Biosimulation of drug metabolism--a yeast based model.

Computationally predicting the metabolic fates of drugs is a very complex task which is owed not only to the huge and diverse biochemical network in the living cell, but also to the majority of in vivo transformations that occur through the action of hepatocytes and gastro-intestinal micro-flora. Thus, xenobiotics are metabolised by more than a single cell type. However, the prediction of metabolic fates is definitely a problem worth solving since it would allow facilitate the development of drugs in a way less relying on animal testing. As a first step in this direction, PharmBiosim is being developed, a biosimulation tool which is based on substantial data reduction and on attributing metabolic fates of drug molecules to functional groups and substituents. This approach works with yeast as a model organism and is restricted to drugs that are mainly transformed by enzymes of the central metabolism, especially sugar metabolism. The reason for the latter is that the qualitative functioning of the involved biochemistry is very similar in diverse cell types involved in drug metabolism. Further it allows for using glycolytic oscillations as a tool to quantify interactions of a drug with this metabolic pathway.

Model evaluation for glycolytic oscillations in yeast biotransformations of xenobiotics.

Anaerobic glycolysis in yeast perturbed by the reduction of xenobiotic ketones is studied numerically in two models which possess the same topology but different levels of complexity. By comparing both models' predictions for concentrations and fluxes as well as steady or oscillatory temporal behavior we answer the question what phenomena require what kind of minimum model abstraction. While mean concentrations and fluxes are predicted in agreement by both models we observe different domains of oscillatory behavior in parameter space. Generic properties of the glycolytic response to ketones are discussed.

Modelling thin-film dewetting on structured substrates and templates: bifurcation analysis and numerical simulations.

We study the dewetting process of a thin liquid film on a chemically patterned solid substrate (template) by means of a thin-film evolution equation incorporating a space-dependent disjoining pressure. Dewetting of a thin film on a homogeneous substrate leads to fluid patterns with a typical length scale, that increases monotonously in time (coarsening). Conditions are identified for the amplitude and periodicity of the heterogeneity that allow to transfer the template pattern onto the liquid structure ("pinning") emerging from the dewetting process. A bifurcation and stability analysis of the possible liquid ridge solutions on a periodically striped substrate reveal parameter ranges where pinning or coarsening ultimately prevail. We obtain an extended parameter range of multistability of the pinning and coarsening morphologies. In this regime, the selected pattern depends sensitively on the initial conditions and potential finite perturbations (noise) in the system as we illustrate with numerical integrations in time. Finally, we discuss the instability to transversal modes leading to a decay of the ridges into rows of drops and show that it may diminish the size of the parameter range where the pinning of the thin film to the template is successful.

Modulated amplitude waves and the transition from phase to defect chaos

The mechanism for transitions from phase to defect chaos in the one-dimensional complex Ginzburg-Landau equation (CGLE) is presented. We describe periodic coherent structures of the CGLE, called modulated amplitude waves (MAWs). MAWs of various periods P occur in phase chaotic states. A bifurcation study of the MAWs reveals that for sufficiently large period, pairs of MAWs cease to exist via a saddle-node bifurcation. For periods beyond this bifurcation, incoherent near-MAW structures evolve towards defects. This leads to our main result: the transition from phase to defect chaos takes place when the periods of MAWs in phase chaos are driven beyond their saddle-node bifurcation.

Simplified replica treatment of various random-energy and random-field models with confinement potential.

A modified version of the replica method recently proposed by the authors [J. Phys. A 32, 585 (1999)] is applied to a certain class of models describing the motion of a particle in a random potential with superposed parabolic confinement. Different types of randomness are considered. Previous treatments of analogous models were based on replica symmetry breaking (RSB). The aim of the paper is to demonstrate that the new method provides reliable results for the average free energy and related quantities without taking into account RSB. The comparison with computer simulations shows satisfactory agreement.