General quasi-equilibrium multivalent binding model to study diverse and complex drug-receptor interactions of biologics

Pharmacokinetics and pharmacodynamics of many biologics are influenced by their complex binding to biological receptors. Biologics consist of diverse groups of molecules with different binding kinetics to its receptors including IgG with simple one-to-one drug receptor bindings, bispecific antibody (BsAb) that binds to two different receptors, and antibodies that can bind to six or more identical receptors. As the binding process is typically much faster than elimination (or internalization) and distribution processes, quasi-equilibrium (QE) binding models are commonly used to describe drug-receptor binding kinetics of biologics. However, no general QE modeling framework is available to describe complex binding kinetics for diverse classes of biologics. In this paper, we describe novel approaches of using differential algebraic equations (DAE) to solve three QE multivalent drug-receptor binding (QEMB) models. The first example describes the binding kinetics of three-body equilibria of BsAb that binds to 2 different receptors for trimer formation. The second example models an engineered IgG variant (Multabody) that can bind to 24 identical target receptors. The third example describes an IgG with modified neonatal Fc receptor (FcRn) binding affinity that competes for the same FcRn receptor as endogenous IgG. The model parameter estimates were obtained by fitting the model to all data simultaneously. The models allowed us to study potential roles of cooperative binding on bell-shaped drug exposure–response relationships of BsAb, and concentration-depended distribution of different drug-receptor complexes for Multabody. This DAE-based QEMB model platform can serve as an important tool to better understand complex binding kinetics of diverse classes of biologics.