Dynamics of a Two-Receptor Binding Model: How Affinities and Capacities Translate into Long- and Short-Term Behaviour and Physiological Corollaries
Willem de Winter (1), Bert Peletier (2), An Vermeulen (1)
(1) Advanced Modeling & Simulation, Clinical Pharmacology, Janssen Research & Development, a Division of Janssen Pharmaceutica NV, Beerse, Belgium; (2) Mathematical Institute, Leiden University, Leiden, The Netherlands
Objectives: We show that data described by a two-receptor model may settle relatively quickly (months) at an apparent steady state, only to rise to a significantly higher final steady state over a much longer period over time (years). The objective of this project is to develop an analytical tool for making predictions about the long-term drug concentrations on the basis of short-term measurements, and for designing optimal dosing regimens.
Methods: The two-receptor model of Snoeck et al , one receptor having high affinity and low capacity, and the other having low affinity but high capacity, was analysed by means of simulations and mathematical analysis. Attention was paid to the relation between drug concentration in plasma and the concentrations at the two receptors. The analysis employed dynamical systems analysis and singular perturbation theory.
Results: Analytical expressions for the lower apparent steady state and the higher final steady state concentrations in plasma and at the receptors were derived and formulas for the time to the apparent and the final steady state were constructed. It was shown how the amount of drug in the large capacity receptor could eventually exceed that in plasma by far. Thus a tool was developed which can be used to predict long term concentrations in the different compartments on the basis of short term data about concentrations in plasma.
Conclusions: When relatively short term data point to a specific model, it is important to analyse the implications of this model for long term behaviour when chronic administration of the drug is considered. This can be done through simulations, but it is better still when analytic expressions are derived for the steady states and for time to steady state, in order to pinpoint the impact of different parameters on these quantities.
 Snoeck E, Jacqmin P, Van Peer A, Danhof M (1999). A combined specific target site binding and pharmacokinetic model to explore the non-linear disposition of draflazine. J Pharmacokinet Biopharm 27(3):257-281