The physiological limits of bispecific monoclonal antibody tissue targeting specificity

ABSTRACT

Bispecific monoclonal antibodies (bsmAbs) are expected to provide targeted drug delivery that overcomes the dose-limiting toxicities often accompanying antibody-drug conjugates (ADC) in clinical practice. Much attention has been paid in the past to target selection, mAb affinities and the payload linker design, but challenges remain. Here, we demonstrate, by physiologically based pharmacokinetic (PBPK) in silico modeling and simulation, that the tissue-targeting accuracy of mono- and bispecific antibody therapeutics is substantially limited by normal physiological characteristics like organ volumes, blood flow rates, lymphatic circulation, and rates of extravasation. Only a small fraction of blood flows through solid tumor, where the diffusion-driven extravasation is relatively slow compared with many other organs. EGFR and HER2 are used as model antigens based on their experimentally measured tissue and tumor expression levels, but the approach is generic and can account for the cellular expression variation of targets. The model confirms experimental observations that only about 0.1–1% of the dosed mAb is likely to reach the tumor, while the rest ends up in healthy tissues due to target-mediated internalization and nonspecific uptake. The model suggests that the dual-positive tumor cell targeting specificity with bispecific antibodies is likely to be higher at lower drug concentrations and doses. However, this can be offset by elevated drug exposure in more accessible healthy tissues, primarily endothelium. The balance of exposure can be shifted toward tumor cells by using higher doses, albeit at the expense of more extensive target engagement elsewhere in the body, suggesting the need to adapt the toxicity of the payload if ADCs are considered. We suggest that PBPK modeling can guide and support biologics and bsmAb development, from target evaluation and drug optimization to therapeutic dose selection.

Introduction

In total, more than 200 monoclonal antibodies (mAbs) have been approved worldwide to treat conditions ranging from immunological and neurological diseases to cancer and infections.¹ While this testifies to the efficacy and safety of mAbs, where the adverse reactions due to off-target effects are typically tolerable and even immunogenicity, if encountered, compromises therapeutic efficacy only, more consequential on-target adverse effects can be dose-limiting, as reviewed by Tabrizi et al.² and Hansel et al.³

On-target toxicity is related to the presence of target antigens in healthy tissues. For example, while EGFR and HER2, two well-studied antigens from the epidermal growth factor receptor family, are often found in excess of a million molecules per tumor cell,^4,5 they are also present in healthy tissues at 25,000–50000 molecules per cell,^6–9 where they play a normal physiological role in angiogenesis.^10,11 Therefore, it is unsurprising that less than 1% of a dosed mAb reaches the solid tumor, as pointed out by Bench et al.¹² The rest is taken up by target-mediated drug disposition (TMDD) or macropinocytosis in healthy tissues alongside endogenous IgG and other plasma proteins.¹³ Target engagement on the healthy cells does not remain inconsequential. It can result in side effects, like dermatitis in the case of EGFR and cardiotoxicity in the case of HER2.³ Increased tissue-targeting specificity to the tumor is, therefore, highly desirable.

Bispecific mAbs (bsmAbs) can bind two different target molecules simultaneously and have been proposed as a modality with improved tissue-targeting potential. This is based on the observation that when two targets are expressed on the surface of the same cell,¹⁴ both Fab arms of the bound antibody can be engaged at the same time, as was demonstrated by Mazor et al.¹⁵ in the case of a bsmAb against CD4 and CD70. The resulting avidity effect¹⁶ enhances effective affinity toward cells expressing both targets at the same time rather than only one or the other. This is supported by quantitative mechanistic modeling by Sengers et al.,¹⁷ which suggests up to 10,000-fold enhanced affinity due to the avidity effect, while the experimental values often lie in the range of 100–1000, according to Einav et al.¹⁸ and Dong et al.¹⁹ A recent publication by Synan et al.²⁰ describes the discovery process of one such bsmAb against p- and LI-cadherins. The workflow started with target identification, followed by in vitro antibody optimization, in vivo evaluation of potency in a preclinical mouse model, and formatting into a bispecific antibody-drug conjugate (bsADC).

Here, we use a physiologically based pharmacokinetic (PBPK) cross-species/cross-modality platform for biologics^21–23 to develop an in silico modeling framework that allows us to analyze the tissue-targeting specificity of bsmAbs. The modeling framework considers the impact of generic factors like organ volumes, blood and lymph flow rates, as well as vascular permeability that describes the tissue distribution, absorption and elimination properties of soluble proteins, be they dosed or endogenous. The model is further furnished with EGFR and HER2 targets at tissue concentrations derived from quantitative protein mass spectrometry.²⁴ The cells making up the tissues were assigned to include those carrying both targets simultaneously, just one or the other, or none at all. This allows us to evaluate the benefits of bsmAbs relative to the comparable monospecific variants.

Materials and methods

PBPK model structure

The PBPK model, as outlined in Supplementary Figure S1a, follows the format introduced for mAbs by Shah and Betts.²¹ The model used in this study is based on two-pore cross-species/cross-modality framework by Sepp et al.²⁵ with the following modifications: the central plasma pool is split into venous and arterial compartments, while small fractions of skin and skeletal muscle are separated as subcutaneous and intramuscular dosing compartments with dedicated draining lymph nodes.²⁶ Solid tumor penetration follows the diffusion-driven well-stirred formalism developed by Thurber et al.²⁷

The typical organ structure accommodates soluble proteins of any size according to the two-pore formalism introduced by Rippe and Haraldsson.²⁸ In PBPK setting, this approach describes the filtration-diffusion exchange of proteins between the organ’s vascular and interstitial compartments, as shown in Figure 1.

Figure 1.

The layout of a typical organ in the two-pore model. Jorg,L and Jorg,S represent fluid flow through the large and small paracellular pores of the vasculature, PSorg denotes the permeability-surface area product, and FcRn is the neonatal fc receptor. X represents the drug. Q_org denotes organ plasma flow and J_org organ lymph flow. Endosomal kd refers to the dissociation constant of FcRn-mAb complex, k_up is fluid uptake by macropinocytosis, k_deg is the rate constant for non-specific endosomal degradation of unbound proteins, k_rec is the FcRn-mAb complex recycling rate constant and FR stands for the fraction of FcRn-mAb recycling complex that is directed to the vascular plasma compartment of the organ. Organ-specific adjustments to the brain, lungs, kidney and tumour compartments are shown in Supplementary Figure S1B.

Macropinocytosis (k_up) into endosomal compartments is postulated to involve only endothelial cells, where endosomal FcRn-mediated recycling (k_rec) and nonspecific degradation (k_deg) take place.^23,24,29,30

The model also includes distinct cellular populations in all organs. Organ endothelial and parenchymal cells are divided into four groups that express both targets simultaneously, just one of the two, or none at all, as shown in Figure 2. The possibility of antibodies cross-linking the targets on two adjacent cells is not incorporated.

Figure 2.

The schematic outline of the reactions between the bsmAb and two cell surface targets: green oval-EGFR and blue oval-HER2. Only binary complexes form when only one of the targets is present on the cell surface. Binary and ternary complexes can form when both targets are present on the cell surface. When there is no target expression, no complexes form. A more detailed scheme also includes non-specific uptake, as shown in Supplementary Figure S2.

The cross-linking step of bsmAb forming a ternary complex on dual-positive cells is expressed in terms of the antigens’ cell surface concentrations using two-dimensional surface reaction kinetics and follows the formalism of Sengers et al. ¹⁷ The surface concentrations are calculated from the tissue concentrations of the respective membrane targets and the number of cells in the organ. The model postulates that any internalized mAb is irreversibly degraded, i.e., there is no recycling back to the cell surface. The internalization rate constant of the ternary complex composed of the bispecific mAb, EGFR and HER2 is postulated to be the sum of rate constants for EGFR and HER2 that were estimated from the plasma PK data for cetuximab and trastuzumab.²⁴ Non-specific clearance in each organ is assigned to different cell populations in proportion to their size.

Physiological parameters and cell numbers

Organ volumes, plasma flow rates and two-pore parameters were taken from our earlier publications.^25,31–33 These are based on the BioDMET database by Graf et al.³⁴ while the pore size values are from Rippe and Haraldsson.²⁸ Half of the organ interstitial volume was assigned as inaccessible to mAbs.³⁵ The solid tumor compartment is defined to have 25 mL volume that contains 100 million cells per mL.³⁶

Organ endothelial cell numbers $\mathit{nE}{C}_{\mathit{organ}}$were calculated using Equation 1

$$\mathit{nE}{C}_{\mathit{organ}}=\frac{{\mathit{V}}_{\mathit{pl},\mathit{organ}}}{V_{\mathit{pl},\mathit{peripheral}}}\cdot \mathit{nE}{C}_{\mathit{total}}$$ (1)

where $V_{\mathit{pl},\mathit{organ}}$ is the organ plasma volume and $V_{\mathit{pl},\mathit{peripheral}}$ is the total peripheral plasma volume across all organs. The peripheral plasma volume is the difference between the total plasma volume and the sum of venous and arterial components, as shown in Equation 2.

$$V_{\mathit{pl},\mathit{peripheral}}=V_{\mathit{pl},\mathit{total}}-V_{\mathit{pl},\mathit{central}}=V_{\mathit{pl},\mathit{total}}-\left(V_{\mathit{pl},\mathit{arterial}}+V_{\mathit{pl},\mathit{venous}}\right)$$ (2)

Organ intracellular volume $V_{\mathit{IC},\mathit{organ}}$ is defined as the difference between the total organ volume $V_{\mathit{organ}}$ and the sum of blood volume $V_{\mathit{bl},\mathit{organ}}$ and interstitial volume $V_{\mathit{IS},\mathit{organ}}$.

$$V_{\mathit{IC},\mathit{organ}}=V_{\mathit{organ}}-\left(V_{\mathit{bl},\mathit{organ}}+V_{\mathit{IS},\mathit{organ}}\right)=V_{\mathit{organ}}-\left(\frac{{\mathit{V}}_{\mathit{pl},\mathit{organ}}}{1-\mathit{HCT}}+V_{\mathit{IS},\mathit{organ}}\right)$$ (3)

where HCT is hematocrit.

The organ parenchymal cell numbers $\mathit{nP}{C}_{\mathit{organ}}$ were calculated by multiplying the ratio of organ and the body intracellular volumes $V_{\mathit{IC},\mathit{total}}$ with the total number of cells in humans $\mathit{nCell}{s}_{\mathit{total}}$³⁷ (Equation 4).

$$\mathit{nP}{C}_{\mathit{organ}}=\frac{{\mathit{V}}_{\mathit{IC},\mathit{organ}}}{V_{\mathit{IC},\mathit{total}}}\cdot \mathit{nCell}{s}_{\mathit{total}}$$ (4)

Target tissue concentrations

EGFR and HER2 tissue concentrations in Model 1 are based on the protein quantitative mass spectrometric values from the PaxDB database,³⁸ which were converted into molarity by Sepp and Muliaditan.²⁴ One million EGFR and HER2 receptors per cell^4,5 were used for the cells in the solid tumor compartment. Target expression on tumor endothelial cells was defined as median from the values for the endothelial cells in all normal tissues, 7.8E4 EGFR and 7.04E4 HER2 molecules per cell.

Models 2–4 encode variants with decreased target expression levels. Model 2 retains the organ-specific receptor number per cell, but decreases the number of target-positive cells by a factor of ten. Model 3 leaves the target-positive cell numbers unchanged, but reduces the target cellular expression level 10-fold. Model 4 combines the lower target-positive cell number of Model 2 with the reduced expression level of Model 3.

In Model 1, the cells in a compartment are divided into four equal fractions carrying no target, just one of the two targets, or both at the same time. The receptor number values on the single- and dual-positive endothelial cells were calculated according to Equation 5.

$$\mathit{n}{R}_{\mathit{target},\mathit{organ},\mathit{va}}=\frac{{\mathit{C}}_{\mathit{target},\mathit{organ},\mathit{va}}\cdot V_{\mathit{organ},\mathit{va}}\cdot N_A}{\mathit{nE}{C}_{\mathit{organ}}}\cdot 2$$ (5)

$N_A$ is the Avogadro number, and $C_{\mathit{target},\mathit{organ},\mathit{va}}$ is the volume concentration equivalent of the target in capillary plasma.

The receptor number values on the target-positive parenchymal cells in each organ were calculated according to Equation 6. These cells can carry just one of the targets (single-positive) or both of them (dual-positive).

$$\mathit{n}{R}_{\mathit{target},\mathit{organ},\mathit{in}}=\frac{{\mathit{C}}_{\mathit{target},\mathit{organ},\mathit{in}}\cdot V_{\mathit{organ},\mathit{in}}\cdot N_A}{\mathit{nP}{C}_{\mathit{organ}}}\cdot 2$$ (6)

where $C_{\mathit{target},\mathit{organ},\mathit{in}}$ is the volume concentration equivalent of the target in the interstitial space.

The statistical multiplier 2 in Equations 5-6 arises from only half of the cells in a compartment carrying either of the two targets. Thus, in any compartment, half of the target is found on single-positive cells and half on dual-positive cells.

Modelling and simulations

The full PBPK model was built in Matlab 2023b SimBiology using computer-assisted assembly.²⁵ Briefly, the template organ outline, shown in Supplementary Figure S2, is used by a script that assembles the full model schematically shown in Supplementary Figure S1, with state variables outlined in Supplementary Table S1. The final model contains 1364 algebraic and 715 ordinary differential equations. These, and the physiological parameters, can be found in the Supplementary Table 2. Although complex, the model is a simplification and does not incorporate all of the known ErbB family receptor tyrosine kinase biology that involves constitutive recycling between membrane-bound and endosomal fractions, homo- and heterodimerization on the cell surface in the absence and presence of different ligands etc.^39,40 Instead, the drug-target complex degradation, as parameterized via TMDD, is interpreted as a single-step irreversible internalization step that removes all bound species at the same time.

Four different mAbs were modeled for comparison purposes: an isotype control mAb with no binding activity (prototyped on mepolizumab,⁴¹ an EGFR-binding mAb prototyped on cetuximab,⁴² a HER2-binding mAb prototyped on trastuzumab⁴³ and a hypothetical bsmAb that combines the monovalent affinities of cetuximab and trastuzumab and where target cross-linking is boosted by the maximum avidity effect of around 10,000 that is expected for bispecific mAbs.¹⁷ Three single-dose intravenous (IV) injections at 0.1, 1, and 10 mg/kg were simulated for each molecule to explore any dose-related effects. The model postulates that the affinities of the mono- and bispecific formats of the monospecific mAbs are the same, i.e., no avidity effect is factored into the monospecific mAb binding. This is based on the experimental observations where the monovalent affinities of cetuximab and trastuzumab, as measured by surface plasmon resonance (SPR), were very similar to the cell binding dissociation equilibrium constants measured by flow cytometry. For trastuzumab, the SPR-measured monovalent Kd = 1.9 nM⁴⁴ is very close to the flow cytometric Kd ≈4 nM.⁴⁵ In the case of cetuximab, the SPR-measured monovalent Kd value is 5 nM,⁴⁶ which is very close to the flow cytometric Kd ≈2.9 nM.⁴⁷

Several diagnostic parameters were defined to describe the drug and target behavior in the model. Receptor occupancy $\mathit{R}{O}_{\mathit{target},\mathit{organ},\mathit{cell},\mathit{compartment}}$ is the ratio of the drug-bound to the total target found on single- or dual-positive cells in the vascular or interstitial compartment of an organ, as shown in Equation 7.

$$\mathit{R}{O}_{\mathit{organ},\mathit{cell},\mathit{compartment}}=1-\frac{\mathit{Targe}{\mathit{t}}_{\mathit{free},\mathit{organ},\mathit{cell},\mathit{compartment}}}{\mathit{Targe}{t}_{\mathit{total},\mathit{organ},\mathit{cell},\mathit{compartment}}}$$ (7)

where cell denotes single- or dual-positive cells.

Intracellular concentrations of the degraded drugs degDrug represent the amounts of the drug that are internalized and catabolized in the cells of a given type. In the case of endothelial cells (EC), Equation 8 is used:

$$\mathit{degDru}{g}_{\mathit{organ},\mathit{cell},\mathit{EC}}=\frac{\mathit{degDru}{\mathit{g}}_{\mathit{cell},\mathit{organ},\mathit{pl}}\cdot V_{\mathit{organ},\mathit{pl}}}{\mathit{nCell}\_\mathit{Adjust}\cdot \mathit{nE}{C}_{\mathit{organ},\mathit{pl}}\cdot V_{\mathit{EC}}}$$ (8)

where $\mathit{degDru}{g}_{\mathit{cell},\mathit{organ},\mathit{pl}}$ is the effective concentration of degraded drug of a given cell type in organ plasma compartment, $V_{\mathit{organ},\mathit{pl}}$is the organ plasma volume, $\mathit{nE}{C}_{\mathit{organ},\mathit{pl}}$is the number of endothelial cells lining the vascular compartment of the organ, $V_{\mathit{EC}}$is the endothelial volume and $\mathit{nCell}\_\mathit{Adjust}$ is the fraction of a given cell type in the compartment.

In the case of the parenchymal cells (PC) Equation 9 is used:

$$\mathit{degDru}{g}_{\mathit{cell},\mathit{organ},\mathit{PC}}=\frac{\mathit{degDru}{\mathit{g}}_{\mathit{cell},\mathit{organ},\mathit{in}}\cdot V_{\mathit{organ},\mathit{in}}}{\mathit{nCell}\_\mathit{Adjust}\cdot V_{\mathit{organ},\mathit{PC}}}$$ (9)

where $\mathit{degDru}{g}_{\mathit{cell},\mathit{organ},\mathit{in}}$ is the effective concentration of degraded drug of a given cell type in the organ interstitial compartment, where $V_{\mathit{organ},\mathit{in}}$ is the organ interstitial accessible volume and $V_{\mathit{organ},\mathit{PC}}$ is the organ parenchymal volume.

The relative cellular concentrations $\mathit{R}{C}_{\mathit{cell},\mathit{organ},\mathit{compartment}}$ characterize the targeting specificity of the drug within a given compartment by dividing the apparent concentration of degraded bsmAb in any cell type of the organ with that in the double-positive tumor parenchymal cells $\mathit{degDru}{g}_{\mathit{AB},\mathit{tumour},\mathit{PC}}$. The RC values are calculated according to Equation 10:

$$\mathit{R}{C}_{\mathit{cell},\mathit{organ},\mathit{EC}}=\frac{\mathit{degDru}{\mathit{g}}_{\mathit{cell},\mathit{organ},\mathit{EC}}}{\mathit{degDru}{g}_{\mathit{AB},\mathit{tumour},\mathit{PC}}}$$ (10)

Fractions unbound (FU) in Equation 11-12 calculate the fractions of the free drug in plasma and interstitial compartments, where the concentrations of free mAb are divided by the sum of all free and bound mAb species present.

$$\mathit{F}{U}_{\mathit{organ},\mathit{pl}}=\frac{\mathit{mA}{\mathit{b}}_{\mathit{organ},\mathit{pl}}}{\mathit{mA}{b}_{\mathit{organ},\mathit{pl}}+\mathit{mAs}\_\mathit{mA}{b}_{\mathit{organ},\mathit{pl}}+\mathit{mBs}\_\mathit{mA}{b}_{\mathit{organ},\mathit{pl}}+\text{breakmAd}\_\mathit{mA}{b}_{\mathit{organ},\mathit{pl}}+\mathit{mBd}\_\mathit{mA}{b}_{\mathit{organ},\mathit{pl}}+\mathit{mAs}\_\mathit{mAb}\_\mathit{mAb}{d}_{\mathit{organ},\mathit{pl}}}$$ (11)

$$\mathit{F}{U}_{\mathit{organ},\mathit{in}}=\frac{\mathit{mA}{\mathit{b}}_{\mathit{organ},\mathit{in}}}{\mathit{mA}{b}_{\mathit{organ},\mathit{in}}+\mathit{mAs}\_\mathit{mA}{b}_{\mathit{organ},\mathit{in}}+\mathit{mBs}\_\mathit{mA}{b}_{\mathit{organ},\mathit{in}}+\text{break}\mathit{mAd}\_\mathit{mA}{b}_{\mathit{organ},\mathit{in}}+\mathit{mBd}\_\mathit{mA}{b}_{\mathit{organ},\mathit{in}}+\mathit{mAs}\_\mathit{mAb}\_\mathit{mAb}{d}_{\mathit{organ},\mathit{in}}}$$ (12)

The model was evaluated and validated using human plasma PK data for mepolizumab,⁴¹ cetuximab⁴²and trastuzumab,⁴³ as shown in Supplementary Figure S3. These three mAbs represent the scenarios of an isotype control mAb with linear PK and the target-related TMDD effects that follow mAb binding to EGFR or HER2. The latter reproduced the model behavior established previously in monospecific mAb format.²⁴

Results

Figure 3 shows the Model 1 concentration-time course predictions in plasma and the interstitial spaces of muscle, liver, and tumor. Isotype control, an inert mAb with no known interactions beyond FcRn, displays dose-linear kinetics with the same terminal half-life at all concentrations and all doses.

Figure 3.

Antibody concentration time course modelling for isotype control, cetuximab, trastuzumab and EGFR-HER2 bsmAb at 0.1, 1 and 10 mg/kg single IV doses in the default target expression level (model 1). Red-plasma (ve_va), green-muscle interstitium (mu_in), blue-liver interstitium (li_in), black-tumour interstitium (ta_in).

Given the highly permeable hepatic vasculature, the liver interstitial concentration is predicted to follow a similar time course. In skeletal muscle interstitium, the steady state develops more slowly due to relatively high interstitial volume. At the same time, the lower permeability of muscle vasculature leads to about 4-fold lower steady-state concentration than in plasma. In the tumor interstitium, the mAb concentration time course is expected to follow the plasma PK once the diffusion-driven exchange has equilibrated the concentrations in a steady state. In the case of cetuximab, trastuzumab and EGFR/HER2-bsmAb, TMDD inflicts non-linear plasma clearance as the mAb dose and circulating concentrations decrease. While the two monospecific parent mAbs are relatively similar PK-wise, the assumed combined internalization rate constant of the bsmAb ternary complex is predicted to accelerate the target-mediated clearance further, resulting in progressively stronger non-linearity. At the lowest dose, the bsmAb is predicted to disappear so quickly from the circulation that only transient exposure lasting a few days is expected to be observed. Supplementary Figure S4 shows the results for the lower target distribution scenarios in Models 2–4. As expected, the impact of TMDD on the mAb PK is diminished at lower tissue target concentrations, be it because of lower receptor number, lower target-positive cell fraction, or the combination of the two. Similar trends for the remaining organs are shown in Supplementary Figure S5. There is no striking difference between the results derived from Models 2 and 3, suggesting the overall 10-fold reduction in target amount achieved through lower cell number or lower receptor number is more impactful than the local cell surface concentrations of the targets.

Antibody-target complex formation depends on mAb affinity and the local concentrations of the drug and the targets. Figure 4 shows the predicted target occupancy time courses for the endothelial and tumor cells. The former are highly exposed to the drug in circulation, while the latter are less accessible in the tumor interstitium.

Figure 4.

The predicted target occupancy for the isotype control mAb, cetuximab, trastuzumab and the bsmAb on single- and dual-positive cells at 10, 1 and 0.1 mg/kg IV bolus dosing. Red-EGFR on EGFR+/HER2- cells, green-EGFR on EGFR+/HER2+ cells, blue-HER2 on EGFR-/HER2+ cells, black-HER2 on EGFR+/HER2+ cells. a) tumour endothelial cells, b) tumour cells.

Figure 4.

(Continued).

The results confirm no target engagement by the isotype control and the lack of discrimination between single- and dual-positive cells by monospecific mAbs in all dosing scenarios and all tissue locations. In the case of the bsmAb, at 10 mg/kg dose, the drug fully engages the targets both on single- and dual-positive endothelial cells for 30–40 days, after which the complexes on the single-positive cells gradually cease to form. In contrast, the avidity-driven binding to the dual-positive cells continues for another five to 10 days, but at rapidly diminishing and low pM plasma concentrations, as can be seen in Figure 3. This defines the conditions where the bsmAb has an advantage over the monospecific ones, at very low drug concentrations that disfavor monovalent complex formation on single-positive cells. At 0.1 and 1 mg/kg dose, limited and transient monospecific mAb target engagement on both single- and dual-positive endothelial cells occurs, while the bsmAb is predicted to be predominantly bound to dual-positive cells for a few days longer than to single-positive cells. In the solid tumor compartment, the interactions mirror those in plasma, but the duration of target engagement is shorter, reflecting the delay and slow rate of diffusion-driven drug extravasation. At 0.1 mg/kg, there is little to no tumor penetration, and hardly any sustained target engagement is predicted. Since tumor cells were assigned one million EGFR and HER2 receptor molecules per cell, their respective black and green color target occupancy profiles on dual-positive cells in the presence of the bispecific mAb overlay in Figure 4b. Notably, at the lowest dose simulated, most of the antibody is engaged and internalized by the targets on the endothelial cells before any extravasation into the tumor occurs. The results for the lower target expression scenarios in Models 2–4 are shown in Supplementary Figures S6 and S7. In these scenarios, TMDD has an increasingly lower impact as the target concentration decreases. There is little difference between modeling scenarios 2 and 3, though. This suggests that the overall target concentration is of greater importance on the PK of the bispecific drug than distribution between single- and dual-positive cell populations.

Due to the target tissue concentrations exceeding the Kd value of the binding reaction and mass action kinetics, a substantial fraction of the mAb will still bind the target even at very low concentrations, as shown in Supplementary Figure S8. However, as the drug concentration decreases, that interaction’s contribution to receptor occupancy becomes negligible.

As shown in Figure 5a for Model 1, the amount of the dosed mAb catabolized in any given organ correlates largely with the organ size and, to a lesser extent, the target expression level, the mAb and the dose, except in the case of solid tumor compartment. In the case of isotype control mAb, the distribution between a given tissue does not depend on the dose or the target expression level. In the case of the target-binding mAbs, the impact of TMDD is higher at lower doses since higher mAb concentrations result in target saturation and relatively higher contribution of nonspecific catabolism. This is most noticeable for the solid tumor compartment, shown in Figure 5b-e, where the target-binding mAbs are taken up and catabolized at 10- to 100-fold higher levels than the non-binding isotype control mAb.

Figure 5.

mAb uptake and degradation in different tissues at different target expression levels. Blue-isotype control, red-cetuximab, yellow-trastuzumab, purple-EGFR/HER2-bsmAb. a) Model 1 - default (high) target expression, all tissues except the tumour, b) Model 1- tumour at default (high) target expression, b) Model 2- tumour at 10-fold lower target-positive cell number, c) Model 3- tumour at 10-fold lower receptor number and d) Model 4- tumour at 10-fold lower cell and receptor numbers.

Figure 5.

(Continued).

The bsmAb advantage over monospecific mAbs is predicted to be more moderate, reaching around 3- to 5-fold at best and to be more pronounced at lower dose and target expression levels. The overall fraction of the injected dose taken up and catabolized in the tumor remains low, varying from 0.1 to 1%. The rest of the dosed mAb is catabolized in the healthy tissues, and this is a suitable measure to characterize the relative exposure of different tissues and cells to the payload molecules in the case of ADCs. Overall, there is a trend for the lower doses and target expression to facilitate higher uptake of the bispecific mAb in the tumor.

Further insight can be gained by looking at the relative uptake of the drug by different cell types in any tissue compartment, which is especially relevant in the ADC context. Using the double-positive target cells in the tumor as the reference point, it becomes possible to evaluate the impact of targeting two receptors at the same time rather than one or the other. Figure 6 presents the results for all mAbs in the context of baseline Model 1.

Figure 6.

mAb uptake and degradation in different cell populations of the vascular endothelium, skeletal muscle, liver, and tumour parenchyma relative to the EGFR+/HER2+ target cells in the tumour. Purple: EGFR⁺/HER2⁻ cells, yellow: EGFR⁻/HER2⁺ cells, orange: EGFR⁺/HER2⁺ cells and blue: EGFR⁻/HER2⁻ cells a) isotype control mAb, b) cetuximab, c) trastuzumab, d) EGFR/HER2 bispecific mAb. Full results for all modelled scenarios are shown in Supplementary Figure S10.

First, in the case of isotype control mAb, all cell types in a given organ compartment contribute equally to mAb uptake and catabolism since there is no target binding. The differences between organs arise primarily due to physiological factors such as relative lymph flow, vascular permeability, capillary plasma, and interstitial volumes. Due to the lack of lymph flow in the tumor compartment, the tumor cells are less exposed to the dosed mAb than any other tissue compartment (except the brain, where the diffusive pathway is missing, too). In the case of target-binding mAbs, the antigen-expressing cells will contribute more to mAb catabolism, with TMDD impact increasing as the dose decreases. It is clear, though, that only bsmAb will achieve any bias toward dual-positive cells, especially at lower doses. The rest of the tissues are shown in Supplementary Figure S10 and follow the same trend. Still, this higher tumor dual-positive cell specificity comes at the cost of relatively higher drug uptake in more highly exposed endothelium. It takes bispecific mAb doses of 1 and 10 mg/kg to achieve higher tumor exposure than in healthy tissues, albeit at the cost of substantial bystander cell engagement in the tumor and elsewhere.

Discussion

MAbs, including ADCs, are often called ‘Magic bullets’ that are expected to engage only the target cells whilst sparing the healthy ones:^48–50 “ … ADCs … guide cytotoxic payloads to the cancer cells”,⁵¹ “ … ADCs deliver the payload directly to tissues guided by the target specificity”⁵² and even “Due to … precise design, it brings about the target cell killing sparing the normal counterpart and free from the toxicities”.⁵³ In contrast, clinical observations point to a very different conclusion, where “Off-target toxicities are a major obstacle to … (ADC) therapy”,⁵⁴ “One of the downfalls of ADCs is that you can struggle to get them into solid tumours”⁵⁵ and “Many … (ADCs) have failed to demonstrate efficacy in the clinic because of dose-limiting toxicity caused by uptake into healthy tissues”.⁵⁶ Thus, the quest for the ultimate magic bullet is still ongoing, with bispecific mAbs and ADCs as frontrunners.⁵⁷ Here, we use holistic PBPD to examine bispecific antibody tissue-targeting accuracy by considering not only the in vitro properties of the mAb, but also dosing and the physiological constraints posed by the tissues and organs that make up the body. The core mechanistic and quantitative aspects of the model have been verified independently. These are bispecific mAb interactions with two cell membrane targets by Sengers et al.¹⁷ tissue distribution, absorption, circulation and elimination of biologics^{21,23,25,31–33} and mass-spectrometric proteomics-based^24,58 tissue target concentrations. The two remaining unknowns relate to the actual avidity coefficient that a cetuximab-trastuzumab-based bispecific mAb can display toward these targets and the internalization rate constant for the cross-linked mAb-EGFR-HER2 ternary complex on dual-positive target cells. No experimental data is available for the dual- and single-positive cell-binding activity of such a bispecific, although the construct has been assembled and described in vitro by Si et al.⁵⁹ In the PBPK model, the approach taken from Sengers et al.¹⁷ affords around a 10,000-fold avidity effect over the respective monovalent affinities. Secondly, there is no direct or indirect measure for the ternary complex internalization rate constant on dual-positive cells either. The model postulates that the ternary complex internalization rate constant is the sum of the respective values estimated for either target separately, i.e., either receptor can independently trigger internalization when in contact with a mAb. These two assumptions strongly favor the bispecific mAb tissue-targeting accuracy. If the actual values were lower, the dual-positive tissue-targeting specificity of the bispecific mAb construct would be compromised.

The principal results of our work are presented in Figures 5 and 6 and Supplementary Figures S9 and 10. These sum up mono- and bispecific mAb tissue uptake differentials and interactions with cell populations in the complex physiological setting where the target expression levels and ratios can vary substantially from one organ to another. Unsurprisingly, just like in the case of monospecific mAbs against EGFR and HER2,²⁴ most of the bsmAb dose is predicted to end up degraded in healthy tissues. This is primarily the consequence of a small fraction that a solid tumor takes up in the body and slow diffusion-dominated tumor penetration of the mAb compared with convection-dominated extravasation in normal tissues. In addition, tissue-based catabolism is the default elimination route for the mAbs, as they are not renally eliminated due to their large size. While the amino acids released in the process of antibody catabolism are of no concern,⁶⁰ the payload molecules of most ADCs are highly toxic, as pointed out by Neff-LaLord⁶¹ and Kraynov.⁶⁰ The cellular exposure simulation results are most relevant for ADCs with non-cleavable linkers where the payload remains confined in the cell where the drug degradation occurred. If this is not the case, the distinction between different cell populations and tissues will diminish.

The model defines two distinct sets of features that affect the tissue-targeting accuracy of bispecific mAbs. In the first category are the drug-related aspects, and in the second are the physiology-related aspects. To an extent, the former can be adjusted during the R&D process by optimizing the bispecific mAb monovalent affinities for the respective targets, the avidity effect and the dosing regimen. Mass action kinetics dictates that when the drug concentration exceeds the monovalent Kd value, there will be increasingly extensive monovalent target engagement and saturation on single-positive cells. The same applies to the targets. If the target concentrations on single-positive cells exceed the respective monovalent Kd values for the bispecific mAb, the drug will be sequestered on such cells even at concentrations below the equilibrium dissociation constant value. Therefore, the dual-positive cell-targeting accuracy of bispecific mAbs can be expected to improve at lower doses and target concentrations when the avidity effect of the bivalent interaction on the dual-positive cells outcompetes the weaker monovalent interactions. The size of the avidity effect is difficult to predict from the first principles for the given mAb-target combinations. In the absence of detailed structural information about the orientation of the molecules in the drug-target complex, screening for the optimal combination may be desirable. In the second category of factors influencing the tissue-targeting accuracy of bispecific mAbs are the constraints imposed by anatomy, physiology, and target distribution between different organs and the cells that make up the organs. Only a tiny fraction of the blood flows through solid tumors, often at irregular rates and in conditions where extravasation is slower than elsewhere due to the absence of paracellular fluid flow in the absence of functioning lymphatics.^62,63 For example, 0.1 mg/kg dose is predicted to result in highly accurate dual-positive cell engagement in the tumor in Figure 6d, yet healthy endothelial cells will experience substantially higher exposure, though still biased toward dual-positive cells. This means that lower doses may actually be suboptimal from the relative exposure perspective, and higher doses of the drug (e.g., 1 and 10 mg/kg plots in Figure 6d) may deliver relatively more payload where needed. In the context of a bispecific ADC for EGFR and HER2, the optimal payload would be a toxin molecule that is not prohibitively toxic at 10 mg/kg ADC doses, e.g., MMAE, while more toxic payloads, those allowing more specific delivery to the dual-positive cells in the tumor, may cause more harm in the periphery. In summary, the dosing conditions and drug properties may need to be optimized for the targets of interest, depending on their tissue distribution and expression level. In the case of cleavable linkers with higher plasma membrane permeability, any diffusion of the free toxin out of the cells where the ADC degradation took place would erode the margin of cellular targeting accuracy and expose bystander cells or other organs of the body, but investigating that scenario is beyond the scope of this work.

The modeling results of this work and the experimental results reported elsewhere do not support the concept of mono- or bispecific mAbs as ‘Magic bullets’, let alone ‘biological missiles’.⁶⁴ The ‘sticky drunkards’ parable suggested by George et al.⁶⁵ appears more appropriate. MAbs, like other proteins, are carried around in plasma and lymphatic circulation in different tissues according to the laws of hydrodynamics until they come into contact and interact with the targets wherever they are expressed. In other words, the high affinity and specificity of mAbs in vitro do not equate with exquisite tissue-targeting specificity in vivo due to the constraints imposed by circulation, extravasation, and dose-dependent target-mediated and nonspecific uptake in healthy tissues. While the properties of the drug can be modulated, to an extent, the physiological features of the body and the target expression patterns place limits on what can be translated to in vivo.

From the drug discovery perspective, substantial differences exist between the reaction conditions in vitro and in vivo that would need to be factored in from the earliest stages of drug discovery. These include target concentrations (for EGFR and HER2, low to high pM levels in vitro vs mid- to high nM levels in vivo) and the impact of complex internalization. In vitro, the diffusion-limited kinetics of binary complex formation can take far longer at pM reactant levels to reach the equilibrium than the typical 1-hour incubation time allows, as was shown by Sengers et al.¹⁷ while high target concentrations can result in the titration of the amount of the target by high-affinity mAbs rather than the affinity of the construct. Both situations will result in an underestimation of the avidity effect. The potential impact of target internalization in vitro vs in vivo has not been reported before. Hence, we explored that aspect too, simulating the binding of the bispecific mAb used in the PBPK model to the cells that expressed both targets as 1 million per cell or just one or the other. The results shown in the Supplementary Figures S11 and S12 align well with the results of the model as applied for CD4/CD70-specific DuetMab,¹⁷ exhibiting time-dependent binding kinetics, except that the maximum avidity effect was around 200–500, rather than 10,000 in the absence of TMDD. This difference is due to the shifting rate-limiting step in the process. At low pM drug concentrations, the formation of the binary complex in bimolecular association reaction becomes slower than the ternary complex internalization on the surface of the cell (ternary complex formation on the cell surface is very fast due to the two-dimensional kinetics of the step). There is no such limitation in the monospecific monovalent interactions, given that diffusion-limited binary complex formation at nM concentrations is about 1000-fold faster than in pM range.

As mentioned above, the ternary complex formation approach applied in the PBPK model to simulate cetuximab-trastuzumab-based bispecific mAb binding to EGFR and HER2 represents the best possible solution and would need to be evaluated experimentally. Interestingly, such bispecific mAb has been assembled and characterized in vitro by Si et al.⁵⁹ As expected, the monovalent affinities of the bispecific construct were unchanged from those of the monospecific parent molecules, but ELISA binding results to the plate-bound peptide ligands showed only about 2- to 4-fold avidity effect. It remains to be seen if this is the genuine property of this particular bsmAb or is related to the assay format, where the plastic-immobilized peptides do not necessarily capture antibody interactions with the intact receptor molecules that are laterally mobile in the plasma membrane. Typically, the antibody discovery process often produces many clonal lineages, and screening different combinations for the highest avidity effect may be desirable, especially if antagonistic activity is not important.

The modeling results demonstrate the interdependence between the dose and the tissue- and cell-targeting accuracy of bispecific mAbs. In general, the lower the dose, the larger the fraction that ends up in dual-positive cells in the tumor (and in other tissues). However, if the targets are present on the endothelial cells, as in the current model, those will be highly exposed while slow diffusion-driven extravasation into the tumor is in progress. An example of this limitation may have been reported by Basse et al.⁶⁶ who found that anti-EGFR/c-Met bispecific mAb causes skin side-effects similar to that of cetuximab.⁶⁷ If so, EGFR might not be the most useful accessory antigen for bispecific mAb targeting purposes, with interstitial concentrations mostly around 100 nM level in most organs. HER2, another common ‘targeting’ antigen,⁶⁸ is likely to be somewhat more suitable, but not much, as the receptor concentrations in interstitial spaces are in mid-nM range (Table 2 in Ref. 24).

In summary, our key findings are:

• High target-binding specificity of mono- and bispecific mAbs in vitro does not necessarily result in high tissue-targeting accuracy in vivo. This is the consequence of physiological constraints of the tissues and organism as a whole, in addition to the peripheral expression of the targets.

• High concentrations and doses result in bsmAb binding not only to the cells that express both targets, but also to those that carry just one or the other

• Low doses and concentrations facilitate bsmAb binding to the cells that express both targets over those that carry just one or the other. Relative exposure in different tissues can still be affected by physiological factors, like exposure to plasma and vascular permeability.

• At low concentrations and doses, the bsmAb may be cleared from circulation before penetrating into tumors, if the target is also expressed on endothelial cells or in the parenchyma of leaky tissues.

• There is likely to be an optimal dose and payload toxicity for different targets in the case of ADCs, where required exposure in tumor needs to be reconciled with minimal on- and off-target target exposure in healthy tissues

• Long infusions at low drug concentrations may allow more accurate dual-positive tissue and cell targeting than bolus dosing, but at the expense of absolute exposure level that is achievable.

• PBPK modeling provides an integrated platform that quantitatively factors in the physiological features of the organism with the properties of the target/s and the drug. As such, it can support mono- and bispecific mAb development and dose prediction throughout the research and development cycle, from target evaluation to preclinical stage and human dose prediction.

Funding Statement

The author(s) reported there is no funding associated with the work featured in this article.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Supplementary material

Supplemental data for this article can be accessed online at https://doi.org/10.1080/19420862.2025.2492236.