The emerging discipline of mathematical pharmacology occupies the space between advanced pharmacometrics and systems biology. A characteristic feature of the approach is application of advance mathematical methods to study the behavior of biological systems as described by mathematical (most often differential) equations. One of the early application of mathematical pharmacology (that was not called this name at the time) was formulation and investigation of the target-mediated drug disposition (TMDD) model and its approximations. The model was shown to be remarkably successful, not only in describing the observed data for drug–target interactions, but also in advancing the qualitative and quantitative understanding of those interactions and their role in pharmacokinetic and pharmacodynamic properties of biologics. The TMDD model in its original formulation describes the interaction of the drug that has one binding site with the target that also has only one binding site. Following the framework developed earlier for drugs with one-to-one binding, this work aims to describe a rigorous approach for working with similar systems and to apply it to drugs that bind to targets with two binding sites. The quasi-steady-state, quasi-equilibrium, irreversible binding, and Michaelis–Menten approximations of the model are also derived. These equations can be used, in particular, to predict concentrations of the partially bound target (RC). This could be clinically important if RC remains active and has slow internalization rate. In this case, introduction of the drug aimed to suppress target activity may lead to the opposite effect due to RC accumulation.
Mathematical pharmacology Target-mediated drug disposition Quasi-equilibrium approximation Quasi-steady-state approximation Irreversible binding approximation Michaelis–Menten approximation Nonlinear pharmacokinetics Targets with two binding sites
This is a preview of subscription content, log in to check access.
Mager DE, Jusko WJ (2001) General pharmacokinetic model for drugs exhibiting target-mediated drug disposition. J Pharmacokinet Pharmacodyn 28:507–532CrossRefPubMedGoogle Scholar
Mager DE, Krzyzanski W (2005) Quasi-equilibrium pharmacokinetic model for drugs exhibiting target-mediated drug disposition. Pharm Res 22(10):1589–1596CrossRefPubMedGoogle Scholar
Gibiansky L, Gibiansky E, Kakkar T, Ma P (2008) Approximations of the target-mediated drug disposition model and identifiability of model parameters. J Pharmacokinet Pharmacodyn 35(5):573–591CrossRefPubMedGoogle Scholar
Gibiansky L, Gibiansky E (2017) Target-mediated drug disposition model for drugs with two binding sites that bind to a target with one binding site. J Pharmacokinet Pharmacodyn. doi:10.1007/s10928-017-9533-1Google Scholar
Yan X, Krzyzanski W (2012) Dose correction for the Michaelis-Menten approximation of the target-mediated drug disposition model. J Pharmacokinet Pharmacodyn 39(2):141–146CrossRefPubMedPubMedCentralGoogle Scholar
Beal SL, Sheiner LB, Boeckmann AJ, Bauer R (eds) (1989–2014) NONMEM users guides. Icon Development Solutions, Ellicott CityGoogle Scholar
Krippendorff BF, Kuester K, Kloft C, Huisinga W (2009) Nonlinear pharmacokinetics of therapeutic proteins resulting from receptor mediated endocytosis. J Pharmacokinet Pharmacodyn 36:239–260CrossRefPubMedPubMedCentralGoogle Scholar
Chakraborty A, Tannenbaum S, Rordorf C, Lowe PJ, Floch D, Gram H, Roy S (2012) Pharmacokinetic and pharmacodynamic properties of canakinumab, a human anti-interleukin-1β monoclonal antibody. Clin Pharmacokinet 51(6):e1–e18CrossRefPubMedPubMedCentralGoogle Scholar