Approximations of Target-Mediated Drug Disposition (TMDD) Equations for Systems with 1:2 and 2:1 Drug-Target Binding Stoichiometry
Leonid Gibiansky, Ekaterina Gibiansky
QuantPharm LLC, North Potomac, MD, USA
Background: TMDD equations were initially written and are used assuming 1:1 stoichiometry of drug-target binding even though many biological systems do not conform to this assumption. Specifically, this assumption is violated for monoclonal antibodies that have two identical binding sites. Although standard TMDD equations provide excellent fit of the observed data, it is of interest to derive correct equations and approximations that assume true binding stoichiometry between the drug and the target.
Objectives: To derive the TMDD model and its approximations for biological systems with 2:1 and 1:2 stoichiometry of drug-target binding.
Methods: TMDD equations for systems with 2:1 and 1:2 drug-target binding were formulated. Equations for total drug and total target concentrations were then derived. Quasi-steady-state (QSS) conditions for two drug-target complexes were used to derive explicit relations that express concentrations of the free drug, the free target, and drug-target complexes via total drug and total target concentrations. These expressions together with differential equations for the total drug and total target concentrations constitute the QSS approximations of the corresponding TMDD systems. QSS systems with zero internalization rate or zero dissociation rate correspond to quasi-equilibrium (QE) or irreversible binding (IB) approximations of the TMDD equations. Michaelis-Menten (MM) approximations were derived assuming that concentrations of the drug-target complexes are much lower than concentrations of the free drug. To check the validity of the derived equations, concentration-time profiles from the full TMDD models and the corresponding QSS approximations were simulated for several dosing regimens.
Results: Simulations demonstrated a good agreement between exact and approximate equations, with some deviations at low concentrations. Additional investigations are planned to investigate applicability of these approximations across the range of system parameters. In addition to predictions of free and total, drug and target concentrations, new approximations also predicted concentrations of two drug-target complexes with different stoichiometry.
Conclusions: QSS, QE, IB, and MM approximations of the TMDD models with 1:2 and 2:1 binding were derived. They can be used to provide a more detailed and precise description of the TMDD systems with 1:2 and 2:1 binding stoichiometry than those of the standard TMDD model.
