Opinion
Factors determining antibody distribution in tumors

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The development of antibody therapies for cancer is increasing rapidly, primarily owing to their specificity. Antibody distribution in tumors is often extremely uneven, however, leading to some malignant cells being exposed to saturating concentrations of antibody, whereas others are completely untargeted. This is detrimental because large regions of cells escape therapy, whereas other regions might be exposed to suboptimal concentrations that promote a selection of resistant mutants. The distribution of antibody depends on a variety of factors, including dose, affinity, antigens per cell and molecular size. Because these parameters are often known or easily estimated, a quick calculation based on simple modeling considerations can predict the uniformity of targeting within a tumor. Such analyses should enable experimental researchers to identify in a straightforward way the limitations in achieving evenly distributed antibody, and design and test improved antibody therapeutics more rationally.

Introduction

Traditional small molecule cancer therapeutics are often marginally selective between tumor cells and healthy tissue, leading to side effects and poor therapeutic indices. Antibodies provide a promising solution with their ability to bind specifically to surface antigens on cancer cells and selectively target the disease. Bound antibodies, in turn, can destroy tumor cells by recruiting immune effectors, blocking proliferative signaling or delivering toxic payloads such as small molecule drugs, biological toxins and radioisotopes 1, 2. For most of these mechanisms, cytotoxicity is limited to the cells that are bound by antibody, such that all of the cells in the tumor must be targeted to achieve a complete therapeutic response (exceptions include long-range radioisotope emissions and other bystander effects.) However, incomplete drug penetration into tumors has long been noted for antibodies 3, 4, 5, and also for chemotherapeutics [6] (Figure 1). This heterogeneous distribution can significantly reduce therapeutic efficacy by leaving a fraction of cells untargeted and viable. A qualitative understanding of the causes of incomplete antibody penetration into tumors is necessary to craft improved targeting molecules and better dosing strategies rationally [7].

Antibody targeting of tumors is a complex process involving extravasation across tumor capillaries, diffusion and binding within the tumor interstitium, plasma clearance, and internalization and catabolism in tumor cells (Figure 2). Furthermore, the clinical presentation of cancer often involves both vascularized solid tumors and prevascular micrometastases embedded in normal tissue, each of which have particular targeting properties and challenges. In particular, solid tumors have heterogeneous vasculature and high interstitial fluid pressure that limit convective flow and antibody extravasation, in addition to large regions of necrosis and hypoxia [8]. Due to the complex nature of tumor targeting, it is difficult to understand or predict antibody distribution without the aid of computational modeling.

Static images of tumors taken after systemic delivery of antibodies reveal regions of high concentration adjacent to areas that have no detectable antibody, a phenomenon often referred to as a ‘binding site barrier’ [9]. Despite the crisp outline of drug penetration shown in Figure 1, this does not result from a discrete morphological or physical barrier. Rather, it is a dynamic, potentially moving front resulting from a balance of opposing rates. The key rates that determine where this boundary is located are shown in schematic and tabular form in Figure 2 and Table 1. In broad terms, antibody penetration from capillary extravasation and diffusion is limited by systemic clearance from the plasma and antibody degradation in the tumor tissue. Here, we consider each of these processes in turn, focusing in particular on parameter values appropriate for antibodies and antibody fragments. We then illustrate how these processes can be reduced to simple ratios of critical rates that can be used to predict antibody penetration in tumors and aid in therapeutic development and testing.

Section snippets

Capillary extravasation

In healthy vasculature, macromolecules move into tissues by convection, transcytosis and diffusion across the capillary wall [8]. However, tumors largely lack draining lymphatics [10] and, consequently, build up interstitial hydrostatic pressure, severely restricting convection [11]. As a result, exit of antibodies from the capillary occurs primarily by diffusion across pores. This causes few problems for small molecules with rapid diffusion rates but puts a significant restriction on the

Systemic clearance

The concentration gradient driving penetration into the tumor is only maintained until the drug has cleared from circulation to a concentration below that present in the tumor. The organ of clearance is a function of the size of the molecule and its interaction with receptors such as the asialoglycoprotein receptor in the liver or neonatal Fc receptor (FcRn) disseminated throughout the endothelial vascular surface area. Whereas small molecule drugs can be heavily influenced by their

Scaling analyses of antibody penetration versus endocytic and systemic clearance

Although each of the rates described in Table 1 are individually important for describing antibody distribution in tumors, it is the relative values of these rates that ultimately determine the extent of antibody penetration. A simple and qualitative approach to considering which processes dominate and which are limiting in a particular situation is to define dimensionless ratios of the rates [24] (Table 2). Three such dimensionless numbers are useful in understanding the tumor penetration

Conclusions

Mathematical modeling of antibody penetration into tumors will be most useful if it can lead to qualitative insights that are incorporated into improved therapeutic design and experimentation. We suggest that calculation of the dimensionless numbers in Table 2 is a straightforward and accessible approach to gain useful perspectives on the dominant rate processes inherent to any tumor-targeting strategy without the need for complex computational tools. Parameter values for the terms present in

Acknowledgements

We thank Jeff Varner, Jules Mattes, Larry Baxter and Jay Tibbitts for helpful critical comments on this review. We are also grateful for the insightful critique of an anonymous reviewer. This work was supported by NIH CA96504 and CA101830.

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