Experimental and mathematical approaches to modeling plant metabolic networks

Avoiding matrix exponentials for large transition rate matrices

Exact methods for the exponentiation of matrices of dimension N can be computationally expensive in terms of execution time (N3) and memory requirements (N2), not to mention numerical precision issues. A matrix often exponentiated in the natural sciences is the rate matrix. Here, we explore five methods to exponentiate rate matrices, some of which apply more broadly to other matrix types. Three of the methods leverage a mathematical analogy between computing matrix elements of a matrix exponential process and computing transition probabilities of a dynamical process (technically a Markov jump process, MJP, typically simulated using Gillespie). In doing so, we identify a novel MJP-based method relying on restricting the number of "trajectory" jumps that incurs improved computational scaling. We then discuss this method's downstream implications on mixing properties of Monte Carlo posterior samplers. We also benchmark two other methods of matrix exponentiation valid for any matrix (beyond rate matrices and, more generally, positive definite matrices) related to solving differential equations: Runge-Kutta integrators and Krylov subspace methods. Under conditions where both the largest matrix element and the number of non-vanishing elements scale linearly with N-reasonable conditions for rate matrices often exponentiated-computational time scaling with the most competitive methods (Krylov and one of the MJP-based methods) reduces to N2 with total memory requirements of N.

Dynamic interactions between SPX proteins, the ubiquitination machinery, and signalling molecules for stress adaptation at a whole-plant level

The plant macronutrient phosphorus is a scarce resource and plant-available phosphate is limiting in most soil types. Generally, a gene regulatory module called the phosphate starvation response (PSR) enables efficient phosphate acquisition by roots and translocation to other organs. Plants growing on moderate to nutrient-rich soils need to co-ordinate availability of different nutrients and repress the highly efficient PSR to adjust phosphate acquisition to the availability of other macro- and micronutrients, and in particular nitrogen. PSR repression is mediated by a small family of single SYG1/Pho81/XPR1 (SPX) domain proteins. The SPX domain binds higher order inositol pyrophosphates that signal cellular phosphorus status and modulate SPX protein interaction with PHOSPHATE STARVATION RESPONSE1 (PHR1), the central transcriptional regulator of PSR. Sequestration by SPX repressors restricts PHR1 access to PSR gene promoters. Here we focus on SPX4 that primarily acts in shoots and sequesters many transcription factors other than PHR1 in the cytosol to control processes beyond the classical PSR, such as nitrate, auxin, and jasmonic acid signalling. Unlike SPX1 and SPX2, SPX4 is subject to proteasomal degradation not only by singular E3 ligases, but also by SCF-CRL complexes. Emerging models for these different layers of control and their consequences for plant acclimation to the environment will be discussed.

Phytoene Synthase: The Key Rate-Limiting Enzyme of Carotenoid Biosynthesis in Plants

Phytoene synthase (PSY) catalyzes the first committed step in the carotenoid biosynthesis pathway and is a major rate-limiting enzyme of carotenogenesis. PSY is highly regulated by various regulators and factors to modulate carotenoid biosynthesis in response to diverse developmental and environmental cues. Because of its critical role in controlling the total amount of synthesized carotenoids, PSY has been extensively investigated and engineered in plant species. However, much remains to be learned on its multifaceted regulatory control and its catalytic efficiency for carotenoid enrichment in crops. Here, we present current knowledge on the basic biology, the functional evolution, the dynamic regulation, and the metabolic engineering of PSY. We also discuss the open questions and gaps to stimulate additional research on this most studied gene/enzyme in the carotenogenic pathway.

An insight to flux-balance analysis for biochemical networks

Systems biology is one of the integrated ways to study biological systems and is more favourable than the earlier used approaches. It includes metabolic pathway analysis, modelling, and regulatory as well as signal transduction for getting insights into cellular behaviour. Among the various techniques of modelling, simulation, analysis of networks and pathways, flux-based analysis (FBA) has been recognised because of its extensibility as well as simplicity. It is widely accepted because it is not like a mechanistic simulation which depends on accurate kinetic data. The study of fluxes through the network is informative and can give insights even in the absence of kinetic data. FBA is one of the widely used tools to study biochemical networks and needs information of reaction stoichiometry, growth requirements, specific measurement parameters of the biological system, in particular the reconstruction of the metabolic network for the genome-scale, many of which have already been built previously. It defines the boundaries of flux distributions which are possible and achievable with a defined set of genes. This review article gives an insight into FBA, from the extension of flux balancing to mathematical representation followed by a discussion about the formulation of flux-balance analysis problems, defining constraints for the stoichiometry of the pathways and the tools that can be used in FBA such as FASIMA, COBRA toolbox, and OptFlux. It also includes broader areas in terms of applications which can be covered by FBA as well as the queries which can be addressed through FBA.

Computational systems biology of cellular processes in Arabidopsis thaliana: an overview

Systems biology strives for gaining an understanding of biological phenomena by studying the interactions of different parts of a system and integrating the knowledge obtained into the current view of the underlying processes. This is achieved by a tight combination of quantitative experimentation and computational modeling. While there is already a large quantity of systems biology studies describing human, animal and especially microbial cell biological systems, plant biology has been lagging behind for many years. However, in the case of the model plant Arabidopsis thaliana, the steadily increasing amount of information on the levels of its genome, proteome and on a variety of its metabolic and signalling pathways is progressively enabling more researchers to construct models for cellular processes for the plant, which in turn encourages more experimental data to be generated, showing also for plant sciences how fruitful systems biology research can be. In this review, we provide an overview over some of these recent studies which use different systems biological approaches to get a better understanding of the cell biology of A. thaliana. The approaches used in these are genome-scale metabolic modeling, as well as kinetic modeling of metabolic and signalling pathways. Furthermore, we selected several cases to exemplify how the modeling approaches have led to significant advances or new perspectives in the field.

Medically Useful Plant Terpenoids: Biosynthesis, Occurrence, and Mechanism of Action

Specialized plant terpenoids have found fortuitous uses in medicine due to their evolutionary and biochemical selection for biological activity in animals. However, these highly functionalized natural products are produced through complex biosynthetic pathways for which we have a complete understanding in only a few cases. Here we review some of the most effective and promising plant terpenoids that are currently used in medicine and medical research and provide updates on their biosynthesis, natural occurrence, and mechanism of action in the body. This includes pharmacologically useful plastidic terpenoids such as p-menthane monoterpenoids, cannabinoids, paclitaxel (taxol®), and ingenol mebutate which are derived from the 2-C-methyl-d-erythritol-4-phosphate (MEP) pathway, as well as cytosolic terpenoids such as thapsigargin and artemisinin produced through the mevalonate (MVA) pathway. We further provide a review of the MEP and MVA precursor pathways which supply the carbon skeletons for the downstream transformations yielding these medically significant natural products.

Flux prediction using artificial neural network (ANN) for the upper part of glycolysis

The selection of optimal enzyme concentration in multienzyme cascade reactions for the highest product yield in practice is very expensive and time-consuming process. The modelling of biological pathways is a difficult process because of the complexity of the system. The mathematical modelling of the system using an analytical approach depends on the many parameters of enzymes which rely on tedious and expensive experiments. The artificial neural network (ANN) method has been successively applied in different fields of science to perform complex functions. In this study, ANN models were trained to predict the flux for the upper part of glycolysis as inferred by NADH consumption, using four enzyme concentrations i.e., phosphoglucoisomerase, phosphofructokinase, fructose-bisphosphate-aldolase, triose-phosphate-isomerase. Out of three ANN algorithms, the neuralnet package with two activation functions, “logistic” and “tanh” were implemented. The prediction of the flux was very efficient: RMSE and R² were 0.847, 0.93 and 0.804, 0.94 respectively for logistic and tanh functions using a cross validation procedure. This study showed that a systemic approach such as ANN could be used for accurate prediction of the flux through the metabolic pathway. This could help to save a lot of time and costs, particularly from an industrial perspective. The R-code is available at: https://github.com/DSIMB/ANN-Glycolysis-Flux-Prediction.

Advances in metabolic flux analysis toward genome-scale profiling of higher organisms

Methodological and technological advances have recently paved the way for metabolic flux profiling in higher organisms, like plants. However, in comparison with omics technologies, flux profiling has yet to provide comprehensive differential flux maps at a genome-scale and in different cell types, tissues, and organs. Here we highlight the recent advances in technologies to gather metabolic labeling patterns and flux profiling approaches. We provide an opinion of how recent local flux profiling approaches can be used in conjunction with the constraint-based modeling framework to arrive at genome-scale flux maps. In addition, we point at approaches which use metabolomics data without introduction of label to predict either non-steady state fluxes in a time-series experiment or flux changes in different experimental scenarios. The combination of these developments allows an experimentally feasible approach for flux-based large-scale systems biology studies.

A kinetic model of sugar metabolism in peach fruit reveals a functional hypothesis of a markedly low fructose-to-glucose ratio phenotype

The concentrations of sugars in fruit vary with fruit development, environment and genotype. In general, there were weak correlations between the variations in sugar concentrations and the activities of enzymes directly related with the synthesis or degradation of sugars. This finding suggests that the relationships between enzyme activities and metabolites are often non-linear and are difficult to assess. To simulate the concentrations of sucrose, glucose, fructose and sorbitol during the development of peach fruit, a kinetic model of sugar metabolism was developed by taking advantage of recent profiling data. Cell compartmentation (cytosol and vacuole) was described explicitly, and data-driven enzyme activities were used to parameterize equations. The model correctly accounts for both annual and genotypic variations, which were observed in 10 genotypes derived from an interspecific cross. They provided important information on the mechanisms underlying the specification of phenotypic differences. In particular, the model supports the hypothesis that a difference in fructokinase affinity could be responsible for a low fructose-to-glucose ratio phenotype, which was observed in the studied population.

Constraint-Based Modeling Highlights Cell Energy, Redox Status and α-Ketoglutarate Availability as Metabolic Drivers for Anthocyanin Accumulation in Grape Cells Under Nitrogen Limitation

Anthocyanin biosynthesis is regulated by environmental factors (such as light, temperature, and water availability) and nutrient status (such as carbon, nitrogen, and phosphate nutrition). Previous reports show that low nitrogen availability strongly enhances anthocyanin accumulation in non carbon-limited plant organs or cell suspensions. It has been hypothesized that high carbon-to-nitrogen ratio would lead to an energy excess in plant cells, and that an increase in flavonoid pathway metabolic fluxes would act as an "energy escape valve," helping plant cells to cope with energy and carbon excess. However, this hypothesis has never been tested directly. To this end, we used the grapevine Vitis vinifera L. cultivar Gamay Teinturier (syn. Gamay Freaux or Freaux Tintorier, VIVC #4382) cell suspension line as a model system to study the regulation of anthocyanin accumulation in response to nitrogen supply. The cells were sub-cultured in the presence of either control (25 mM) or low (5 mM) nitrate concentration. Targeted metabolomics and enzyme activity determinations were used to parametrize a constraint-based model describing both the central carbon and nitrogen metabolisms and the flavonoid (phenylpropanoid) pathway connected by the energy (ATP) and reducing power equivalents (NADPH and NADH) cofactors. The flux analysis (2 flux maps generated, for control and low nitrogen in culture medium) clearly showed that in low nitrogen-fed cells all the metabolic fluxes of central metabolism were decreased, whereas fluxes that consume energy and reducing power, were either increased (upper part of glycolysis, shikimate, and flavonoid pathway) or maintained (pentose phosphate pathway). Also, fluxes of flavanone 3β-hydroxylase, flavonol synthase, and anthocyanidin synthase were strongly increased, advocating for a regulation of the flavonoid pathway by alpha-ketoglutarate levels. These results strongly support the hypothesis of anthocyanin biosynthesis acting as an energy escape valve in plant cells, and they open new possibilities to manipulate flavonoid production in plant cells. They do not, however, support a role of anthocyanins as an effective mechanism for coping with carbon excess in high carbon to nitrogen ratio situations in grape cells. Instead, constraint-based modeling output and biomass analysis indicate that carbon excess is dealt with by vacuolar storage of soluble sugars.

Mathematical Modeling Approaches in Plant Metabolomics

The experimental analysis of a plant metabolome typically results in a comprehensive and multidimensional data set. To interpret metabolomics data in the context of biochemical regulation and environmental fluctuation, various approaches of mathematical modeling have been developed and have proven useful. In this chapter, a general introduction to mathematical modeling is presented and discussed in context of plant metabolism. A particular focus is laid on the suitability of mathematical approaches to functionally integrate plant metabolomics data in a metabolic network and combine it with other biochemical or physiological parameters.

First principle-based models in plant suspension cell cultures: a review

In this work, the development and application of published models for describing the behavior of plant cell cultures is reviewed. The structure of each type of model is analyzed and the new tendencies for the modeling of biotechnological processes that can be applied in plant cell cultures are presented. This review is a tool for clarifying the main features that characterize each type of model in the field of plant cell cultures and can be used as a support on the selection of the more suitable model type, taking into account the purpose of specific research.

Metabolomics, Standards, and Metabolic Modeling for Synthetic Biology in Plants

Life on earth depends on dynamic chemical transformations that enable cellular functions, including electron transfer reactions, as well as synthesis and degradation of biomolecules. Biochemical reactions are coordinated in metabolic pathways that interact in a complex way to allow adequate regulation. Biotechnology, food, biofuel, agricultural, and pharmaceutical industries are highly interested in metabolic engineering as an enabling technology of synthetic biology to exploit cells for the controlled production of metabolites of interest. These approaches have only recently been extended to plants due to their greater metabolic complexity (such as primary and secondary metabolism) and highly compartmentalized cellular structures and functions (including plant-specific organelles) compared with bacteria and other microorganisms. Technological advances in analytical instrumentation in combination with advances in data analysis and modeling have opened up new approaches to engineer plant metabolic pathways and allow the impact of modifications to be predicted more accurately. In this article, we review challenges in the integration and analysis of large-scale metabolic data, present an overview of current bioinformatics methods for the modeling and visualization of metabolic networks, and discuss approaches for interfacing bioinformatics approaches with metabolic models of cellular processes and flux distributions in order to predict phenotypes derived from specific genetic modifications or subjected to different environmental conditions.

Modeling and Classification of Kinetic Patterns of Dynamic Metabolic Biomarkers in Physical Activity

The objectives of this work were the classification of dynamic metabolic biomarker candidates and the modeling and characterization of kinetic regulatory mechanisms in human metabolism with response to external perturbations by physical activity. Longitudinal metabolic concentration data of 47 individuals from 4 different groups were examined, obtained from a cycle ergometry cohort study. In total, 110 metabolites (within the classes of acylcarnitines, amino acids, and sugars) were measured through a targeted metabolomics approach, combining tandem mass spectrometry (MS/MS) with the concept of stable isotope dilution (SID) for metabolite quantitation. Biomarker candidates were selected by combined analysis of maximum fold changes (MFCs) in concentrations and P-values resulting from statistical hypothesis testing. Characteristic kinetic signatures were identified through a mathematical modeling approach utilizing polynomial fitting. Modeled kinetic signatures were analyzed for groups with similar behavior by applying hierarchical cluster analysis. Kinetic shape templates were characterized, defining different forms of basic kinetic response patterns, such as sustained, early, late, and other forms, that can be used for metabolite classification. Acetylcarnitine (C2), showing a late response pattern and having the highest values in MFC and statistical significance, was classified as late marker and ranked as strong predictor (MFC = 1.97, P < 0.001). In the class of amino acids, highest values were shown for alanine (MFC = 1.42, P < 0.001), classified as late marker and strong predictor. Glucose yields a delayed response pattern, similar to a hockey stick function, being classified as delayed marker and ranked as moderate predictor (MFC = 1.32, P < 0.001). These findings coincide with existing knowledge on central metabolic pathways affected in exercise physiology, such as β-oxidation of fatty acids, glycolysis, and glycogenolysis. The presented modeling approach demonstrates high potential for dynamic biomarker identification and the investigation of kinetic mechanisms in disease or pharmacodynamics studies using MS data from longitudinal cohort studies.

Human metabolism is controlled through basic kinetic regulatory mechanisms, where the overall system aims to maintain a state of homeostasis. In response to external perturbations, such as environmental influences, nutrition or physical exercise, circulating metabolites show specific kinetic response patterns, which can be computationally modeled. In this work, we searched for dynamic metabolic biomarker candidates and analyzed specific kinetic mechanisms from longitudinal metabolic concentration data, obtained through a cycle ergometry stress test. In total, 110 metabolites measured from blood samples of 47 individuals were analyzed using tandem mass spectrometry (MS/MS). Dynamic biomarker candidates could be selected based on the amplitudes of changes in metabolite concentrations and the significance of statistical hypothesis testing. We were able to characterize specific kinetic patterns for groups of similarly behaving metabolites. Kinetic shape templates were identified, defining basic kinetic response patterns to physical exercise, such as sustained, early, late and other shape forms. The presented approach contributes to a better understanding of (patho)physiological biochemical mechanisms in human health, disease or during drug therapy, by offering tools for classifying dynamic biomarker candidates and for modeling and characterizing kinetic regulatory mechanisms from longitudinal experimental data.

Integration of metabolomics data into metabolic networks

Metabolite levels together with their corresponding metabolic fluxes are integrative outcomes of biochemical transformations and regulatory processes and they can be used to characterize the response of biological systems to genetic and/or environmental changes. However, while changes in transcript or to some extent protein levels can usually be traced back to one or several responsible genes, changes in fluxes and particularly changes in metabolite levels do not follow such rationale and are often the outcome of complex interactions of several components. The increasing quality and coverage of metabolomics technologies have fostered the development of computational approaches for integrating metabolic read-outs with large-scale models to predict the physiological state of a system. Constraint-based approaches, relying on the stoichiometry of the considered reactions, provide a modeling framework amenable to analyses of large-scale systems and to the integration of high-throughput data. Here we review the existing approaches that integrate metabolomics data in variants of constrained-based approaches to refine model reconstructions, to constrain flux predictions in metabolic models, and to relate network structural properties to metabolite levels. Finally, we discuss the challenges and perspectives in the developments of constraint-based modeling approaches driven by metabolomics data.

Moving toward a comprehensive map of central plant metabolism

Decades of intensive study have led to the discovery of the main pathways involved in central metabolism but only some of the pathways and regulatory networks in which they are embedded. In this review, we discuss techniques used to assemble these pathways into a systems biology framework that can enable accurate modeling of the response of central metabolism to changes, including ways to perturb metabolic systems and assemble the resulting data into a meaningful network. Critically, these networks are of such size and complexity that it is possible to derive them only if data from different groups can be comprehensively and meaningfully combined. We conclude that it is essential to establish common standards for the description of experimental conditions and data collection and to store this information in databases to which the whole community can contribute.

A detailed view on sulphur metabolism at the cellular and whole-plant level illustrates challenges in metabolite flux analyses

Understanding the dynamics of physiological process in the systems biology era requires approaches at the genome, transcriptome, proteome, and metabolome levels. In this context, metabolite flux experiments have been used in mapping metabolite pathways and analysing metabolic control. In the present review, sulphur metabolism was taken to illustrate current challenges of metabolic flux analyses. At the cellular level, restrictions in metabolite flux analyses originate from incomplete knowledge of the compartmentation network of metabolic pathways. Transport of metabolites through membranes is usually not considered in flux experiments but may be involved in controlling the whole pathway. Hence, steady-state and snapshot readings need to be expanded to time-course studies in combination with compartment-specific metabolite analyses. Because of species-specific differences, differences between tissues, and stress-related responses, the quantitative significance of different sulphur sinks has to be elucidated; this requires the development of methods for whole-sulphur metabolome approaches. Different cell types can contribute to metabolite fluxes to different extents at the tissue and organ level. Cell type-specific analyses are needed to characterize these contributions. Based on such approaches, metabolite flux analyses can be expanded to the whole-plant level by considering long-distance transport and, thus, the interaction of roots and the shoot in metabolite fluxes. However, whole-plant studies need detailed empirical and mathematical modelling that have to be validated by experimental analyses.

Kinetic modeling of plant metabolism and its predictive power: peppermint essential oil biosynthesis as an example

The integration of mathematical modeling with analytical experimentation in an iterative fashion is a powerful approach to advance our understanding of the architecture and regulation of metabolic networks. Ultimately, such knowledge is highly valuable to support efforts aimed at modulating flux through target pathways by molecular breeding and/or metabolic engineering. In this article we describe a kinetic mathematical model of peppermint essential oil biosynthesis, a pathway that has been studied extensively for more than two decades. Modeling assumptions and approximations are described in detail. We provide step-by-step instructions on how to run simulations of dynamic changes in pathway metabolites concentrations.

The metabolic response of cultured tomato cells to low oxygen stress

The storage of fruits and vegetables under a controlled atmosphere can induce low oxygen stress, which can lead to post-harvest losses through the induction of disorders such as core breakdown and browning. To gain better understanding of the metabolic response of plant organs to low oxygen, cultured tomato cells (Lycopersicum esculentum) were used as a model system to study the metabolic stress response to low oxygen (0 and 1 kPa O2). By adding 13C labelled glucose, changes in the levels of polar metabolites and their 13C label accumulation were quantified. Low oxygen stress altered the metabolite profile of tomato cells, with the accumulation of the intermediates of glycolysis in addition to increases in lactate and sugar alcohols. 13C label data showed reduced label accumulation in almost all metabolites except lactate and some sugar alcohols. The results showed that low oxygen stress in tomato cell culture activated fermentative metabolism and sugar alcohol synthesis while inhibiting the activity of the TCA cycle and the biosynthesis of metabolites whose precursors are derived from central metabolism, including fluxes to most organic acids, amino acids and sugars.

Metabolic flux analysis of plastidic isoprenoid biosynthesis in poplar leaves emitting and nonemitting isoprene

The plastidic 2-C-methyl-D-erythritol-4-phosphate (MEP) pathway is one of the most important pathways in plants and produces a large variety of essential isoprenoids. Its regulation, however, is still not well understood. Using the stable isotope 13C-labeling technique, we analyzed the carbon fluxes through the MEP pathway and into the major plastidic isoprenoid products in isoprene-emitting and transgenic isoprene-nonemitting (NE) gray poplar (Populus×canescens). We assessed the dependence on temperature, light intensity, and atmospheric [CO2]. Isoprene biosynthesis was by far (99%) the main carbon sink of MEP pathway intermediates in mature gray poplar leaves, and its production required severalfold higher carbon fluxes compared with NE leaves with almost zero isoprene emission. To compensate for the much lower demand for carbon, NE leaves drastically reduced the overall carbon flux within the MEP pathway. Feedback inhibition of 1-deoxy-D-xylulose-5-phosphate synthase activity by accumulated plastidic dimethylallyl diphosphate almost completely explained this reduction in carbon flux. Our data demonstrate that short-term biochemical feedback regulation of 1-deoxy-d-xylulose-5-phosphate synthase activity by plastidic dimethylallyl diphosphate is an important regulatory mechanism of the MEP pathway. Despite being relieved from the large carbon demand of isoprene biosynthesis, NE plants redirected only approximately 0.5% of this saved carbon toward essential nonvolatile isoprenoids, i.e. β-carotene and lutein, most probably to compensate for the absence of isoprene and its antioxidant properties.

Applications of kinetic modeling to plant metabolism

The importance of kinetic modeling for understanding the control and regulation of complex metabolic networks is increasingly being recognized. Kinetic models encapsulate the available kinetic information of all the enzymes in a pathway, and then calculate the complex behavior that emerges from the interactions between these network components. Kinetic models are particularly useful because they can simulate untested scenarios and thus explore pathway behavior beyond the realm of what is experimentally available or currently feasible. Models can also suggest new experiments in a directed approach.This chapter provides a brief introduction to kinetic modeling and its application to plant metabolic pathways. A two-pronged strategy is followed: first, a method is presented for further analysis of existing published models, with references to the relevant databases housing such models and instructions on how to load the models into simulation software. Next, the requirements for and processes of constructing and validating a kinetic model from scratch are outlined. To conclude, potential applications of models are summarized.

Simulating labeling to estimate kinetic parameters for flux control analysis

An important aspect of kinetic modeling is the ability to provide predictive information on network control and dynamic responses to genetic or environmental perturbations based on innate enzyme kinetics. In a top-down approach to model assembly, unknown kinetic parameters are calculated using experimental data such as metabolite pool concentrations and transient labeling patterns after supply of an isotopically labeled substrate. These kinetic parameters can then be used to calculate flux control coefficients for every reaction in a network, which aids in the identification of enzymatic reactions that exert the most control over the network as a whole. This chapter describes a modeling approach to estimate kinetic parameters which are then used to perform metabolic control analysis. An example is provided for the benzenoid network of Petunia hybrida; however, the methodologies can be applied to any small segment of metabolism.

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.

Insight into the functioning of metabolic control to meet changing demands is a first step in rational engineering of biological systems towards a desired behavior. Metabolic control analysis provides the means to examine the impact of change of reaction fluxes on a specific target flux based on kinetic modeling, but suffers from limitations of the kinetic approach. Here, we introduce and analyze structural metabolic control as a framework to overcome these limitations. We utilize functional centrality, a framework based on the Shapley value from cooperative game theory and flux balance analysis, to determine the contribution of individual reactions to the functions accomplished by a metabolic network. These contributions, in turn, depend on the control exerted on the remaining network. Functional centrality provides the mathematical means to gain further understanding of metabolic control. The potential applications range from facilitating strategies of rational strain design to drug target identification.

Analysis of metabolic flux using dynamic labelling and metabolic modelling

Metabolic fluxes and the capacity to modulate them are a crucial component of the ability of the plant cell to react to environmental perturbations. Our ability to quantify them and to attain information concerning the regulatory mechanisms that control them is therefore essential to understand and influence metabolic networks. For all but the simplest of flux measurements labelling methods have proven to be the most informative. Both steady-state and dynamic labelling approaches have been adopted in the study of plant metabolism. Here the conceptual basis of these complementary approaches, as well as their historical application in microbial, mammalian and plant sciences, is reviewed, and an update on technical developments in label distribution analyses is provided. This is supported by illustrative cases studies involving the kinetic modelling of secondary metabolism. One issue that is particularly complex in the analysis of plant fluxes is the extensive compartmentation of the plant cell. This problem is discussed from both theoretical and experimental perspectives, and the current approaches used to address it are assessed. Finally, current limitations and future perspectives of kinetic modelling of plant metabolism are discussed.

Granger causality in integrated GC-MS and LC-MS metabolomics data reveals the interface of primary and secondary metabolism

Metabolomics has emerged as a key technique of modern life sciences in recent years. Two major techniques for metabolomics in the last 10 years are gas chromatography coupled to mass spectrometry (GC-MS) and liquid chromatography coupled to mass spectrometry (LC-MS). Each platform has a specific performance detecting subsets of metabolites. GC-MS in combination with derivatisation has a preference for small polar metabolites covering primary metabolism. In contrast, reversed phase LC-MS covers large hydrophobic metabolites predominant in secondary metabolism. Here, we present an integrative metabolomics platform providing a mean to reveal the interaction of primary and secondary metabolism in plants and other organisms. The strategy combines GC-MS and LC-MS analysis of the same sample, a novel alignment tool MetMAX and a statistical toolbox COVAIN for data integration and linkage of Granger Causality with metabolic modelling. For metabolic modelling we have implemented the combined GC-LC-MS metabolomics data covariance matrix and a stoichiometric matrix of the underlying biochemical reaction network. The changes in biochemical regulation are expressed as differential Jacobian matrices. Applying the Granger causality, a subset of secondary metabolites was detected with significant correlations to primary metabolites such as sugars and amino acids. These metabolic subsets were compiled into a stoichiometric matrix N. Using N the inverse calculation of a differential Jacobian J from metabolomics data was possible. Key points of regulation at the interface of primary and secondary metabolism were identified.

Metabolic network flux analysis for engineering plant systems

Metabolic network flux analysis (NFA) tools have proven themselves to be powerful aids to metabolic engineering of microbes by providing quantitative insights into the flows of material and energy through cellular systems. The development and application of NFA tools to plant systems has advanced in recent years and are yielding significant insights and testable predictions. Plants present substantial opportunities for the practical application of NFA but they also pose serious challenges related to the complexity of plant metabolic networks and to deficiencies in our knowledge of their structure and regulation. By considering the tools available and selected examples, this article attempts to assess where and how NFA is most likely to have a real impact on plant biotechnology.

Mathematical modeling of plant metabolism-from reconstruction to prediction

Due to their sessile lifestyle, plants are exposed to a large set of environmental cues. In order to cope with changes in environmental conditions a multitude of complex strategies to regulate metabolism has evolved. The complexity is mainly attributed to interlaced regulatory circuits between genes, proteins and metabolites and a high degree of cellular compartmentalization. The genetic model plant Arabidopsis thaliana was intensely studied to characterize adaptive traits to a changing environment. The availability of genetically distinct natural populations has made it an attractive system to study plant-environment interactions. The impact on metabolism caused by changing environmental conditions can be estimated by mathematical approaches and deepens the understanding of complex biological systems. In combination with experimental high-throughput technologies this provides a promising platform to develop in silico models which are not only able to reproduce but also to predict metabolic phenotypes and to allow for the interpretation of plant physiological mechanisms leading to successful adaptation to a changing environment. Here, we provide an overview of mathematical approaches to analyze plant metabolism, with experimental procedures being used to validate their output, and we discuss them in the context of establishing a comprehensive understanding of plant-environment interactions.

FluxMap: a VANTED add-on for the visual exploration of flux distributions in biological networks

BACKGROUND

The quantification of metabolic fluxes is gaining increasing importance in the analysis of the metabolic behavior of biological systems such as organisms, tissues or cells. Various methodologies (wetlab or drylab) result in sets of fluxes which require an appropriate visualization for interpretation by scientists. The visualization of flux distributions is a necessary prerequisite for intuitive flux data exploration in the context of metabolic networks.

RESULTS

We present FluxMap, a tool for the advanced visualization and exploration of flux data in the context of metabolic networks. The template-based flux data import assigns flux values and optional quality parameters (e. g. the confidence interval) to biochemical reactions. It supports the discrimination between mass and substance fluxes, such as C- or N-fluxes. After import, flux data mapping and network-based visualization allow the interactive exploration of the dataset. Various visualization options enable the user to adapt layout and network representation according to individual purposes.

CONCLUSIONS

The Vanted add-on FluxMap comprises a comprehensive set of functionalities for visualization and advanced visual exploration of flux distributions in biological networks. It is available as a Java open source tool from http://www.vanted.org/fluxmap.

Dynamic regulatory on/off minimization for biological systems under internal temporal perturbations

Background

Flux balance analysis (FBA) together with its extension, dynamic FBA, have proven instrumental for analyzing the robustness and dynamics of metabolic networks by employing only the stoichiometry of the included reactions coupled with adequately chosen objective function. In addition, under the assumption of minimization of metabolic adjustment, dynamic FBA has recently been employed to analyze the transition between metabolic states.

Results

Here, we propose a suite of novel methods for analyzing the dynamics of (internally perturbed) metabolic networks and for quantifying their robustness with limited knowledge of kinetic parameters. Following the biochemically meaningful premise that metabolite concentrations exhibit smooth temporal changes, the proposed methods rely on minimizing the significant fluctuations of metabolic profiles to predict the time-resolved metabolic state, characterized by both fluxes and concentrations. By conducting a comparative analysis with a kinetic model of the Calvin-Benson cycle and a model of plant carbohydrate metabolism, we demonstrate that the principle of regulatory on/off minimization coupled with dynamic FBA can accurately predict the changes in metabolic states.

Conclusions

Our methods outperform the existing dynamic FBA-based modeling alternatives, and could help in revealing the mechanisms for maintaining robustness of dynamic processes in metabolic networks over time.

Kinetic modelling of plant metabolic pathways

This paper provides a review of kinetic modelling of plant metabolic pathways as a tool for analysing their control and regulation. An overview of different modelling strategies is presented, starting with those approaches that only require a knowledge of the network stoichiometry; these are referred to as structural. Flux-balance analysis, metabolic flux analysis using isotope labelling, and elementary mode analysis are briefly mentioned as three representative examples. The main focus of this paper, however, is a discussion of kinetic modelling, which requires, in addition to the stoichiometry, a knowledge of the kinetic properties of the constituent pathway enzymes. The different types of kinetic modelling analysis, namely time-course simulation, steady-state analysis, and metabolic control analysis, are explained in some detail. An overview is presented of strategies for obtaining model parameters, as well as software tools available for simulation of such models. The kinetic modelling approach is exemplified with discussion of three models from the general plant physiology literature. With the aid of kinetic modelling it is possible to perform a control analysis of a plant metabolic system, to identify potential targets for biotechnological manipulation, as well as to ascertain the regulatory importance of different enzymes (including isoforms of the same enzyme) in a pathway. Finally, a framework is presented for extending metabolic models to the whole-plant scale by linking biochemical reactions with diffusion and advective flow through the phloem. Future challenges include explicit modelling of subcellular compartments, as well as the integration of kinetic models on the different levels of the cellular and organizational hierarchy.

Model-based confirmation of alternative substrates of mitochondrial electron transport chain

Discrimination of metabolic models based on high throughput metabolomics data, reflecting various internal and external perturbations, is essential for identifying the components that contribute to the emerging behavior of metabolic processes. Here, we investigate 12 different models of the mitochondrial electron transport chain (ETC) in Arabidopsis thaliana during dark-induced senescence in order to elucidate the alternative substrates to this metabolic pathway. Our findings demonstrate that the coupling of the proposed computational approach, based on dynamic flux balance analysis, with time-resolved metabolomics data results in model-based confirmations of the hypotheses that, during dark-induced senescence in Arabidopsis, (i) under conditions where the main substrate for the ETC are not fully available, isovaleryl-CoA dehydrogenase and 2-hydroxyglutarate dehydrogenase are able to donate electrons to the ETC, (ii) phytanoyl-CoA does not act even as an indirect substrate of the electron transfer flavoprotein/electron-transfer flavoprotein:ubiquinone oxidoreductase complex, and (iii) the mitochondrial γ-aminobutyric acid transporter has functional significance in maintaining mitochondrial metabolism. Our study provides a basic framework for future in silico studies of alternative pathways in mitochondrial metabolism under extended darkness whereby the role of its components can be computationally discriminated based on available molecular profile data.

Relative and accurate measurement of protein abundance using 15N stable isotope labeling in Arabidopsis (SILIA)

In the quantitative proteomic studies, numerous in vitro and in vivo peptide labeling strategies have been successfully applied to measure differentially regulated protein and peptide abundance. These approaches have been proven to be versatile and repeatable in biological discoveries. (15)N metabolic labeling is one of these widely adopted and economical methods. However, due to the differential incorporation rates of (15)N or (14)N, the labeling results produce imperfectly matched isotopic envelopes between the heavy and light nitrogen-labeled peptides. In the present study, we have modified the solid Arabidopsis growth medium to standardize the (15)N supply, which led to a uniform incorporation of (15)N into the whole plant protein complement. The incorporation rate (97.43±0.11%) of (15)N into (15)N-coded peptides was determined by correlating the intensities of peptide ions with the labeling efficiencies according to Gaussian distribution. The resulting actual incorporation rate (97.44%) and natural abundance of (15)N/(14)N-coded peptides are used to re-calculate the intensities of isotopic envelopes of differentially labeled peptides, respectively. A modified (15)N/(14)N stable isotope labeling strategy, SILIA, is assessed and the results demonstrate that this approach is able to differentiate the fold change in protein abundance down to 10%. The machine dynamic range limitation and purification step will make the precursor ion ratio deriving from the actual ratio fold change. It is suggested that the differentially mixed (15)N-coded and (14)N-coded plant protein samples that are used to establish the protein abundance standard curve should be prepared following a similar protein isolation protocol used to isolate the proteins to be quantitated.

The multiplicity of hairy root cultures: prolific possibilities

Hairy root cultures (HRCs), induced by Agrobacterium rhizogenes infection, have been established from a wide variety of plant species. HRCs accumulate phytochemicals to levels comparable to that of intact plants and are usually stable in their biosynthetic capacity. When optimized for liquid cultures, hairy roots can be grown in industrial-scale bioreactors providing a convenient, abundant and sustainable source of phytochemicals. Due to their ease of propagation and growth in confined environments, HRCs have also been used in recent years in the synthesis of recombinant therapeutic proteins, especially those that have been challenging to express in bacteria, yeast and mammalian expression systems. Although phytochemicals are recognized for their important roles in plant and human health, large gaps still exist in understanding how phytochemicals (in particular, secondary/specialized metabolites) are synthesized in plants. This review presents recent developments and findings in phytochemical and recombinant protein production, as well as new revelations in gene discovery and biochemical pathway elucidation, by the utilization of HRCs. Although many challenges still exist for industrial applications of HRCs, the immediate future of this diverse system, especially for the bench-side scientists, is still found to be promising and abounding in possibilities.

Quantitative measurement of phosphopeptides and proteins via stable isotope labeling in Arabidopsis and functional phosphoproteomic strategies

Protein phosphorylation is one type of posttranslational modification, which regulates a large number of cellular processes in plant cells. As an emerging powerful biotechnology that integrates all aspects of advantages from mass spectrometry, bioinformatics, and genomics, phosphoproteomics offers us an unprecedented high-throughput methodology with high sensitivity and dashing speed in identifying a large complement of phosphoproteins from plant cells within a relatively short period of time. Needless to say, phosphoproteomics has become an integral portion of life sciences, which penetrates various research disciplines of biology, agriculture, and forestry and irreversibly changes the way by which plant scientists study biological problems.Because phosphorylation/dephosphorylation of protein is dynamic in cells and the amount of phosphoproteins is low, the preservation of a phosphor group onto phosphosite throughout protein purification as well as enrichment of these phosphoproteins during purification has become a serious technical issue. To overcome difficulties commonly associated with phosphoprotein isolation, phosphopeptides' enrichment, and mass spectrometry analysis, we have developed a urea-based phosphoprotein purification protocol for plants, which instantly denatures plant proteins once the total cell content comes into contact with the UEB solution. To measure the alteration of phosphorylation on a phosphosite using mass spectrometer, an in vivo (15)N metabolic labeling method (SILIA, i.e., stable isotope labeling in Arabidopsis) has been developed and applied for Arabidopsis differential phosphoproteomics. Thus far, hundreds of signaling-specific phosphoproteins have been identified using both label-free and (15)N-labeled differential phosphoproteomic approach. The phosphoproteomics has allowed us to identify a number of signaling components mediating plant cell signaling in Arabidopsis. It is envisaged that a huge number of phosphosites will continue to be uncovered from phosphoproteomics in the near future, which will become instrumental for the development of plant phosphor-relay networks and molecular systems biology.

Central metabolic fluxes in the endosperm of developing maize seeds and their implications for metabolic engineering

¹⁴C labeling experiments performed with kernel cultures showed that developing maize endosperm is more efficient than other non-photosynthetic tissues such as sunflower and maize embryos at converting maternally supplied substrates into biomass. To characterize the metabolic fluxes in endosperm, maize kernels were labeled to isotopic steady state using ¹³C-labeled glucose. The resultant labeling in free metabolites and biomass was analyzed by NMR and GC-MS. After taking into account the labeling of substrates supplied by the metabolically active cob, the fluxes through central metabolism were quantified by computer-aided modeling. The flux map indicates that 51-69% of the ATP produced is used for biomass synthesis and up to 47% is expended in substrate cycling. These findings point to potential engineering targets for improving yield and increasing oil contents by, respectively, reducing substrate cycling and increasing the commitment of plastidic carbon into fatty acid synthesis at the level of pyruvate kinase.

Quantifying the labeling and the levels of plant cell wall precursors using ion chromatography tandem mass spectrometry

The biosynthesis of cell wall polymers involves enormous fluxes through central metabolism that are not fully delineated and whose regulation is poorly understood. We have established and validated a liquid chromatography tandem mass spectrometry method using multiple reaction monitoring mode to separate and quantify the levels of plant cell wall precursors. Target analytes were identified by their parent/daughter ions and retention times. The method allows the quantification of precursors at low picomole quantities with linear responses up to the nanomole quantity range. When applying the technique to Arabidopsis (Arabidopsis thaliana) T87 cell cultures, 16 hexose-phosphates (hexose-Ps) and nucleotide-sugars (NDP-sugars) involved in cell wall biosynthesis were separately quantified. Using hexose-P and NDP-sugar standards, we have shown that hot water extraction allows good recovery of the target metabolites (over 86%). This method is applicable to quantifying the levels of hexose-Ps and NDP-sugars in different plant tissues, such as Arabidopsis T87 cells in culture and fenugreek (Trigonella foenum-graecum) endosperm tissue, showing higher levels of galacto-mannan precursors in fenugreek endosperm. In Arabidopsis cells incubated with [U-(13)C(Fru)]sucrose, the method was used to track the labeling pattern in cell wall precursors. As the fragmentation of hexose-Ps and NDP-sugars results in high yields of [PO(3)](-)/or [H(2)PO(4)](-) ions, mass isotopomers can be quantified directly from the intensity of selected tandem mass spectrometry transitions. The ability to directly measure (13)C labeling in cell wall precursors makes possible metabolic flux analysis of cell wall biosynthesis based on dynamic labeling experiments.

Mathematical modeling-guided evaluation of biochemical, developmental, environmental, and genotypic determinants of essential oil composition and yield in peppermint leaves

We have previously reported the use of a combination of computational simulations and targeted experiments to build a first generation mathematical model of peppermint (Menthaxpiperita) essential oil biosynthesis. Here, we report on the expansion of this approach to identify the key factors controlling monoterpenoid essential oil biosynthesis under adverse environmental conditions. We also investigated determinants of essential oil biosynthesis in transgenic peppermint lines with modulated essential oil profiles. A computational perturbation analysis, which was implemented to identify the variables that exert prominent control over the outputs of the model, indicated that the essential oil composition should be highly dependent on certain biosynthetic enzyme concentrations [(+)-pulegone reductase and (+)-menthofuran synthase], whereas oil yield should be particularly sensitive to the density and/or distribution of leaf glandular trichomes, the specialized anatomical structures responsible for the synthesis and storage of essential oils. A microscopic evaluation of leaf surfaces demonstrated that the final mature size of glandular trichomes was the same across all experiments. However, as predicted by the perturbation analysis, differences in the size distribution and the total number of glandular trichomes strongly correlated with differences in monoterpenoid essential oil yield. Building on various experimental data sets, appropriate mathematical functions were selected to approximate the dynamics of glandular trichome distribution/density and enzyme concentrations in our kinetic model. Based on a chi2 statistical analysis, simulated and measured essential oil profiles were in very good agreement, indicating that modeling is a valuable tool for guiding metabolic engineering efforts aimed at improving essential oil quality and quantity.

RNAi suppression of Arogenate Dehydratase1 reveals that phenylalanine is synthesized predominantly via the arogenate pathway in petunia petals

l-Phe, a protein building block and precursor of numerous phenolic compounds, is synthesized from prephenate via an arogenate and/or phenylpyruvate route in which arogenate dehydratase (ADT) or prephenate dehydratase, respectively, plays a key role. Here, we used Petunia hybrida flowers, which are rich in Phe-derived volatiles, to determine the biosynthetic routes involved in Phe formation in planta. Of the three identified petunia ADTs, expression of ADT1 was the highest in petunia petals and positively correlated with endogenous Phe levels throughout flower development. ADT1 showed strict substrate specificity toward arogenate, although with the lowest catalytic efficiency among the three ADTs. ADT1 suppression via RNA interference in petunia petals significantly reduced ADT activity, levels of Phe, and downstream phenylpropanoid/benzenoid volatiles. Unexpectedly, arogenate levels were unaltered, while shikimate and Trp levels were decreased in transgenic petals. Stable isotope labeling experiments showed that ADT1 suppression led to downregulation of carbon flux toward shikimic acid. However, an exogenous supply of shikimate bypassed this negative regulation and resulted in elevated arogenate accumulation. Feeding with shikimate also led to prephenate and phenylpyruvate accumulation and a partial recovery of the reduced Phe level in transgenic petals, suggesting that the phenylpyruvate route can also operate in planta. These results provide genetic evidence that Phe is synthesized predominantly via arogenate in petunia petals and uncover a novel posttranscriptional regulation of the shikimate pathway.

Metabolomics for functional genomics, systems biology, and biotechnology

Metabolomics now plays a significant role in fundamental plant biology and applied biotechnology. Plants collectively produce a huge array of chemicals, far more than are produced by most other organisms; hence, metabolomics is of great importance in plant biology. Although substantial improvements have been made in the field of metabolomics, the uniform annotation of metabolite signals in databases and informatics through international standardization efforts remains a challenge, as does the development of new fields such as fluxome analysis and single cell analysis. The principle of transcript and metabolite cooccurrence, particularly transcriptome coexpression network analysis, is a powerful tool for decoding the function of genes in Arabidopsis thaliana. This strategy can now be used for the identification of genes involved in specific pathways in crops and medicinal plants. Metabolomics has gained importance in biotechnology applications, as exemplified by quantitative loci analysis, prediction of food quality, and evaluation of genetically modified crops. Systems biology driven by metabolome data will aid in deciphering the secrets of plant cell systems and their application to biotechnology.

Analysis of metabolic flux phenotypes for two Arabidopsis mutants with severe impairment in seed storage lipid synthesis

Major storage reserves of Arabidopsis (Arabidopsis thaliana) seeds are triacylglycerols (seed oils) and proteins. Seed oil content is severely reduced for the regulatory mutant wrinkled1 (wri1-1; At3g54320) and for a double mutant in two isoforms of plastidic pyruvate kinase (pkpbeta(1)pkpalpha; At5g52920 and At3g22960). Both already biochemically well-characterized mutants were now studied by (13)C metabolic flux analysis of cultured developing embryos based on comparison with their respective genetic wild-type backgrounds. For both mutations, in seeds as well as in cultured embryos, the oil fraction was strongly reduced while the fractions of proteins and free metabolites increased. Flux analysis in cultured embryos revealed changes in nutrient uptakes and fluxes into biomass as well as an increase in tricarboxylic acid cycle activity for both mutations. While in both wild types plastidic pyruvate kinase (PK(p)) provides most of the pyruvate for plastidic fatty acid synthesis, the flux through PK(p) is reduced in pkpbeta(1)pkpalpha by 43% of the wild-type value. In wri1-1, PK(p) flux is even more reduced (by 82%), although the genes PKpbeta(1) and PKpalpha are still expressed. Along a common paradigm of metabolic control theory, it is hypothesized that a large reduction in PK(p) enzyme activity in pkpbeta(1)pkpalpha has less effect on PK(p) flux than multiple smaller reductions in glycolytic enzymes in wri1-1. In addition, only in the wri1-1 mutant is the large reduction in PK(p) flux compensated in part by an increased import of cytosolic pyruvate and by plastidic malic enzyme. No such limited compensatory bypass could be observed in pkpbeta(1)pkpalpha.

Metabolic flux analysis in plants: coping with complexity

Theory and experience in metabolic engineering both show that metabolism operates at the network level. In plants, this complexity is compounded by a high degree of compartmentation and the synthesis of a very wide array of secondary metabolic products. A further challenge to understanding and predicting plant metabolic function is posed by our ignorance about the structure of metabolic networks even in well-studied systems. Metabolic flux analysis (MFA) provides tools to measure and model the functioning of metabolism, and is making significant contributions to coping with their complexity. This review gives an overview of different MFA approaches, the measurements required to implement them and the information they yield. The application of MFA methods to plant systems is then illustrated by several examples from the recent literature. Next, the challenges that plant metabolism poses for MFA are discussed together with ways that these can be addressed. Lastly, new developments in MFA are described that can be expected to improve the range and reliability of plant MFA in the coming years.

Bidirectionality and compartmentation of metabolic fluxes are revealed in the dynamics of isotopomer networks

Isotope labeling is one of the few methods of revealing the in vivo bidirectionality and compartmentalization of metabolic fluxes within metabolic networks. We argue that a shift from steady state to dynamic isotopomer analysis is required to deal with these cellular complexities and provide a review of dynamic studies of compartmentalized energy fluxes in eukaryotic cells including cardiac muscle, plants, and astrocytes. Knowledge of complex metabolic behaviour on a molecular level is prerequisite for the intelligent design of genetically modified organisms able to realize their potential of revolutionizing food, energy, and pharmaceutical production. We describe techniques to explore the bidirectionality and compartmentalization of metabolic fluxes using information contained in the isotopic transient, and discuss the integration of kinetic models with MFA. The flux parameters of an example metabolic network were optimized to examine the compartmentalization of metabolites and and the bidirectionality of fluxes in the TCA cycle of Saccharomyces uvarum for steady-state respiratory growth.