Mathematical models of purine metabolism in man

Curto, Raúl E.; Voit, Eberhard O.; Sorribas, Albert; Cascante, Marta

doi:10.1016/s0025-5564(98)10001-9

Cited by 69 publications

(73 citation statements)

References 97 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Curto et al [13] observed in a model of purine metabolism in man that the stoichiometry of branched systems is destroyed using the S-system formulation for predictions of new steady states when the deviation from the operating point is extensive. Xanthine occurs at a branch point, and can be degraded by either of two fluxes: it can be converted into urate, in a reaction catalysed by xanthine oxidase or xanthine dehydrogenase, with a flux of 2.3 mmol´min 21 ; alternatively it can be excreted, with a flux of 0.03 mmol´min…”

Section: Discussionmentioning

confidence: 99%

“…The matrix equations proposed here to analyse this problem indicate that the deviation of flux stoichiometry will be more pronounced when the system is more sensitive to changes in the flux distribution ratio between the two branches in response to the perturbation. Accordingly, if we analyse the previous example of the S-system model of purine metabolism in man [13] we see that the ratio of fluxes in the two branches is 2.3/ 0.03 = 76.7 in the reference steady state. With deficiency in hypoxanthine phosphoribosyltransferase this ratio changes about 100-fold to 14.0/21.5 = 0.65, and the consequent violation of stoichiometry is very important, whereas it only decreases by a factor of five in the case of excessive activity of ribosephosphate pyrophosphokinase, and the violation of stoichiometry is moderate.…”

mentioning

confidence: 90%

“…At the operating point it is equivalent to an elasticity coefficient defined in metabolic control analysis, with the difference that in control analysis there is no implication that it is a constant. In generalized mass action each individual reaction is a unit of representation, but in S-systems the individual reaction fluxes are aggregated into net fluxes through each internal metabolite pool of the metabolic pathway; in this way, a steady state is represented simply as the balance between two terms from Kirchhoff's node equations, one representing the aggregation of the incoming fluxes and the other the aggregation of the outgoing fluxes.The S-system way of representing a system has several advantages [11] but it also has some disadvantages, and several authors have reported that it fails to predict the new steady state correctly when this is far from the operating point in a complex branched metabolic pathway such as the tricarboxylic acid cycle in Dictyostelium discoideum [12] or purine metabolism in man [13].Although metabolic control analysis has often been applied without aggregating elementary fluxes into net fluxes through pools of enzyme-catalysed reactions, such aggregation is not prohibited, and the advantages and disadvantages of aggregation described here also have importance in control analysis if aggregation is used to simplify a complex model. The general strategy used has been to simplify the system into modules or blocks that communicate via one or more explicit intermediates; this approach is called as modular [14,15] or top-down control analysis [16,17].…”

mentioning

confidence: 99%

“…The S-system way of representing a system has several advantages [11] but it also has some disadvantages, and several authors have reported that it fails to predict the new steady state correctly when this is far from the operating point in a complex branched metabolic pathway such as the tricarboxylic acid cycle in Dictyostelium discoideum [12] or purine metabolism in man [13].…”

mentioning

confidence: 99%

“…The aggregation may produce a spurious reduction in the number of degrees of freedom of the system at steady state, because the stoichiometric relationships are not accurately expressed by the system equations [20]. Curto et al [13] observed that the stoichiometry of branched systems is destroyed using the S-system formulation for predictions of new steady states when the deviation from the operating point is extensive, and they illustrated the biochemical and clinical importance of these inaccuracies with a model of purine metabolism in man. For example, in modelling deficiency of hypoxanthine phosphoribosyltransferase they found that the inaccuracy in the flux stoichiometry of S-system models became significant for large deviations from the operating point.…”

mentioning

confidence: 99%

See 4 more Smart Citations

Advantages and disadvantages of aggregating fluxes into synthetic and degradative fluxes when modelling metabolic pathways

Atauri

Curto

Puigjaner

et al. 1999

European Journal of Biochemistry

Self Cite

View full text Add to dashboard Cite

It is now widely accepted that mathematical models are needed to predict the behaviour of complex metabolic networks in the cell, in order to have a rational basis for planning metabolic engineering with biotechnological or therapeutical purposes. The great complexity of metabolic networks makes it crucial to simplify them for analysis, but without violating key principles of stoichiometry or thermodynamics. We show here, however, that models for branched complex systems are sometimes obtained that violate the stoichiometry of fluxes at branch points and as a result give unrealistic metabolite concentrations at the steady state. This problem is especially important when models are constructed with the S-system form of biochemical systems theory. However, the same violation of stoichiometry can occur in metabolic control analysis if control coefficients are assumed to be constant when trying to predict the effects of large changes. We derive the appropriate matrix equations to analyse this type of problem systematically and to assess its extent in any given model. Keywords: flux aggregation, metabolic control analysis, biochemical systems theory, metabolism, kinetic models.The metabolic activities of living cells are accomplished by a regulated and highly coupled network of enzyme-catalysed reactions and selective transport systems. The complexity of the networks makes it necessary to construct models to understand and predict their behaviour, but these are always simplifications of reality. Several approaches for modelling biochemical pathways have appeared over the last 30 years, and with the help of computers it is not difficult to simulate behaviour of simple metabolic pathways with a set of equations representing kinetics of the enzymes in the pathway. However, dealing with complex systems and progressing further in the field requires a theoretical basis for formulating different strategies for simplifying the complexity and relating local properties of enzymes with global properties of the pathway.To fulfil this purpose two approaches to the analysis of complex biochemical systems have emerged in the past two decades, biochemical systems theory [1±3] and metabolic control analysis [4±6]. The need for these derives from the large numbers of components in such systems and the nonlinear interactions between them. Both are based on sensitivity theory, but whereas biochemical systems theory uses explicit methods metabolic control analysis uses implicit methods [7±10]. Equivalent matrix equations have been developed in both formalisms to relate the response of a whole system to a perturbation (logarithmic gains in biochemical systems theory, or control coefficients in metabolic control analysis) and the local responses of individual enzymes to changes in their substrate concentrations (kinetic orders or elasticity coefficients).Two variants of biochemical systems theory have long been distinguished, generalized mass action and S-systems. In both variants each rate law is simplified by writing it as a product of p...

show abstract

Section: Discussionmentioning

confidence: 99%

mentioning

confidence: 90%