Ronny Schuster

Refined algorithm and computer program for calculating all non–negative fluxes admissible in steady states of biochemical reaction systems with or without some flux rates fixed

A refined algorithm together with a computer procedure for determining the complete set of non-negative, steady-state fluxes in biochemical reaction systems of any complexity, with or without some flux rates fixed, is given. It is shown that this set is a convex polyhedron, which may or may not be bounde. The algorithm is illustrated by several examples; one of them concerns intermediary metabolism. A computer code in standard C is presented.

Detecting strictly detailed balanced subnetworks in open chemical reaction networks

The notion “strictly detailed balanced subnetwork” is introduced, for chemical reaction networks which are open and spatially homogeneous, to refer to any set of reactions the net rates of which vanish in each asymptotically stable steady state, regardless of the kinetic parameters of any reaction in the whole network. Necessary and sufficient conditions for sets of reactions to be strictly detailed balanced subnetworks are derived. An algorithm for detecting all reactions belonging to such subnetworks in systems of arbitrary stoichiometry is given, justified and applied to a realistic biochemical system. A computer program in PASCAL, performing the essential parts of this algorithm, is added.

Interrelations between glycolysis and the hexose monophosphate shunt in erythrocytes as studied on the basis of a mathematical model

A mathematical model is presented which comprises the reactions of glycolysis, the hexose monophosphate shunt (HMS) and the glutathione system in erythrocytes. The model is used to calculate stationary and time-dependent metabolic states of the cell in vitro and in vivo. The model properly accounts for the following metabolic features observed in vitro: (a) stimulation of the oxidative pentose pathway after addition of pyruvate due to a NADP-dependent lactate dehydrogenase as coupling enzyme between glycolysis and the oxidative pentose pathway, (b) relative share of the oxidative pentose pathway in the total consumption of glucose amounting to approximately 10% in the normal case and to approximately 90% under conditions of oxidative stress excreted by methylene blue. From the application of the model to in vivo conditions it is predicted that (c) under normal conditions glycolysis and the HMS are independently regulated by the energetic and oxidative load, respectively, (d) under conditions of enhanced energetic or oxidative load both glycolysis and the HMS are mainly controlled by the hexokinase; in this situation the highest possible values of the energetic and oxidative load which are compatible with cell integrity are strongly coupled and considerably restricted in comparison with the normal case, (e) the stationary states possess bifurcation points at high and low values of the energetic load.

A GENERALIZATION OF WEGSCHEIDER'S CONDITION. IMPLICATIONS FOR PROPERTIES OF STEADY STATES AND FOR QUASI-STEADY-STATE APPROXIMATION

A generalization of Wegschciders condition concerning equilibrium constants in chemically reacting systems is formulated, which is then proved to be a necessary and sufficient condition for detailed balancing. In order to include a large multitude of rate laws, a generalized mass action kinetics is considered which comprises usual mass action kinetics and all reversible enzyme kinetics and which is consistent with basic postulates of irreversible thermodynamics for ideal mixtures. Reaction systems of arbitrary stoichiometry are considered. They may contain reactants with fixed concentrations, as is characteristic for models of biochemical reaction networks. Existence, uniqueness, and global asymptotic stability of equilibrium states for reaction systems endowed with generalized man action kinetics are proved. Using these results, he generalized Wegscheider condition is shown to be a sufficient criterion for the applicability of the quasi-steady-state approximation.

Simplification of complex kinetic models used for the quantitative analysis of nuclear magnetic resonance or radioactive tracer studies

A method for simplifying the mathematical models describing the dynamics of tracers (e.g.13C, 31P, 14C, as used in NMR studies or radioactive tracer experiments) in (bio-)chemical reaction systems is presented. This method is appropriate in the cases where the system includes reactions, the rates of which differ by several orders of magnitude. The basic idea is to adapt the rapid-equilibrium approximation to tracer systems. It is shown with the aid of the Perron–Frobenius theorem that for tracer systems, the conditions for applicability of this approximation are satisfied whenever some reactions are near equilibrium. It turns out that the specific enrichments of all of the labelled atoms that are connected by fast reversible reactions can be grouped together as ‘pool variables’. The reduced system contains fewer parameters and can, thus, be fitted more easily to experimental data. Moreover, the method can be employed for identifying non-equilibrium and near-equilibrium reactions from experimentally measured specific enrichments of tracer. The reduction algorithm is illustrated by studying a model of the distribution of 13C-tracers in the pentose phosphate pathway.

THE POSSIBLE CONSEQUENCES OF LARGE-SCALE ENZYME ALTERATIONS ON THE METABOLIC EFFICIENCY OF RED BLOOD CELLS AS STUDIED ON THE BASIS OF A MATHEMATICAL MODEL

Based on a comprehensive mathematical model of the energy and redox metabolism of human erythrocytes we calculated stationary metabolic states of the cell varying the activity of the participating enzymes by several orders of magnitude. To compare the computational results with clinical and experimental data reported for various enzymopathies of the red cell, the three essential metabolic variables ATP, GSH and osmolarity were included in a “homeostasis function” which allows us to estimate the range of enzyme activities in which the metabolic alterations should be either tolerable, associated with non-chronic or chronic hemolytic diseases, or letal.

Calculation of Metabolic Fluxes by Mathematical Modeling of Carbon-13 Distribution in Metabolites. II. Application to the Study of C6 Cell Metabolism

The metabolism of the rat C6 cell line has been extensively studied1–4, because these cells constitute a model of malignant glioma. As neoplastic cells preferentially utilize the relatively inefficient Embden-Meyerhof pathway for satisfying their energy requirements, the carbohydrate metabolism, up to now, was in the center of interest. Besides glycolysis, C6 cells have been shown to possess non-negligible activities of the hexose monophosphate shunt (HMPS), and glycogen synthesis.

Calculation of Metabolic Fluxes by Mathematical Modeling of Carbon-13 Distribution in Metabolites. I. Presentation of the Mathematical Model

Carbon-13 (13C) NMR spectroscopy in connection with the use of 13C-enriched substrates is a powerful technique for metabolic studies, e.g. for specifying the structure of metabolic pathways, determining flux rates or investigating reaction mechanisms1–9. However, owing to the complexity of many biological systems, it is often impossible to directly obtain this information from the experimental data. In many cases, mathematical models which describe the isotopic distribution as a function of fluxes turn out to be necessary1–9.