Antibodies have very low rates of extravasation, making transport across the vasculature a considerable barrier. For directly conjugated antibody therapeutics, the resulting concentration profile, where the blood often contains a 100-fold to 1,000-fold higher concentration of therapeutic than surrounding tissue (4-6), obviously limits efficacy. When combined with a long circulatory half-life, the elevated blood concentration often results in bone marrow toxicity before therapeutic toxicity throughout a solid tumor is reached.

Once out of the vasculature, there are further obstructions to tumor permeation by antibody drugs. The specific architecture of solid tumors, such as limited convective flow, high interstitial pressure, and a dense extracellular matrix, acts to limit penetration (3). The well-studied impediment of the “binding site barrier” (7, 8) results from the intersection of the slow diffusion and fast association rates of high affinity antibodies. The combined effect of these rates is that binding sites closest to the vasculature are occupied before further penetration occurs. This phenomenon results in a highly heterogeneous distribution of drug-with areas of saturation surrounding the blood supply and a complete lack of antibody in more distal regions (9). Depending on the mode of cell killing, such a heterogeneous distribution can be highly undesirable.

To evade these barriers to penetration, numerous alterations have been made to the composition of the protein drug itself (1). Decreased size increases both extravasation and diffusivity (10, 11), whereas albumin binding domains (9, 12) and interactions with FcRn (13, 14) have been engineered to lengthen plasma residence time and allow more therapeutic to extravasate before clearance. Low affinity binders have been shown to circumvent the binding site barrier and allow a more homogeneous distribution of therapeutic (8) at the unacceptable cost, however, of significantly reducing the amount of antibody retained in the tumor.

Despite these efforts, solid tumor penetration remains an elusive goal. To account for the various processes affecting penetration, the simplified scaling model of Thurber et al. (4) describes the relevant kinetic rates and processes determining penetration in spherical micrometastases and vascularized tumors. For the purposes of the present experiments with spheroids, the relationships for micrometastases will be tested. Rearrangement of the Thiele modulus, a dimensionless group describing the ratio of catabolism to transport, yields an expression predicting the distance (R) that a prevascular spheroidal metastasis will be penetrated by an antibody (Eq. A).

Whereas many of the variables in this expression relate to the properties of the antibody, such as the dose ([Ab]_surface), void fraction (ε), and diffusivity (D), the remaining terms describe antigen properties which could set intrinsic limits to penetration. These terms include the antigen expression level ([Ag]_tumor) and turnover rate (k_e). Intuitively, it is clear how each of these variables could limit the penetration of a high affinity therapeutic: the distance each antibody can penetrate before binding depends on the density of binding sites; and as bound antigen is turned over and replaced, new binding sites are exposed. In fact, if turnover occurs on a timescale comparable with vascular escape and diffusion, the result is a bottomless sink for therapeutic and a limit to further tissue penetration.

In this study, spheroids were grown in a hanging drop (17), allowed to adhere to coverslips, incubated in the presence of various fluorescently labeled antibodies, and imaged by confocal microscopy. Raw images (Fig. 1A) were analyzed to determine the average distance that antibody penetrated into the spheroid at a given time. After acquisition, images were gated to generate a binary version (Fig. 1B), such that background signal was excluded. A circular region of interest was drawn around each spheroid, and pixel-by-pixel intensity was taken along a bisecting diagonal line as the region of interest was rotated in 18 projections around 360° (Fig. 1C). The number of pixels above the selected intensity threshold was summed and then averaged over all projections, giving the diameter of the spheroid that had been penetrated by label. The macro for this analysis may be found in the supplementary materials.⁵

Equation A predicts that penetration distance, R, will increase proportionally to [Ab]_surface and inversely proportional to [Ag]_tumor. Accordingly, a 10-fold decrease in antigen density is expected to yield a 10-fold increase in penetration distance. Similarly, the model also predicts that a 10-fold decrease in antigen density will negate the effect of a 10-fold decrease in antibody dose.

To experimentally test these predictions, spheroids were incubated in either a given concentration of fluorescent anti-A33 antibody or a mixture of fluorescent antibody and nonfluorescent competitor. The nonfluorescent competitor functions to occupy a fraction of binding sites, as both antibodies diffuse through the spheroid, blocking the fluorescent antibody from binding and allowing it to diffuse further into the spheroid before encountering an available binding site. Accordingly, the nonfluorescent competitor acts as a means to effectively tune the density of available antigen binding sites.

When spheroids were incubated in either a given concentration of fluorescent anti-A33 antibody or a mixture of one-tenth that concentration of fluorescent and nine-tenths nonfluorescent competitor antibody, penetration was indeed equivalent (Fig. 2A)—as would be expected given that the total antibody dose is equivalent in both cases. The decrease in fluorescent antibody dose worsens the signal to noise ratio; however, the equivalence of total dose leads to equivalent penetration distance, as can be seen in representative images at 24 hours (Fig. 2B and C).

For a given dose of fluorescent antibody, penetration distance is predicted to vary proportionally to [Ag]_tumor. Therefore, when available [Ag]_tumor is decreased 10-fold due to the presence of unlabeled competitor, the model predicts that the penetration distance will increase by a factor of 10—close to the value observed at a concentration of 0.15 nmol/L at 24 hours (Fig. 2D, black columns). At higher concentrations (gray columns) and later time points, this ratio decreases to 1, as the spheroids become completely saturated to their centers under both conditions (error bars represent the variation in spheroid size). As predicted theoretically (4, 5) and shown experimentally previously (20), increasing antibody dose is one route to overcoming the binding site barrier.

To explore the dependence on antigen density by an independent method, spheroids were grown from cell lines expressing different levels of antigen. SW1222 cells express one-fifth as much A33 antigen as LS174T cells (data not shown). This 5-fold decrease in antigen density is predicted to lead to a 5 increase in penetration distance. As can be seen at 12 hours, 1.5 nmol/L antibody almost completely penetrates the SW1222 spheroid while advancing only a few cell layers in an LS174T spheroid (Fig. 3A versus B). The relative distance that the antibody front penetrates in each spheroid cell type was quantified and is given over a range of concentrations at 12 hours (Fig. 3C). When these penetration distances are taken as a ratio, they agree well with the model prediction (Fig. 3D).

To study the effect of internalization rate on penetration, we used antibodies against CEA that exhibit differing internalization rates. Despite binding to the same cellular target, M85151a and M111147 display an ~3-fold difference in internalization rate.⁶ This difference is likely related to antibody M85151a's recognition of two epitopes per CEA molecule, allowing cross-linking of the antigen. When the increased internalization rate of M85151a and a 2-fold increase in binding sites are incorporated into the model, M111147 is predicted to penetrate into spheroids 2.3-fold further than M85151a. Indeed, when LS174T spheroids were incubated with each of these antibodies, there were clear differences in penetration. The more quickly internalizing M85151a (t_1/2, 5 hours) clearly penetrates the spheroid to a lesser extent than M111147 (t_1/2, 13 hours). Figure 4A and B are representative sections of spheroids labeled with M85151a and MS111147, respectively. To quantitatively compare the difference in penetration, the ratio of the penetration distances of slow to fast internalizing antibodies was taken at various concentrations (Fig. 4C). Here again, at early times and low concentrations, before spheroids become saturated and the ratio approaches unity, the data were found to agree well with the model prediction of a 2.3-fold difference.

Thus, both antigen turnover and antigen density have significant effects on tumor penetration and should be considered in the selection of targets. Whereas a high antigen density is beneficial for increasing the exposure of each cell to the therapeutic, excessively high density inhibits penetration and increases heterogeneity. Likewise, antigen turnover results in continual replenishment of available binding sites and can thereby act as a bottomless sink for therapeutic and block further tissue penetration. Figure 5 compares two alternative antigens. Both A33 and CEA are present at similar expression levels in LS174T cells and each has a long history of study as a target in radioimmunotherapy of colon cancer (21-25). However, CEA has a metabolic turnover halflife of 15 hours,⁵ whereas the halflife of A33 stretches out to almost 60 hours (16). Even the seemingly slow internalization rate of CEA has a significant effect on tumor penetration. Figure 5A and B present the distance penetrated by various antibody doses over time. A 150 nmol/L concentration of anti-CEA antibody has saturated the spheroid by the first time point, at 6 hours. Therefore, at this concentration, the increase in the penetration distance beyond that at 6 hours is due to growth of the spheroid, and this line represents the maximum penetration distance achievable. At low concentrations, penetration arrests when antibody diffusion comes to steady-state with antigen turnover (Fig. 5A). This arrest is evident as a stalled fluorescence front, which can be observed in 24-hour and 48-hour images of cells exposed to 1.5 nmol/L anti-CEA antibody (Fig. 5C, top). As a result, at this concentration of therapeutic, cells at the center of the spheroid will never be exposed.

In contrast, the slower internalization rate of A33 not only allows 1.5 nmol/L antibody (Fig. 3C, center) to continue to progress toward the center, but even 0.07 nmol/L doses (bottom) continue to progress and reach the spheroid center eventually. Significantly, antibodies to A33 have been shown to accomplish penetration to the core of tumors in vivo in clinical trials (21, 22)—an unusual result for an IgG. We hypothesize that the slow rate of antigen turnover contributes significantly to this highly desirable attribute.

Therapeutic strategies, such as pretargeted radioimmunotherapy, antibody-directed enzyme prodrug therapy, and antibody-dependent cellular cytotoxicity, rely on sustained accessibility of the tumor-bound therapeutic to a second agent and are therefore negatively effected by internalization. As a means to study the effect of internalization and turnover on the surface accessibility of antibody over time, spheroids were grown in antibody, washed, incubated in fresh media, and imaged daily to follow the fate of bound antibody. Over the period of observation, fluorescent signal may decrease due to antibody internalization and degradation or unbinding and diffusion out of the spheroid or, in the case of CEA, when antigen is shed. As in previous experiments, spheroids continue to grow over the period of observation. Therefore, fluorescence is also diluted via the division of labeled cells. Figure 6A shows the observed patterns of staining over the course of 4 days after removal of label. A33 and CEA show dramatically different staining patterns: A33 antibody remains relatively evenly distributed throughout the spheroid, whereas CEA exhibits a punctuate localization pattern.

However, less attention has been paid to the properties of the target antigen that might pose intrinsic limits to penetration. Previous theory predicts that both the expression level and turnover rate of the antigen can affect penetration (4, 5). This study provides experimental evidence that under some circumstances antigen properties can be the determining factor in tumor penetration and supports the selection of antigens with slower turnover and lower expression.

As this report shows, antigen density can have a dramatic effect on tumor penetration. Of course, the greater penetration observed with lower antigen density is in direct opposition to the practice of selecting highly expressed tumor antigens to increase the amount of drug to which each cell is exposed. And, somewhat ironically, to the extent that expression level has been manipulated in targeting, it has been to up-regulate expression via IFN-γ treatment (27), which, as shown here, would be predicted to decrease overall penetration depths.

Similarly, the data presented in this study has significant implications for the models used in the study of immunotherapy. Such models have often used cell lines that grossly overexpress the target antigen or have been modified in ways that can affect turnover, such as by transfection. Accordingly, the resulting distribution of drug in such models may be highly artifactual. To accurately capture antibody distribution, accurate recapitulation of antigen properties is required.

In practice, once an antigen is expressed at levels sufficient to recruit a lethal dose of therapeutic, additional antigen counterproductively leads to poorer tumor penetration and a more heterogeneous dosing of the tumor. Because the level of expression sufficient to induce cytotoxicity may vary widely depending on the mode of therapy used, bounds for optimal antigen expression levels will be case specific. Highly potent toxic modalities, such as a emitters or some protein toxins, may be best suited for low antigen expression, whereas other less potent therapeutics may require high expression to be effective. Likewise, for some modes of toxicity, such as therapies using radionuclides with long deposition distances, complete penetration may be unnecessary as untargeted cells can accumulate a toxic dose via crossfire or other local environment effects. Nonetheless, regardless of the expression level required for cytotoxic effect, incremental expression above that level incurs a cost in terms of reduced penetration.

We have also shown that turnover can set an inherent limit to penetration: if the target is replaced at a rate similar to the diffusion of the therapeutic through tissue, complete penetration may be impossible. Here too, however, the preferred antigen turnover rate will depend on the mechanism of cell killing, because internalization is critical to immunotoxin and antibody-drug conjugate therapies, for example. Slow turnover remains desirable for penetration, but internalization is necessary for efficacy in such cases—leaving the goals of reaching distal cells and high drug activity in direct opposition. In contrast, two-step therapies, such as antibody-directed enzyme prodrug therapy, pretargeted radioimmunotherapy, or effector function rely on persistent surface localization and antibody/antigen turnover acts to directly decrease cell killing. Because altering a single variable can have multiple and even competing effects, it is instructive to look to quantitative, predictive models to assess such tradeoffs when designing therapies. The complexity of relationships between transport, binding, and other kinetic processes can lead to nonintuitive outcomes, which are captured by a properly formulated model.

The data presented here underscore the reality that tumor-specific expression is truly only the first criteria that a target antigen must meet. Depending on its other properties, use of certain modes of therapy may be highly inadvisable. Therefore, selection from among the repertoire of toxic mechanisms should take into account the properties of the target antigen. Differences between A33 and CEA, the two targets used in this study, highlight the importance of such target-tailored therapy design. The more rapid turnover of CEA has multiple implications. First, a greater dose of therapeutic is required to achieve equivalent penetration. Secondly, as time passes, progressively less targeting drug remains surface localized and able to bind a second agent in a two-step therapy. Conversely, more molecules of immunotoxin would be internalized during a given period of time, likely making CEA the preferred target for immunotoxin therapy, relative to A33.

In contrast, the relative stability of A33 is especially promising for two-step therapies. Observations made here as to the ability of antibodies to A33 to penetrate spheroids at even extremely low doses are paralleled by experience in the clinic, where even the necrotic centers of tumors are labeled (21, 22) and where antibody is detectable a month and a half after administration. This stable profile would allow for both improved dosing of distal cells, as well as the recruitment of the toxic effector at a level similar to antigen expression. The fact that clinically observed differences between the penetration of antibodies against A33 relative to other targets are reproduced here suggests both that the spheroids used here are a reasonably representative model of in vivo tumors and that antigen properties are indeed relevant to clinical biodistribution results.

Whereas antibody therapeutics have well-demonstrated difficulty in penetrating tissue, this difficulty is generally ascribed to their large size. However, there is a significant body of literature describing the inability of even small molecule drugs to penetrate tissue. Clearly, if even orders of magnitude changes in size, extravasation, and diffusivity cannot lead to thorough tumor penetration, there are other variables that must have a considerable effect on distribution and penetration. Minchinton and Tannock provide an excellent review of the distribution of small molecules in tumors as a factor in therapeutic outcome (2). Many of the factors cited to influence antibody penetration also figure prominently for small molecules, and it is likely that the target properties explored here can play a similar role in determining the distribution and efficacy of small molecules.

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