Target-mediated drug disposition model for drugs that bind to more than one target.

Until recently, most therapeutic monoclonal antibodies (mAb) were designed to bind only one target. However, several existing mAbs bind to soluble and membrane forms of the same receptor. Moreover, design of bi-specific and multi-specific proteins that bind to more than one target is a promising direction of drug design. The pharmacokinetics and pharmacodynamics of these drugs may be described by the target-mediated drug disposition (TMDD). This work extended the TMDD model to drugs that bind more than one target. The quasi-steady-state (QSS) and Michaelis-Menten (MM) approximations of the model were also derived. Identifiability of model parameters was studied by simulations. The drug and target parameters used in simulations were chosen to imitate a monoclonal antibody that binds to the soluble (S) and membrane-bound (M) targets. The data were simulated for 224 subjects using the full TMDD model and dosing that mimicked typical Phase I and Phase II designs with rich sampling. Four population pharmacokinetic models were fitted to the free (unbound) drug and total (unbound and bound to the drug) S-target data: a one-target QSS model that simultaneously described the free drug and the total S-target (M1), a model with parallel linear and MM elimination that described the free drug combined with a separate S-target model that utilized the free drug concentrations but did not influence them (M2), a two-target QSS model where the S-target was described by the QSS approximation while the contribution of the M-target was described by the MM elimination term (M3), and a two-target full TMDD model (M4). The influence of relative contributions of the S and M-targets to target-mediated elimination on identifiability of the model parameters was investigated. The influence of assay sensitivity and availability of the total rather than free drug concentration measurements were also investigated. The results indicated that for the dosing regimens and system parameters investigated in this work the pharmacokinetic data alone did not allow to distinguish influences of the two targets. When the drug and S-target data were available, the model M1 described the data with the deficiencies of the fit visible only at the lowest dose level. However, the parameter estimates were strongly biased. The model M2 improved the fit and provided the precise estimates of the S-target parameters. However, no information concerning the M-target could be obtained from this model. The model M3 provided an excellent description of the data and the unbiased estimates of all the parameters. It also provided the unbiased estimates of change from baseline of the unobservable M-target concentrations. The models M1-M3 were robust while M4 was unstable despite the prohibitively long run time. The results were similar when the total rather than free drug was measured. The M-target parameters were estimated only when M-target elimination was at least comparable to S-target elimination. Improvement of the assay sensitivity has not resulted in marked improvement of the parameter estimates. In summary, for the cases investigated in this work the QSS approximation of the two-target TMDD model provided the unbiased and robust estimates of all the relevant TMDD parameters.