The tumor spheroid model system for measuring scFv penetration provides valuable insights into key aspects of antibody tumor targeting. Antibody distribution is dependent on a variety of variables, and penetration to the center of a spheroid is not simply a binary result. The dose, antigen density, spheroid size, incubation time, and all the other variables present in the clearance and Thiele moduli affect the results. The spheroids used here most closely resemble prevascular micrometastases in normal tissue. Other physiologic barriers, such as lowered concentrations in normal tissue and inefficient extravasation across tumor capillaries, are not reproduced in the spheroid model system. Therefore the in vitro results are not intended to directly mimic the in vivo results. Nevertheless, the fundamental processes of diffusion, binding, and endocytosis that determine distribution in spheroids are expected to closely replicate those acting in vivo.
The distribution of scFvs in these spheroids lacks a major barrier to penetration in solid tumors, namely the capillary wall. Due to elevated interstitial pressure, convection in the tumor is negligible, and the dominate mode of transport is diffusion (3
), similar to the spheroids. Therefore, although the supply of antibodies is severely limited compared with these spheroids (and therefore the effective concentrations are very low), the distribution is expected to follow the same principles. Poor extravasation of macromolecules in tumors (22
) results in concentrations outside the tumor capillary that can be 100- to 1,000-fold below that found in the plasma (21
). The modeling results can then be modified to account for these additional complications present in vascularized tumors in vivo
. Because the transport barriers in the spheroid system also exist in vivo
, it is a necessary condition that a spheroid be saturated for the corresponding tumor to be saturated. Spheroid saturation is not sufficient to predict in vivo
saturation because additional barriers exist (e.g., capillary extravasation and systemic clearance.) Modeling for the case of solid tumors compared with spheroids and metastases has been carried out previously and shown to agree with published data (5
These experiments have shown that two simple model scaling criteria can predict the distribution of antibody fragments in spheroids. The clearance modulus, which predicts the exposure time required to saturate spheroids, and the Thiele modulus, which predicts the concentration required to overcome internalization to reach the center of a spheroid, are criteria that quantitatively capture the major determinants in antibody distribution.
Experiments with high-affinity scFvs show steep gradients as the “core” of unbound antigen “shrinks” when antibody binds the outer layers of cells. These high-affinity antibodies bind at saturating concentrations “from the outside in” (, bottom
). Most IgG molecules travel through tumor tissue in this “shrinking core” fashion (saturating cell layer after cell layer) due to their rapid binding to free antigen, slow diffusion coefficients (9
), and slow dissociation caused by multivalent interactions. They are often internalized before they have a chance to dissociate and diffuse farther into the tissue (23
), resulting in shrinking core penetration with effectively irreversible binding. However, with newer protein engineering techniques (scFvs, Fabs, single domain antibodies, and alternative protein scaffolds), these new proteins, which are often smaller and monovalent, can exhibit “nonshrinking core” transport in tumor tissue.
Lower affinity scFvs display a more diffuse gradient, yielding more homogenous labeling of the spheroids with lower amounts of bound antibody; they bind antigen at subsaturating concentrations “from the bottom up” (, top
). If a significant fraction of antigen must be bound for the desired effect, however, much higher concentrations have to be used with the lower affinity fragments. As mentioned previously, antibody and antibody fragment concentrations in solid tumors are often very low in vivo
. The rapid dissociation and high fraction of unbound scFv allows the lower affinity monovalent scFv to penetrate more homogenously (21
). Increasing the valency would hinder complete dissociation and result in distributions similar to higher affinity binders. Unfortunately, it is the same ability to rapidly dissociate that allows scFv to diffuse back out of the tissue once the surrounding concentration has dropped.
The poor retention of lower affinity binders has implications for both imaging and pretargeting therapies. As systemic antibody is cleared from the circulation, the total signal of low-affinity antibodies will be reduced in the tumor tissue. Even if a residualizing radioisotope is used for imaging, much of this is lost due to diffusion out of the tissue before it can be internalized during the waiting period while clearance is reducing background levels. For pretargeting techniques, a waiting period is again required for normal tissue levels to drop. The surface concentration is the variable of interest because this is the only antibody accessible to secondary agents. In the retention experiment, diffusion out of the spheroid occurred much more rapidly for the low affinity scFv, resulting in higher surface concentrations for the sm3E antibody than shMFE.
Although antibody fragments rapidly diffuse in and out of spheroids, similar to a micrometastasis, the retention in solid tumors is predicted to be very different. Because the capillary wall is a significant barrier to extravasation, once the antibody has reached the tumor tissue, it is very slow to intravasate back into the blood. Thus, for large molecules, this enhanced permeability and retention (“EPR”) effect occurs relatively independent of affinity. For smaller molecules with higher permeabilities, binding is predicted to be more important in preventing loss from the tumor due to a lower EPR effect.
Antigen labeling in the IHC experiment shows extensive CEA heterogeneity in the spheroids, as was seen on a per-cell basis in the flow cytometry experiments, and this is an important point for therapy. Looking at the merged images, the lowest concentration spheroid clearly has antigen in the center that has not been reached by sm3E. At the highest concentration, virtually every area of high antigen concentration has correspondingly high scFv concentrations, indicative of saturation. The middle concentration is more interesting. With this size spheroid, a 3 nmol/L concentration of scFv is predicted to penetrate to the center, and there is sm3E in the center as seen in the green channel. However, there is also a region in the bottom left side with very high antigen concentration that is not completely saturated by scFv. The local increase in antigen concentration (and possibly decrease in void fraction, diffusion coefficient, etc.) has apparently prevented saturation of this region. The live-cell imaging experiments would not have picked up on the high local antigen density because they only analyze the antibody fragment fluorescence signal. These IHC experiments better capture the local heterogeneities found in solid tumors and metastases. In the live-cell experiments, however, the relationship between dose and penetration distance is more clearly established despite the complicating factor of antigen heterogeneity. This antigen heterogeneity can result in antibody heterogeneity even after full antigen saturation.
A small number of fundamental processes dictate the distribution of antibodies and antibody fragments in tumor tissue, and the scaling criteria (Thiele and clearance moduli) capture these rates to better understand and predict penetration. The moduli simply relate the supply and demand of free antibody. As a bolus dose clears the plasma and normal tissues, the supply of antibody entering the tumor tissue continually shrinks, and the demand for antibody remains high as more layers of cells are bound. The clearance modulus captures this ratio and predicts the penetration distance before clearance. Similarly, even with a steady supply entering from the circulation, demand for antibody to replace molecules that were internalized or degraded may immobilize all the free antibody before it can reach every cell. This is in effect the distance that the Thiele modulus predicts.
The implications of these experiments and scaling criteria lend insight into optimizing antibody and antibody fragment imaging and therapy experiments. To target all cells with a high-affinity binder, the dose must exceed the limitations posed by clearance and internalization as given in the scaling criteria. Decreasing the clearance rate far below the antigen turn-over rate will not increase penetration into the tissue, as antibody metabolism becomes rate limiting. Lower affinity binders result in a more homogenous distribution when the Kd is large enough to reduce the scaling moduli below one. Unfortunately, the total amount entering the tumor is still small, and the fraction that is bound is even less. For prevascular metastases and proteins with high permeability, retention of these antibodies will also be poor. For imaging experiments, penetration of antibodies and fragments (and the associated signal) is directly proportional to the AUC. Increasing clearance rates reduces background noise, but it also decreases signal. A more optimal plasma profile would have an extended period of high concentration for tumor uptake followed by rapid clearance, advocating the use of clearing agents. A similar strategy would benefit pretargeting methods.
Understanding the major determinants for antibody and antibody fragment uptake, distribution, and retention in tumors and micrometastases can point to ways of improving and optimizing therapies. The requirements of bound antibody, total antibody uptake, and retention required for successful imaging and therapeutic modalities can be compared with the actual values attainable as predicted by the model based on all the relevant variables: dose, clearance, internalization, extravasation, diffusion, antigen density, and tumor vascular density. The choice of antigen target, antibody fragment size, and other protein engineering decisions can be made rationally to optimize the desired therapeutic or imaging result. Improvements in protein engineering, imaging sensitivity and resolution, toxin conjugates, Fc effector functions, signal blockade, and other areas relevant to antibody targeting will further push developments in antibody-based therapies for the diagnosis and treatment of cancer.