Note on importance of correct stoichiometric assumptions for modeling of monoclonal antibodies

Pharmacokinetic modeling of monoclonal antibodies (mAbs) with non-linear binding is based on equations of the target-mediated drug disposition (Mager and Jusko, J Pharmacokinet Pharmacodyn 28:507-532, 2001). These equations demonstrated their utility in countless examples and drug development programs. The model assumes that the mAb drug and the target have only one binding site each while, in reality, most antibodies have two binding sites. Thus, the currently used model does not correspond to the biological process that it aims to describe. The correct mechanistic model should take into account both binding sites. We investigated, using simulations, whether this discrepancy is important and when it is advisable to use a model with correct stoichiometric 2-to-1 ratio. We show that for soluble targets when elimination rate of the drug-target complex is comparable with the elimination rate of the drug or lower, and when measurements of both total drug and total target concentrations are available, the model with 1-to-1 (monovalent) binding cannot describe data simulated from the model with 2-to-1 (bivalent) binding. In these cases, models with correct stoichiometric assumptions may be necessary for an adequate description of the observed data. Also, a model with allosteric binding that encompasses both 2-to-1 and 1-to-1 binding models as particular cases was proposed and applied. It was shown to be identifiable given the detailed concentration data of total drug and total target.