From structure to dynamics of metabolic pathways: application to the plant mitochondrial TCA cycle

Seasonality Affects Low-Molecular-Weight Organic Acids and Phenolic Compounds' Composition in Scots Pine Litterfall

BACKGROUND AND AIMS

Secondary plant metabolites, including organic acids and phenolic compounds, have a significant impact on the properties of organic matter in soil, influencing its structure and function. How the production of these compounds in foliage that falls to the forest floor as litterfall varies across tree age and seasonality are of considerable interest for advancing our understanding of organic matter dynamics.

METHODS

Monthly, we collected fallen needles of Scots pine (Pinus sylvestris L.) across stands of five different age classes (20, 40, 60, 80, and 100 years) for one year and measured the organic acids and phenolic compounds.

RESULTS

Seven low-molecular-weight organic acids and thirteen phenolic compounds were detected in the litterfall. No differences were observed across stand age. Significant seasonal differences were detected. Most compounds peaked during litterfall in the growing season. Succinic acid was the most prevalent organic acid in the litterfall, comprising 78% of total organic acids (351.27 ± 34.27 µg g- 1), and was 1.5 to 11.0 times greater in the summer than all other seasons. Sinapic acid was the most prevalent phenolic compound in the litterfall (42.15 µg g- 1), representing 11% of the total phenolic compounds, and was 39.8 times greater in spring and summer compared to autumn and winter. Growing season peaks in needle concentrations were observed for all thirteen phenolic compounds and two organic acids (lactic, succinic). Citric acid exhibited a definitive peak in late winter into early spring.

CONCLUSIONS

Our results highlight the seasonal dynamics of the composition of secondary plant metabolites in litterfall, which is most different at the onset of the growing season. Fresh inputs of litterfall at this time of emerging biological activity likely have seasonal impacts on soil's organic matter composition as well.

Stable Isotope Tracer Technique and Network Pharmacology to Reveal Antidepressant Targets and Active Components of Xiaoyao San

In recent years, the research of mitochondrial dysfunction in depression has drawn the focus of researchers. Our research group previously found that Xiaoyao San (XYS) has improved the mitochondrial structure and the blocked tricarboxylic acid cycle (TCA cycle) in the hippocampal tissue of chronic unpredictable mild stress (CUMS) rats. However, the specific targets and active components of XYS remain unclear, and the potential to improve hippocampal mitochondrial TCA cycle disorder was also unexplored. In this research, a strategy to combine stable isotope-resolved metabolomics (SIRM), network pharmacology and transmission electron microscopy (TEM) was used to explore the potential, targets of action, and active components of XYS to improve hippocampal mitochondrial TCA cycle disorder of CUMS rats. The results of TEM showed that the ultrastructure of hippocampal mitochondria could be improved by XYS. A combination of SIRM and molecular docking showed that pyruvate carboxylase (PC), ATP citrate lyase (ACLK), glutamate dehydrogenase (GLDH), glutamate oxaloacetate transaminase (GOT) and pyruvate dehydrogenase (PDH) were targets of XYS to improve TCA cycle disorder. In addition, troxerutin was found to be the most potential active component of XYS to improve TCA cycle disorder. The above research results can provide new insights for the development of antidepressant drugs.

Ca2+-dependent oxidation of exogenous NADH and NADPH by the mitochondria of spring wheat and its relation with AOX capacity and ROS content at high temperatures

Mitochondria are sources of reactive oxygen species (ROS) in a plant cell under high temperature. Mitochondrial alternative NAD(P)H dehydrogenases (type II NAD(P)H DHs) and cyanide-resistant oxidase (AOX) can regulate ROS production, but their role at high temperatures is unknown. This study investigates the influence heat acclimation (37 °C) and heat shock (50 °C) temperatures on ROS content, activity and protein abundance of external Ca²⁺-dependent NAD(P)H DHs (NDB) and AOX in mitochondria of 4- and 8-day-old seedlings of spring wheat (Triticum aestivum L., var. Novosibirskya 29). The shoots of 4-day-old seedlings contained more carbohydrates, had a higher rate of total respiration and a high rate of oxidation of exogenous NADH, a greater AOX capacity and a lower of ROS content, as compared to leaves of 8-day-old seedlings, and were more resistant to heat shock. The activity of external NADH DH was higher than the one of NADPH DH in mitochondria of both shoots and leaves. At 37 °C, high NADH oxidation was associated with increased AOX capacity in mitochondria of both shoots and leaves, whereas NADPH oxidation with COX capacity. At 50 °C, the NADPH oxidation by shoots' mitochondria increased and the NADH oxidation stayed high. The content of NDB and AOX proteins depends on heat treatments and differs between mitochondria of shoots and leaves. Our data indicate that Ca²⁺-dependent type II NAD(P)H DHs can regulate the ROS content and together with AOX are involved in heat tolerance, depending on the development phase of spring wheat and is, probably, tissue-specific.

An Arabidopsis GCMS chemical ionization technique to quantify adaptive responses in central metabolism

We present a methodology to survey central metabolism in 13CO2-labeled Arabidopsis (Arabidopsis thaliana) rosettes by ammonia positive chemical ionization-gas chromatography-mass spectrometry. This technique preserves the molecular ion cluster of methyloxime/trimethylsilyl-derivatized analytes up to 1 kDa, providing unambiguous nominal mass assignment of >200 central metabolites and 13C incorporation rates into a subset of 111 from the tricarboxylic acid (TCA) cycle, photorespiratory pathway, amino acid metabolism, shikimate pathway, and lipid and sugar metabolism. In short-term labeling assays, we observed plateau labeling of ∼35% for intermediates of the photorespiratory cycle except for glyoxylate, which reached only ∼4% labeling and was also present at molar concentrations several fold lower than other photorespiratory intermediates. This suggests photorespiratory flux may involve alternate intermediate pools besides the generally accepted route through glyoxylate. Untargeted scans showed that in illuminated leaves, noncyclic TCA cycle flux and citrate export to the cytosol revert to a cyclic flux mode following methyl jasmonate (MJ) treatment. MJ also caused a block in the photorespiratory transamination of glyoxylate to glycine. Salicylic acid treatment induced the opposite effects in both cases, indicating the antagonistic relationship of these defense signaling hormones is preserved at the metabolome level. We provide complete chemical ionization spectra for 203 Arabidopsis metabolites from central metabolism, which uniformly feature the unfragmented pseudomolecular ion as the base peak. This unbiased, soft ionization technique is a powerful screening tool to identify adaptive metabolic trends in photosynthetic tissue and represents an important advance in methodology to measure plant metabolic flux.

Generalized Structural Kinetic Modeling: A Survey and Guide

Many current challenges involve understanding the complex dynamical interplay between the constituents of systems. Typically, the number of such constituents is high, but only limited data sources on them are available. Conventional dynamical models of complex systems are rarely mathematically tractable and their numerical exploration suffers both from computational and data limitations. Here we review generalized modeling, an alternative approach for formulating dynamical models to gain insights into dynamics and bifurcations of uncertain systems. We argue that this approach deals elegantly with the uncertainties that exist in real world data and enables analytical insight or highly efficient numerical investigation. We provide a survey of recent successes of generalized modeling and a guide to the application of this modeling approach in future studies such as complex integrative ecological models.

Phylogenetics and biochemistry elucidate the evolutionary link between l-malate and l-lactate dehydrogenases and disclose an intermediate group of sequences with mix functional properties

The NAD(P)-dependent malate dehydrogenases (MDH) (EC 1.1.1.37) and NAD-dependent lactate dehydrogenases (LDH) (EC. 1.1.1.27) form a large superfamily that has been characterized in organisms belonging to the three Domains of Life. MDH catalyzes the reversible conversion of the oxaloacetate into malate, while LDH operates at the late stage of glycolysis by converting pyruvate into lactate. Phylogenetic studies proposed that the LDH/MDH superfamily encompasses five main groups of enzymes. Here, starting from 16,052 reference proteomes, we reinvestigated the relationships between MDH and LDH. We showed that the LDH/MDH superfamily encompasses three main families: MDH1, MDH2, and a large family encompassing MDH3, LDH, and L-2-hydroxyisocaproate dehydrogenases (HicDH) sequences. An in-depth analysis of the phylogeny of the MDH3/LDH/HicDH family and of the nature of three important amino acids, located within the catalytic site and involved in binding and substrate discrimination, revealed a large group of sequences displaying unexpected combinations of amino acids at these three critical positions. This group branched in-between canonical MDH3 and LDH sequences. The functional characterization of several enzymes from this intermediate group disclosed a mix of functional properties, indicating that the MDH3/LDH/HicDH family is much more diverse than previously thought, and blurred the frontier between MDH3 and LDH enzymes. Present-days enzymes of the intermediate group are a valuable material to study the evolutionary steps that led to functional diversity and emergence of allosteric regulation within the LDH/MDH superfamily.

Transcriptome analysis reveals key genes regulating signaling and metabolic pathways during the growth of moso bamboo (Phyllostachys edulis) shoots

Moso bamboo (Phyllostachys edulis), a high-value bamboo used to produce food (young shoots), building, and industrial goods. To explore key candidate genes regulating signal transduction and metabolic processes during the initiation of stem elongation in moso bamboo, a transcriptome analysis of the shoots during three successive early elongation stages was performed. From cluster and differential expression analyses, 2984 differentially expressed genes (DEGs) were selected for an enrichment analysis. The DEGs were significantly enriched in the plant hormone signal transduction, sugar and starch metabolism, and energy metabolism pathways. Consequently, the DEG expression patterns of these pathways were analyzed, and the plant endogenous hormone and carbon metabolite (including sucrose, total soluble sugar, and starch) contents for each growth stage, of the shoot, were determined. The cytokinin-signaling pathway was continuously active in the three successive elongation stages, in which several cytokinin-signaling genes played indispensable roles. Additionally, many key DEGs regulating sugar, starch metabolism, and energy conversion, which are actively involved in energy production and substrate synthesis during the continuous growth of the shoots, were found. In summary, our study lays a foundation for understanding the mechanisms of moso bamboo growth and provides useful gene resources for breeding through genetic engineering.

Modeling Plant Metabolism: From Network Reconstruction to Mechanistic Models

Mathematical modeling of plant metabolism enables the plant science community to understand the organization of plant metabolism, obtain quantitative insights into metabolic functions, and derive engineering strategies for manipulation of metabolism. Among the various modeling approaches, metabolic pathway analysis can dissect the basic functional modes of subsections of core metabolism, such as photorespiration, and reveal how classical definitions of metabolic pathways have overlapping functionality. In the many studies using constraint-based modeling in plants, numerous computational tools are currently available to analyze large-scale and genome-scale metabolic networks. For ¹³C-metabolic flux analysis, principles of isotopic steady state have been used to study heterotrophic plant tissues, while nonstationary isotope labeling approaches are amenable to the study of photoautotrophic and secondary metabolism. Enzyme kinetic models explore pathways in mechanistic detail, and we discuss different approaches to determine or estimate kinetic parameters. In this review, we describe recent advances and challenges in modeling plant metabolism.

Citrate valve integrates mitochondria into photosynthetic metabolism

While in heterotrophic cells and in darkness mitochondria serve as main producers of energy, during photosynthesis this function is transferred to chloroplasts and the main role of mitochondria in bioenergetics turns to be the balance of the level of phosphorylation of adenylates and of reduction of pyridine nucleotides to avoid over-energization of the cell and optimize major metabolic fluxes. This is achieved via the establishment and regulation of local equilibria of the tricarboxylic acid (TCA) cycle enzymes malate dehydrogenase and fumarase in one branch and aconitase and isocitrate dehydrogenase in another branch. In the conditions of elevation of redox level, the TCA cycle is transformed into a non-cyclic open structure (hemicycle) leading to the export of the tricarboxylic acid (citrate) to the cytosol and to the accumulation of the dicarboxylic acids (malate and fumarate). While the buildup of NADPH in chloroplasts provides operation of the malate valve leading to establishment of NADH/NAD⁺ ratios in different cell compartments, the production of NADH by mitochondria drives citrate export by establishing conditions for the operation of the citrate valve. The latter regulates the intercompartmental NADPH/NADP⁺ ratio and contributes to the biosynthesis of amino acids and other metabolic products during photosynthesis.

Fernie A. Plant Mitochondrial Carriers: Molecular Gatekeepers That Help to Regulate Plant Central Carbon Metabolism

The evolution of membrane-bound organelles among eukaryotes led to a highly compartmentalized metabolism. As a compartment of the central carbon metabolism, mitochondria must be connected to the cytosol by molecular gates that facilitate a myriad of cellular processes. Members of the mitochondrial carrier family function to mediate the transport of metabolites across the impermeable inner mitochondrial membrane and, thus, are potentially crucial for metabolic control and regulation. Here, we focus on members of this family that might impact intracellular central plant carbon metabolism. We summarize and review what is currently known about these transporters from in vitro transport assays and in planta physiological functions, whenever available. From the biochemical and molecular data, we hypothesize how these relevant transporters might play a role in the shuttling of organic acids in the various flux modes of the TCA cycle. Furthermore, we also review relevant mitochondrial carriers that may be vital in mitochondrial oxidative phosphorylation. Lastly, we survey novel experimental approaches that could possibly extend and/or complement the widely accepted proteoliposome reconstitution approach.

Isotopic labelling reveals the efficient adaptation of wheat root TCA cycle flux modes to match carbon demand under ammonium nutrition

Proper carbon (C) supply is essential for nitrogen (N) assimilation especially when plants are grown under ammonium (NH4+) nutrition. However, how C and N metabolic fluxes adapt to achieve so remains uncertain. In this work, roots of wheat (Triticum aestivum L.) plants grown under exclusive NH4+ or nitrate (NO3-) supply were incubated with isotope-labelled substrates (15NH4+, 15NO3-, or [13C]Pyruvate) to follow the incorporation of 15N or 13C into amino acids and organic acids. Roots of plants adapted to ammonium nutrition presented higher capacity to incorporate both 15NH4+ and 15NO3- into amino acids, thanks to the previous induction of the NH4+ assimilative machinery. The 15N label was firstly incorporated into [15N]Gln vía glutamine synthetase; ultimately leading to [15N]Asn accumulation as an optimal NH4+ storage. The provision of [13C]Pyruvate led to [13C]Citrate and [13C]Malate accumulation and to rapid [13C]2-OG consumption for amino acid synthesis and highlighted the importance of the anaplerotic routes associated to tricarboxylic acid (TCA) cycle. Taken together, our results indicate that root adaptation to ammonium nutrition allowed efficient assimilation of N thanks to the promotion of TCA cycle open flux modes in order to sustain C skeleton availability for effective NH4+ detoxification into amino acids.

Revealing instabilities in a generalized triadic supply network: A bifurcation analysis

Supply networks are exposed to instabilities and thus a high level of risk. To mitigate this risk, it is necessary to understand how instabilities are formed in supply networks. In this paper, we focus on instabilities in inventory dynamics that develop due to the topology of the supply network. To be able to capture these topology-induced instabilities, we use a method called generalized modeling, a minimally specified modeling approach adopted from ecology. This method maps the functional dependencies of production rates on the inventory levels of different parts and products, which are imposed by the network topology, to a set of elasticity parameters. We perform a bifurcation analysis to investigate how these elasticities affect the stability. First, we show that dyads and serial supply chains are immune to topology-induced instabilities. In contrast, in a simple triadic network, where a supplier acts as both a first and a second tier supplier, we can identify instabilities that emerge from saddle-node, Hopf, and global homoclinic bifurcations. These bifurcations lead to different types of dynamical behavior, including exponential convergence to and divergence from a steady state, temporary oscillations around a steady state, and co-existence of different types of dynamics, depending on initial conditions. Finally, we discuss managerial implications of the results.

Formulation, construction and analysis of kinetic models of metabolism: A review of modelling frameworks

Kinetic models are critical to predict the dynamic behaviour of metabolic networks. Mechanistic kinetic models for large networks remain uncommon due to the difficulty of fitting their parameters. Recent modelling frameworks promise new ways to overcome this obstacle while retaining predictive capabilities. In this review, we present an overview of the relevant mathematical frameworks for kinetic formulation, construction and analysis. Starting with kinetic formalisms, we next review statistical methods for parameter inference, as well as recent computational frameworks applied to the construction and analysis of kinetic models. Finally, we discuss opportunities and limitations hindering the development of larger kinetic reconstructions.

Altered levels of AtHSCB disrupts iron translocation from roots to shoots

Plants overexpressing AtHSCB and hscb knockdown mutants showed altered iron homeostasis. The overexpression of AtHSCB led to activation of the iron uptake system and iron accumulation in roots without concomitant transport to shoots, resulting in reduced iron content in the aerial parts of plants. By contrast, hscb knockdown mutants presented the opposite phenotype, with iron accumulation in shoots despite the reduced levels of iron uptake in roots. AtHSCB play a key role in iron metabolism, probably taking part in the control of iron translocation from roots to shoots. Many aspects of plant iron metabolism remain obscure. The most known and studied homeostatic mechanism is the control of iron uptake in the roots by shoots. Nevertheless, this mechanism likely involves various unknown sensors and unidentified signals sent from one tissue to another which need to be identified. Here, we characterized Arabidopsis thaliana plants overexpressing AtHSCB, encoding a mitochondrial cochaperone involved in [Fe-S] cluster biosynthesis, and hscb knockdown mutants, which exhibit altered shoot/root Fe partitioning. Overexpression of AtHSCB induced an increase in root iron uptake and content along with iron deficiency in shoots. Conversely, hscb knockdown mutants exhibited increased iron accumulation in shoots and reduced iron uptake in roots. Different experiments, including foliar iron application, citrate supplementation and iron deficiency treatment, indicate that the shoot-directed control of iron uptake in roots functions properly in these lines, implying that [Fe-S] clusters are not involved in this regulatory mechanism. The most likely explanation is that both lines have altered Fe transport from roots to shoots. This could be consistent with a defect in a homeostatic mechanism operating at the root-to-shoot translocation level, which would be independent of the shoot control over root iron deficiency responses. In summary, the phenotypes of these plants indicate that AtHSCB plays a role in iron metabolism.

Monte-Carlo modeling of the central carbon metabolism of Lactococcus lactis: insights into metabolic regulation

Metabolic pathways are complex dynamic systems whose response to perturbations and environmental challenges are governed by multiple interdependencies between enzyme properties, reactions rates, and substrate levels. Understanding the dynamics arising from such a network can be greatly enhanced by the construction of a computational model that embodies the properties of the respective system. Such models aim to incorporate mechanistic details of cellular interactions to mimic the temporal behavior of the biochemical reaction system and usually require substantial knowledge of kinetic parameters to allow meaningful conclusions. Several approaches have been suggested to overcome the severe data requirements of kinetic modeling, including the use of approximative kinetics and Monte-Carlo sampling of reaction parameters. In this work, we employ a probabilistic approach to study the response of a complex metabolic system, the central metabolism of the lactic acid bacterium Lactococcus lactis, subject to perturbations and brief periods of starvation. Supplementing existing methodologies, we show that it is possible to acquire a detailed understanding of the control properties of a corresponding metabolic pathway model that is directly based on experimental observations. In particular, we delineate the role of enzymatic regulation to maintain metabolic stability and metabolic recovery after periods of starvation. It is shown that the feedforward activation of the pyruvate kinase by fructose-1,6-bisphosphate qualitatively alters the bifurcation structure of the corresponding pathway model, indicating a crucial role of enzymatic regulation to prevent metabolic collapse for low external concentrations of glucose. We argue that similar probabilistic methodologies will help our understanding of dynamic properties of small-, medium- and large-scale metabolic networks models.

iTRAQ-based quantitative proteomics analysis revealed alterations of carbohydrate metabolism pathways and mitochondrial proteins in a male sterile cybrid pummelo

Comprehensive and quantitative proteomic information on citrus floral bud is significant for understanding male sterility of the cybrid pummelo (G1+HBP) with nuclear genome of HBP and foreign mitochondrial genome of G1. Scanning electron microscopy and transmission electron microscopy analyses of the anthers showed that the development of pollen wall in G1+HBP was severely defective with a lack of exine and sporopollenin formation. Proteomic analysis was used to identify the differentially expressed proteins between male sterile G1+HBP and fertile type (HBP) with the aim to clarify their potential roles in anther development and male sterility. On the basis of iTRAQ quantitative proteomics, we identified 2235 high-confidence protein groups, 666 of which showed differentially expressed profiles in one or more stages. Proteins up- or down-regulated in G1+HBP were mainly involved in carbohydrate and energy metabolism (e.g., pyruvate dehydrogenase, isocitrate dehydrogenase, ATP synthase, and malate dehydrogenase), nucleotide binding (RNA-binding proteins), protein synthesis and degradation (e.g., ribosome proteins and proteasome subunits). Additionally, the proteins located in mitochondria also showed changed expression patterns. These findings provide a valuable inventory of proteins involved in floral bud development and contribute to elucidate the mechanism of cytoplasmic male sterility in the cybrid pummelo.

What controls fleshy fruit acidity? A review of malate and citrate accumulation in fruit cells

Fleshy fruit acidity is an important component of fruit organoleptic quality and is mainly due to the presence of malic and citric acids, the main organic acids found in most ripe fruits. The accumulation of these two acids in fruit cells is the result of several interlinked processes that take place in different compartments of the cell and appear to be under the control of many factors. This review combines analyses of transcriptomic, metabolomic, and proteomic data, and fruit process-based simulation models of the accumulation of citric and malic acids, to further our understanding of the physiological mechanisms likely to control the accumulation of these two acids during fruit development. The effects of agro-environmental factors, such as the source:sink ratio, water supply, mineral nutrition, and temperature, on citric and malic acid accumulation in fruit cells have been reported in several agronomic studies. This review sheds light on the interactions between these factors and the metabolism and storage of organic acids in the cell.

The dynamics of hybrid metabolic-genetic oscillators

The synthetic construction of intracellular circuits is frequently hindered by a poor knowledge of appropriate kinetics and precise rate parameters. Here, we use generalized modeling (GM) to study the dynamical behavior of topological models of a family of hybrid metabolic-genetic circuits known as "metabolators." Under mild assumptions on the kinetics, we use GM to analytically prove that all explicit kinetic models which are topologically analogous to one such circuit, the "core metabolator," cannot undergo Hopf bifurcations. Then, we examine more detailed models of the metabolator. Inspired by the experimental observation of a Hopf bifurcation in a synthetically constructed circuit related to the core metabolator, we apply GM to identify the critical components of the synthetically constructed metabolator which must be reintroduced in order to recover the Hopf bifurcation. Next, we study the dynamics of a re-wired version of the core metabolator, dubbed the "reverse" metabolator, and show that it exhibits a substantially richer set of dynamical behaviors, including both local and global oscillations. Prompted by the observation of relaxation oscillations in the reverse metabolator, we study the role that a separation of genetic and metabolic time scales may play in its dynamics, and find that widely separated time scales promote stability in the circuit. Our results illustrate a generic pipeline for vetting the potential success of a circuit design, simply by studying the dynamics of the corresponding generalized model.

Boolean versus continuous dynamics in modules with two feedback loops

We investigate the dynamical behavior of simple networks, namely loops with an additional internal regulating connection. Continuous dynamics for mRNA and protein concentrations is compared to a Boolean model for gene activity. Using a generalized method and within a single framework, we study different continuous models and different types of regulatory functions, and establish conditions under which the system can display stable oscillations or stable fixed points. These conditions depend only on general features such as the degree of cooperativity of the regulating interactions and the logical structure of the interactions. There are no simple rules for deciding when Boolean and continuous dynamics agree with each other, but we identify several relevant criteria.

A MATLAB toolbox for structural kinetic modeling

SUMMARY

Structural kinetic modeling (SKM) enables the analysis of dynamical properties of metabolic networks solely based on topological information and experimental data. Current SKM-based experiments are hampered by the time-intensive process of assigning model parameters and choosing appropriate sampling intervals for Monte-Carlo experiments. We introduce a toolbox for the automatic and efficient construction and evaluation of structural kinetic models (SK models). Quantitative and qualitative analyses of network stability properties are performed in an automated manner. We illustrate the model building and analysis process in detailed example scripts that provide toolbox implementations of previously published literature models.

AVAILABILITY

The source code is freely available for download at http://bioinformatics.uni-potsdam.de/projects/skm.

CONTACT

girbig@mpimp-golm.mpg.de.

Understanding regulation of metabolism through feasibility analysis

Understanding cellular regulation of metabolism is a major challenge in systems biology. Thus far, the main assumption was that enzyme levels are key regulators in metabolic networks. However, regulation analysis recently showed that metabolism is rarely controlled via enzyme levels only, but through non-obvious combinations of hierarchical (gene and enzyme levels) and metabolic regulation (mass action and allosteric interaction). Quantitative analyses relating changes in metabolic fluxes to changes in transcript or protein levels have revealed a remarkable lack of understanding of the regulation of these networks. We study metabolic regulation via feasibility analysis (FA). Inspired by the constraint-based approach of Flux Balance Analysis, FA incorporates a model describing kinetic interactions between molecules. We enlarge the portfolio of objectives for the cell by defining three main physiologically relevant objectives for the cell: function, robustness and temporal responsiveness. We postulate that the cell assumes one or a combination of these objectives and search for enzyme levels necessary to achieve this. We call the subspace of feasible enzyme levels the feasible enzyme space. Once this space is constructed, we can study how different objectives may (if possible) be combined, or evaluate the conditions at which the cells are faced with a trade-off among those. We apply FA to the experimental scenario of long-term carbon limited chemostat cultivation of yeast cells, studying how metabolism evolves optimally. Cells employ a mixed strategy composed of increasing enzyme levels for glucose uptake and hexokinase and decreasing levels of the remaining enzymes. This trade-off renders the cells specialized in this low-carbon flux state to compete for the available glucose and get rid of over-overcapacity. Overall, we show that FA is a powerful tool for systems biologists to study regulation of metabolism, interpret experimental data and evaluate hypotheses.

Respiratory carbon fluxes in leaves

Leaf respiration is a major metabolic process that drives energy production and growth. Earlier works in this field were focused on the measurement of respiration rates in relation to carbohydrate content, photosynthesis, enzymatic activities or nitrogen content. Recently, several studies have shed light on the mechanisms describing the regulation of respiration in the light and in the dark and on associated metabolic flux patterns. This review will highlight advances made into characterizing respiratory fluxes and provide a discussion of metabolic respiration dynamics in relation to important biological functions.

Discovering the role of mitochondria in the iron deficiency-induced metabolic responses of plants

In plants, iron (Fe) deficiency-induced chlorosis is a major problem, affecting both yield and quality of crops. Plants have evolved multifaceted strategies, such as reductase activity, proton extrusion, and specialised storage proteins, to mobilise Fe from the environment and distribute it within the plant. Because of its fundamental role in plant productivity, several issues concerning Fe homeostasis in plants are currently intensively studied. The activation of Fe uptake reactions requires an overall adaptation of the primary metabolism because these activities need the constant supply of energetic substrates (i.e., NADPH and ATP). Several studies concerning the metabolism of Fe-deficient plants have been conducted, but research focused on mitochondrial implications in adaptive responses to nutritional stress has only begun in recent years. Mitochondria are the energetic centre of the root cell, and they are strongly affected by Fe deficiency. Nevertheless, they display a high level of functional flexibility, which allows them to maintain the viability of the cell. Mitochondria represent a crucial target of studies on plant homeostasis, and it might be of interest to concentrate future research on understanding how mitochondria orchestrate the reprogramming of root cell metabolism under Fe deficiency. In this review, I summarise what it is known about the effect of Fe deficiency on mitochondrial metabolism and morphology. Moreover, I present a detailed view of the possible roles of mitochondria in the development of plant responses to Fe deficiency, integrating old findings with new and discussing new hypotheses for future investigations.

Decomposing flux distributions into elementary flux modes in genome-scale metabolic networks

MOTIVATION

Elementary flux mode (EFM) is a fundamental concept as well as a useful tool in metabolic pathway analysis. One important role of EFMs is that every flux distribution can be decomposed into a set of EFMs and a number of methods to study flux distributions originated from it. Yet finding such decompositions requires the complete set of EFMs, which is intractable in genome-scale metabolic networks due to combinatorial explosion.

RESULTS

In this article, we proposed an algorithm to decompose flux distributions into EFMs in genome-scale networks. It is an iterative scheme of a mixed integer linear program. Unlike previous optimization models to find pathways, any feasible solutions can become EFMs in our algorithm. This advantage enables the algorithm to approximate the EFM of largest contribution to an objective reaction in a flux distribution. Our algorithm is able to find EFMs of flux distributions with complex structures, closer to the realistic case in which a cell is subject to various constraints. A case of Escherichia coli growth in the Lysogeny broth (LB) medium containing various carbon sources was studied. Essential metabolites and their syntheses were located. Information on the contribution of each carbon source not obvious from the apparent flux distribution was also revealed. Our work further confirms the utility of finding EFMs by optimization models in genome-scale metabolic networks.

CONTACT

joshua.chan@connect.polyu.hk

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Modelling dynamic plant cells

A major challenge in plant biology is to understand how functions in plant cells emerge from interactions between molecular components. Computational and mathematical modelling can encapsulate the relationships between molecular components and reveal how biological functions emerge. We review recent progress in modelling in metabolism, growth, signalling and circadian rhythms in plant cells. We discuss challenges and opportunities for future directions.

Boolean versus continuous dynamics on simple two-gene modules

We investigate the dynamical behavior of simple modules composed of two genes with two or three regulating connections. Continuous dynamics for mRNA and protein concentrations is compared to a Boolean model for gene activity. Using a generalized method, we study within a single framework different continuous models and different types of regulatory functions, and establish conditions under which the system can display stable oscillations. These conditions depend only on general features such as the ratio of the relevant time scales, the degree of cooperativity of the regulating interactions, and the logical structure of the interactions. Our results combine and generalize the findings of several disconnected previous studies.

Not just a circle: flux modes in the plant TCA cycle

The tricarboxylic acid (TCA) cycle is one of the iconic pathways in metabolism. The cycle is commonly thought of in terms of energy metabolism, being responsible for the oxidation of respiratory substrates to drive ATP synthesis. However, the reactions of carboxylic acid metabolism are embedded in a larger metabolic network and the conventional TCA cycle is only one way in which the component reactions can be organised. Recent evidence from labelling studies and metabolic network models suggest that the organisation of carboxylic acid metabolism in plants is highly dependent on the metabolic and physiological demands of the cell. Thus, alternative, non-cyclic flux modes occur in leaves in the light, in some developing oilseeds, and under specific physiological circumstances such as anoxia.

On the stability of metabolic cycles

We investigate the stability properties of two different classes of metabolic cycles using a combination of analytical and computational methods. Using principles from structural kinetic modeling (SKM), we show that the stability of metabolic networks with certain structural regularities can be studied using a combination of analytical and computational techniques. We then apply these techniques to a class of single input, single output metabolic cycles, and find that the cycles are stable under all conditions tested. Next, we extend our analysis to a small autocatalytic cycle, and determine parameter regimes within which the cycle is very likely to be stable. We demonstrate that analytical methods can be used to understand the relationship between kinetic parameters and stability, and that results from these analytical methods can be confirmed with computational experiments. In addition, our results suggest that elevated metabolite concentrations and certain crucial saturation parameters can strongly affect the stability of the entire metabolic cycle. We discuss our results in light of the possibility that evolutionary forces may select for metabolic network topologies with a high intrinsic probability of being stable. Furthermore, our conclusions support the hypothesis that certain types of metabolic cycles may have played a role in the development of primitive metabolism despite the absence of regulatory mechanisms.

Which metabolic pathways generate and characterize the flux space? A comparison among elementary modes, extreme pathways and minimal generators

Important efforts are being done to systematically identify the relevant pathways in a metabolic network. Unsurprisingly, there is not a unique set of network-based pathways to be tagged as relevant, and at least four related concepts have been proposed: extreme currents, elementary modes, extreme pathways, and minimal generators. Basically, there are two properties that these sets of pathways can hold: they can generate the flux space--if every feasible flux distribution can be represented as a nonnegative combination of flux through them--or they can comprise all the nondecomposable pathways in the network. The four concepts fulfill the first property, but only the elementary modes fulfill the second one. This subtle difference has been a source of errors and misunderstandings. This paper attempts to clarify the intricate relationship between the network-based pathways performing a comparison among them.

Stability of metabolic correlations under changing environmental conditions in Escherichia coli--a systems approach

BACKGROUND

Biological systems adapt to changing environments by reorganizing their cellular and physiological program with metabolites representing one important response level. Different stresses lead to both conserved and specific responses on the metabolite level which should be reflected in the underlying metabolic network.

METHODOLOGY/PRINCIPAL FINDINGS

Starting from experimental data obtained by a GC-MS based high-throughput metabolic profiling technology we here develop an approach that: (1) extracts network representations from metabolic condition-dependent data by using pairwise correlations, (2) determines the sets of stable and condition-dependent correlations based on a combination of statistical significance and homogeneity tests, and (3) can identify metabolites related to the stress response, which goes beyond simple observations about the changes of metabolic concentrations. The approach was tested with Escherichia coli as a model organism observed under four different environmental stress conditions (cold stress, heat stress, oxidative stress, lactose diauxie) and control unperturbed conditions. By constructing the stable network component, which displays a scale free topology and small-world characteristics, we demonstrated that: (1) metabolite hubs in this reconstructed correlation networks are significantly enriched for those contained in biochemical networks such as EcoCyc, (2) particular components of the stable network are enriched for functionally related biochemical pathways, and (3) independently of the response scale, based on their importance in the reorganization of the correlation network a set of metabolites can be identified which represent hypothetical candidates for adjusting to a stress-specific response.

CONCLUSIONS/SIGNIFICANCE

Network-based tools allowed the identification of stress-dependent and general metabolic correlation networks. This correlation-network-based approach does not rely on major changes in concentration to identify metabolites important for stress adaptation, but rather on the changes in network properties with respect to metabolites. This should represent a useful complementary technique in addition to more classical approaches.

Plasma amino acid analysis for diagnosis and amino acid-based metabolic networks

PURPOSE OF REVIEW

To highlight the usefulness of amino acid profiling in clinical diagnosis and current developments in analysis revealing underlying metabolic relationships.

RECENT FINDINGS

Recent innovations in metabolomics and systems biology enable high throughput measurement of diverse amino acids and the subsequent data mining for various uses. Recent studies show new possibilities of using plasma amino acid analysis as biomarker discovery tools by generating diagnostic indices through systematic computation. Such studies show that amino acid-based clinical diagnostic indices for hepatic fibrosis in type C hepatitis patients can be generated. In addition, several studies show the potential of treating amino acid profile data as a metabolomic subset, which can be integrated through the analysis of correlation with different types of 'omics' data for describing metabolite-to-metabolite or metabolite-to-gene interaction networks.

CONCLUSION

Amino acid profiling of biological samples could be used to generate indices that could be used for clinical diagnosis and is a useful tool for understanding metabolic implications under various physiological conditions. Although further improvements in analytical methods are needed, amino acids could be useful indicators for facilitating nutritional management of specific physiological and pathological states.

Parameter inference for biochemical systems that undergo a Hopf bifurcation

The increasingly widespread use of parametric mathematical models to describe biological systems means that the ability to infer model parameters is of great importance. In this study, we consider parameter inferability in nonlinear ordinary differential equation models that undergo a bifurcation, focusing on a simple but generic biochemical reaction model. We systematically investigate the shape of the likelihood function for the model's parameters, analyzing the changes that occur as the model undergoes a Hopf bifurcation. We demonstrate that there exists an intrinsic link between inference and the parameters' impact on the modeled system's dynamical stability, which we hope will motivate further research in this area.

Teaching (and learning from) metabolomics: the 2006 PlantMetaNet ETNA Metabolomics Research School

Under the auspices of the European Training and Networking Activity programme of the European Union, a 'Metabolic Profiling and Data Analysis' Plant Genomics and Bioinformatics Summer School was hosted in Potsdam, Germany between 20 and 29 September 2006. Sixteen early career researchers were invited from the European Union partner nations and the so-called developing nations (Appendix). Lectures from invited leading European researchers provided an overview of the state of the art of these fields and seeded discussion regarding major challenges for their future advancement. Hands-on experience was provided by an example experiment - that of defining the metabolic response of Arabidopsis to treatment of a commercial herbicide of defined mode of action. This experiment was performed throughout the duration of the course in order to teach the concepts underlying extraction and machine handling as well as to provide a rich data set with which the required computation and statistical skills could be illustrated. Here we review the state of the field by describing both key lectures given at and practical aspects taught at the summer school. In addition, we disclose results that were obtained using the four distinct technical platforms at the different participating institutes. While the effects of the chosen herbicide are well documented, this study looks at a broader number of metabolites than in previous investigations. This allowed, on the one hand, not only to characterise further effects of the herbicide than previously observed but also to detect molecules other than the herbicide that were obviously present in the commercial formulation. These data and the workshop in general are all discussed in the context of the teaching of metabolomics.

Getting to grips with the plant metabolic network

Research into plant metabolism has a long history, and analytical approaches of ever-increasing breadth and sophistication have been brought to bear. We now have access to vast repositories of data concerning enzymology and regulatory features of enzymes, as well as large-scale datasets containing profiling information of transcripts, protein and metabolite levels. Nevertheless, despite this wealth of data, we remain some way off from being able to rationally engineer plant metabolism or even to predict metabolic responses. Within the past 18 months, rapid progress has been made, with several highly informative plant network interrogations being discussed in the literature. In the present review we will appraise the current state of the art regarding plant metabolic network analysis and attempt to outline what the necessary steps are in order to further our understanding of network regulation.

Computational approaches to the topology, stability and dynamics of metabolic networks

Cellular metabolism is characterized by an intricate network of interactions between biochemical fluxes, metabolic compounds and regulatory interactions. To investigate and eventually understand the emergent global behavior arising from such networks of interaction is not possible by intuitive reasoning alone. This contribution seeks to describe recent computational approaches that aim to asses the topological and functional properties of metabolic networks. In particular, based on a recently proposed method, it is shown that it is possible to acquire a quantitative picture of the possible dynamics of metabolic systems, without assuming detailed knowledge of the underlying enzyme-kinetic rate equations and parameters. Rather, the method builds upon a statistical exploration of the comprehensive parameter space to evaluate the dynamic capabilities of a metabolic system, thus providing a first step towards the transition from topology to function of metabolic pathways. Utilizing this approach, the role of feedback mechanisms in the maintenance of stability is discussed using minimal models of cellular pathways.