Numerical validation and properties of a rapid binding approximation of a target-mediated drug disposition pharmacokinetic model

Target mediated drug disposition (TMDD) describes the phenomenon where high affinity binding of a drug to its pharmacological target (enzymes or receptors) significantly alters the pharmacokinetic profile of the drug. A rapid binding model replaces the often inestimable binding micro-constants (kon and koff) of TMDD models with the equilibrium dissociation constant (KD) by assuming rapid binding of the drug to its target. The purpose of this study is to examine the validity of the rapid binding assumption and the pharmacokinetic properties of this model. Temporal profiles of free drug in plasma and a non-specific distribution site, free receptor, and the pharmacodynamically relevant, drug–receptor complex obtained from the rapid binding model compared favorably with the full TMDD model for small values of the parameter ɛ, which represents the ratio of the time required for drug–receptor binding relative to the time required for drug to be cleared from the system. The effect of escalating drug doses on the temporal characteristics and the comparison between the two models has been numerically investigated. A closer match between the full and rapid binding models is observed for high doses. Analysis for very large doses (Dose/Vc) relative to endogenous steady-state receptor concentration (Rss), reveals that the rapid binding model reduces to a standard two compartmental model with a plasma compartment with linear drug elimination and a peripheral compartment. Decreasing clearance with increasing dose and decreasing Rss indicates that for drugs exhibiting TMDD, the relative ratio of Rss and dose is an important determinant of the pharmacokinetic properties rather than the individual parameters alone. An analytical solution derived for clearance shows that the primary elements of the apparent clearance of the drug are the linear clearance given by kelVc, the non-linear clearance due to drug–receptor complex internalization (kint), and the ratio of AUC values of the receptor complex to that of free drug. Overall, simulations and analytical techniques applied here provide a better understanding of the validity of the rapid binding model and provide guidelines for its application.