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

The paper extended the TMDD model to drugs with two identical binding sites (2-1 TMDD). The quasi-steady-state (2-1 QSS), quasi-equilibrium (2-1 QE), irreversible binding (2-1 IB), and Michaelis-Menten (2-1 MM) approximations of the model were derived. Using simulations, the 2-1 QSS approximation was compared with the full 2-1 TMDD model. As expected and similarly to the standard TMDD for monoclonal antibodies (mAb), 2-1 QSS predictions were nearly identical to 2-1 TMDD predictions, except for times of fast changes following initiation of dosing, when equilibrium has not yet been reached. To illustrate properties of new equations and approximations, several variations of population PK data for mAbs with soluble (slow elimination of the complex) or membrane-bound (fast elimination of the complex) targets were simulated from a full 2-1 TMDD model and fitted to 2-1 TMDD models, to its approximations, and to the standard (1-1) QSS model. For a mAb with a soluble target, it was demonstrated that the 2-1 QSS model provided nearly identical description of the observed (simulated) free drug and total target concentrations, although there was some minor bias in predictions of unobserved free target concentrations. The standard QSS approximation also provided a good description of the observed data, but was not able to distinguish between free drug concentrations (with no target attached and both binding site free) and partially bound drug concentrations (with one of the binding sites occupied by the target). For a mAb with a membrane-bound target, the 2-1 MM approximation adequately described the data. The 2-1 QSS approximation converged 10 times faster than the full 2-1 TMDD, and its run time was comparable with the standard QSS model.