Antibody Coadministration as a Strategy to Overcome Binding-Site Barrier for ADCs: a Quantitative Investigation

Abstract

It has been proposed that the binding-site barrier (BSB) for antibody-drug conjugates (ADCs) can be overcome with the help of antibody coadministration. However, broad utility of this strategy remains in question. Consequently, here, we have conducted in vivo experiments and pharmacokinetics-pharmacodynamics (PK-PD) modeling and simulation (M&S) to further evaluate the antibody coadministration hypothesis in a quantitative manner. Two different Trastuzumab-based ADCs, T-DM1 (no bystander effect) and T-vc-MMAE (with a bystander effect), were evaluated in high-HER2 (N87) and low-HER2 (MDA-MB-453) expressing tumors, with or without the coadministration of 1, 3, or 8-fold higher Trastuzumab. The tumor growth inhibition (TGI) data was quantitatively characterized using a semi-mechanistic PK-PD model to determine the nature of drug interaction for each coadministration regimen, by estimating the interaction parameter ψ. It was found that the coadministration strategy improved ADC efficacy under certain conditions and had no impact on ADC efficacy in others. The benefit was more pronounced for N87 tumors with very high antigen expression levels where the effect on treatment was synergistic (a synergistic drug interaction, ψ = 2.86 [2.6–3.12]). The benefit was diminished in tumor with lower antigen expression (MDA-MB-453) and payload with bystander effect. Under these conditions, the coadministration regimens resulted in an additive or even less than additive benefit (ψ ≤ 1). As such, our results suggest that while antibody coadministration may be helpful for ADCs in certain circumstances, one should not broadly apply this strategy to all the scenarios without first identifying the costs and benefits of this approach.

INTRODUCTION

Antibody-drug conjugates (ADCs) are promising anti-cancer molecules that utilize targeted monoclonal antibodies (mAbs) to deliver highly potent cytotoxic agents (payloads) to antigen overexpressing tumor cells (1–3). They aim to improve the therapeutic index compared with conventional chemotherapy (4). At present, there are 4 FDA-approved ADCs in the market and ~ 85 molecules in clinical development (5). While these molecules are promising, their clinical success is often limited by poor tumor penetration and distribution at the clinically relevant doses (6). Indeed, a recent statistic highlights that > 90% of the ADCs discontinued from clinical development were indicated for solid tumors and not hematological malignancies (5). These limitations stem from the inherent design of an ADC, which is developed to target an overexpressed and rapidly internalizing antigen on the tumor cells (7,8). High antigen expression and internalization have been known to limit the distribution of antibody-based molecules in the perivascular regions of a tumor, resulting in the formation of the binding-site-barrier (BSB). The extent of this barrier could be more prominent for ADCs compared with conventional mAbs because of the lower doses used in the clinic (6–8). Many studies in the clinic have demonstrated antibody heterogeneity in these dose-ranges (9–18). In addition, this barrier can be more detrimental for ADCs that do not exhibit any bystander effect, because the released drug molecules would not be able to kill the cells that are not reachable by the ADC. Thus, there is need to develop pharmacokinetic (PK) strategies that can enhance the efficacy of ADCs by facilitating more homogeneous distribution within solid tumors (1,19,20).

Cilliers et al. (6) have recently presented one such strategy, where using imaging experiments and mathematical modeling, they have proposed that coadministration of Trastuzumab could lead to more homogeneous distribution of T-DM1 in HER2 overexpressing N87 tumors. Their analysis revealed that 3-fold higher Trastuzumab coadministration will not affect tumor exposure of T-DM1, but 8-fold higher Trastuzumab may lead to a reduction in tumor exposure of ADC. They have further evaluated this strategy for any improvement in the efficacy of T-DM1, by performing tumor growth inhibition (TGI) studies in N87 tumor-bearing mice (21). They found that coadministration of 1, 3, and 8-fold higher Trastuzumab led to an improvement in the efficacy of 3.6 mg/kg T-DM1 compared with the ADC alone. While these studies provide a solid proof-of-concept for the coadministration hypothesis, there is a need to further evaluate this hypothesis in a more quantitative manner, at multiple ADC dose levels, across different ADC molecules (with or without the bystander effect), and across tumors with different antigen expression levels (low or high).

In this paper, we have further evaluated the antibody coadministration hypothesis (6,21) in a more quantitative manner, using a diverse set of in vivo experiments and pharmacokinetics-pharmacodynamics (PK-PD) modeling and simulation (M&S). Figure 1a summarizes different experimental conditions that we have evaluated in the presented work using TGI studies. Two different mouse tumor models generated using low HER2 expressing MDA-MB-453 and high HER2 expressing N87 cells were evaluated. In addition, two different Trastuzumab-based ADCs were evaluated: T-DM1 that is expected to demonstrated minimal bystander effect, and T-vc-MMAE that has been shown to demonstrate notable bystander effect (22). The ADCs were also evaluated at two different dose levels, and Trastuzumab was coadministered at 3- and/or 8-fold higher doses. We hypothesized that the proposed set of experiments will help us evaluate the beneficial effects of antibody coadministration under various scenarios with varying degrees of BSB. Typically, one would expect greater benefits for ADCs with minimal bystander effect in high-antigen expressing tumors. We have evaluated these expectations by performing quantitative characterization of the observed TGI data using a semi-mechanistic PK-PD model (Fig. 1b) (23), which is capable of identifying if antibody coadministration leads to synergistic, additive, or less than additive drug interaction with ADCs.

Fig. 1.

a A schematic diagram highlighting the hypothesis associated with the proposed coadministration strategy to overcome the binding-site barrier (BSB) for antibody-drug conjugates (ADCs). (A1): A scenario where T-DM1 (no bystander effect) is administered in HER2-low versus HER2-high tumors. More BSB will be observed in HER2-high tumors leading to restrictive distribution of ADC. (A2): A scenario where T-vc-MMAE (with bystander effect) is administered in HER2-low versus HER2-high tumors. More BSB will be observed in HER2-high tumors, however, released payload could diffuse into deeper portions of the tissues, leading to more homogeneous payload exposures. (A3): A scenario where T-DM1 is coadministered with naked Trastuzumab in HER2-low versus HER2-high tumors. Coadministration leads to deeper distribution of T-DM1 and hence more homogeneous payload exposure. (A4): A scenario where T-vc-MMAE is coadministered with naked Trastuzumab in HER2-low versus HER2-high tumors. Coadministration leads to deeper distribution of T-vc-MMAE within the tumor tissues, and the payload could also diffuse into the neighboring cells to induce more homogenous exposure. b A schematic of the proposed semi-mechanistic PK-PD model that was used to evaluate the nature of drug interaction when antibody was coadministered with ADCs during the TGI studies. The model operates with two different 2-compartment pharmacokinetic (PK) models, associated with ADC and antibody. A hybrid killing function shuttles the growing tumor cells (using biphasic saturable growth rate) to non-growing phases using a series of transit compartments, which eventually leads to tumor cell death (model equations are listed in supplementary text).

MATERIALS AND METHODS

Cell Lines

HER2-expressing cell lines used for the development of mouse tumor models were MDA-MB-453 and NCI-N87. MDA-MB-453 cells are known to express ~ 250,000 receptors/cell (24), and N87 cells are known to express ~ 950,000 receptors/cell (25), which makes them low and high HER2 expressing cell lines, respectively. Both cell lines were procured from ATCC® and cultured in Leibovitz’s L-15 and RPMI-1640 growth mediums, respectively, supplemented with 10% fetal bovine serum (ATCC®) and gentamicin (Sigma®).

Antibody and Antibody-Drug Conjugates

Three molecules utilized for the investigation were Trastuzumab (TTmAb), Trastuzumab Emtansine (T-DM1), and Trastuzumab-valine-citrulline monomethyl auristatin E (T-vc-MMAE). Both Trastuzumab (Herceptin®, Genentech) and T-DM1 (Kadcylla®, Genentech) were obtained commercially, and T-vc-MMAE was synthesized and characterized in-house. Detailed methodology on the synthesis and characterization of T-vc-MMAE has been previously published by us (22,25). Briefly, Trastuzumab was conjugated with valine-citrulline MMAE (drug-linker solution) using cysteine-based conjugation method, resulting in a heterogeneous formulation with an average drug: antibody ratio (DAR) of ~ 4.

Development of Xenograft Mouse Models

Male severe combined immunodeficient (SCID, NOD.CB17-Prkdc^scid/J) mice (~ 6 weeks old) were purchased from Jackson Laboratory, USA. After acclimation, mice were subcutaneously implanted (in the right flank) with ~ 10 million tumor cells (MDA-MB-453 or N87) suspended in their growth medium. All procedures involving animals were conducted in accordance with the Institutional Animal Care and Use Committee (IACUC) at State University of New York at Buffalo.

Tumor Growth Inhibition Studies

Monotherapy of Investigated Molecules in HER2-High N87 Xenografts

A total of 58 SCID mice were subcutaneously implanted with N87 cells, and the treatment was initiated 4–6 weeks post implantation when the tumor volumes reached ~ 250–350 mm³. At day 0, mice were randomly assigned to 9 different groups: control (no treatment, n = 10), 1 mg/kg T-DM1 (n = 3), 3.6 mg/kg T-DM1 (n = 5), 1 mg/kg T-vc-MMAE (n = 11), 3 mg/kg T-vc-MMAE (n = 7), 3.6 mg/kg T-vc-MMAE (n = 5), 10 mg/kg T-vc-MMAE (n = 7), 3 mg/kg TTmAb (n = 5), and 10.8 mg/kg TTmAb (n = 5).

Monotherapy of Investigated Molecules in HER2-Low MDA-MB-453 Xenografts

A total of 63 SCID mice were subcutaneously implanted with MDA-MB-453 cells, and the treatment was initiated ~ 8 weeks after implantation when the tumor volumes reached ~ 250–350 mm³. At day 0, mice were randomly assigned to 9 different groups: control (no treatment, n = 7), 0.36 mg/kg T-DM1 (n = 7), 3.6 mg/kg T-DM1 (n = 7), 0.36 mg/kg T-vc-MMAE (n = 7), 3.6 mg/kg T-vc-MMAE (n = 7), 1 mg/kg TTmAb (n = 7), 3.6 mg/kg TTmAb (n = 7), 10.8 mg/kg TTmAb (n = 7), and 28.8 mg/kg TTmAb (n = 7).

Coadministration Therapy in N87 and MDA-MB-453 Xenografts

A total of 57 SCID mice were subcutaneously implanted with MDA-MB-453 cells, and the treatment was initiated ~ 8 weeks after implantation when the tumor volumes reached ~ 250–350 mm³. At day 0, mice were randomly divided into 8 different treatment groups, and the following combinations were investigated. 3.6 mg/kg T-DM1 coadministered with 1-fold higher TTmAb (n = 7), 0.36 mg/kg T-DM1 coadministered with 3-fold higher TTmAb (n = 7), 3.6 mg/kg T-DM1 coadministered with 3-fold higher TTmAb (n = 7), 3.6 mg/kg T-DM1 coadministered with 8-fold higher TTmAb (n = 7), 3.6 mg/kg T-vc-MMAE coadministered with 1-fold higher TTmAb (n = 7), 0.36 mg/kg T-vc-MMAE coadministered with 3-fold higher TTmAb (n = 7), 3.6 mg/kg T-vc-MMAE coadministered with 3-fold higher TTmAb (n = 8), and 3.6 mg/kg T-vc-MMAE coadministered with 8-fold higher TTmAb (n = 7).

A total of 18 SCID mice were subcutaneously implanted with N87 cells, and the treatment was initiated 4–6 weeks post implantation when the tumor volumes reached ~ 250–350 mm³. At day 0, mice were divided into 4 different treatment groups, and the following combination regimens were investigated. 3.6 mg/kg T-DM1 coadministered with 3-fold higher TTmAb (n = 5), 1 mg/kg T-DM1 coadministered with 3-fold higher TTmAb (n = 3), 3.6 mg/kg T-vc-MMAE coadministered with 3-fold higher TTmAb (n = 5), and 1 mg/kg T-vc-MMAE coadministered with 3-fold higher TTmAb (n = 5).

Data Analysis

Tumor volumes were calculated by measuring length (L, longest diameter) and breadth (B) using vernier caliper, and implementation of the following expression: $\frac{1}{2}\times \text{L}\times {\text{B}}^2$. Tumor volumes for control and treatment groups were measured twice a week until tumor volume exceeded > 2500 mm³ or was completely regressed/maintained stasis for a prolonged duration of time (~ 120 days). The sample size for each treatment arm varied due to the availability of tumor-bearing animals and incorporation of additional treatment groups within the study design.

Mathematical Modeling to Quantitatively Investigate the Effect of Antibody Coadministration on ADC Efficacy

A population PK-PD modeling approach was adopted to characterize TGI data and to quantitatively determine the additive, synergistic or less than additive effect of antibody administration on ADC efficacy. Mathematical modeling was supplemented in addition to observed mean data, due to the huge variability in tumor growth profiles and different sample sizes among various treatment groups. All the equations associated with the model are provided in the supplementary material. The 1st step of our approach involved development of individual PK-PD relationships for the efficacy of T-DM1, T-vc-MMAE, and TTmAb, in N87 and MDA-MB-453 tumor models. This was accomplished using the semi-mechanistic PK-PD model shown in Fig. 1b. The PK of each molecule in tumor-bearing mice was obtained from our previous publications (1,26) and was assumed to be consistent across the present study. The PK was characterized using a 2-compartment model with linear elimination from the central compartment. An additional non-specific deconjugation rate (K^Dec) from the central compartment was added for characterizing the PK of two ADCs. This process represents nonspecific shedding of drug (payload) molecules from the ADC (1,20,26–28). The growth of each tumor model in the absence of drug exposure was characterized using our previously published hybrid growth model (26,27,29). This model switches the tumor growth from early exponential growth $\left(K_g^{Ex}\right)$ to a linear growth $\left(K_g^{Lin}\right)$, followed by a plateau at higher tumor volumes. The efficacy of drugs was modeled using linear or non-linear killing rates, which shuttled growing tumor cells into non-growing phases as a function of drug exposure in the plasma (30) (Fig. 1b). It was assumed that all the variability in tumor volume profiles stemmed from the variability in tumor growth rates, which were assumed to follow a log-normal distribution. The PK-PD model was fitted to all individual tumor growth profiles, and the parameters related to the growth of N87 and MDA-MB-453 tumors, and the efficacy of T-DM1, T-vc-MMAE, and TTmAb in these tumors was estimated.

In the 2nd step, TGI profiles of animals administered with different combination regimens were characterized, by combining individual killing rates of ADC and antibody in the following hybrid killing function (23):

$$\text{Kill}=f\left({\text{C}}_{\text{p}}^{\text{ADC}}\right)+\psi \cdot f\left({\text{C}}_{\text{p}}^{\text{mAb}}\right)$$ (1)

where ψ represents the interaction term, which provides an indication of the nature of drug interaction when antibody is coadministered with ADC. A value of > 1 suggests a synergistic interaction, a value of 1 suggests an additive interaction, and a value < 1 suggests less than additive interaction. To characterize the TGI data from coadministration studies, the efficacy parameters for each drug molecule and the growth parameters for each tumor model were fixed to values estimated in Step 1, and only the parameters related to tumor growth variability and drug interaction (i.e., ψ) were estimated. To assess the predictive nature of the model, visual predictive checks (VPC) were also generated. One thousand monte-carlo simulations were performed for each treatment regimen, and 5th, 50th, and 95th percentiles were calculated to compare with the observed tumor growth profiles. Modeling and simulation was performed using stochastic approximation expectation maximization (SAEM) algorithm in Monolix version 8 (Lixoft®) (31).

RESULTS

Tumor Growth Inhibition Studies

HER2-High N87 Xenografts at 3.6 mg/kg ADC (High Dose)

Figures 2a and b show the observed TGI data in N87 tumor-bearing mice, where the efficacy of 3.6 mg/kg ADCs was evaluated in the presence or absence of 3-fold higher TTmAb. It was observed that 3.6 mg/kg T-vc-MMAE (Fig. 2b) was more efficacious than 3.6 mg/kg T-DM1 (Fig. 2a). Three-fold higher TTmAb (i.e., 10.8 mg/kg), administered alone, also demonstrated minor tumor growth inhibition when compared with the control (which has been observed previously at high doses (32,33)). The time to reach > 1000 mm³ tumor volume was observed to be 24 days for 10.8 mg/kg Trastuzumab group, compared with 16 days for the control group. When both ADCs were coadministered with 3-fold higher TTmAb, there was an evident improvement in the efficacy of ADCs. The extent of improvement was found to be more significant for T-DM1 (Fig. 2a) compared with T-vc-MMAE (Fig. 2b), which may be due to already high efficacy of T-vc-MMAE in N87 tumors at the given dose. Coadministration of 3-fold higher Trastuzumab led to the regression of N87 tumors by T-DM1, which was not the case when T-DM1 was given alone. The time to reach > 1000 mm³ tumor volume was 42 days when T-DM1 was coadministered with 3-fold higher TTmAb, compared with 21 days when T-DM1 was given alone. In case of T-vc-MMAE, when 3-fold higher Trastuzumab was coadministered, the initial extent of tumor regression did not change but the duration of response lasted for a longer time. The time to reach > 500 mm³ tumor volume was 83 days when T-vc-MMAE was coadministered with TTmAb, compared with 54 days when T-vc-MMAE was administered alone.

Fig. 2.

a–d TGI data in N87 and MDA-MB-453 tumor models from the high dose groups. 3.6 mg/kg of ADCs was evaluated as monotherapy or in combination with 3-fold higher Trastuzumab. Key: blue, ADC alone; green, Trastuzumab alone; red, combination of ADC and Trastuzumab; black, control

HER2-Low MDA-MB-453 Xenografts at 3.6 mg/kg ADC (High Dose)

Figures 2c and d show the TGI data in MDA-MB-453 tumors, following administration of 3.6 mg/kg ADCs in the presence or absence of 3-fold higher TTmAb. It was observed that 3.6 mg/kg T-vc-MMAE, 3.6 mg/kg T-DM1, and 3-fold higher Trastuzumab (i.e., 10.8 mg/kg) alone were highly efficacious in this tumor model. T-vc-MMAE exhibited higher efficacy than T-DM1 in MDA-MB-453 tumors as well. When both ADCs were coadministered with 3-fold higher TTmAb, no significant enhancement in the efficacy was observed, which may be due to already high efficacy ADCs at the given dose. However, it is hard to decide the nature of this interaction based on visualization. Therefore, mathematical modeling was employed to quantitatively and objectively decide the nature of this interaction later.

Figure 3 shows the efficacy of T-DM1 and T-vc-MMAE in MDA-MB-453 tumor model following coadministration of different dose-equivalents of Trastuzumab (i.e., 1-, 3-, and 8-fold higher than 3.6 mg/kg). The tumor growth profiles are plotted on a log-linear scale to provide better visual clarity of the observed differences. Interestingly, we observed a dose-dependent increase in the efficacy of Trastuzumab alone, which was unexpected and contrary to what is reported for the in vitro system by Barok et al. (24) (Supplementary Figure 33). When Trastuzumab was coadministered with T-DM1 or T-vc-MMAE, there was an improvement in the efficacy of ADCs, but this was not statistically significant. Nonetheless, mathematical modeling of the data is performed later to further examine the nature of this drug interaction.

Fig. 3.

TGI data in MDA-MB-453 tumors plotted on a log Y-axis. 3.6 mg/kg of ADCs was evaluated as a monotherapy, or in combination with 1-, 3-, and 8-fold higher Trastuzumab. Key: blue, ADC alone; green, Trastuzumab alone; red, combination of ADC and Trastuzumab; black, control

HER2-High N87 Xenografts at 1 mg/kg ADC (Low Dose)

Figures 4a and b show the TGI data in N87 tumor-bearing mice, where 1 mg/kg of ADC (T-DM1 or T-vc-MMAE) was administered alone or in combination with 3-fold higher TTmAb (i.e., 3 mg/kg). At the tested dose levels, no significant efficacy was observed for monotherapies (ADC or antibody) or combination therapies. When T-DM1 was compared with T-vc-MMAE, it was found that T-vc-MMAE was slightly more efficacious than T-DM1 at 1 mg/kg. However, there was a notable variability in the data, and hence, the actual nature of drug interaction following antibody coadministration was further evaluated using mathematical modeling.

Fig. 4.

a–d TGI data in N87 and MDA-MB-453 tumor models from the low dose groups. N87 tumors were administered with 1 mg/kg ADCs, and MDA-MB-453 tumors were administered with 0.36 mg/kg ADCs, as monotherapy or in combination with 3-fold higher Trastuzumab. Key: blue, ADC alone; green, Trastuzumab alone; red, combination of ADC and Trastuzumab; black, control

HER2-Low MDA-MB-453 Xenografts at 0.36 mg/kg ADC (Low Dose)

Figures 4c and d show the TGI data in MDA-MB-453 tumor-bearing mice, where 0.36 mg/kg of ADC (T-DM or T-vc-MMAE) was administered alone or in combination with 3-fold higher TTmAb (i.e., 1 mg/kg). For this tumor model as well, no significant efficacy was observed for monotherapies (ADC or antibody) or combination therapies at the tested dose levels. Interestingly, TTmAb alone was found to exhibit slightly higher efficacy than combination therapy; however, this observation is confounded by the variability in the data. Nonetheless, the nature of observed drug interaction was further confirmed using mathematical modeling.

Mathematical Modeling to Evaluate the Nature of Drug Interaction Following Antibody Coadministration

The 1st step of quantitative evaluation was to establish a PK-PD relationship for each investigational molecule (i.e., T-DM1, T-vc-MMAE, and TTmAb) as a monotherapy in MDA-MB-453 and N87 tumors. Figures 5 and 6 show the fitting results in the form of visual predictive checks (VPCs), which were generated following the development of individual PK-PD relationships for each molecule in MDA-MB-453 (Fig. 5) and N87 (Fig. 6) tumors. The predictions for individual animals (IPRED) and goodness of fits (GoF) plots are provided in the Supplementary Figures 1–8 for N87 tumors and Supplementary Figures 13–20 for MDA-MB-453 tumors. All the estimated parameters associated with the growth of N87 and MDA-MB-453 tumors and the efficacy of each investigational molecule in the two mouse models are listed in Table I. It was found that the chosen PK-PD models were able to characterize the observed data reasonably well, and the VPCs reflected that ~ 90% of the observed data was within 90% confidence intervals for all the treatment groups.

Fig. 5.

a–q Visual predictive checks (VPCs) for TGI data generated in MDA-MB-453 tumor model. Solid lines represent median and dotted lines represent 5th and 95th percentiles. Model predictions are superimposed over the observed data for each cohort. Key: blue, ADC alone; green, Trastuzumab alone; red, combination of ADC and Trastuzumab; black, control

Fig. 6.

a–k Visual predictive checks (VPCs) for TGI data generated in N87 tumor model. Solid lines represent median and dotted lines represent 5th and 95th percentiles. Model predictions are superimposed over the observed data for each cohort. Key: blue, ADC alone; green, Trastuzumab alone; red, combination of ADC and Trastuzumab; black, control

Table I.

A List of Published or Estimated Model Parameters That Were Used to Drive the Proposed Semi-mechanistic PK-PD Model

Parameter	Definition	Value (CV %)	Unit	Source
Parameters associated with plasma pharmacokinetics
CLTTmAb, CLDTTmAb	Central and distributional clearances of Trastuzumab	0.033, 0.0585	L/day/Kg	In house
V1TTmAb, V2TTmAb	Central and peripheral volumes of distribution for Trastuzuma	0.084, 0.051	L/day/Kg	In house
$K_{dec}^{T-DM1}$ $K_{dec}^{T-vc-MMAE}$	1st order deconjugation rate of payload (i.e., DM1 and MMAE respectively) from ADC in the systemic circulation	0.241, 0.353	L/day/Kg	(1) In house
Parameters associated with TGI of N87 bearing mice
$K_g^{EX}$, ${\omega }^{K_g^{Ex}}$	Mean and standard deviation of random effects associated with exponential N87 tumor growth rate	0.121 (47.5%), 0.861 (43.9%)	1/day	Estimated
$K_g^{Lin}$, ${\omega }^{K_g^{Lin}}$	Mean and standard deviation of random effects associated with linear N87 tumor growth rate	57.2 (21.6%), 0.426 (34%)	mm3/day	Estimated
TVmax	Maximum carrying capacity of N87 tumors	5000	mm3	Fixed
χ	Constant for switching from exponential to linear growth patterns	20	Unitless	Fixed
$K_{Kill}^{T-DM1}$	Linear killing rate constant of T-DM1	1.66E−3 (25.9%)	1/day	Estimated
$K_{Max}^{T-vc-MMAE}$ $K{C}_{50}^{T-vc-MMAE}$	Maximum killing rate and systemic T-vc-MMAE concentration inducing 50% of maximum killing respectively	0.188 (4.5%), 0.19 (43.9%)	/day, nM	Estimated
$K_{Kill}^{TTmAb}$	Linear killing rate constant of Trastuzumab	5.17E−4 (17.8%)	1/day	Estimated
${\tau }^{T-DM1}$, ${\tau }^{T-vc-MMAE}$, ${\tau }^{TTmab}$	Transit time associated with N87 tumor killing with T-DM1, T-vc-MMAE, and Trastuzumab respectively	2.9 (28.2%), 0.308 (11.2%), 1.97 (26%)	Day	Estimated
Parameters associated with TGI of MDA-MB-453 bearing mice
$K_g^{Ex}$, ${\omega }^{K_g^{Ex}}$	Mean and standard deviation of random effects associated with exponential MDA-MB-453 tumor growth rate	0.0225 (7.16%), 0.182 (28.8%)	1/day
$K_{Kill}^{T-DM1}$	Linear killing rate constant of T-DM1	4.34E−3 (5.61%	1/day	Estimated
$K_{Kill}^{T-vc-MMAE}$	Linearkilling rate constant of T-vc-MMAE	5.45E−3 (4.3%)	1/day	Estimated
$K_{Max}^{TT-mAb}$, $K{C}_{50}^{TTmAb}$	Maximum killing rate and systemic Trastuzumab concentration inducing 50% of maximum killing respectively	0.354 (11.5%), 110 (23.2 %)	1/day, nM	Estimated
${\tau }^{T-DM1}$, ${\tau }^{T-vc-MMAE}$, ${\tau }^{TTmAb}$	Transit time associated with MDA-MB-453 tumor killing with T-DM1, T-vc-MMAE, and Trastuzumab respectively	8.42 (7.87%), 3.41 (10.3 %), 0.03 (10.1%)	1/day	Estimated
Parameter associated with synergistic efficacy (Ψ) upon coadministration of ADC with antibody
$\begin{array}{l}{\Psi }_{T-DM1}^{3fold}\\ \left(N87\right)\end{array}$	Interaction term associated with coadministration of T-DM1 and 3-fold higher Trastuzumab	2.86 (4.52%) confidence interval [2.6–3.12]	Unitless	Estimated
$\begin{array}{l}{\Psi }_{T-VC-MMSE}^{3fold}\\ \left(N87\right)\end{array}$	Interaction term associated with coadministration of T-vc-MMAE and 3-fold higher Trastuzumab	0.39 (37.4%) confidence interval [0.1–0.69]	Unitless	Estimated
$\begin{array}{l}{\Psi }_{T-DM1}^{3fold}\\ \left(MDA-MB-453\right)\end{array}$	Interaction term associated with coadministration of T-DM1 and 3-fold higher Trastuzumab	0.565 (8.2%) confidence interval [0.472–0.657]	Unitless	Estimated
$\begin{array}{l}{\Psi }_{T-vc-MMAE}^{3fold}\\ \left(MDA-MB-453\right)\end{array}$	Interaction term associated with coadministration of T-vc-MMAE and 3-fold higher Trastuzumab	0.577 (14.3%) confidence interval [0.412–0.742]	Unitless	Estimated
$\begin{array}{l}{\Psi }_{T-DM1}^{1fold}\\ \left(MDA-MB-453\right)\end{array}$	Interaction term associated with coadministration of T-DM1 and 1-fold higher Trastuzumab	0.1 (10.8 %) confidence interval [0.08–0.12]	Unitless	Estimated
$\begin{array}{l}{\Psi }_{T-vc-MMAE}^{1fold}\\ \left(MDA-MB-453\right)\end{array}$	Interaction term associated with coadministration of T-vc-MMAE and 1-fold higher Trastuzumab	1.36 (20.5 %) confidence interval [0.8–1.92]	Unitless	Estimated
$\begin{array}{l}{\Psi }_{T-DM1}^{8fold}\\ \left(MDA-MB-453\right)\end{array}$	Interaction term associated with coadministration of T-DM1 and 8-fold higher Trastuzumb	0.382 (16.4 %) confidence interval [0.257–0.507]	Unitless	Estimated
$\begin{array}{l}{\Psi }_{T-vc-MMAE}^{8fold}\\ \left(MDA-MB-453\right)\end{array}$	Interaction term associated with coadministration of T-vc-MMAE and 8-fold higher Trastuzumab	0.577 (14.3 %) confidence interval [0.412–0.742]	Unitless	Estimated

Since a biphasic growth profile was observed for N87 tumors, both exponential $\left(K_g^{Ex}\right)$ and linear $\left(K_g^{Lin}\right)$ growth rates were estimated using the hybrid growth model (29), along with the associated inter-subject variability. In case of MDA-MB-453, a single exponential growth rate was able to characterize the tumor growth data reasonably well. For most of the monotherapy treatments, TGI data from only two different dose levels were available. Consequently, a linear killing rate $\left(K_{\text{Kill}}^{\text{Drug}}\right)$ was utilized to facilitate the characterization of this data. However, whenever > 2 dose levels were available, a non-linear killing rate was applied with parameters related to maximum killing rate $\left(K_{\max }^{\text{Drug}}\right)$ and plasma concentrations that induces 50% of maximal killing $\left({\text{KC}}_{50}^{\text{Drug}}\right)$. Examples of such data include T-vc-MMAE efficacy in N87 tumors (Supplementary Figure 5), and Trastuzumab efficacy in MDA-MB-453 tumors (Supplementary Figure 19).

Modeling analysis confirmed the observed data that T-vc-MMAE demonstrated the highest efficacy in both tumor models, followed by T-DM1 and TTmAb.

The 2nd step of quantitative evaluation was to fix the parameters for monotherapies and estimate only the parameter associated with drug interaction (ψ), by characterizing the data from coadministration therapies. For each combination therapy, the data from different dose levels were pooled together to estimate the value of ψ. The VPC plots from the fitting of coadministration data are provided in Figs. 5 and 6, which reveals that ~ 90% of the observed data was within 90% confidence intervals. The predictions for individual animals (IPRED) and goodness of fits (GoF) plots are provided in Supplementary Figures 9–12 for N87 tumors, and Supplementary Figures 21–32 for MDA-MB-453 tumors. Model estimated values of ψ are listed in Table I, along with the estimated precision (% CV) and confidence intervals. It was found that the coadministration therapy that led to the estimated value of ψ >1 (2.86, CI 2.6–3.12) for T-DM1 administration with 3-fold higher Trastuzumab in N87 (HER2-high) tumors. This result indicates a synergistic drug interaction for this combination. All other coadministration regimens in either N87 or MDA-MB-453 tumors resulted in a ψ value < 1, meaning the effect was always additive or less than additive following coadministration of TTmAb with T-DM1 or T-vc-MMAE.

DISCUSSION

ADC targets are often chosen based on their high expression levels on cancer cells and faster internalization rate, both of which are desired properties to deliver an efficacious amount of payload within the cancer cells (7,8). However, these desirable properties could also be detrimental for the overall efficacy of ADCs. Rapid binding and internalization of ADCs upon extravasation limits their exposure to the perivascular regions of the tumor, resulting in the formation of a virtual barrier known as the binding-site barrier (BSB). BSB impedes the entry of ADCs into the deeper portions of the tumor and may impact the efficacy of ADCs in an adverse manner. In addition, the presence of a BSB may be more prominent for ADCs compared with antibodies since the ADCs are administered at relatively lower doses due to the dose-limiting toxicities from the payload. Historically, several strategies have been investigated to help the antibodies overcome the BSB, including reduction in the affinity and alteration in the size (34–36). Coadministration of competing molecules that interfere with the binding of antibody to the antigen has also been evaluated to overcome the BSB for antibodies. For example, Abuqayyas and Balthasar have proposed coadministration of a high-affinity anti-trastuzumab peptide (H98) as a strategy to overcome the BSB for Trastuzumab (37). They have hypothesized that this strategy would facilitate deeper penetration of Trastuzumab within the tumor. Similarly, Pak et al. have proposed the presence of shed antigen as a strategy to overcome the BSB for immunotoxins within a solid tumor (7,8).

More recently, Cilliers et al. have proposed coadministration of naked antibody as a strategy to overcome the BSB for ADCs in a solid tumor using ado-Trastuzumab emtansine (T-DM1) as a model system (6). Because of its high expression and significant internalization, HER2-targeted agents often show heterogeneity (35,38,39), making it useful for studying the BSB. They first demonstrated the presence of BSB for T-DM1 at a clinically approved dose of 3.6 mg/kg in N87 tumor-bearing mouse model. Subsequently, using imaging and mathematical modeling, they highlighted how the BSB could be overcome by coadministration of 3 or 8-fold higher Trastuzumab. Finally, they demonstrated an improvement in the efficacy of T-DM1 for N87 tumors when coadministered with 1, 3, or 8-fold higher Trastuzumab. However, whether the coadministration of antibody leads to just an additive effect or truly a synergistic effect was not quantitatively evaluated. In addition, generalization of this approach towards other doses, tumor models, and ADCs remains in question (6,40). For instance, if an ADC can demonstrate the bystander effect and its payload can diffuse across the tumor, it may not experience severe BSB, and improvement in its efficacy following antibody coadministration may not be as notable (40). Consequently, here, we have quantitatively evaluated the beneficial effects of Trastuzumab coadministration on the efficacy of two different Trastuzumab-based ADCs (T-DM1 with minimal bystander effect and T-vc-MMAE with notable bystander effect), at two different dose levels, in two different HER2 expression tumor models (high HER2 expressing N87 tumor and low HER2 expressing MDA-MB-453 tumor) (Fig. 1a).

TGI studies (Figs. 2, 3, and 4) revealed that in both the tumor models, T-vc-MMAE was more efficacious than T-DM1. While this difference may stem from the inherent difference in the sensitivity of the two tumor models towards the released drug (i.e., MMAE versus Lys-mcc-DM1), it is more likely to stem from the ability of T-vc-MMAE to exhibit bystander effect. In fact, in vitro cell killing assays indicate similar potency between T-vc-MMAE (190 pM IC50(22)) and T-DM1 (82 pM IC50(21)). TGI studies also revealed that Trastuzumab had significantly higher efficacy in HER2-low MDA-MB-453 tumors compared with HER-2 high N87 tumors. In fact, there was a dose-dependent increase in the efficacy of Trastuzumab in MDA-MB-453 tumors in vivo. This result was unexpected, considering that Barok et al. (24) have shown that MDA-MB-453 cells are inherently insensitive to Trastuzumab in vitro (Supplementary Figure 33), and a SCID mouse model was used to reduce immune effects. The observed discrepancy may stem from the evolution of the cells in vivo, which may have rendered them responsive to Trastuzumab.

Efficacy studies with coadministration of T-vc-MMAE or T-DM1 with 1, 3, or 8-fold higher Trastuzumab revealed that coadministration strategy was more beneficial for HER2-high N87 tumors compared with HER2 low MDA-MB-453 tumors. This observation may stem from the presence of more prominent BSB in antigen overexpressing tumors, which could be overcome with the help of antibody coadministration. Moreover, the efficacy studies revealed that the benefit of the coadministration strategy in N87 tumors was more pronounced at the higher ADC doses. This may seem counterintuitive, as the BSB phenomenon is supposed to be reduced at a higher dose. However, the BSB only disappears upon saturation of the tumor, and N87 tumors are not saturated at the 0.36–3.6 mg/kg ADC doses. In fact, at very low doses relative to expression, the ADC may not even saturate the first few perivascular cell layers, so the addition of unconjugated antibody would not improve ADC penetration into the tumor.

To quantitatively evaluate the nature of drug interaction following antibody coadministration, a mathematical modeling approach was employed. A semi-mechanistic population PK-PD model was developed and used to characterize all the TGI data. By estimating the value of drug interaction parameter ψ, the nature of a given drug interaction was identified. It was observed that when 3-fold higher Trastuzumab was coadministered with 3.6 mg/kg T-DM1 in N87 tumors, there was a synergistic drug interaction. This observation was consistent with the observation reported by Cilliers et al. and suggests that the observed effect was greater than what one can achieve by just an additive effect of monotherapies. All other coadministration therapies in HER2-high or HER2-low tumors with T-DM1 or T-vc-MMAE (Fig. 1a, Table I) resulted in ψ values < 1, indicating less than additive effect. Of note, although they did not reach statistical significance, coadministration did improve the efficacy in the MDA-MB-453 model with non-bystander (Fig. 5c, k, l, and m) and bystander (Fig. 5e, o, p, and q) payloads. It also improved efficacy in the N87 model with DM1 (Fig. 6c and i) and MMAE (Fig. 6d and k). The synergistic values for the N87 tumors suggest that the high dose of ADC results in “overkill” of the targeted cells with the addition of unconjugated antibody, which has little efficacy by itself. The payload reaches more cells while maintaining lethal payload delivery, resulting in greater TGI than the ADC or unconjugated antibody dose alone. In all other cases, the higher antibody uptake results in less than additive effects. This could be due to reaching a greater number of cells with antibody coadministration but less efficient killing of these cells due to lower payload per cell. At the low doses, increased antibody dosing may not even saturate the first few cell layers, so antibody coadministration may not improve penetration. It is anticipated that very high levels of coadministered antibody may even compete with the ADC for the target receptor, enough to cause an adverse effect on the efficacy of ADC. This result was not seen even at high antibody doses (8:1 ratio) with the lower expressing MDA-MB-453 cells likely because of the notable efficacy of the antibody itself in this model (e.g., Fig. 4c and d, green lines).

Thus, while antibody coadministration may be beneficial to overcome the BSB for ADCs, this strategy needs to be implemented in a meticulous way. First, the target expression level/internalization rate relative to the ADC maximum tolerated dose provides an indication of whether a BSB will exist. Sub-saturating doses are likely to result in heterogeneous distribution while saturating doses result in more uniform uptake (paralleling antigen expression (36,41)). Next, it is important to determine the potency and delivery of the payload relative to the single-cell dose needed for cell death. High levels of cellular delivery relative to potency can result in significant “overkill” of a few cells and spreading the antibody dose deeper into the tissue can result in a synergistic increase in TGI (as seen with N87 tumors). Models with low ADC delivery per cell can have the TGI reduced below that of the ADC alone if the antibody coadministration lowers cellular uptake such that no cells receive a lethal dose, although this was not seen in these data. Most of the tumors resulted in less than additive TGI (i.e., ψ < 1) where the additional cells receiving payload outweighed the reduction in number of payloads per cell. Under these circumstances, the “cost-benefit” ratio depends heavily on any drawbacks from a higher antibody dose. A broad application of the coadministration strategy in all the scenarios may lead to detrimental effect in certain cases. Outcomes of our experimental results in HER2-low MDA-MB-453 tumors, where the coadministration strategy consistently led to a less than additive TGI (i.e., ψ < 1), also suggest utility of this approach in improving therapeutic window of ADCs for heterogeneous targets (e.g., EGFR, HER2, and PSMA) where on-target/off-tumor toxicities could be circumvented. Since the clinical importance of BSB and overcoming the BSB to improve the efficacy of antibody-based therapies is still not clear, how the proposed antibody coadministration therapy will improve the clinical efficacy of ADCs remains to be seen.

If one was to summarize the cost-benefit analysis, there are 6 potential advantages to higher antibody doses and 3 potential limitations, each depending on the specific agent (antibody, target, payload, and linker). The potential benefits include the following: (1) better tissue penetration and payload cell killing (6,21), (2) improved receptor signaling blockade (e.g., trastuzumab (42)), (3) increased Fc-effector functions from better tumor cell coverage (43), (4) higher antibody doses to minimize target-mediated drug disposition and increase tumor uptake(44,45), (5) lower target-mediated toxicity from the payload by blocking receptor-mediated uptake in healthy tissue (46), and (6) lower DAR-dependent clearance if a higher dose and lower DAR strategy is used to increase the antibody dose (47). The three potential limitations are as follows: (1) dilution of the per cell payload delivery below the necessary threshold for cell death (particularly with very low antigen expression of < 10 K receptors/cell (48) or with lower potency payloads (49,50)), (2) targets with high (unconjugated) antibody toxicity (e.g., EGFR), and (3) greater material costs due to higher antibody doses. Although, the supra-high dose of naked antibody may not be feasible for all therapeutic targets, clinical studies with Trastuzumab have revealed that a dose up to 6 mg/kg Q1W were tolerable in HER2+ breast cancer patients (51), which results in a 5-fold higher dose-level in comparison to 3.6 mg/kg T-DM1 administered Q3W. Finally, resistance mechanisms are an important concern (52), but these do not fall clearly in either category. Significant “overkill” of a few cells may reduce the likelihood of multi-drug resistance pumps or transporters enabling escape from therapy in some circumstances (53), but maximizing multiple mechanisms of action (receptor signaling blockade, Fc-effector mediated immune cell killing, and payload-mediated death (54)) along with the potential to delivery more total payload to the tumor in some instances (minimizing TMDD and/or lower DAR-dependent clearance) may more than compensate in others. The multitude of antibodies, targets, payloads, and linkers makes broader generalizations impractical, and each ADC must be analyzed individually.

In sum, here, we have quantitatively evaluated the potential of antibody coadministration therapy as a strategy to overcome the BSB effect for ADCs in solid tumors. Both experimental results and mathematical modeling indicated that this strategy could be more beneficial for ADCs that do not show the bystander effect. For ADCs with significant bystander effect, the coadministration strategy may not result in as large an improvement in efficacy. Our results also indicate that the coadministration strategy could be more beneficial for tumors with very high-antigen expression levels, as these tumors demonstrate more prominent BSB. It was also found that the beneficial effect of antibody coadministration could be dose-dependent, and at low doses, the amount of ADC in the tumor may be too limited to demonstrate any improvement in the efficacy following more homogenous distribution of ADC in the tumor. Collectively, the results and mathematical model provided here should provide further guidance on optimizing the drug to antibody ratio (effectively achieved with antibody coadministration) for ADCs based on payload potency, bystander effects, target expression and internalization, and ADC doses.