IV-13 Leonid Gibiansky Monoclonal Antibody-Drug Conjugates (ADC): TMDD Equations, Approximations, and Identifiability of Model Parameters

Leonid Gibiansky, Ekaterina Gibiansky

QuantPharm LLC, North Potomac, MD, USA

Objectives: To derive equations that describe antibody-drug conjugate (ADC) distribution, deconjugation, elimination and interaction with the target; to derive Michaelis-Menten approximation of these equations; to investigate identifiability of model parameters given typically available measurements and clinically feasible sampling scheme.

Methods: Equations of that describe concentration-time course of the ADC - target system that includes the naked antibody, ADCs with various loads, free drug, free target, and various antibody ADC-target complexes were derived. Michaelis-Menten approximation of these equations was derived based on the assumption of fast internalization of the ADC-target complex. Identifiability of the model parameters was investigated using optimal design PFIM software [1]. The parsimonious model flexible enough to describe the typically available measurements yet simple enough to be identifiable was suggested. Various generalizations of the proposed model were discussed.

Results: The ADC system can be described using the general TMDD framework with an additional element that accounts for the deconjugation process. Given the typically available measurements, parameters of the individual ADC species (ADCs with specific drug loads) are not identifiable. Assumptions that relate ADC and ADC-target parameters with different drug loads are required. In particular, the system where ADC model parameters do not depend on the drug load is identifiable. The system where parameters linearly depend on the drug load also can be identifiable. Similarly, deconjugation rate of individual ADC species can be identifiable only under specific assumptions on how deconjugation rate depends on the drug load; the individual ADC deconjugation rates cannot be estimated from the typically available data.

Conclusions: Michaelis-Menten approximation of the TMDD model can be used to describe the interaction of ADC with the target when internalization rate is fast. Assumptions that describe dependence of the ADC parameters on drug load are necessary to make the system identifiable. In particular, the system with ADC parameters linearly dependent on the drug load can be identifiable.

References: [1] Bazzoli C, Retout S, Mentré F. Design evaluation and optimisation in multiple response nonlinear mixed effect models: PFIM 3.0. Computer Methods and Programs in Biomedicine, 2010, 98: 55-65; http://www.pfim.biostat.fr