The stability and robustness of metabolic states: identifying stabilizing sites in metabolic networks

The dynamic behavior of metabolic networks is governed by numerous regulatory mechanisms, such as reversible phosphorylation, binding of allosteric effectors or temporal gene expression, by which the activity of the participating enzymes can be adjusted to the functional requirements of the cell. For most of the cellular enzymes, such regulatory mechanisms are at best qualitatively known, whereas detailed enzyme-kinetic models are lacking. To explore the possible dynamic behavior of metabolic networks in cases of lacking or incomplete enzyme-kinetic information, we present a computational approach based on structural kinetic modeling. We derive statistical measures for the relative impact of enzyme-kinetic parameters on dynamic properties (such as local stability) and apply our approach to the metabolism of human erythrocytes. Our findings show that allosteric enzyme regulation significantly enhances the stability of the network and extends its potential dynamic behavior. Moreover, our approach allows to differentiate quantitatively between metabolic states related to senescence and metabolic collapse of the human erythrocyte. We think that the proposed method represents an important intermediate step on the long way from topological network analysis to detailed kinetic modeling of complex metabolic networks

Understanding the regulation of aspartate metabolism using a model based on measured kinetic parameters

The aspartate-derived amino-acid pathway from plants is well suited for analysing the function of the allosteric network of interactions in branched pathways. For this purpose, a detailed kinetic model of the system in the plant model Arabidopsis was constructed on the basis of in vitro kinetic measurements. The data, assembled into a mathematical model, reproduce in vivo measurements and also provide non-intuitive predictions. A crucial result is the identification of allosteric interactions whose function is not to couple demand and supply but to maintain a high independence between fluxes in competing pathways. In addition, the model shows that enzyme isoforms are not functionally redundant, because they contribute unequally to the flux and its regulation. Another result is the identification of the threonine concentration as the most sensitive variable in the system, suggesting a regulatory role for threonine at a higher level of integration

Evaluation of rate law approximations in bottom-up kinetic models of metabolism.

BackgroundThe mechanistic description of enzyme kinetics in a dynamic model of metabolism requires specifying the numerical values of a large number of kinetic parameters. The parameterization challenge is often addressed through the use of simplifying approximations to form reaction rate laws with reduced numbers of parameters. Whether such simplified models can reproduce dynamic characteristics of the full system is an important question.ResultsIn this work, we compared the local transient response properties of dynamic models constructed using rate laws with varying levels of approximation. These approximate rate laws were: 1) a Michaelis-Menten rate law with measured enzyme parameters, 2) a Michaelis-Menten rate law with approximated parameters, using the convenience kinetics convention, 3) a thermodynamic rate law resulting from a metabolite saturation assumption, and 4) a pure chemical reaction mass action rate law that removes the role of the enzyme from the reaction kinetics. We utilized in vivo data for the human red blood cell to compare the effect of rate law choices against the backdrop of physiological flux and concentration differences. We found that the Michaelis-Menten rate law with measured enzyme parameters yields an excellent approximation of the full system dynamics, while other assumptions cause greater discrepancies in system dynamic behavior. However, iteratively replacing mechanistic rate laws with approximations resulted in a model that retains a high correlation with the true model behavior. Investigating this consistency, we determined that the order of magnitude differences among fluxes and concentrations in the network were greatly influential on the network dynamics. We further identified reaction features such as thermodynamic reversibility, high substrate concentration, and lack of allosteric regulation, which make certain reactions more suitable for rate law approximations.ConclusionsOverall, our work generally supports the use of approximate rate laws when building large scale kinetic models, due to the key role that physiologically meaningful flux and concentration ranges play in determining network dynamics. However, we also showed that detailed mechanistic models show a clear benefit in prediction accuracy when data is available. The work here should help to provide guidance to future kinetic modeling efforts on the choice of rate law and parameterization approaches

Detailed Enzyme Kinetics in Terms of Biochemical Species: Study of Citrate Synthase

The compulsory-ordered ternary catalytic mechanism for two-substrate two-product enzymes is analyzed to account for binding of inhibitors to each of the four enzyme states and to maintain the relationship between the kinetic constants and the reaction equilibrium constant. The developed quasi-steady flux expression is applied to the analysis of data from citrate synthase to determine and parameterize a kinetic scheme in terms of biochemical species, in which the effects of pH, ionic strength, and cation binding to biochemical species are explicitly accounted for in the analysis of the data. This analysis provides a mechanistic model that is consistent with the data that have been used support competing hypotheses regarding the catalytic mechanism of this enzyme

Targeting pathogen metabolism without collateral damage to the host

The development of drugs that can inactivate disease-causing cells (e.g. cancer cells or parasites) without causing collateral damage to healthy or to host cells is complicated by the fact that many proteins are very similar between organisms. Nevertheless, due to subtle, quantitative differences between the biochemical reaction networks of target cell and host, a drug can limit the flux of the same essential process in one organism more than in another. We identified precise criteria for this â €network-based' drug selectivity, which can serve as an alternative or additive to structural differences. We combined computational and experimental approaches to compare energy metabolism in the causative agent of sleeping sickness, Trypanosoma brucei, with that of human erythrocytes, and identified glucose transport and glyceraldehyde-3-phosphate dehydrogenase as the most selective antiparasitic targets. Computational predictions were validated experimentally in a novel parasite-erythrocytes co-culture system. Glucose-transport inhibitors killed trypanosomes without killing erythrocytes, neurons or liver cells

Unpredictability of metabolism—the key role of metabolomics science in combination with next-generation genome sequencing

Next-generation sequencing provides technologies which sequence whole prokaryotic and eukaryotic genomes in days, perform genome-wide association studies, chromatin immunoprecipitation followed by sequencing and RNA sequencing for transcriptome studies. An exponentially growing volume of sequence data can be anticipated, yet functional interpretation does not keep pace with the amount of data produced. In principle, these data contain all the secrets of living systems, the genotype–phenotype relationship. Firstly, it is possible to derive the structure and connectivity of the metabolic network from the genotype of an organism in the form of the stoichiometric matrix N. This is, however, static information. Strategies for genome-scale measurement, modelling and predicting of dynamic metabolic networks need to be applied. Consequently, metabolomics science—the quantitative measurement of metabolism in conjunction with metabolic modelling—is a key discipline for the functional interpretation of whole genomes and especially for testing the numerical predictions of metabolism based on genome-scale metabolic network models. In this context, a systematic equation is derived based on metabolomics covariance data and the genome-scale stoichiometric matrix which describes the genotype–phenotype relationship

Simultaneous determination of low free Mg2+ and pH in human sickle cells using 31P NMR spectroscopy.

The concentrations of free magnesium, [Mg(2+)](free), [H(+)], and [ATP] are important in the dehydration of red blood cells from patients with sickle cell anemia, but they are not easily measured. Consequently, we have developed a rapid, noninvasive NMR spectroscopic method using the phosphorus chemical shifts of ATP and 2,3-diphosphoglycerate (DPG) to determine [Mg(2+)](free) and pH(i) simultaneously in fully oxygenated whole blood. The method employs theoretical equations expressing the observed chemical shift as a function of pH, K(+), and [Mg(2+)](free), over a pH range of 5.75-8.5 and [Mg(2+)](free) range 0-5 mm. The equations were adjusted to allow for the binding of hemoglobin to ATP and DPG, which required knowledge of the intracellular concentrations of ATP, DPG, K(+), and hemoglobin. Normal oxygenated whole blood (n = 33) had a pH(i) of 7.20 +/- 0.02, a [Mg(2+)](free) of 0.41 +/- 0.03 mm, and [DPG] of 7.69 +/- 0.47 mm. Under the same conditions, whole sickle blood (n = 9) had normal [ATP] but significantly lower pH(i) (7.10 +/- 0.03) and [Mg(2+)](free) (0.32 +/- 0.05 mm) than normal red cells, whereas [DPG] (10.8 +/- 1.2 mm) was significantly higher. Because total magnesium was normal in sickle cells, the lower [Mg(2+)](free) could be attributed to increased [DPG] and therefore greater magnesium binding capacity of sickle cells

Formulating genome‐scale kinetic models in the post‐genome era

The biological community is now awash in high-throughput data sets and is grappling with the challenge of integrating disparate data sets. Such integration has taken the form of statistical analysis of large data sets, or through the bottom–up reconstruction of reaction networks. While progress has been made with statistical and structural methods, large-scale systems have remained refractory to dynamic model building by traditional approaches. The availability of annotated genomes enabled the reconstruction of genome-scale networks, and now the availability of high-throughput metabolomic and fluxomic data along with thermodynamic information opens the possibility to build genome-scale kinetic models. We describe here a framework for building and analyzing such models. The mathematical analysis challenges are reflected in four foundational properties, (i) the decomposition of the Jacobian matrix into chemical, kinetic and thermodynamic information, (ii) the structural similarity between the stoichiometric matrix and the transpose of the gradient matrix, (iii) the duality transformations enabling either fluxes or concentrations to serve as the independent variables and (iv) the timescale hierarchy in biological networks. Recognition and appreciation of these properties highlight notable and challenging new in silico analysis issues