Application of PBPK modeling to predict monoclonal antibody disposition in plasma and tissues in mouse models of human colorectal cancer

Abstract

This investigation evaluated the utility of a physiologically based pharmacokinetic (PBPK) model, which incorporates model parameters representing key determinants of monoclonal antibody (mAb) target-mediated disposition, to predict, a priori, mAb disposition in plasma and in tissues, including tumors that express target antigens. Monte Carlo simulation techniques were employed to predict the disposition of two mAbs, 8C2 (as a non-binding control mouse IgG1 mAb) and T84.66 (a high-affinity murine IgG1 anti-carcinoembryonic antigen mAb), in mice bearing no tumors, or bearing colorectal HT29 or LS174T xenografts. Model parameters were obtained or derived from the literature. ¹²⁵I-T84.66 and ¹²⁵I-8C2 were administered to groups of SCID mice, and plasma and tissue concentrations were determined via gamma counting. The PBPK model well-predicted the experimental data. Comparisons of the population predicted versus observed areas under the plasma concentration versus time curve (AUC) for T84.66 were 95.4 ± 67.8 versus 84.0 ± 3.0, 1,859 ± 682 versus 2,370 ± 154, and 5,930 ± 1,375 versus 5,960 ± 317 (nM × day) at 1, 10, and 25 mg/kg in LS174T xenograft-bearing SCID mice; and 215 ± 72 versus 233 ± 30, 3,070 ± 346 versus 3,120 ± 180, and 7,884 ± 714 versus 7,440 ± 626 in HT29 xenograft-bearing mice. Model predicted versus observed 8C2 plasma AUCs were 312.4 ± 30 versus 182 ± 7.6 and 7,619 ± 738 versus 7,840 ± 24.3 (nM × day) at 1 and 25 mg/kg. High correlations were observed between the predicted median plasma concentrations and observed median plasma concentrations (r ² = 0.927, for all combinations of treatment, dose, and tumor model), highlighting the utility of the PBPK model for the a priori prediction of in vivo data.

Appendices

Appendix 1

See Tables 5, 6, 7.

Table 5 Parameter symbols and definitions

Table 6 Organ-specific parameter values

Table 7 PBPK model parameters

Appendix 2

Model equations

• 1. Plasma

  $$ \begin{aligned} V_{p} \frac{{dC_{plasma} }}{dt} = (Q_{lung} - L_{lung} ) \times C_{lung}^{V} - (L_{gut} + L_{spleen} + Q_{liver} + Q_{heart} + Q_{kidney} + Q_{skin} + Q_{muscle} \\ & + Q_{tumor} ) \times C_{plasma} + \left( {\frac{1}{Tau} \times X_{lymph} } \right) \quad \quad \quad \,C_{plasma} (0) = \frac{Dose}{{V_{p} }} \\ \end{aligned} $$

  (1)

• 2. Lung

  • 2.1. Vascular space

    $$ \begin{aligned} V_{lung}^{V} \frac{{dc_{lung}^{V} }}{dt} = (Q_{liver} - L_{liver} ) \times C_{liver}^{V} + (Q_{heart} - L_{heart} ) \times C_{heart}^{V} + (Q_{kidney} - L_{kidney} ) \times C_{kidney}^{V} \\ & + (Q_{skin} - L_{skin} ) \times C_{skin}^{V} + (Q_{muscle} - L_{muscle} ) \times C_{muscle}^{V} + (Q_{tumor} - L_{tumor} ) \\ & \times C_{tumor}^{V} + ( FR \times R1 \times (1 - fu_{lung} ) \times C_{lung}^{E,total} \times V_{lung}^{E} ) - (Q_{lung} - L_{lung} ) \times C_{lung}^{V} \\ & - ( R1 \times C_{lung}^{V} \times V_{lung}^{V} ) - ((1 - \sigma_{lung}^{V} ) \times L_{lung} \times C_{lung}^{V} ) \\ \end{aligned} $$

    (2)

  • 2.2. Endothelial space

    $$ \begin{aligned} V_{lung}^{E} \frac{{dc_{lung}^{E,total} }}{dt} = \left( { R1 \times C_{lung}^{V} \times V_{lung}^{V} } \right) - \left( {fu_{lung} \times CL_{lung} \times C_{lung}^{E,total} } \right) \\ & - \left( {\left( {1 - fu_{lung} } \right) \times R1 \times C_{lung}^{E,total} \times V_{lung}^{E} } \right) + \left( {R1 \times C_{lung}^{IS} \times V_{lung}^{IS} } \right) \\ \end{aligned} $$

    (3)

• 2.3. Interstitial space

  $$ \begin{aligned} V_{lung}^{IS} \frac{{dc_{lung}^{IS,total} }}{dt} = \left( {\left( {1 - \sigma_{lung}^{V} } \right) \times L_{lung} \times C_{lung}^{V} } \right) + \left( {\left( {1 - FR} \right) \times R1 \times \left( {1 - fu_{lung} } \right) \times C_{lung}^{E,total} \times V_{lung}^{E} } \right) \\ & - \left( {\left( {1 - \sigma_{lung}^{L} } \right) \times L_{lung} \times C_{lung}^{IS} } \right) - R1 \times C_{lung}^{IS} \times V_{lung}^{IS} \\ \end{aligned} $$

  (4)

• 3. Liver

  • 3.1. Vascular space

    $$ \begin{aligned} V_{liver}^{V} \frac{{dc_{liver}^{V} }}{dt} = (Q_{gut} - L_{gut} ) \times C_{gut}^{V} + (Q_{spleen} - L_{spleen} ) \times C_{spleen}^{V} + ((Q_{liver} - Q_{gut} - Q_{spleen} + L_{gut} \\ & + L_{spleen} ) \times C_{plasma} ) - (Q_{liver} - L_{liver} ) \times C_{liver}^{V} + (FR \times R1 \times (1 - fu_{liver} ) \times C_{liver}^{E,total} \\ & \times V_{liver}^{E} ) - ( R1 \times C_{liver}^{V} \times V_{liver}^{V} ) - ((1 - \sigma_{liver}^{V} ) \times L_{liver} \times C_{liver}^{V} ) \\ \end{aligned} $$

    (5)

  • 3.2. Endothelial space

    $$ \begin{aligned} V_{lung}^{E} \frac{{dc_{lung}^{E,total} }}{dt} = \left( { R1 \times C_{liver}^{V} \times V_{liver}^{V} } \right) - \left( {fu_{liver} \times CL_{liver} \times C_{liver}^{E,total} } \right) \\ & - \left( {\left( {1 - fu_{liver} } \right) \times R1 \times C_{liver}^{E,total} \times V_{lung}^{E} } \right) + \left( {R1 \times C_{liver}^{IS} \times V_{liver}^{IS} } \right) \\ \end{aligned} $$

    (6)

  • 3.3. Interstitial space

    $$ \begin{aligned} V_{liver}^{IS} \frac{{dc_{liver}^{IS} }}{dt} = \left( {\left( {1 - \sigma_{liver}^{V} } \right) \times L_{liver} \times C_{liver}^{V} } \right) + \left( {\left( {1 - FR} \right) \times R1 \times \left( {1 - fu_{liver} } \right) \times C_{liver}^{E,total} \times V_{liver}^{E} } \right) \\ & - \left( {\left( {1 - \sigma_{liver}^{L} } \right) \times L_{liver} \times C_{liver}^{IS} } \right) - R1 \times C_{liver}^{IS} \times V_{liver}^{IS} \\ \end{aligned} $$

    (7)

• 4. Tumor

  • 4.1. Vascular space

    $$ \begin{aligned} V_{tumor}^{V} \frac{{dc_{tumor}^{V} }}{dt} = Q_{tumor} \times C_{plasma} - (Q_{tumor} - L_{tumor} ) \times C_{tumor}^{V} + (FR \times R1 \times (1 - fu_{tumor} ) \times C_{tumor}^{E,total} \\ & \times V_{tumor}^{E} ) - ( R1 \times C_{tumor}^{V} \times V_{tumor}^{V} ) - ((1 - \sigma_{tumor}^{V} ) \times L_{tumor} \times C_{tumor}^{V} ) \\ \end{aligned} $$

    (8)

  • 4.2. Endothelial space

    $$ \begin{aligned} V_{tumor}^{E} \frac{{dc_{tumor}^{E,total} }}{dt} = \left( { R1 \times C_{tumor}^{V} \times V_{tumor}^{V} } \right) - \left( {fu_{tumor} \times CL_{tumor} \times C_{tumor}^{E,total} } \right) \\ & - \left( {\left( {1 - fu_{tumor} } \right) \times R1 \times C_{tumor}^{E,total} \times V_{tumor}^{E} } \right) + \left( {R1 \times fu_{tumor}^{IS,cell} \times C_{tumor}^{IS} \times V_{tumor}^{IS} } \right) \\ \end{aligned} $$

    (9)

  • 4.3. Interstitial space

    $$ \begin{aligned} V_{{tumor}}^{{IS}} \frac{{dc_{{tumor}}^{{IS}} }}{{dt}} & = \left( {(1 - \sigma _{{tumor}}^{V} ) \times L_{{tumor}} \times C_{{tumor}}^{V} } \right) + \left( {(1 - FR) \times R1 \times (1 - fu_{{tumor}} ) \times C_{{tumor}}^{{E,total}} \times V_{{tumor}}^{E} } \right) \\ & - \left( {(1 - \sigma _{{tumor}}^{L} ) \times L_{{tumor}} \times fu_{{tumor}}^{{IS,cell}} \times C_{{tumor}}^{{IS}} } \right) - R1 \times fu_{{tumor}}^{{IS,cell}} \times C_{{tumor}}^{{IS}} \times V_{{tumor}}^{{IS}} - (1 - fu_{{tumor}}^{{IS,cell}} ) \times C_{{tumor}}^{{IS}} \\ & \times k_{int} \times V_{{tumor}}^{{IS}} \\ \end{aligned} $$

    (10)

  Please note: The model assumes an instantaneous binding equilibrium between unbound mAb and mAb in complex with tumor antigens. Binding to the target receptor influences the rate of mass loss from the interstitial space via convection (through influence on $fu_{tumor}^{IS,cell}$) and via target-mediated clearance (via influence on $(1 - fu_{tumor}^{IS,cell} )$).

• 5. Other organs (i)

  • 5.1. Vascular space

    $$ \begin{aligned} V_{i}^{V} \frac{{dc_{i}^{V} }}{dt} = Q_{i} \times C_{plasma} - (Q_{i} - L_{i} ) \times C_{i}^{V} + ( FR \times R1 \times (1 - fu_{i} ) \times C_{i}^{E,total} \times V_{i}^{E} ) - ( R1 \times C_{i}^{V} \times V_{i}^{V} ) \\ & - ((1 - \sigma_{i}^{V} ) \times L_{i} \times C_{i}^{V} ) \\ \end{aligned} $$

    (11)

  • 5.2 Endothelial space

    $$ \begin{aligned} V_{i}^{E} \frac{{dc_{i}^{E,total} }}{dt} = \left( { R1 \times C_{i}^{V} \times V_{i}^{V} } \right) - \left( {fu_{i} \times CL_{i} \times C_{i}^{E,total} } \right) - \left( {\left( {1 - fu_{i} } \right) \times R1 \times C_{i}^{E,total} \times V_{i}^{E} } \right) \\ & + \left( {R1 \times C_{i}^{IS} \times V_{i}^{IS} } \right) \\ \end{aligned} $$

    (12)

  • 5.3. Interstitial space

    $$ \begin{aligned} V_{i}^{IS} \frac{{dc_{i}^{IS} }}{dt} = \left( {\left( {1 - \sigma_{i}^{V} } \right) \times L_{i} \times C_{i}^{V} } \right) + \left( {\left( {1 - FR} \right) \times R1 \times \left( {1 - fu_{i} } \right) \times C_{i}^{E,total} \times V_{i}^{E} } \right) \\ & - \left( {\left( {1 - \sigma_{i}^{L} } \right) \times L_{i} \times C_{i}^{IS} } \right) - R1 \times C_{i}^{IS} \times V_{i}^{IS} \\ \end{aligned} $$

    (13)

• 6. Lymph node

  $$ \frac{{dX_{lymph} }}{dt} = \left( {\mathop \sum \nolimits (1 - \sigma_{i}^{l} ) \times L_{i} \times C_{i}^{IS} )} \right) + \left( {1 - \sigma_{tumor}^{l} } \right) \times L_{tumor} \times fu_{tumor}^{IS,cell} \times C_{tumor}^{IS} - \frac{1}{Tau} \times X_{lymph} $$

  (14)

• 7. For each organ, the $fu_{i}$ to organ FcRn in the endosomal space was described as follow:

  $$ fu_{i} = 1 - \frac{1}{{2 \times C_{i}^{E,total} }} \times \left[ {\left( {K_{d}^{FcRn} + nPt_{i} + C_{i}^{E,total} } \right) - \sqrt {\left( {K_{d}^{FcRn} + nPt_{i} + C_{i}^{E,total} } \right)^{2} - \left( {4 \times nPt_{i} \times C_{i}^{E,total} } \right)} } \right] $$

  (15)
  $$ C_{i}^{E,total} = C_{i}^{E,endogenous} + C_{i}^{E,exogenous} $$

  (16)

  For tumor compartment, the $fu_{tumor}^{IS,cell}$ to tumor antigens in the interstitial space was described as follow:

  $$ \begin{aligned} fu_{{tumor}}^{{IS,cell}} = & 1 - \frac{1}{{2 \times C_{{tumor}}^{{IS,total}} }} \\ \times & \left[ {\left( {K_{{d_{{tumor}} }}^{{CEA}} + FA \times nPt_{{tumor}}^{{CEA}} + C_{{tumor}}^{{IS}} } \right)} \right] \\ - & \sqrt {\left( {K_{{d_{{tumor}} }}^{{CEA}} + FA \times nPt_{{tumor}}^{{CEA}} + C_{{tumor}}^{{IS,total}} } \right)^{2} - \left( {4 \times FA \times nPt_{{tumor}}^{{CEA}} + C_{{tumor}}^{{IS,total}} } \right)} \\ \end{aligned} $$

  (17)

• 8. Total antibody concentration was calculated as follow

  $$ C_{i}^{total} = \frac{{C_{i}^{V} \times V_{i}^{V} + C_{i}^{E} \times V_{i}^{E} + C_{i}^{IS} \times V_{i}^{IS} }}{{V_{i}^{total} }} $$

  (18)

  For tumor compartment total tumor volume was defined using an exponential growth function, which represents the sum of all sub-compartments

  $$ V_{tumor}^{total} = V_{tumor}^{V} + V_{tumor}^{E} + V_{tumor}^{IS} + V_{tumor}^{Cellular} $$

  (19)