Peiming Ma
Amgen Inc.
Objectives: To illustrate a rigorous way with which simplifications of the general TMD model are derived; to organize TMD models including MM, Qss and RB models; and to identify some confusions in application.
Methods: TMD of a drug refers to the phenomenon that drug interaction with target significantly influences drug disposition. When amount/capacity of accessible target relative to drug is limited, TMD typically manifests nonlinear PK. Many biologics bind to target with high affinity and specificity, and exhibit TMD.
A general TMD model was proposed [1], followed by simplifications of RB and Qss models [2,3]. However, it is not always clear besides fewer equations or parameters why simplifications are indeed so, and not uncommon to see confusions in application.
Results: We present recent work on organizing various TMD models and compare them using known examples. We follow a model scheme in [4] with C, R, and M as drug, target, and drug-target complex concentrations. The association and dissociation processes are governed by a second- and a first-order rate constants kon and koff. The complex may internalize or degrade with a rate constant kmet.
A direct simplification of the general TMD model is to assume constant total target Rtot [1]. Other simplifications can be made by modifying some differential equations with e.g. RB and Qss assumptions. However, a broad assumption can be the basis for many simplification: R∙C = κ M – α R – β C + γ. This algebraic equation replaces one of the differential equations, and the resultant equations form a simplification. The Qss assumption R∙C = KmM, where Km = (koff + kmet)/kon, is a special case. Under Qss assumption the MM and Qss models can be directly simplified from the general TMD model. As a second example, if κ, β=0, α = Km, γ = Vmax/kon for a constant Vmax, the simplification is a model of central, peripheral, and receptor compartments with or MM distribution from the central to receptor compartment and linear elimination from both. This was briefly discussed in [1].
Note that the labeling of KD and Km is the only difference between the RB and Qss models, which are indistinguishable for model fitting. Thus, upon fitting either model, we need to ask whether or not the fitted parameter KD of the RB model is actually Km, and vice versa.
Conclusions: Our work should provide a more rigorous basis for theoretical and practical research of TMD models, important for investigating PK-PD relationships of many biologics.
References:
[1] Mager and Jusko, J Pharmacokinet Pharmacodyn 28(6):507-532, 2001
[2] Mager and Krzyzanski, Pharm Res. 2005;22(10):1589-96.
[3] Gibiansky, Gibiansky, Kakkar, and Ma, J Pharmacokinet Pharmacodyn. 2009;35:573-91
[4] Ma, Pharm Res. 2011, Pharm Res, DOI 10.1007/s11095-011-0615-2
Reference: PAGE 21 (2012) Abstr 2307 [www.page-meeting.org/?abstract=2307]
Poster: New Modelling Approaches