Target-mediated drug disposition model for drugs with N > 2 binding sites that bind to a target with one binding site

Abstract

The paper extended the TMDD model to drugs with more than two (N > 2) identical binding sites (N-to-one TMDD). The quasi-steady-state (N-to-one QSS), quasi-equilibrium (N-to-one QE), irreversible binding (N-to-one IB), and Michaelis-Menten (N-to-one MM) approximations of the model were derived. To illustrate properties of new equations and approximations, N = 4 case was investigated numerically. Using simulations, the N-to-one QSS approximation was compared with the full N-to-one TMDD model. As expected, and similarly to the standard TMDD for monoclonal antibodies (mAb), N-to-one QSS predictions were nearly identical to N-to-one TMDD predictions, except for times of fast changes following initiation of dosing, when equilibrium has not yet been reached. Predictions for mAbs with soluble targets (slow elimination of the complex) were simulated from the full 4-to-one TMDD model and were fitted to the 4-to-one TMDD model and to its QSS approximation. It was demonstrated that the 4-to-one QSS model provided nearly identical description of not only the observed (simulated) total drug and total target concentrations, but also unobserved concentrations of the free drug, free target, and drug-target complexes. For mAb with a membrane-bound target, the 4-to-one MM approximation adequately described the data. The 4-to-one QSS approximation converged 8 times faster than the full 4-to-one TMDD.

Keywords: Drugs with many binding sites; Irreversible binding approximation; Michaelis–Menten approximation; Nonlinear pharmacokinetics; Quasi-equilibrium approximation; Quasi-steady-state approximation; Target-mediated drug disposition.