New Equilibrium Models of Drug-Receptor Interactions Derived from Target-Mediated Drug Disposition

In vivo analyses of pharmacological data are traditionally based on a closed system approach not incorporating turnover of target and ligand-target kinetics, but mainly focussing on ligand-target binding properties. This study incorporates information about target and ligand-target kinetics parallel to binding. In a previous paper, steady-state relationships between target- and ligand-target complex versus ligand exposure were derived and a new expression of in vivo potency was derived for a circulating target. This communication is extending the equilibrium relationships and in vivo potency expression for (i) two separate targets competing for one ligand, (ii) two different ligands competing for a single target and (iii) a single ligand-target interaction located in tissue. The derived expressions of the in vivo potencies will be useful both in drug-related discovery projects and mechanistic studies. The equilibrium states of two targets and one ligand may have implications in safety assessment, whilst the equilibrium states of two competing ligands for one target may cast light on when pharmacodynamic drug-drug interactions are important. The proposed equilibrium expressions for a peripherally located target may also be useful for small molecule interactions with extravascularly located targets. Including target turnover, ligand-target complex kinetics and binding properties in expressions of potency and efficacy will improve our understanding of within and between-individual (and across species) variability. The new expressions of potencies highlight the fact that the level of drug-induced target suppression is very much governed by target turnover properties rather than by the target expression level as such.Analysis and Stochastic

Travelling wave solutions for degenerate pseudo-parabolic equation modelling two-phase flow in porous media

We discuss a pseudo-parabolic equation modelling two-phase flow in porous media, which includes a dynamic capillary pressure term. We extend results obtained previously for linear higher order terms and investigate the existence of travelling wave solutions in the non-linear and degenerate case. These cases may lead to non-smooth travelling waves, as well as to a discontinuous capillary pressure

A new class of entropy solutions of the Buckley-Leverett equation.

We discuss an extension of the Buckley-Leverett (BL) equation describing two-phase flow in porous media. This extension includes a third order mixed derivatives term and models the dynamic effects in the pressure difference between the two phases. We derive existence conditions for travelling wave solutions of the extended model. This leads to admissible shocks for the original BL equation, which violate the Oleinik entropy condition and are therefore called nonclassical. In this way we obtain non-monotone weak solutions of the BL problem consisting of steady states separated by shocks, confirming results obtained experimentall

A new class of entropy solutions of the Buckley-Leverett equation.

We discuss an extension of the Buckley-Leverett (BL) equation describing two-phase flow in porous media. This extension includes a third order mixed derivatives term and models the dynamic effects in the pressure difference between the two phases. We derive existence conditions for travelling wave solutions of the extended model. This leads to admissible shocks for the original BL equation, which violate the Oleinik entropy condition and are therefore called nonclassical. In this way we obtain non-monotone weak solutions of the BL problem consisting of steady states separated by shocks, confirming results obtained experimentall

Topics in Mathematical Pharmacology

Mathematical analysis of pharmacological models is becoming increasingly rel- evant for drug development. Emphasis on mechanistic models has grown and qualitative understanding of complex biological systems has improved a great deal. In this paper we present two examples of basic modular processes which are involved in a wide range of physiological systems. The first model concerns the interaction of a drug with its target, the way the compounds bind and then elicit an effect. The second model is central in signal trans- duction across the cell wall. Both models demonstrate the complex and interesting dynamics which is directly relevant for the impact of the drug. Analysis and Stochastic