Asymptotic analysis of a TMDD model: when a reaction contributes to the destruction of its product

The multi-scale dynamics of a two-compartment with first order absorption Target-Mediated Drug Disposition (TMDD) pharmacokinetics model is analysed, using the Computational Singular Perturbation (CSP) algorithm. It is shown that the process evolves along two Slow Invariant Manifolds (SIMs), on which the most intense components of the model are equilibrated, so that the less intensive are the driving ones. The CSP tools allow for the identification of the components of the TMDD model that (i) constrain the evolution of the process on the SIMs, (ii) drive the system along the SIMs and (iii) generate the fast time scales. Among others, such diagnostics identify (i) the factors that determine the start and the duration of the period in which the ligand-receptor complex acts and (ii) the processes that determine its degradation rate. The counterintuitive influence of the process that transfers the ligand from the tissue to the main compartment, as it is manifested during the final stage of the process, is studied in detail.