Dynamics of target-mediated drug disposition: how a drug reaches its target

We study the dynamics of drug–target interaction and the way it impacts the shape of drug versus time graphs through the derivation of accurate closed-form approximations, which reveal explicitly the relevance of rate constants in the system and can be used to compute such critical quantities as the area under the ligand (drug) curve, the clearance and the terminal slope λ _z . We also use these approximations to verify the validity of well-known approximate models, in particular the rapid binding model (Mager and Krzyzanski, Pharm Res 22:1589–1596, 2005) and the quasi-steady state model (Gibiansky et al., J Pharmacokinet Pharmacodyn 35:573–591, 2008).