The modelling of metabolic systems. Structure, control and optimality.
Heinrich R, Schuster S
This article gives an overview of recent developments in the modelling of the structure, control and optimality of metabolic networks. In particular, methods of algebraically analysing the topology of such networks are presented. By these methods, conservation relations and elementary modes of functioning (biochemical routes) can be detected. The principles of metabolic control analysis are outlined. Various recent extensions of this theory are presented, such as an analysis in terms of time dependent variables and modular analysis. Evolutionary optimisation principles are applied to explain the catalytic efficiency of single enzymes as well as the structural design of metabolic pathways. Special results concern the optimal distribution of ATP consuming and ATP producing reactions in glycolysis.
Control analysis of metabolic systems involving quasi-equilibrium reactions.
Kholodenko BN, Schuster S, Garcia J, Westerhoff HV, Cascante M
1998 Mar 2; 1379(3): 337-52. PubMed: 9545597.
Reactions for which the rates are extremely sensitive to changes in the concentrations of variable metabolite concentrations contribute little to the control of biochemical reaction networks. Yet they do interfere with the calculation of the system's behaviour, both in terms of numerical integration of the rate equations and in terms of the analysis of metabolic control. We here present a way to solve this problem systematically for systems with time hierarchies. We identify the fast reactions and fast metabolites, group them apart from the other ("slow") reactions and metabolites, and then apply the appropriate quasi-equilibrium condition for the fast subsystem. This then makes it possible to eliminate the fast reactions and their elasticity coefficients from the calculations, allowing the calculation of the control coefficients of the slow reactions in terms of the elasticity coefficients of the slow reactions. As expected, the elasticity coefficients of the fast reactions drop out of the calculations, and they are irrelevant for control at the time resolution of the steady state of the slow reactions. The analysis, when applied iteratively, is expected to be particularly valuable for the control analysis of living cells, where a time hierarchy exists, the fastest being at the level of enzyme kinetics and the slowest at gene expression.
Mitochondria as an important factor in the maintenance of constant amplitudes of cytosolic calcium oscillations.
Marhl M, Schuster S, Brumen M
Theoretical models of intracellular calcium oscillations have hitherto focused on the endoplasmic reticulum (ER) as an internal calcium store. These models reproduced the large variability in oscillation frequency observed experimentally. In the present contribution, we extend our earlier model [Marhl et al., Biophys. Chem., 63 (1997) 221] by including, in addition to the ER, mitochondria as calcium stores. Simple plausible rate laws are used for the calcium uptake into, and release from, the mitochondria. It is demonstrated with the help of this extended model that mitochondria are likely to act in favour of frequency encoding by enabling the maintenance of fairly constant amplitudes over wide ranges of frequency.
Elementary Modes Analysis Illustrated with Human Red Cell Metabolism.
In: BioThermoKinetics in the Post Genomic Era. (C. Larsson, I.-L. Pahlman and L. Gustafsson, eds.)
pp.332-339. BID: 12.
Publisher: Chalmers, Goeteborg
Influence of Calcium Binding to Proteins on Calcium Oscillations and ER Membrane Potential Oscillations. A Mathematical Model.
Schuster S, Marhl M, Brumen M, Heinrich R
In: Information Processing in Cells and Tissues. (R. Paton and M. Holcombe)
pp.137-150. BID: 13.
Publisher: Plenum Press, New York
Modelling the interrelation between the transmembrane potential and pH difference across membranes with electrogenic proton transport upon build-up of the proton-motive force.
Schuster S, Ouhabi R, Rigoulet M, Mazat JP
1998; 45: 181-192. PID: 357.