We worked exclusively with the recombinant immunotoxins (RIT), which are molecules made partly of tumor-specific antibody and partly of a potent protein toxin. Our collaborator, Dr. Ira Pastan, and his group are making and testing these molecules as a new class of potent and specific anti-cancer protein drugs. We published the initial mathematical model of the RIT delivery process five years ago (Chen et al., Annals of Biomedical Engineering, 36: 486-512, 2008). The model considers a tumor as a collection of N identical representative units (RUs), which is a spherical unit of approximately 100 micron diameter centered around a spherical blood vessel, which serves as the source of the RIT. The advantage of this model is that it can handle tumors of any size while handling only one RU of a reasonable, constant size. The model consists of two main sets of differential equations. One set describes the kinetic steps that the RIT molecules go through within each RU, which include extravasation from the blood vessel into the tumor ECS, diffusion in ECS, binding to the surface antigen, internalization by endocytosis, travel through endosomal compartments, translocation into the cytosol, and finally intoxication of the cell. The other set of differential equations describe the growth, death, and movement of tumor cells within each RU and their flow in and out of the RUs. Cells move because the number of cells increases when the tumor grows and because intoxicated cells die and are cleared, creating an empty space into which neighboring cells move in. This model reproduces the experimental volume change with time of human tumors growing in mice in response to the administration of different doses of RIT and demonstrates the well-known binding site barrier effect. It also identified some two dozen factors that are involved in the delivery process, some of which affect the efficacy of the RIT much more than others. We have since improved upon this model by re-writing the entire set of differential equations to make the model quantitatively more precise and by including the effect of antigen shedding, which was not included in the original model. When applied to the mesothelin-targeting RIT called SS1P, the new model gave accurate accounting of all the RITs that enter the tumor tissue at all times. (Pak et al., Cancer Res 72:3143-52, 2012.) In accordance with the experimental data (Zhang et al., Clin Cancer Res 12:4695, 2006), the model indicates that only about 0.5% of the injected dose enters the tumor tissue of approximately 100 cc size growing in mice. Most of the RITs that enter the tumor tissue are degraded in the endosomal compartment within the tumor cells, again as expected from many earlier studies. A major, unexpected prediction is that antigen shedding greatly enhances, not retards, the efficacy of the RITs. The main reason for this effect is that the shed antigen acts as a protective reservoir, which releases the bound antigen at later times and at places far away from the blood vessel. The idea that there was a reservoir of RITs in the system had been suggested by experimental data (Zhang et al., Cancer Res 70:1082, 2010), although concrete nature of the reservoir had not been identified. We have now further improved the model by (1) allowing all molecular species to back-permeate from the tumor extra-cellular space to the blood, (2) making the permeation rate constant to vary with the tumor size, (3) damping tumor growth exponentially by tumor size (Laird, British Journal of Cancer 13:490-502, 1964), (4) describing the toxin enzymatic action by Michaelis-Menten type kinetics rather than by simple exponential, (5) recognizing the presence (assumed to be 50%) of non-tumor cells in the tumor tissue, and (6) increasing the radius of the RU from 38 to 50 microns. We applied this modified model to LMB-2 targeting CD25 as well as to SS1P targeting mesothelin. These changes resulted in a much better fit to the experimental data in both cases. Comparison of the two cases brought out the large influence of the number of antigen molecules on the surface. The new model shows that shedding is beneficial only when there are more than half million antigen molecules per cell on the surface, which is the case for mesothelin. However, when there are fewer than this number of antigens, which is the case for CD-25, shedding in fact reduces the efficacy of RIT. The model also predicts that LMB-2 must be degraded faster in the endosome than SS1P, which suggests that the two RITs enter different endosomal compartments upon endocytosis. A manuscript reporting these results is in preparation.