An interval approach for dealing with flux distributions and elementary modes activity patterns

This work introduces the use of an interval representation of fluxes. This representation can be useful in two common situations: (a) when fluxes are uncertain due to the lack of accurate measurements and (b) when the flux distribution is partially unknown. In addition, the interval representation can be used for other purposes such as dealing with inconsistency or representing a range of behaviour. Two main problems are addressed. On the one hand, the translation of a metabolic flux distribution into an elementary modes or extreme pathways activity pattern is analysed. In general, there is not a unique solution for this problem but a range of solutions. To represent the whole solution region in an easy way, it is possible to compute the alpha-spectrum (i.e., the range of possible values for each elementary mode or extreme pathway activity). Herein, a method is proposed which, based on the interval representation of fluxes, makes it possible to compute the alpha-spectrum from an uncertain or even partially unknown flux distribution. On the other hand, the concept of the flux-spectrum is introduced as a variant of the metabolic flux analysis methodology that presents some advantages: applicable when measurements are insufficient (underdetermined case), integration of uncertain measurements, inclusion of irreversibility constraints and an alternative procedure to deal with inconsistency. Frequently, when applying metabolic flux analysis the available measurements are insufficient and/or uncertain and the complete flux distribution cannot be uniquely calculated. The method proposed here allows the determination of the ranges of possible values for each non-calculable flux, resulting in a flux region called flux-spectrum. In order to illustrate the proposed methods, the example of the metabolic network of CHO cells cultivated in stirred flasks is used.     

Metabolic flux distributions in Penicillium chrysogenum during fed-batch cultivations

Based on a review of the Penicillium chrysogenum biochemistry a stoichiometric model has been set up. The model considers 61 internal fluxes and there are 49 intracellular metabolites which are assumed to be in pseudo-steady state. In addition to the intracellular fluxes the model considers the uptake of 21 amino acids. From the stoichiometric model the maximum theoretical yield of penicillin V is calculated to 0.43 mol/mol glucose. If biosynthesis of cysteine is by direct sulfhydrylation rather than by transsulfuration, the maximum theoretical yield is about 20% higher, i.e., 0.50 mol/mol glucose. The theoretical yield decreases substantially if alpha-aminoadipate is converted to 6-oxo-piperidine-2-carboxylic acid (OPC). If only 40% of the alpha-aminoadipate is recycled, the maximum theoretical yield is 0.31 mol/mol glucose. The uptake rates of glucose, lactate, gamma-aminobutyrate, and 21 amino acids were measured during fed-batch cultivations. The rates of formation of penicillin V, delta-(L-alpha)-aminoadipyl-L-cysteinyl-D-valine (ACV), OPC, and the pool of isopenicillin N, 6-APA, and 8-HPA were also measured. Finally the synthesis rates of the biomass constituents RNA/DNA, protein, lipid, carbohydrate, and amino carbohydrate were measured. From these measured rates and the stoichiometric model the metabolic fluxes through the different intracellular pathways are calculated. The calculations show that penicillin formation is accompanied by a large flux through the pentose phosphate (PP) pathway due to a large requirement for nicotinamide-adenine dinucleotide phosphate (NADPH) used in the biosynthesis of cysteine. If cysteine is added to the medium, the flux through the PP pathway decreases. From the stoichiometric model Y(xATP) is calculated to 87 mmol adenosine triphosphate (ATP)/g dry weight (DW), and from the flux calculations m(ATP) is found to 3 mmol ATP/g DW/h. (c) 1995 John Wiley & Sons, Inc.     

System-level insights into yeast metabolism by thermodynamic analysis of elementary flux modes

One of the most obvious phenotypes of a cell is its metabolic activity, which is defined by the fluxes in the metabolic network. Although experimental methods to determine intracellular fluxes are well established, only a limited number of fluxes can be resolved. Especially in eukaryotes such as yeast, compartmentalization and the existence of many parallel routes render exact flux analysis impossible using current methods. To gain more insight into the metabolic operation of S. cerevisiae we developed a new computational approach where we characterize the flux solution space by determining elementary flux modes (EFMs) that are subsequently classified as thermodynamically feasible or infeasible on the basis of experimental metabolome data. This allows us to provably rule out the contribution of certain EFMs to the in vivo flux distribution. From the 71 million EFMs in a medium size metabolic network of S. cerevisiae, we classified 54% as thermodynamically feasible. By comparing the thermodynamically feasible and infeasible EFMs, we could identify reaction combinations that span the cytosol and mitochondrion and, as a system, cannot operate under the investigated glucose batch conditions. Besides conclusions on single reactions, we found that thermodynamic constraints prevent the import of redox cofactor equivalents into the mitochondrion due to limits on compartmental cofactor concentrations. Our novel approach of incorporating quantitative metabolite concentrations into the analysis of the space of all stoichiometrically feasible flux distributions allows generating new insights into the system-level operation of the intracellular fluxes without making assumptions on metabolic objectives of the cell.     

Exploiting zebrafish to help understand human cardiac arrhythmia

Commentary to:

Hassel D, Scholz EP, Trano N et al. Deficient zebrafish Ether-a-Go-Go-related gene channel gating causes short-QT syndrome in zebrafish reggae mutants. Circulation 2008; 117:866-75.     

Metabolic flux network and analysis of fermentative hydrogen production

Fermentative hydrogen production (FHP) has received a great R & D interest in recent decades, as it offers a potential means of producing H₂ from a variety of renewable resources, even wastewater via a low energy continuous process. Various extracellular metabolites including ethanol, acetate, butyrate and lactate can be produced during the fermentation, building a complex metabolic network of the FHP. Except for the recognition of its complexity, the metabolic flux network has not been well understood. Studies on biochemical reactions and metabolic flux network associated with the FHP in anaerobic fermentation system have only been drawn attention in recent years. This review summarizes the biochemical reactions taking place in the metabolic network of FHP. We discuss how the key operation factors influence metabolism in the FHP process. Recently developed and applied technologies for metabolic flux analysis have been described. Future studies on the metabolic network to enhance fermentative hydrogen production by strict anaerobes are recommended. It is expected that this review can provide useful information in terms of fundamental knowledge and update technology for scientists and research engineers in the field of biological hydrogen production.     

Pollen allergen reports help to understand preseason symptoms

Early symptoms of pollen allergies arefrequently reported before pollination periodof allergenic plant starts. At northernlatitudes the main concern is Betulaceae-trees(alders, hazel, birches). Pollen allergeninformation, based on the analysis of actualairborne allergen concentrations, beside thetraditional pollen reports, based on pollencounts, has been given in SW Finland since1998. 1–2 weeks before the onset of floweringpollen allergens are detected airborne inquantities high enough to provoke symptoms.Information is given on radio and in localnewspapers. During the first season of the newservice (1998) we carried out a questionnairestudy. The results showed that new informationservice, though not as frequently used as wehad hoped for, was useful to allergic personsfor starting their medication in time. Theyalso received explanation for their earlierinexplicable symptoms. We recommend bothinformation services to be run concurrently togive the best information to the public.     

ACoM: A classification method for elementary flux modes based on motif finding

Elementary flux mode analysis is a powerful tool for the theoretical study of metabolic networks. However, when the networks are complex, the determination of elementary flux modes leads to combinatorial explosion of their number which prevents from drawing simple conclusions from their analysis. To deal with this problem we have developed a method based on the Agglomeration of Common Motifs (ACoM) for classifying elementary flux modes. We applied this algorithm to describe the decomposition into elementary flux modes of the central carbon metabolism in Bacillus subtilis and of the yeast mitochondrial energy metabolism. ACoM helps to give biological meaning to the different elementary flux modes and to the relatedness between reactions. ACoM, which can be viewed as a bi-clustering method, can be of general use for sets of vectors with values 0, +1 or −1.     

Finding elementary flux modes in metabolic networks based on flux balance analysis and flux coupling analysis: application to the analysis of Escherichia coli metabolism

Elementary modes (EMs) are steady-state metabolic flux vectors with minimal set of active reactions. Each EM corresponds to a metabolic pathway. Therefore, studying EMs is helpful for analyzing the production of biotechnologically important metabolites. However, memory requirements for computing EMs may hamper their applicability as, in most genome-scale metabolic models, no EM can be computed due to running out of memory. In this study, we present a method for computing randomly sampled EMs. In this approach, a network reduction algorithm is used for EM computation, which is based on flux balance-based methods. We show that this approach can be used to recover the EMs in the medium- and genome-scale metabolic network models, while the EMs are sampled in an unbiased way. The applicability of such results is shown by computing “estimated” control-effective flux values in Escherichia coli metabolic network.     

Study of metabolic network of Cupriavidus necator DSM 545 growing on glycerol by applying elementary flux modes and yield space analysis

A metabolic network consisting of 48 reactions was established to describe intracellular processes during growth and poly-3-hydroxybutyrate (PHB) production for Cupriavidus necator DSM 545. Glycerol acted as the sole carbon source during exponential, steady-state cultivation conditions. Elementary flux modes were obtained by the program Metatool and analyzed by using yield space analysis. Four sets of elementary modes were obtained, depending on whether the pair NAD/NADH or FAD/FADH₂ contributes to the reaction of glycerol-3-phosphate dehydrogenase (GLY-3-P DH), and whether 6-phosphogluconate dehydrogenase (6-PG DH) is present or not. Established metabolic network and the related system of equations provide multiple solutions for the simultaneous synthesis of PHB and biomass; this number of solutions can be further increased if NAD/NADH or FAD/FADH₂ were assumed to contribute in the reaction of GLY-3-P DH. As a major outcome, it was demonstrated that experimentally determined yields for biomass and PHB with respect to glycerol fit well to the values obtained in silico when the Entner–Doudoroff pathway (ED) dominates over the glycolytic pathway; this is also the case if the Embden–Meyerhof–Parnas pathway dominates over the ED.     

Using mathematical models to help understand biological pattern formation

One of the characteristics of biological systems is their ability to produce and sustain spatial and spatio-temporal pattern. Elucidating the underlying mechanisms responsible for this phenomenon has been the goal of much experimental and theoretical research. This paper illustrates this area of research by presenting some of the mathematical models that have been proposed to account for pattern formation in biology and considering their implications.