Modeling of Drugs with Target-Mediated Disposition
Leonid Gibiansky
QuantPharm LLC, North Potomac, MD, USA
Objectives: To introduce Target-Mediated Drug Disposition (TMDD) model, discuss underlying assumptions and model properties, describe TMDD model approximations, discuss specific conditions when each of the approximation should be used, and describe experience-based recommendations on how to develop a robust model that retains all major TMDD features.
Methods: The term TMDD refers to the biological processes and models where drug-target binding significantly influences both pharmacodynamics (PD) and pharmacokinetics (PK). These are typical for the biologic drugs with high specificity to the intended target. The TMDD model describes the processes on the widely different time scales: fast drug-target binding and relatively slow drug distribution and elimination. Given the typical clinically relevant sampling, this model is rarely identifiable thus requiring use of approximations. Various TMDD approximations have been developed. Selection of the appropriate model requires understanding of the biology and assumptions underlying each of the approximations, careful examination of the available data and model diagnostics.
Results: Investigation of the TMDD equations identified distinct phases in the concentration time profiles. The initial fast phase reflects drug-target binding processes. This phase is followed by a slow phase where the drug, target, and drug-target complex are in a slowly changing equilibrium. Several approximations that differ by the underlying assumptions have been developed. The quasi-steady state (QSS) approximation describes the TMDD system where the elimination of the drug-target complex is much slower than the elimination of the free target. In this case, the drug-target complex contributes significantly to the drug kinetics. This model is especially robust if the total target concentration measurements are also available. The QSS approximation was successful in describing PK and PD of monoclonal antibodies that target soluble receptors. When the drug-target complex is eliminated faster than the free target, the QSS equations can be simplified to result in the Michaelis-Menten (MM) approximation. The MM approximation can also be derived assuming irreversible binding and low free receptor concentrations. The MM approximation was shown to describe PK of many monoclonal antibodies that target membrane receptors. For drugs that bind to both soluble and membrane receptors, the QSS approximation of the two-target TMDD equations can be used. Diagnostic plots play an important role in model selection: dose dependence of the model fit or random effects indicates model deficiency. Identifiability of model parameters is another important factor in the TMDD model selection. To be able to provide a reliable description of the data and insights into biology of the system, the approximation should be flexible enough to describe the data but parsimonious to allow precise estimation of all model parameters.
Conclusions: Modeling of drugs with TMDD requires careful examination of the underlying biology, the available data, and model diagnostics to develop the robust model that describes the observed data and is identifiable given the available data.
