Fig. 1. Schematic illustration of the model. (a) Model 1: one-compartment model. Targeted NPs, plasma proteins and receptors co-exist within the single compartment. The plasma proteins interact nonspecifically to the NPs with ultraweak affinity. The maximum NP binding capacity is 2 proteins/NP (in the actual simulations the maximum binding capacities were 1, 6 and 10 proteins/NP for NPs of different radii). Binding of the first plasma protein does not interfere with NP-receptor complexation, whereas binding of the second protein shields the targeting moiety and prevents receptor complexation. The rate of systemic clearance from the compartment is size-dependent, being the fastest for free NPs and the slowest for NPs with 2 bound proteins (differences in clearance rates are represented with arrows of different widths). Simulations were performed to understand the cooperative action of ultraweak interactions, systemic clearance rate, and NP radius/binding capacity on the extent of receptor occupancy in the single compartment. (b) Model 2: two-compartment model. NPs are initially present in the main (‘plasma’) compartment but can reach a second, peripheral (‘tumor’) compartment. Proteins in both compartments interact nonspecifically to the NPs with ultraweak affinity. The rate of NP transfer between compartments is size-dependent, being the fastest for free NPs and the slowest for NPs with 2 bound proteins. NP clearance takes place through the main compartment as in Model 1. Simulations were performed to understand the cooperative action of ultraweak interactions, systemic clearance rate, inter-compartment transfer rates, and NP radius/binding capacity on the accumulation of NPs into the tumor compartment.