Multiscale Modeling of Antibody-Drug Conjugates: Connecting Tissue and Cellular Distribution to Whole Animal Pharmacokinetics and Potential Implications for Efficacy

Abstract

Antibody-drug conjugates exhibit complex pharmacokinetics due to their combination of macromolecular and small molecule properties. These issues range from systemic concerns, such as deconjugation of the small molecule drug during the long antibody circulation time or rapid clearance from nonspecific interactions, to local tumor tissue heterogeneity, cell bystander effects, and endosomal escape. Mathematical models can be used to study the impact of these processes on overall distribution in an efficient manner, and several types of models have been used to analyze varying aspects of antibody distribution including physiologically based pharmacokinetic (PBPK) models and tissue-level simulations. However, these processes are quantitative in nature and cannot be handled qualitatively in isolation. For example, free antibody from deconjugation of the small molecule will impact the distribution of conjugated antibodies within the tumor. To incorporate these effects into a unified framework, we have coupled the systemic and organ-level distribution of a PBPK model with the tissue-level detail of a distributed parameter tumor model. We used this mathematical model to analyze new experimental results on the distribution of the clinical antibody-drug conjugate Kadcyla in HER2-positive mouse xenografts. This model is able to capture the impact of the drug-antibody ratio (DAR) on tumor penetration, the net result of drug deconjugation, and the effect of using unconjugated antibody to drive ADC penetration deeper into the tumor tissue. This modeling approach will provide quantitative and mechanistic support to experimental studies trying to parse the impact of multiple mechanisms of action for these complex drugs.

Keywords: Herceptin; Kadcyla; Krogh cylinder; ado-trastuzumab emtansine; antibody tissue penetration; drug-antibody ratio (DAR).

Figure 1

Multi-scale PBPK-Krogh cylinder model diagram. A, PBPK model tracks systemic distribution of both antibody and ADC. Solid black lines correspond to antibody/ADC flow and green dotted lines correspond to metabolite flow. B, representative organ compartment model. All organs except the tumor and carcass are divided into vascular, interstitial, and metabolite compartments. The endothelial compartment is added in the carcass to account for FcRn recycling. C, the tumor compartment is modeled by a 1-D Krogh cylinder tissue model with permeability (P) across the endothelium (extravasation) and diffusion (D) through the surrounding tissue. D, cellular-scale model showing binding, internalization, and degradation rates of both antibody and ADC.

Figure 2

Heterogeneous ADC distribution. A, graphic depiction of T-DM1 tumor distribution with co-administration of trastuzumab. Without a carrier dose of trastuzumab, tumor distribution of T-DM1 is perivascular. Co-administration of T-DM1 with ‘carrier’ doses of trastuzumab (at constant T-DM1 doses) results in significantly more T-DM1 tumor penetration. B, immunofluorescence imaging following co-administration of 3.6 mg/kg of AlexaFluor 680 tagged T-DM1 (green) with trastuzumab at 0:1, 3:1, and 8:1 ratios (0 mg/kg, 10.8 mg/kg, and 28.8 mg/kg unlabeled trastuzumab, respectively). Immunofluorescence staining with CD31-AF555 (red) shows tumor vasculature. Window leveling of images is different. Scale bar = 200 μm.

Figure 3

PBPK model results and experimental biodistribution data. PBPK model shows systemic distribution of 3.6 mg/kg T-DM1 with trastuzumab at 0:1 (black), 3:1 (red), and 8:1 (blue) ratios (trastuzumab:T-DM1, N=3 mice for each). 0:1 and 3:1 distributions overlap since the tumor is below saturation at these dosing levels. At 8:1 ratio, the dose is slightly above tumor saturation resulting in lower tumor %ID/g and slower clearance. Experimental data shows T-DM1 distribution at 24 hours for the respective ratios; data points were shifted slightly for visibility. The PBPK results are similar despite widely differing distribution seen within the tumors in Fig. 2.

Figure 4

Quantitative Krogh cylinder simulation results and immunofluorescence imaging results. A, model predictions of bound T-DM1 with co-administration of trastuzumab at 0:1, 3:1, and 8:1 ratios 24 hours post injection. B, experimental validation of model predictions. Whole tumor (bottom) and inset (top) T-DM1 (green) distribution following injection of 3.6mg/kg T-DM1 with trastuzumab at 0:1, 3:1, and 8:1 ratios. Immunofluorescence staining with CD31-AF555 (red) shows tumor vasculature. I and M show regions of inflammatory cells and muscle, respectively. Window leveling between different carrier dose images is different. Scale bar = 50 μm (top) and 1 mm (bottom).

Figure 5

Prediction of T-DM1 distribution versus trastuzumab carrier dose. Predicted perivascular tumor distribution following dosage with T-DM1 and trastuzumab for tumor cells expressing 1 × 10⁶ receptors per cell, A, and 3 × 10⁵ receptors per cell, B, corresponding to ∼3+ and ∼2+ IHC staining, respectively. From 0 to 3.6 mg/kg total dose only T-DM1 is dosed. After 3.6 mg/kg the T-DM1 dose is kept constant (3.6 mg/kg) and trastuzumab carrier dose is increased.

Figure 6

Literature review of efficacy with constant small molecule dose but differing DAR and antibody doses. A, at a constant small molecule dose, ADCs with a higher DAR and lower antibody dose (black) are generally less efficacious than ADCs with a lower DAR and higher antibody dose (gray). Blue arrows correspond to six cases where a constant small molecule dose delivered with a higher antibody dose improved efficacy and is predicted to have increased tissue penetration. In one case the reverse was true (green arrow); however, here the small molecule had an IC₅₀ reported to be greater than the K_D of the antibody due to a less toxic payload. This would require saturation of cells with a high DAR antibody for efficacy. Red lines and boxes correspond to the estimated difference in small molecule AUC between different DAR/antibody doses using literature reports of DAR-dependent deconjugation and clearance rates in a pharmacokinetic model. The pharmacokinetic analysis is outlined in the supplementary data. B, DAR-dependent clearance can significantly affect the efficacy, making it difficult to parse tumor penetration effects from small molecule AUC.

Figure 7

Predicted and experimental impact of carrier dose on total tumor uptake. A, bound and internalized uptake of T-DM1 in tumor with increasing trastuzumab carrier dose. Prior to saturation, the addition of a carrier dose (or equivalently, delivering a constant small molecule dose while lowering the DAR) does not lower total tumor uptake of a constant T-DM1 dose (3.6 mg/kg). It only changes the distribution. B, experimentally measured %ID/g of T-DM1 at respective ratios. Differences of %ID/g were not statistically significant between the 0:1 to 8:1.

Figure 8

Impact of carrier dose/DAR on healthy tissue targeting. A, graphic depiction of specific binding added to the heart organ compartment. A bound compartment was added to represent the low levels of HER2 antigen expressed in the heart. B, Bound and internalized T-DM1 (constant 3.6 mg/kg dose) in heart compartment with increasing trastuzumab carrier dose shows lower healthy tissue uptake with a carrier dose or lower DAR. The y-axis is normalized to initial unbound antigen in heart.