Do elementary flux modes combine linearly at the "atomic" level?: integrating tracer-based metabolomics data and elementary flux modes

The elementary flux modes (EFMs) approach is an efficient computational tool to predict novel metabolic pathways. Elucidating the physiological relevance of EFMs in a particular cellular state is still an open challenge. Different methods have been presented to carry out this task. However, these methods typically use little experimental data, exploiting methodologies where an a priori optimization function is used to deal with the indetermination underlying metabolic networks. Available “omics” data represent an opportunity to refine current methods. In this article we discuss whether (or not) metabolomics data from isotope labeling experiments (ILEs) and EFMs can be integrated into a linear system of equations. Aside from refining current approaches to infer the physiological relevance of EFMs, this question is important for the integration of metabolomics data from ILEs into metabolic networks, which generally involve non-linear relationships. As a result of our analysis, we concluded that in general the concept of EFMs needs to be redefined at the atomic level for the modeling of ILEs. For this purpose, the concept of Elementary Carbon Modes (ECMs) is introduced.     

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.     

Elementary Flux Mode Analysis Revealed Cyclization Pathway as a Powerful Way for NADPH Regeneration of Central Carbon Metabolism

NADPH regeneration capacity is attracting growing research attention due to its important role in resisting oxidative stress. Besides, NADPH availability has been regarded as a limiting factor in production of industrially valuable compounds. The central carbon metabolism carries the carbon skeleton flux supporting the operation of NADPH-regenerating enzyme and offers flexibility in coping with NADPH demand for varied intracellular environment. To acquire an insightful understanding of its NADPH regeneration capacity, the elementary mode method was employed to compute all elementary flux modes (EFMs) of a network representative of central carbon metabolism. Based on the metabolic flux distributions of these modes, a cluster analysis of EFMs with high NADPH regeneration rate was conducted using the self-organizing map clustering algorithm. The clustering results were used to study the relationship between the flux of total NADPH regeneration and the flux in each NADPH producing enzyme. The results identified several reaction combinations supporting high NADPH regeneration, which are proven to be feasible in cells via thermodynamic analysis and coincident with a great deal of previous experimental report. Meanwhile, the reaction combinations showed some common characteristics: there were one or two decarboxylation oxidation reactions in the combinations that produced NADPH and the combination constitution included certain gluconeogenesis pathways. These findings suggested cyclization pathways as a powerful way for NADPH regeneration capacity of bacterial central carbon metabolism.     

Metabolic pathway analysis of glycerol metabolism in Klebsiella pneumoniae incorporating oxygen regulatory system

It is well known that environmental and genetic perturbations have major effects on the metabolic behavior of cells. In this work, a model that utilizes existing knowledge of oxygen and redox sensing/regulatory system to assist elementary flux modes (EFMs) has been developed and was carried out to predict the metabolic potential of Klebsiella pneumoniae for the production of 1,3‐propanediol (1,3‐PD) under anaerobic and aerobic conditions. It was found that the theoretical optimal 1,3‐PD yield could reach to 0.844 mol mol^?1 if the pentose phosphate pathway (PPP), and transhydrogenase had a high flux under anaerobic condition. However, PPP had little influence on the theoretical 1,3‐PD yield, and the flux through tricarboxylic acid (TCA) cycle was high under aerobic conditions. In addition, the effect of oxygen level on the 1,3‐PD and biomass was further analyzed. © 2009 American Institute of Chemical Engineers Biotechnol. Prog., 2009     

Pathway analysis of NAD+ metabolism

NAD(+) is well known as a crucial cofactor in the redox balance of metabolism. Moreover, NAD(+) is degraded in ADP-ribosyl transfer reactions, which are important components of multitudinous signalling reactions. These include reactions linked to DNA repair and aging. In the present study, using the concept of EFMs (elementary flux modes), we established all of the potential routes in a network describing NAD(+) biosynthesis and degradation. All known biosynthetic pathways, which include de novo synthesis starting from tryptophan as well as the classical Preiss-Handler pathway and NAD(+) synthesis from other vitamin precursors, were detected as EFMs. Moreover, several EFMs were found that degrade NAD(+), represent futile cycles or have other functionalities. The systematic analysis and comparison of the networks specific for yeast and humans document significant differences between species with regard to the use of precursors, biosynthetic routes and NAD(+)-dependent signalling.     

Quantification of metabolism in Saccharomyces cerevisiae under hyperosmotic conditions using elementary mode analysis

Yeast metabolism under hyperosmotic stress conditions was quantified using elementary mode analysis to obtain insights into the metabolic status of the cell. The fluxes of elementary modes were determined as solutions to a linear program that used the stoichiometry of the elementary modes as constraints. The analysis demonstrated that distinctly different sets of elementary modes operate under normal and hyperosmotic conditions. During the adaptation phase, elementary modes that only produce glycerol are active, while elementary modes that yield biomass, ethanol, and glycerol become active after the adaptive phase. The flux distribution in the metabolic network, calculated using the fluxes in the elementary modes, was employed to obtain the flux ratio at key nodes. At the glucose 6-phosphate (G6P) node, 25% of the carbon influx was diverted towards the pentose phosphate pathway under normal growth conditions, while only 0.3% of the carbon flux was diverted towards the pentose phosphate pathway during growth at 1?M NaCl, indicating that cell growth is arrested under hyperosmotic conditions. Further, objective functions were used in the linear program to obtain optimal solution spaces corresponding to the different accumulation rates. The analysis demonstrated that while biomass formation was optimal under normal growth conditions, glycerol synthesis was closer to optimal during adaptation to osmotic shock.     

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.     

Interplay between Constraints,Objectives, and Optimality for Genome-Scale Stoichiometric Models

High-throughput data generation and genome-scale stoichiometric models have greatly facilitated the comprehensive study of metabolic networks. The computation of all feasible metabolic routes with these models, given stoichiometric, thermodynamic, and steady-state constraints, provides important insights into the metabolic capacities of a cell. How the feasible metabolic routes emerge from the interplay between flux constraints, optimality objectives, and the entire metabolic network of a cell is, however, only partially understood. We show how optimal metabolic routes, resulting from flux balance analysis computations, arise out of elementary flux modes, constraints, and optimization objectives. We illustrate our findings with a genome-scale stoichiometric model of Escherichia coli metabolism. In the case of one flux constraint, all feasible optimal flux routes can be derived from elementary flux modes alone. We found up to 120 million of such optimal elementary flux modes. We introduce a new computational method to compute the corner points of the optimal solution space fast and efficiently. Optimal flux routes no longer depend exclusively on elementary flux modes when we impose additional constraints; new optimal metabolic routes arise out of combinations of elementary flux modes. The solution space of feasible metabolic routes shrinks enormously when additional objectives---e.g. those related to pathway expression costs or pathway length---are introduced. In many cases, only a single metabolic route remains that is both feasible and optimal. This paper contributes to reaching a complete topological understanding of the metabolic capacity of organisms in terms of metabolic flux routes, one that is most natural to biochemists and biotechnologists studying and engineering metabolism.     

Moderate plant–soil feedbacks have small effects on the biodiversity–productivity relationship: A field experiment

Plant–soil feedback (PSF) has gained attention as a mechanism promoting plant growth and coexistence. However, most PSF research has measured monoculture growth in greenhouse conditions. Translating PSFs into effects on plant growth in field communities remains an important frontier for PSF research. Using a 4‐year, factorial field experiment in Jena, Germany, we measured the growth of nine grassland species on soils conditioned by each of the target species (i.e., 72 PSFs). Plant community models were parameterized with or without these PSF effects, and model predictions were compared to plant biomass production in diversity–productivity experiments. Plants created soils that changed subsequent plant biomass by 40%. However, because they were both positive and negative, the average PSF effect was 14% less growth on “home” than on “away” soils. Nine‐species plant communities produced 29 to 37% more biomass for polycultures than for monocultures due primarily to selection effects. With or without PSF, plant community models predicted 28%–29% more biomass for polycultures than for monocultures, again due primarily to selection effects. Synthesis: Despite causing 40% changes in plant biomass, PSFs had little effect on model predictions of plant community biomass across a range of species richness. While somewhat surprising, a lack of a PSF effect was appropriate in this site because species richness effects in this study were caused by selection effects and not complementarity effects (PSFs are a complementarity mechanism). Our plant community models helped us describe several reasons that even large PSF may not affect plant productivity. Notably, we found that dominant species demonstrated small PSF, suggesting there may be selective pressure for plants to create neutral PSF. Broadly, testing PSFs in plant communities in field conditions provided a more realistic understanding of how PSFs affect plant growth in communities in the context of other species traits.     

Varicones and Growth Cones: Two Neurite Terminals in PC12 Cells

The rat adrenal pheochromocytoma PC12 cell line is one of the traditional models for the study of neurite outgrowth and growth cone behavior. To clarify to what extent PC12 neurite terminals can be compared to neuronal growth cones, we have analyzed their morphology and protein distribution in fixed PC12 cells by immunocytochemistry. Our results show that that PC12 cells display a special kind of neurite terminal that includes a varicosity in close association with a growth cone. This hybrid terminal, or “varicone”, is characterized by the expression of specific markers not typically present in neuronal growth cones. For example, we show that calpain-2 is a specific marker of varicones and can be detected even before the neurite develops. Our data also shows that a fraction of PC12 neurites end in regular growth cones, which we have compared to hippocampal neurites as a control. We also report the extraordinary incidence of varicones in the literature referred to as “growth cones”. In summary, we provide evidence of two different kinds of neurite terminals in PC12 cells, including a PC12-specific terminal, which implies that care must be taken when using them as a model for neuronal growth cones or neurite outgrowth.     

Structural robustness of metabolic networks with respect to multiple knockouts

We present a generalised framework for analysing structural robustness of metabolic networks, based on the concept of elementary flux modes (EFMs). Extending our earlier study on single knockouts [Wilhelm, T., Behre, J., Schuster, S., 2004. Analysis of structural robustness of metabolic networks. IEE Proc. Syst. Biol. 1(1), 114-120], we are now considering the general case of double and multiple knockouts. The robustness measures are based on the ratio of the number of remaining EFMs after knockout vs. the number of EFMs in the unperturbed situation, averaged over all combinations of knockouts. With the help of simple examples we demonstrate that consideration of multiple knockouts yields additional information going beyond single-knockout results. It is proven that the robustness score decreases as the knockout depth increases.We apply our extended framework to metabolic networks representing amino acid anabolism in Escherichia coli and human hepatocytes, and the central metabolism in human erythrocytes. Moreover, in the E. coli model the two subnetworks synthesising amino acids that are essential and those that are non-essential for humans are studied separately. The results are discussed from an evolutionary viewpoint. We find that E. coli has the most robust metabolism of all the cell types studied here. Considering only the subnetwork of the synthesis of non-essential amino acids, E. coli and the human hepatocyte show about the same robustness.     

Structural Control of Metabolic Flux

Organisms have to continuously adapt to changing environmental conditions or undergo developmental transitions. To meet the accompanying change in metabolic demands, the molecular mechanisms of adaptation involve concerted interactions which ultimately induce a modification of the metabolic state, which is characterized by reaction fluxes and metabolite concentrations. These state transitions are the effect of simultaneously manipulating fluxes through several reactions. While metabolic control analysis has provided a powerful framework for elucidating the principles governing this orchestrated action to understand metabolic control, its applications are restricted by the limited availability of kinetic information. Here, we introduce structural metabolic control as a framework to examine individual reactions'' potential to control metabolic functions, such as biomass production, based on structural modeling. The capability to carry out a metabolic function is determined using flux balance analysis (FBA). We examine structural metabolic control on the example of the central carbon metabolism of Escherichia coli by the recently introduced framework of functional centrality (FC). This framework is based on the Shapley value from cooperative game theory and FBA, and we demonstrate its superior ability to assign “share of control” to individual reactions with respect to metabolic functions and environmental conditions. A comparative analysis of various scenarios illustrates the usefulness of FC and its relations to other structural approaches pertaining to metabolic control. We propose a Monte Carlo algorithm to estimate FCs for large networks, based on the enumeration of elementary flux modes. We further give detailed biological interpretation of FCs for production of lactate and ATP under various respiratory conditions.     

Scent of a killer: How could killer yeast boost its dispersal?

Vector‐borne parasites often manipulate hosts to attract uninfected vectors. For example, parasites causing malaria alter host odor to attract mosquitoes. Here, we discuss the ecology and evolution of fruit‐colonizing yeast in a tripartite symbiosis—the so‐called “killer yeast” system. “Killer yeast” consists of Saccharomyces cerevisiae yeast hosting two double‐stranded RNA viruses (M satellite dsRNAs, L‐A dsRNA helper virus). When both dsRNA viruses occur in a yeast cell, the yeast converts to lethal toxin‑producing “killer yeast” phenotype that kills uninfected yeasts. Yeasts on ephemeral fruits attract insect vectors to colonize new habitats. As the viruses have no extracellular stage, they depend on the same insect vectors as yeast for their dispersal. Viruses also benefit from yeast dispersal as this promotes yeast to reproduce sexually, which is how viruses can transmit to uninfected yeast strains. We tested whether insect vectors are more attracted to killer yeasts than to non‑killer yeasts. In our field experiment, we found that killer yeasts were more attractive to Drosophila than non‐killer yeasts. This suggests that vectors foraging on yeast are more likely to transmit yeast with a killer phenotype, allowing the viruses to colonize those uninfected yeast strains that engage in sexual reproduction with the killer yeast. Beyond insights into the basic ecology of the killer yeast system, our results suggest that viruses could increase transmission success by manipulating the insect vectors of their host.     

Elementary Flux Modes Analysis of Functional Domain Networks Allows a Better Metabolic Pathway Interpretation

Metabolic network analysis is an important step for the functional understanding of biological systems. In these networks, enzymes are made of one or more functional domains often involved in different catalytic activities. Elementary flux mode (EFM) analysis is a method of choice for the topological studies of these enzymatic networks. In this article, we propose to use an EFM approach on networks that encompass available knowledge on structure-function. We introduce a new method that allows to represent the metabolic networks as functional domain networks and provides an application of the algorithm for computing elementary flux modes to analyse them. Any EFM that can be represented using the classical representation can be represented using our functional domain network representation but the fine-grained feature of functional domain networks allows to highlight new connections in EFMs. This methodology is applied to the tricarboxylic acid cycle (TCA cycle) of Bacillus subtilis, and compared to the classical analyses. This new method of analysis of the functional domain network reveals that a specific inhibition on the second domain of the lipoamide dehydrogenase (pdhD) component of pyruvate dehydrogenase complex leads to the loss of all fluxes. Such conclusion was not predictable in the classical approach.     

Phenotypic characterization of <Emphasis Type="Italic">Corynebacterium glutamicum</Emphasis> using elementary modes towards synthesis of amino acids

Elementary flux mode (EFM) analysis is a powerful tool to represent the metabolic network structure and can be further utilized for flux analysis. The method enables characterization and quantification of feasible phenotypes in microbes. EFM analysis was employed to characterize the phenotype of Corynebacterium glutamicum to yield various amino acids. The metabolic network of C. glutamicum yielded 62 elementary modes by incorporating the accumulation of amino acids namely, lysine, alanine, valine, glutamine and glutamate. The analysis also allowed us to compute the maximum theoretical yield for the synthesis of various amino acids. These 62 elementary modes were further used to obtain optimal phenotypic space towards accumulation of biomass and lysine. The study indicated that the optimal solution space from 62 elementary modes forms a super space which incorporates various mutants including lysine producing strain of C. glutamicum. The analysis was also extended to obtain sensitivity of the network to variation in the stoichiometry of NADP in the definition of biomass.     

Imaging Ca2+ Dynamics in Cone Photoreceptor Axon Terminals of the Mouse Retina

Retinal cone photoreceptors (cones) serve daylight vision and are the basis of color discrimination. They are subject to degeneration, often leading to blindness in many retinal diseases. Calcium (Ca²⁺), a key second messenger in photoreceptor signaling and metabolism, has been proposed to be indirectly linked with photoreceptor degeneration in various animal models. Systematically studying these aspects of cone physiology and pathophysiology has been hampered by the difficulties of electrically recording from these small cells, in particular in the mouse where the retina is dominated by rod photoreceptors. To circumvent this issue, we established a two-photon Ca²⁺ imaging protocol using a transgenic mouse line that expresses the genetically encoded Ca²⁺ biosensor TN-XL exclusively in cones and can be crossbred with mouse models for photoreceptor degeneration. The protocol described here involves preparing vertical sections (“slices”) of retinas from mice and optical imaging of light stimulus-evoked changes in cone Ca²⁺ level. The protocol also allows “in-slice measurement” of absolute Ca²⁺ concentrations; as the recordings can be followed by calibration. This protocol enables studies into functional cone properties and is expected to contribute to the understanding of cone Ca²⁺ signaling as well as the potential involvement of Ca²⁺ in photoreceptor death and retinal degeneration.     

Semantics-Based Composition of Integrated Cardiomyocyte Models Motivated by Real-World Use Cases

Semantics-based model composition is an approach for generating complex biosimulation models from existing components that relies on capturing the biological meaning of model elements in a machine-readable fashion. This approach allows the user to work at the biological rather than computational level of abstraction and helps minimize the amount of manual effort required for model composition. To support this compositional approach, we have developed the SemGen software, and here report on SemGen’s semantics-based merging capabilities using real-world modeling use cases. We successfully reproduced a large, manually-encoded, multi-model merge: the “Pandit-Hinch-Niederer” (PHN) cardiomyocyte excitation-contraction model, previously developed using CellML. We describe our approach for annotating the three component models used in the PHN composition and for merging them at the biological level of abstraction within SemGen. We demonstrate that we were able to reproduce the original PHN model results in a semi-automated, semantics-based fashion and also rapidly generate a second, novel cardiomyocyte model composed using an alternative, independently-developed tension generation component. We discuss the time-saving features of our compositional approach in the context of these merging exercises, the limitations we encountered, and potential solutions for enhancing the approach.     

Not all scale-free networks are born equal: the role of the seed graph in PPI network evolution

The (asymptotic) degree distributions of the best-known “scale-free” network models are all similar and are independent of the seed graph used; hence, it has been tempting to assume that networks generated by these models are generally similar. In this paper, we observe that several key topological features of such networks depend heavily on the specific model and the seed graph used. Furthermore, we show that starting with the “right” seed graph (typically a dense subgraph of the protein–protein interaction network analyzed), the duplication model captures many topological features of publicly available protein–protein interaction networks very well.