Bibliography

(eng): We address efficient modeling of the intracellular action of a drug binding to the nuclear pregnane X receptor. The binded complex enters the cell nucleus and acts on DNA, resulting in enhanced production of an enzyme which metabolizes, among others, co-administered drugs. Pharmacodynamic modeling is traditionally based on a compartmental approach, which simplifies the complex processes in the human body through the definition of a small number of compartments representing organs, tissues, cells, cytoplasm or abstract units. Inside a compartment, the concentrations of all substances are assumed to be distributed homogeneously, i.e. there is no spatial dependence. They lead to a system of ODEs for the time-dependence of the concentrations of the active substances. We will present an extension of a model from the literature for the action of the tuberculose-drug Rifampicin. The extension consists of a first attempt to add spatial resolution for substances that are active in the cytoplasm. Spatial resolution can be benecifial to analyze important issues like, among others, local exceeding of toxic drug levels, delay of transport and drug-drug interactions. We address efficient solution of the linear systems arising when numerically integrating the resulting PDE's and consider some preconditioning techniques based on properties of the underlying biochemical network.