# A Cell-Level Systems PK-PD Model to Characterize In Vivo Efficacy of ADCs

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Cell Lines

#### 2.2. Tool ADC

^{®}, Genentech, South San Francisco, CA, USA) was conjugated with valine-citrulline MMAE (drug-linker solution) using random conjugation method, resulting in a heterogeneous formulation with an average drug: antibody ratio (DAR) of ~4. Detailed protocol for synthesis and characterization of T-vc-MMAE has been published before [14,16].

#### 2.3. Development of Xenograft Mouse Models

^{scid}/J) mice were purchased at the age of six weeks from Jackson Laboratory, ME, USA. After acclimation to their new housing conditions for two weeks, mice were subcutaneously implanted in the right dorsal flank with ~10 million tumor cells (N87 or GFP-MCF7) suspended in the growth medium with no FBS. To facilitate faster growth of GFP-MCF7 tumors, mice were supplemented with 1µg of 17β-estradiol valerate (Sigma

^{®}, St. Louis, MO, USA) in 50 µL of pharmaceutical grade peanut oil (Sigma

^{®}), by subcutaneous injection every 4 days [17] until the termination of the study. All procedures involving animals, including housing and care, method of euthanasia, and experimental protocols were conducted in accordance with the Institutional Animal Care and Use Committee (IACUC) at State University of New York at Buffalo. The permission for the animal experiments was provided by IACUC under the approval number PHC26114Y on 1 October 2014.

#### 2.4. Development of Bioanalytical Techniques

_{2}EDTA at 4 °C followed by centrifugation for 15 min at 1000 RPM. Plasma and tumor lysate sample were then divided into three groups associated with detection of each analyte. Standard curves were generated using plasma and tumor lysate samples from untreated animals and spiking with different concentrations of either trastuzumab (for ELISA) or MMAE (for LC-MS/MS). Detailed methodology, development, and validation of all three bioanalytical techniques have been published before [14].

#### 2.5. Tumor Pharmacokinetic Studies

^{3}. All the animals from each group were treated with single 10 mg/kg dose of T-vc-MMAE intravenously. At 24 h, 72 h, and 168 h after ADC administration, three animals from each group were sacrificed to collect blood and tumor samples. In addition, a blood sample was also collected from each animal at 10 min after ADC dose via retro-orbital sampling. Blood samples were immediately processed to extract plasma, and all the plasma and tumor samples were stored at −80 °C until further analysis.

#### 2.6. Tumor Growth Inhibition Studies

^{3}. On day 0, mice from each group (A and B) were further randomly divided into four equal subgroups (n = 7), either control (A1 and B1) or treatment (A2-4 and B2-4). GFP-MCF7 bearing mice were injected with a single intravenous dose of 3 mg/kg (A2), 5 mg/kg (A3) or 10 mg/kg (A4) ADC. N87 bearing mice were injected with a single intravenous dose of 1 mg/kg (B2), 3 mg/kg (B3), or 10 mg/kg (B4) ADC. Tumor volumes were calculated based on tumor length (L) and breadth (B) using the following formula: $\frac{1}{2}\times \mathrm{L}\times {\mathrm{B}}^{2}$. Tumor volumes in all the groups were measured twice a week until either tumor volume exceeded the permissible limit or was completely regressed for a prolonged duration of time (i.e., ~3 week).

#### 2.7. Development of In-Vivo systems PK-PD Model for T-vc-MMAE ADC

#### 2.7.1. Plasma PK Model for ADC

#### 2.7.2. Tumor Distribution Model for ADC

#### 2.7.3. Single Cell Disposition Model for ADC

^{8}tumor cells per gram of tumor [21], simultaneous interaction of T-vc-MMAE and free MMAE in the extracellular and intracellular space of each tumor cell is accounted for. The equations pertaining to the growth of the tumor ($\mathrm{TV}$, in L) in the absence of any tumor growth inhibition are provided below (Equations (1) and (2)):

#### 2.7.4. Characterization of Intracellular Occupancy of Tubulin with MMAE

#### 2.7.5. Linking Intracellular Occupancy of Tubulin to Tumor-Growth Inhibition

## 3. Parameter Estimation, Model Fitting and Simulations

^{®}(University of California at Berkeley, Berkeley, CA, USA), and PK data fitting was performed using maximum likelihood (ML) estimation method of ADAPT-5 software (BMSR, Los Angeles, CA, USA) [23]. The following variance model (Equation (24)) was used:

^{®}) [24], where log-normal distribution was assumed for IIV in $\mathrm{Kmax}$ and $\mathsf{\tau}$ parameters.

## 4. Results

#### 4.1. Plasma and Tumor PK Studies:

#### 4.2. Tumor Growth Inhibition Studies:

^{3}tumor volume for these mice was found to be 15, 33, and 48 days for 3, 5, and 10 mg/kg dose groups, compared to nine days for the control group. In N87 tumor bearing mice, there was an evident tumor regression at the higher dose-levels, and 10 mg/kg dose resulted in complete regression of the tumor. Time to achieve >1000 mm

^{3}tumor volume for these mice was found to be 24 and 33 days for 1 and 3 mg/kg dose groups, compared to 24 days for the control group.

#### 4.3. Development of the Systems PK-PD Model for ADC:

#### 4.3.1. Plasma PK Model for T-vc-MMAE:

#### 4.3.2. Tumor Distribution Model for T-vc-MMAE

#### 4.3.3. Prediction of Intracellular Occupancy of Tubulin

#### 4.3.4. Linking Intracellular Tubulin Occupancy to Tumor Growth Inhibition

## 5. Discussion

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

^{®}) for their continuous support and discussions on implementation of complex models in ADAPT 5 and Monolix v8 software, respectively.

## Conflicts of Interest

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**Figure 1.**A schematic diagram of the systems pharmacokinetics-pharmacodynamics (PK-PD) model for antibody-drug conjugates (ADCs).

**Plasma PK:**Disposition of Trastuzumab-Valine-Citrulline-Monomethyl Auristatin E (T-vc-MMAE) in systemic and peripheral spaces is characterized using a two-compartment model with linear clearance from the central compartment. Processes associated with non-specific shedding of MMAE and catabolic clearance of T-vc-MMAE contribute to the formation of unconjugated MMAE, which is also characterized using a two-compartment model with distribution to peripheral tissues and linear clearance from the central compartment.

**Tumor Distribution:**the distribution of T-vc-MMAE and unconjugated MMAE was assumed to be driven from their central compartment to tumor extracellular space using two diffusive processes, i.e., surface and vascular exchange.

**Single Cell Disposition:**once in the extracellular space, T-vc-MMAE was assumed to bind to HER2 receptors and internalize into the endosomal/lysosomal space of each cell. Upon enzymatic degradation and linker cleavage, unconjugated MMAE was assumed to release in the cytoplasmic space and either bind to intracellular tubulin or efflux out in the extracellular space.

**Single Cell Killing:**occupancy of intracellular tubulin with MMAE drives the killing of cells and shuttles the growing cells into non-growing phases. Upon the death of each cell, the intracellular content becomes part of tumor extracellular space, which can distribute back into other cells or diffuse out in the systemic circulation.

**Figure 2.**Plasma and tumor pharmacokinetic data (mean ± standard deviation) for three analytes (n = 3): unconjugated MMAE (green), total MMAE (purple), and total trastuzumab (red), after 10 mg/kg intravenous dose of T-vc-MMAE in GFP-MCF7 (

**A1**and

**A2**) and N87 (

**B1**and

**B2**) tumor bearing mice. Comparative tumor pharmacokinetics of 10 mg/kg T-vc-MMAE in GFP-MCF7 (green) and N87 (red) tumors for total trastuzumab (

**C1**), total MMAE (

**C2**) and unconjugated MMAE (

**C3**).

**Figure 3.**Tumor growth inhibition (TGI) profiles (mean ± standard deviation) in GFP-MCF7 (

**A**) and N87 (

**B**) tumors of either control (black, n = 7) or after single intravenous administration of T-vc-MMAE at 1 mg/kg (green, n = 7)), 3 mg/kg (red, n = 7), 5 mg/kg (pink, n = 7), and 10 mg/kg (blue, n = 7).

**Figure 4.**Model fittings for plasma and tumor pharmacokinetics of 10 mg/kg of intravenous 10 mg/kg T-vc-MMAE (

**A**) Observed and model fitted profiles for plasma pharmacokinetics of total trastuzumab (red), total MMAE (purple), and unconjugated MMAE (green) in GFP-MCF7 and N87 tumor bearing mice. (

**B**and

**C**) Observed and model fitted profiles for tumor pharmacokinetics of total trastuzumab (

**B1**and

**C1**), free MMAE (

**B2**and

**C2**), and total MMAE (

**B3**and

**C3**) in GFP-MCF7 (green) and N87 (red) tumor bearing mice.

**Figure 5.**Simulations for intracellular occupancy of tubulin with MMAE (${\mathrm{Occ}}_{\mathrm{Tub}}$) in GFP-MCF7 (

**A**) and N87 (

**B**) tumor bearing mice after administration of single intravenous dose of 1 mg/kg (green), 3 mg/kg (red), 5 mg/kg (pink), and 10 mg/kg (blue) T-vc-MMAE.

**Figure 6.**Observed and model predicted tumor growth profiles in GFP-MCF7 (green) and N87 (red) tumor bearing mice in either control group (

**A1**,

**B1**) or after 1 mg/kg (

**B2**), 3 mg/kg (

**A2**,

**B3**), 5 mg/kg (

**A3**), and 10 mg/kg (

**A4**,

**B4**) T-vc-MMAE.

**Table 1.**A list of literature derived, or model estimated parameters used for the systems PK-PD model of T-vc-MMAE.

Parameter | Definition | Value (CV %) | Unit | Source |
---|---|---|---|---|

Parameters associated with plasma pharmacokinetics of T-vc-MMAE | ||||

${\mathrm{CL}}_{\mathrm{ADC}}$, ${\mathrm{CLD}}_{\mathrm{ADC}}$ | Central and distributional clearances of T-vc-MMAE | 0.033 (4.8%), 0.0585 (12.6%) | L/day/Kg | Estimated |

$\mathrm{V}{1}_{\mathrm{ADC}}$, $\mathrm{V}{2}_{\mathrm{ADC}}$ | Central and peripheral volumes of distribution for T-vc-MMAE | 0.084 (7.3%), 0.051 (5.2%) | L/Kg | Estimated |

${\mathrm{CL}}_{\mathrm{Drug}}$, ${\mathrm{CLD}}_{\mathrm{Drug}}$ | Central and distributional clearances of free MMAE | 18.40, 1.84 | L/day/Kg | [11] |

$\mathrm{V}{1}_{\mathrm{Drug}}$, $\mathrm{V}{2}_{\mathrm{Drug}}$ | Central and peripheral volumes of distribution for T-vc-MMAE | 0.136, 0.523 | L/Kg | [11] |

${\mathrm{K}}_{\mathrm{dec}}^{\mathrm{P}}$ | Non-specific deconjugation of MMAE from T-vc-MMAE | 0.323 (8.8%) | 1/day | Estimated |

Parameters associated with tumor distribution of T-vc-MMAE | ||||

${\mathrm{R}}_{\mathrm{Cap}}$ | Radius of the tumor blood capillary | 8.0 | µm | [18,19,20] |

${\mathrm{R}}_{\mathrm{Krogh}}$ | An average distance between two capillaries | 75.0 | µm | [18,19,20] |

${\mathrm{P}}_{\mathrm{ADC}}$, ${\mathrm{P}}_{\mathrm{Drug}}$ | The rates of permeability of T-vc-MMAE and MMAE across the blood vessels respectively | 334, 21000 | µm/day | [18,19,20] |

${\mathrm{D}}_{\mathrm{ADC}}$, ${\mathrm{D}}_{\mathrm{Drug}}$ | The rates of diffusion of T-vc-MMAE and MMAE across the blood vessels respectively | 0.022, 0.25 | cm^{2}/day | [18,19,20] |

${\mathsf{\epsilon}}_{\mathrm{ADC}}$, ${\mathsf{\epsilon}}_{\mathrm{Drug}}$ | Tumor void volume for T-vc-MMAE and MMAE | 0.24, 0.44 | Unitless | [18,19,20] |

${\mathrm{R}}_{\mathrm{Tumor}}$ | Radius of a spherical tumor calculated based on varying tumor volume (TV) where: $\mathrm{TV}\left(\mathrm{t}\right)=\frac{4}{3}{\ast \mathsf{\pi}\ast \mathrm{R}}^{3}{}_{\mathrm{Tumor}}$ | Dynamic | cm | |

Parameters associated with single cell disposition of T-vc-MMAE | ||||

${\mathrm{K}}_{\mathrm{on}}^{\mathrm{ADC}}$ | Second order association rate constant between T-vc-MMAE and HER2 receptor | 0.03 | 1/nM/h | [14] |

${\mathrm{K}}_{\mathrm{off}}^{\mathrm{ADC}}$ | First order dissociation rate constant between T-vc-MMAE and HER2 receptor | 0.014 | 1/h | [14] |

${\mathrm{K}}_{\mathrm{int}}^{\mathrm{ADC}}$ | Internalization rate of HER2-ADC complex inside the cell | 0.11 | 1/h | [14] |

${\mathrm{K}}_{\mathrm{deg}}^{\mathrm{ADC}}$ | Intracellular degradation of T-vc-MMAE in endosomal/lysosomal space | 0.353 | 1/h | [14] |

${\mathrm{K}}_{\mathrm{on}}^{\mathrm{Tub}}$ | Second order association rate constant between cytoplasmic MMAE and intracellular tubulin protein | 0.0183 | 1/nM/h | [14] |

${\mathrm{K}}_{\mathrm{off}}^{\mathrm{Tub}}$ | First order dissociation rate constant between MMAE-tubulin complex | 0.545 | 1/h | [14] |

${\mathrm{Tub}}^{\mathrm{tot}}$ | Total concentration of intracellular tubulin in a single cell | 65 | nM | [11,14] |

${\mathrm{K}}_{\mathrm{in}}^{\mathrm{Drug}}$ | First order influx rate of MMAE from extracellular to intracellular space | 8.33 | 1/h | [14] |

${\mathrm{K}}_{\mathrm{out}}^{\mathrm{Drug}}$ | First order efflux rate of MMAE from intracellular to extracellular space | 0.046 | 1/h | [11] |

${\mathrm{Ag}}_{\mathrm{N}87}^{\mathrm{ex}}$, ${\mathrm{Ag}}_{\mathrm{MCF}7}^{\mathrm{ex}}$ | Model estimated HER2 receptor count on each tumor cell in N87 and GFP-MCF7 tumors in vivo | 185,000 (2.8%), 22,400 (3.2%) | Numbers/Cell | Estimated |

Parameters associated with single cell killing of T-vc-MMAE in tumors | ||||

$\mathrm{Kmax}$ | First order killing rate of MMAE in each tumor cell (either GFP-MCF7 or N87) | 1.03 (31.3%) | 1/day | Estimated |

$\mathrm{KC}50$ | Percentage of intracellular occupancy to tubulin by MMAE which leads to 50% of maximum killing | 96.8 (13.2%) | Percentage | Estimated |

$\mathsf{\tau}$ | Transit time associated with the killing | 2.03 | Day | Estimated |

${\mathrm{IIV}}^{\mathrm{Kmax}}$, ${\mathrm{IIV}}^{\mathsf{\tau}}$ | Inter-subject variability associated with Kmax and ‘Tau’ values assuming log-normal distribution | 10.16 (47%), 19.4 (32%) | Percentage | Estimated |

$\mathsf{\gamma}$ | Curve-fitting parameter associated with sigmoidal tubulin occupancy-killing relationship | 15.02 (38.6%) | Unitless | Estimated |

${\mathrm{DT}}^{\mathrm{N}87}$, ${\mathrm{DT}}^{\mathrm{MCF}7}$ | Doubling time of N87 and GFP-MCF7 tumors | 13.5 (11.4%), 10.6 (18.7%) | Day | Estimated |

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**MDPI and ACS Style**

Singh, A.P.; Guo, L.; Verma, A.; Wong, G.G.-L.; Shah, D.K.
A Cell-Level Systems PK-PD Model to Characterize In Vivo Efficacy of ADCs. *Pharmaceutics* **2019**, *11*, 98.
https://doi.org/10.3390/pharmaceutics11020098

**AMA Style**

Singh AP, Guo L, Verma A, Wong GG-L, Shah DK.
A Cell-Level Systems PK-PD Model to Characterize In Vivo Efficacy of ADCs. *Pharmaceutics*. 2019; 11(2):98.
https://doi.org/10.3390/pharmaceutics11020098

**Chicago/Turabian Style**

Singh, Aman P., Leiming Guo, Ashwni Verma, Gloria Gao-Li Wong, and Dhaval K. Shah.
2019. "A Cell-Level Systems PK-PD Model to Characterize In Vivo Efficacy of ADCs" *Pharmaceutics* 11, no. 2: 98.
https://doi.org/10.3390/pharmaceutics11020098