A Systems Pharmacology Model for Drug Delivery to Solid Tumors by Antibody-Drug Conjugates: Implications for Bystander Effects

Abstract

Antibody-drug conjugates (ADCs) are cancer drugs composed of a humanized antibody linked to a cytotoxic payload, allowing preferential release of payload in cancer cells expressing the antibody-targeted antigen. Here, a systems pharmacology model is used to simulate ADC transport from blood to tumor tissue and ADC uptake by tumor cells. The model includes effects of spatial gradients in drug concentration in a three-dimensional network of tumor blood vessels with realistic geometry and accounts for diffusion of ADC in the tumor extracellular space, binding to antigen, internalization, intracellular processing, and payload efflux from cells. Cells that process an internalized ADC-antigen complex may release payload that can be taken up by other "bystander" cells. Such bystander effects are included in the model. The model is used to simulate conditions in previous experiments, showing good agreement with experimental results. Simulations are used to analyze the relationship of bystander effects to payload properties and single-dose administrations. The model indicates that exposure of payload to cells distant from vessels is sensitive to the free payload diffusivity in the extracellular space. When antigen expression is heterogeneous, the model indicates that the amount of payload accumulating in non-antigen-expressing cells increases linearly with dose but depends only weakly on the percentage of antigen-expressing cells. The model provides an integrated mechanistic framework for understanding the effects of spatial gradients on drug distribution using ADCs and for designing ADCs to achieve more effective payload distribution in solid tumors, thereby increasing the therapeutic index of the ADC.

Keywords: capillaries; diffusion; drug transport; mathematical model; vascular permeability.

Figure 1.. ADC transport and reactions including bystander effects.

Smooth boundary denotes Ag⁻ cell; wavy boundary denotes Ag⁺ cell; orange (blue) color denotes cell containing free (no) payload. A. Steps in ADC transport and reaction. 1. ADC (green circles) is carried into the tumor via convection in plasma. 2. ADC passes across the vessel wall into the tumor interstitial space. 3. ADC diffuses through the interstitial space. 4. ADC binds to target antigen expressed on the cell membrane. 5. ADC-antigen complex is internalized by the cell and undergoes lysosomal degradation to release payload. 6. Payload passively effluxes from the cell (orange arrow) and diffuses to other cells, creating a possible bystander effect. 7. Payload is released by the cell, enters blood vessels and is washed out in plasma. B-E. Payload distribution in absence and presence of bystander effects. B. Heterogeneous antigen expression. Cells containing ADC do not release payload, so payload does not reach Ag^‒ cells. C. Heterogeneous antigen expression, with heterogeneous bystander effect. Cells containing ADC release payload, which diffuses and is taken up by Ag^‒ cells, and also by more distant Ag⁺ cells. D. Homogeneous antigen expression, no bystander effect. ADC transport into cells is restricted by the binding-site barrier, and cells containing ADC do not release payload to reach distant cells. E. Homogeneous antigen expression with spatial bystander effect. Cells containing ADC release payload, which diffuses and is taken up by more distant cells.

Figure 2.. Microvessel network.

A. Network used for computational model. Flow rates in nl/min and flow directions are indicated for each vessel segment. Vessel segment color indicates the magnitude of flow rate. B. Distribution of tissue point distances from the nearest vessel for the microvessel network. For comparison, the distribution of distances for the Krogh cylinder geometry with the same mean vessel diameter and the same vessel length per tissue volume is also shown. The Krogh cylinder has a tissue radius of 52.96 μm and a capillary radius of 5.59 μm.

Figure 3.

Intratumoral antibody distributions. A. Comparison between results of Rhoden et al. (27) and model simulations of antibody distribution in a solid tumor for doses 2, 15, 50, 100 and 500 μg of the sm3e antibody. Experimental data: relative mean fluorescent intensity (MFI). Model predictions: fractional antigen saturation defined as (total antibody)/(total antigen), where total antibody is the sum of bound antibody and free antibody. B-D. Predicted spatial distributions of antibody concentration in a plane through the tissue domain for doses 5, 15 and 50 μg of antibody. Black and gray lines show projections of vessel positions. Vessels whose midpoints are within 50 μm of the contour plane are shown in gray. Parameters values are listed in Table II.

Figure 4.. Intratumoral payload concentrations.

A. Model predictions and experimental results from Alley et al. (28) of intratumoral payload time course for a 1.5 mg/kg dose of h1f6-mcMMAF. B. Model predictions and experimental results from Li et al. (28) of intratumoral concentration of MMAE from two ADCs (cAC10-vcMMAE, h1F6-vcMMAE) for three doses (0.5, 1, 3 mg/kg) measured at 72 hours. C. Model predictions and experimental results from Li et al. (28) of intratumoral payload time course for a 2 mg/kg dose of cAC10-vcMMAE. Parameter values are listed in Table II.

Figure 5.. Cellular exposure to payload and payload washout.

A, B. Peak intracellular payload concentration ($\overline{C_{max}^{int}}$) averaged over 10 μm intervals of distance from the nearest vessel, for three levels of payload diffusivity (D_payload = 1, 10, 100 μm²/s). A. Dose = 1 mg/kg, DAR = 4. B. Dose = 1 mg/kg, DAR = 4 together with 9 mg/kg, DAR = 0, resulting in an effective average DAR = 0.4. C, D. Area under the payload concentration curve in plasma at time t, AUC(t), due to payload washout. C. Dose = 1 mg/kg, DAR = 4. D. Dose = 1 mg/kg, DAR = 4 together with 9 mg/kg, DAR = 0. No DAR-dependent deconjugation was assumed. Parameter values are listed in Table III. In each case, results are also shown for a payload with no bystander effect.

Figure 6.. Dependence of cellular exposure to payload on distance to the nearest vessel, percentage of Ag⁺ cells, and dose.

Values of $\overline{C_{max}^{int}}$ are averaged over cells within 10-μm intervals of distance from the nearest vessel, for 30%, 50% and 90% Ag⁺ cells and correspondingly 70%, 50% and 10% Ag⁻ cells, and for doses of 1, 5, 10 mg/kg. Bars represent one standard deviation above the mean. The fractional antigen saturation as defined in the Figure 3 caption was calculated for cells within 10 μm to vessels: 0.15, 0.116, 0.088 for 30%, 50%, 90% Ag⁺ cells at 1 mg/kg respectively, 0.551, 0.448, 0.36, for 30%, 50%, 90% Ag⁺ cells at 5 mg/kg respectively and 0.806, 0.681, 0.574 for 30%, 50%, 90% Ag⁺ cells at 10 mg/kg respectively. Values of $\overline{C_{max}^{int}}$ for 70%, 50% and 10% Ag⁻ cells are emphasized on the axes. Parameter values are listed in Table III.

Figure 7.. Spatial minimum values of cellular exposure in tissue region for varying doses and percentages of Ag⁺ and Ag⁻ cells.

Minimum values of $\overline{C_{max}^{int}}$ for doses of 1, 5, 10 mg/kg are shown for 30%, 50% and 90% Ag⁺ cells and correspondingly 70%, 50% and 10% Ag⁻ cells. Parameter values are listed in Table III.