A Modeling and Experimental Investigation of the Effects of Antigen Density, Binding Affinity, and Antigen Expression Ratio on Bispecific Antibody Binding to Cell Surface Targets

Despite the increasing number of multivalent antibodies, bispecific antibodies, fusion proteins, and targeted nanoparticles that have been generated and studied, the mechanism of multivalent binding to cell surface targets is not well understood. Here, we describe a conceptual and mathematical model of multivalent antibody binding to cell surface antigens. Our model predicts that properties beyond 1:1 antibody:antigen affinity to target antigens have a strong influence on multivalent binding. Predicted crucial properties include the structure and flexibility of the antibody construct, the target antigen(s) and binding epitope(s), and the density of antigens on the cell surface. For bispecific antibodies, the ratio of the expression levels of the two target antigens is predicted to be critical to target binding, particularly for the lower expressed of the antigens. Using bispecific antibodies of different valencies to cell surface antigens including MET and EGF receptor, we have experimentally validated our modeling approach and its predictions and observed several nonintuitive effects of avidity related to antigen density, target ratio, and antibody affinity. In some biological circumstances, the effect we have predicted and measured varied from the monovalent binding interaction by several orders of magnitude. Moreover, our mathematical framework affords us a mechanistic interpretation of our observations and suggests strategies to achieve the desired antibody-antigen binding goals. These mechanistic insights have implications in antibody engineering and structure/activity relationship determination in a variety of biological contexts.

Effect of small-molecule-binding affinity on tumor uptake in vivo: a systematic study using a pretargeted bispecific antibody

Small-molecule ligands specific for tumor-associated surface receptors have wide applications in cancer diagnosis and therapy. Achieving high-affinity binding to the desired target is important for improving detection limits and for increasing therapeutic efficacy. However, the affinity required for maximal binding and retention remains unknown. Here, we present a systematic study of the effect of small-molecule affinity on tumor uptake in vivo with affinities spanning a range of three orders of magnitude. A pretargeted bispecific antibody with different binding affinities to different DOTA (1,4,7,10-tetraazacyclododecane-1,4,7,10-tetraacetic acid)-based small molecules is used as a receptor proxy. In this particular system targeting carcinoembryonic antigen, a small-molecule-binding affinity of 400 pmol/L was sufficient to achieve maximal tumor targeting, and an improvement in affinity to 10 pmol/L showed no significant improvement in tumor uptake at 24 hours postinjection. We derive a simple mathematical model of tumor targeting using measurable parameters that correlates well with experimental observations. We use relations derived from the model to develop design criteria for the future development of small-molecule agents for targeted cancer therapeutics.

Practical theoretic guidance for the design of tumor-targeting agents

Theoretical analyses of targeting agent pharmacokinetics provides specific guidance with respect to desirable design objectives such as agent size, affinity, and target antigen. These analyses suggest that IgG-sized macromolecular constructs exhibit the most favorable balance between systemic clearance and vascular extravasation, resulting in maximal tumor uptake. Quantitative predictions of the effects of dose and binding affinity on tumor uptake and penetration are also provided. The single bolus dose required for saturation of xenografted tumors in mice can be predicted from knowledge of antigen expression level and metabolic half-life. The role of high binding affinity in tumor uptake can be summarized as: essential for small peptides, less important for antibodies, and negligible for nanoparticles.

Dose dependence of intratumoral perivascular distribution of monoclonal antibodies

Intravenously delivered antibodies have been previously found to distribute in a perivascular fashion in a variety of tumor types and despite targeting a range of different antigens. Properties of both the antibody and the targeted antigen, such as the administered dose, binding affinity, and antigen metabolic half-life, are predicted to influence the observed perivascular distribution. Here, the effect of antibody dose on the perivascular distribution is determined using an unbiased image analysis approach to quantify the microscopic distribution of the antibody around thousands of blood vessels per tumor. This method allows the quantitative determination of the localization of blood vessels, extravasated antibody, and tumor antigen following the administration of antibody doses covering two orders of magnitude in the dose range commonly utilized in preclinical studies. A mathematical model of antibody extravasation, diffusion, binding, and endocytosis in a Krogh cylinder geometry with parameters directly measured or taken from the literature is quantitatively consistent with the experimentally determined profiles. A previously reported scaling analysis is employed to extend these results to any tumor model in which the antigen density and turnover rate are known, allowing facile quantitative prediction of the minimum antibody dose required for complete tumor saturation.

Spontaneous phosphoinositide 3-kinase signaling dynamics drive spreading and random migration of fibroblasts

During directed cell migration (chemotaxis), cytoskeletal dynamics are stimulated and spatially biased by phosphoinositide 3-kinase (PI3K) and other signal transduction pathways. Live-cell imaging using total internal reflection fluorescence (TIRF) microscopy revealed that, in the absence of soluble cues, 3'-phosphoinositides are enriched in a localized and dynamic fashion during active spreading and random migration of mouse fibroblasts on adhesive surfaces. Surprisingly, we found that PI3K activation is uncoupled from classical integrin-mediated pathways and feedback from the actin cytoskeleton. Inhibiting PI3K significantly impairs cell motility, both in the context of normal spreading and when microtubules are dissociated, which induces a dynamic protrusion phenotype as seen by TIRF in our cells. Accordingly, during random migration, 3'-phosphoinositides are frequently localized to regions of membrane protrusion and correlate quantitatively with the direction and persistence of cell movement. These results underscore the importance of localized PI3K signaling not only in chemotaxis but also in basal motility/migration of fibroblasts.