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We develop and analyze mathematical models for receptor-mediated transcytosis of monoclonal antibodies (MAb) targeting the transferrin receptor (TfR) or the insulin receptor (IR), which are expressed at the blood-brain barrier (BBB). The mass-action kinetic model for both the TfR and IR antibodies were solved numerically to generate predictions for the concentrations of all species in all compartments considered. Using these models, we estimated the rates of MAb endocytosis into brain capillary endothelium, which forms the BBB in vivo, the rates of MAb exocytosis from the intra-endothelial compartment into brain extracellular space, and the rates of receptor recycling from the endothelial space back to the luminal endothelial plasma membrane. Our analysis highlights the optimal rates of MAb association with the targeted receptor. An important role of the endogenous ligand, transferrin (Tf) or insulin, in receptor-mediated-transport (RMT) of the associated MAb was found and was attributed to the five order magnitude difference between plasma concentrations of Tf (25,000 nM) and insulin (0.3 nM). Our modeling shows that the very high plasma concentration of Tf leads to only 5% of the endothelial TfR expressed on the luminal endothelial membrane.

Mathematical Models of Blood-Brain Barrier Transport of Monoclonal Antibodies Targeting the Transferrin Receptor and the Insulin Receptor