A modeling analysis of the effects of molecular size and binding affinity on tumor targeting

A diverse array of tumor targeting agents ranging in size from peptides to nanoparticles is currently under development for applications in cancer imaging and therapy. However, it remains largely unclear how size differences among these molecules influence their targeting properties. Here, we develop a simple, mechanistic model that can be used to understand and predict the complex interplay between molecular size, affinity, and tumor uptake. Empirical relationships between molecular radius and capillary permeability, interstitial diffusivity, available volume fraction, and plasma clearance were obtained using data in the literature. These relationships were incorporated into a compartmental model of tumor targeting using MATLAB to predict the magnitude, specificity, time dependence, and affinity dependence of tumor uptake for molecules across a broad size spectrum. In the typical size range for proteins, the model uncovers a complex trend in which intermediate-sized targeting agents (MW, approximately 25 kDa) have the lowest tumor uptake, whereas higher tumor uptake levels are achieved by smaller and larger agents. Small peptides accumulate rapidly in the tumor but require high affinity to be retained, whereas larger proteins can achieve similar retention with >100-fold weaker binding. For molecules in the size range of liposomes, the model predicts that antigen targeting will not significantly increase tumor uptake relative to untargeted molecules. All model predictions are shown to be consistent with experimental observations from published targeting studies. The results and techniques have implications for drug development, imaging, and therapeutic dosing.