞCv;SP  kcat;SP Cv;SP Vv;SP dt  JL;SP ð1
 rL ÞCv;SP  Ci;SP PeL;SP  PSL;SP Cv;SP  RSP ePes;SP  1  JS;SP ð1
 rS ÞCv;SP  Ci;SP PeS;SP  PSS;SP Cv;SP  RSP ePes;SP  1

dCi;SP ¼ JL;SP ð1  rL ÞCv;SP dt
þ PSL;SP Cv;SP 

Vv;T

 Ci;SP PeL;SP RSP ePes;SP  1

dCm;T ¼ kcat;ag Ci;T Vi;T  CLT Cm;T dt

For kidney: For vascular space Vv;K

dCv;K ¼ QK CB  ðQK  LK ÞCv;K  kcat;K Cv;K Vv;K dt
 Ci;K PeL;K  JL;K ð1  rL ÞCv;K  PSL;K Cv;K  Pes;K  1 R e K
Ci;K PeS;K  JS;K ð1  rS ÞCv;K  PSS;K Cv;K  RK ePes;K  1

Vi;K


 dCi;K Ci;K PeL;K ¼ JL;K ð1  rL ÞCv;K þ PSL;K Cv;K  Pe dt RK e s;K  1
Ci;K PeS;K þ JS;K ð1  rS ÞCv;K þ PSS;K Cv;K  RK ePes;K  1  LK Ci;K

For catabolites

dCm;SP ¼ kcat;SP Cv;SP Vv;SP  CLSP Cm;SP dt

MAb concentration in the spleen is given by: CTOT;SP ¼

 kcat;ag Cbi;ag Vi;T

For interstitial space

For catabolites



dt

  ¼ kfag Cfi;T Bmax  Cbi;ag Vi;T  krag Cbi;ag Vi;T

MAb concentration in the tumor is given by:   Cv;T Vv;T þ Cfi;T þ Cbi;ag þ Cm;T Vi;T CTOT;T ¼ VT

þ JS;SP ð1
 rS ÞCv;SP  Ci;SP PeS;SP  LSP Ci;SP þ PSS;SP Cv;SP  RSP ePes;SP  1

Vv;SP

dCbi;ag

For catabolites

For interstitial space Vi;SP

dCv;T ¼ QT CB  ðQT  LT ÞCv;T  JL;T ð1  rL ÞCv;T dt ! Cfi;T PeL;T  JS;T ð1  rS ÞCv;T  PSL;T Cv;T  RT ePes;T  1 ! Cfi;T PeS;T  PSS;T Cv;T  RT ePes;T  1



Cv;SP þ Cm;SP Vv;SP þ Ci;SP Vi;SP VSP

Vv;K

dCm;K ¼ kcat;K Cv;K Vv;K þ Qk Cm;B  UCm;K Vv;K dt

MAb concentration in the kidney is given by:   Cv;K þ Cm;K Vv;K þ Ci;K Vi;K CTOT;K ¼ VK

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For heart: For vascular space dCv;H ¼ QH CB  ðQH  LH ÞCv;H  kcat;H Cv;H Vv;H dt
 Ci;H PeL;H  JL;H ð1  rL ÞCv;H  PSL;H Cv;H  Pes;H  1 R e H
 Ci;H PeS;H  JS;H ð1  rS ÞCv;H  PSS;H Cv;H  Pe RH e s;H  1

Vv;H

For interstitial space Vi;H


 dCi;H Ci;H PeL;H ¼ JL;H ð1  rL ÞCv;H þ PSL;H Cv;H  Pes;H  1 dt R e H
 Ci;H PeS;H þ JS;H ð1  rS ÞCv;H þ PSS;H Cv;H  RH ePes;H  1  LH Ci;H

For catabolites Vv;H

dCm;H ¼ kcat;H Cv;H Vv;H  CLH Cm;H dt

MAb concentration in the heart is given by:   Cv;H þ Cm;H Vv;H þ Ci;H Vi;H CTOT;H ¼ VH For carcass: For vascular space Vv;RB

dCv;RB ¼ QRB CB  ðQRB  LRB ÞCv;RB þ krec Cend;RB Vv;RB dt  kint Cv;RB ð1  rL ÞCv;RB
Vv;RB  JL;RB Ci;RB PeL;RB  PSL;RB Cv;RB  RRB ePes;RB  1  JS;RB ð1
 rS ÞCv;RB  Ci;RB PeS;RB  PSS;RB Cv;RB  RRB ePes;RB  1

For interstitial space Vi;RB

dCi;RB ¼ JL;RB ð1  rL ÞCv;RB dt
þ PSL;RB Cv;RB 

 Ci;RB PeL;RB RRB ePes;RB  1

þ JS;RB ð1
 rS ÞCv;RB  Ci;RB PeS;RB  LRB Ci;RB þ PSS;RB Cv;RB  Pe RRB e s;RB  1 For endosomal space Vv;RB

dCend;RB ¼ kint Cv;RB Vv;RB  krec Cend;RB Vv;RB dt  kcat;RB Cend;RB Vv;RB

For catabolites Vv;RB

dCm;RB ¼ kcat;RB Cv;RB Vv;RB  CLRB Cm;RB dt

MAb concentration in the carcass is given by: 

CTOT;RB

 Cv;RB þ Cend;RB þ Cm;RB Vv;RB þ Ci;RB Vi;RB ¼ VRB

Nomenclature (units) Bmax Bound antibody concentration at saturation, equal to the maximum tumor-associated antigen concentration in the tumor tissue (M) Cb Antibody concentration in blood (M) Cv,org Antibody concentration in the vascular space of the tumor (M) Ci,org MAb concentration in the interstitium of each organ (M) Cm,org Concentration of catabolite(s) in each organ (M) CTOT, org Average concentration in each organ (M) CLorg Catabolite clearance rate for each organ (ml/h) Jorg Net flux of MAb across blood vessels (moles/h) Jiso,org Fluid recirculation flow rate for each organ (ml/h) JL,org, JS,org Transcapillary fluid flow rate for each organ through large and small pores, respectively (ml/h) kfag Association rate constant for the binding of antibody to tumor-associated antigen (M− 1h− 1) krag Dissociation rate constant for the binding of antibody to tumor-associated antigen (h− 1) kint Rate constant for IgG internalization in the intracellular compartment (h− 1) kcat Rate constant for lysosomal degradation of intracellular IgG (h− 1) krec Rate constant for recycling of FcRn-bound IgG to plasma (h− 1) Lorg Lymph flow rate of each organ (ml/h) Qorg Blood flow rate to each organ (ml/h) PeL,org, PeS,org Péclet number; ratio of convection to diffusion across large and small pores, respectively (dimensionless) PSL,org, PSS,org Permeability-surface area product for organ for large and small pores, respectively (ml/h) U Urinary excretion rate constant (h− 1) Vi,org Volume of interstitial space of each organ (ml) Vv,org Volume of vascular space of each organ (ml) Vc,org Volume of cellular space of each organ (ml) Vorg Total volume of each organ (ml) αL, αS Fraction of hydraulic conductivity accounted for by large and small pores, respectively (dimensionless) σL, σS Osmotic reflection coefficient for large and small pores, respectively (dimensionless)

Subscripts B Blood H Heart K Kidney LU Lung LI Liver RB Carcass SP Spleen T Tumor TOT Total (or average) L Large pore S Small pore i Interstitial v Vascular end Endosomal

PBPK model for MAb CC49 and scFv constructs

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