title: Theoretical analysis of antibody targeting of tumor spheroids: importance of dosage for penetration, and affinity for retention.
abstract: The interplay among antibody/antigen binding kinetics, antibody diffusion, and antigen metabolic turnover together determines the depth of penetration of antitumor antibodies into prevascular tumor spheroid cell clumps. A sharp boundary between an outer shell of bound high-affinity antibody and an inner antibody-free core has been previously observed and mathematically modeled and was termed the "binding site barrier." We show here that this process is well described by a simplified shrinking core model wherein binding equilibration is much more rapid than diffusion. This analysis provides the following experimentally testable predictions: (a) the binding site barrier is a moving boundary whose velocity is proportional to the time integral of antibody concentration at the spheroid surface (i.e. plasma antibody AUC); (b) the velocity of this moving boundary is independent of binding affinity, if the affinity is sufficiently high to strongly favor antibody/antigen complex formation at prevailing antibody concentrations; and (c) maximum tumor retention is achieved when the antibody/antigen dissociation rate approaches the rate of antigen metabolic turnover. The consistency of these predictions with published experimental results is demonstrated. The shrinking core model provides a simple analytic relationship predicting the effects of altered antibody pharmacokinetics, antibody molecular weight, antigen turnover rate, antigen expression level, and micrometastasis size on antibody penetration and retention. For example, a formula is provided for predicting the bolus dose necessary to accomplish tumor saturation as a function of antibody and tumor properties. Furthermore, this analysis indicates certain attributes necessary for an optimal tumor targeting agent.
authors.affiliation: Department of Chemical Engineering and Division of Biological Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
authors.forename: Christilyn P
authors.initials: CP
authors.lastname: Graff
authors.forename: K Dane
authors.initials: KD
authors.lastname: Wittrup
mesh_terms: D000818:Animals; D000906:Antibodies / Q000276:immunology / Q000378:metabolism*; D000936:Antigen-Antibody Complex / Q000096:biosynthesis; D000951:Antigens, Neoplasm / Q000096:biosynthesis / Q000276:immunology / Q000378:metabolism; D006801:Humans; D007128:Immunoglobulin Fragments / Q000378:metabolism; D007700:Kinetics; D008545:Melanoma / Q000276:immunology / Q000378:metabolism; D051379:Mice; D018448:Models, Immunological; D009369:Neoplasms / Q000276:immunology / Q000378:metabolism*; D018874:Spheroids, Cellular / Q000276:immunology / Q000378:metabolism; D014018:Tissue Distribution; D014183:Transplantation, Heterologous
chemical_list: D000906:Antibodies; D000936:Antigen-Antibody Complex; D000951:Antigens, Neoplasm; D007128:Immunoglobulin Fragments