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A mathematical pharmacokinetic/anti-drug-antibody (PK/ADA) model was constructed for quantitatively assessing immunogenicity for therapeutic proteins. The model is inspired by traditional pharmacokinetic/pharmacodynamic (PK/PD) models, and is based on the observed impact of ADA on protein drug clearance. The hypothesis for this work is that altered drug PK contains information about the extent and timing of ADA generation. By fitting drug PK profiles while accounting for ADA-mediated drug clearance, the model provides an approach to characterize ADA generation during the study, including the maximum ADA response, sensitivity of ADA response to drug dose level, affinity maturation rate, time lag to observe an ADA response, and the elimination rate for ADA-drug complex. The model also provides a mean to estimate putative concentration-time profiles for ADA, ADA-drug complex, and ADA binding affinity-time profile. When simulating ADA responses to various drug dose levels, bell-shaped dose-response curves were generated. The model contains simultaneous quantitative modeling and provides estimation of the characteristics of therapeutic protein drug PK and ADA responses in vivo. With further experimental validation, the model may be applied to the simulation of ADA response to therapeutic protein drugs in silico, or be applied in subsequent PK/PD models.

A Mathematical Model of the Effect of Immunogenicity on Therapeutic Protein Pharmacokinetics