Mathematical modeling of plant metabolic pathways

Model-assisted analysis for tuning anthocyanin composition in grape berries

Anthocyanin composition is responsible for the red colour of grape berries and wines, and contributes to their organoleptic quality. However, anthocyanin biosynthesis is under genetic, developmental and environmental regulation, making its targeted fine-tuning challenging. We constructed a mechanistic model to simulate the dynamics of anthocyanin composition throughout grape ripening in Vitis vinifera, employing a consensus anthocyanin biosynthesis pathway. The model was calibrated and validated using six datasets from eight cultivars and 37 growth conditions. Tuning the transformation and degradation parameters allowed us to accurately simulate the accumulation process of each individual anthocyanin under different environmental conditions. The model parameters were robust across environments for each genotype. The coefficients of determination (R2) for the simulated versus observed values for the six datasets ranged from 0.92 to 0.99, while the relative root mean square errors (RRMSEs) were between 16.8 and 42.1 %. The leave-one-out cross-validation for three datasets showed R2 values of 0.99, 0.96 and 0.91, and RRMSE values of 28.8, 32.9 and 26.4 %, respectively, suggesting a high prediction quality of the model. Model analysis showed that the anthocyanin profiles of diverse genotypes are relatively stable in response to parameter perturbations. Virtual experiments further suggested that targeted anthocyanin profiles may be reached by manipulating a minimum of three parameters, in a genotype-dependent manner. This model presents a promising methodology for characterizing the temporal progression of anthocyanin composition, while also offering a logical foundation for bioengineering endeavours focused on precisely adjusting the anthocyanin composition of grapes.

Rethinking the potential productivity of crassulacean acid metabolism by integrating metabolic dynamics with shoot architecture, using the example of Agave tequilana

Terrestrial CAM plants typically occur in hot semiarid regions, yet can show high crop productivity under favorable conditions. To achieve a more mechanistic understanding of CAM plant productivity, a biochemical model of diel metabolism was developed and integrated with 3-D shoot morphology to predict the energetics of light interception and photosynthetic carbon assimilation. Using Agave tequilana as an example, this biochemical model faithfully simulated the four diel phases of CO2 and metabolite dynamics during the CAM rhythm. After capturing the 3-D form over an 8-yr production cycle, a ray-tracing method allowed the prediction of the light microclimate across all photosynthetic surfaces. Integration with the biochemical model thereby enabled the simulation of plant and stand carbon uptake over daily and annual courses. The theoretical maximum energy conversion efficiency of Agave spp. is calculated at 0.045-0.049, up to 7% higher than for C3 photosynthesis. Actual light interception, and biochemical and anatomical limitations, reduced this to 0.0069, or 15.6 Mg ha-1  yr-1 dry mass annualized over an 8-yr cropping cycle, consistent with observation. This is comparable to the productivity of many C3 crops, demonstrating the potential of CAM plants in climates where little else may be grown while indicating strategies that could raise their productivity.

Enhancing control systems of higher plant culture chambers via multilevel structural mechanistic modelling

Modelling higher plant growth is of strategic interest for modern agriculture as well as for the development of bioregenerative life support systems for space applications, where crop growth is expected to play an essential role. The capability of constraint-based metabolic models to cope the diel dynamics of plants growth is integrated into a multilevel modelling approach including mass and energy transfer and enzyme kinetics. Lactuca sativa is used as an exemplary crop to validate, with experimental data, the approach presented as well as to design a novel model-based predictive control strategy embedding metabolic information. The proposed modelling strategy predicts with high accuracy the dynamics of gas exchange and the distribution of fluxes in the metabolic network whereas the control architecture presented can be useful to manage higher plants chambers and open new ways of merging metabolome and control algorithms.

Non-linearity of Metabolic Pathways Critically Influences the Choice of Machine Learning Model

The use of machine learning (ML) in life sciences has gained wide interest over the past years, as it speeds up the development of high performing models. Important modeling tools in biology have proven their worth for pathway design, such as mechanistic models and metabolic networks, as they allow better understanding of mechanisms involved in the functioning of organisms. However, little has been done on the use of ML to model metabolic pathways, and the degree of non-linearity associated with them is not clear. Here, we report the construction of different metabolic pathways with several linear and non-linear ML models. Different types of data are used; they lead to the prediction of important biological data, such as pathway flux and final product concentration. A comparison reveals that the data features impact model performance and highlight the effectiveness of non-linear models (e.g., QRF: RMSE = 0.021 nmol·min-1 and R2 = 1 vs. Bayesian GLM: RMSE = 1.379 nmol·min-1 R2 = 0.823). It turns out that the greater the degree of non-linearity of the pathway, the better suited a non-linear model will be. Therefore, a decision-making support for pathway modeling is established. These findings generally support the hypothesis that non-linear aspects predominate within the metabolic pathways. This must be taken into account when devising possible applications of these pathways for the identification of biomarkers of diseases (e.g., infections, cancer, neurodegenerative diseases) or the optimization of industrial production processes.

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.

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.

Approximating the stabilization of cellular metabolism by compartmentalization

Biochemical regulation in compartmentalized metabolic networks is highly complex and non-intuitive. This is particularly true for cells of higher plants showing one of the most compartmentalized cellular structures across all kingdoms of life. The interpretation and testable hypothesis generation from experimental data on such complex systems is a challenging step in biological research and biotechnological applications. While it is known that subcellular compartments provide defined reaction spaces within a cell allowing for the tight coordination of complex biochemical reaction sequences, its role in the coordination of metabolic signals during metabolic reprogramming due to environmental fluctuations is less clear. In the present study, we numerically analysed the effects of environmental fluctuations in a subcellular metabolic network with regard to the stability of an experimentally observed steady state in the genetic model plant Arabidopsis thaliana. Applying a method for kinetic parameter normalization, several millions of probable enzyme kinetic parameter constellations were simulated and evaluated with regard to the stability information of the metabolic homeostasis. Information about the stability of the metabolic steady state was derived from real parts of eigenvalues of Jacobian matrices. Our results provide evidence for a differential stabilizing contribution of different subcellular compartments. We could identify stabilizing and destabilizing network components which we could classify according to their subcellular localization. The findings prove that a highly dynamic interplay between intracellular compartments is preliminary for an efficient stabilization of a metabolic homeostasis after environmental perturbation. Further, our results provide evidence that feedback-inhibition originating from the cytosol and plastid seem to stabilize the sucrose homeostasis more efficiently than vacuolar control. In summary, our results indicate stabilizing and destabilizing network components in context of their subcellular organization.

Grassland species differentially regulate proline concentrations under future climate conditions: an integrated biochemical and modelling approach

Proline (Pro) is a versatile metabolite playing a role in the protection of plants against environmental stresses. To gain a deeper understanding of the regulation of Pro metabolism under predicted future climate conditions, including drought stress, elevated temperature and CO2 , we combined measurements in contrasting grassland species (two grasses and two legumes) at multiple organisational levels, that is, metabolite concentrations, enzyme activities and gene expression. Drought stress (D) activates Pro biosynthesis and represses its catabolism, and elevated temperature (DT) further elevated its content. Elevated CO2 attenuated the DT effect on Pro accumulation. Computational pathway control analysis allowed a mechanistic understanding of the regulatory changes in Pro metabolism. This analysis indicates that the experimentally observed coregulation of multiple enzymes is more effective in modulating Pro concentrations than regulation of a single step. Pyrroline-5-carboxylate synthetase (P5CS) and pyrroline-5-carboxylate reductase (P5CR) play a central role in grasses (Lolium perenne, Poa pratensis), and arginase (ARG), ornithine aminotransferase (OAT) and P5CR play a central role in legumes (Medicago lupulina, Lotus corniculatus). Different strategies in the regulation of Pro concentrations under stress conditions were observed. In grasses the glutamate pathway is activated predominantly, and in the legumes the ornithine pathway, possibly related to differences in N-nutritional status.

ENISI SDE: A New Web-Based Tool for Modeling Stochastic Processes

Modeling and simulations approaches have been widely used in computational biology, mathematics, bioinformatics and engineering to represent complex existing knowledge and to effectively generate novel hypotheses. While deterministic modeling strategies are widely used in computational biology, stochastic modeling techniques are not as popular due to a lack of user-friendly tools. This paper presents ENISI SDE, a novel web-based modeling tool with stochastic differential equations. ENISI SDE provides user-friendly web user interfaces to facilitate adoption by immunologists and computational biologists. This work provides three major contributions: (1) discussion of SDE as a generic approach for stochastic modeling in computational biology; (2) development of ENISI SDE, a web-based user-friendly SDE modeling tool that highly resembles regular ODE-based modeling; (3) applying ENISI SDE modeling tool through a use case for studying stochastic sources of cell heterogeneity in the context of CD4+ T cell differentiation. The CD4+ T cell differential ODE model has been published [8] and can be downloaded from biomodels.net. The case study reproduces a biological phenomenon that is not captured by the previously published ODE model and shows the effectiveness of SDE as a stochastic modeling approach in biology in general and immunology in particular and the power of ENISI SDE.

A systems biology approach toward understanding seed composition in soybean

BACKGROUND

The molecular, biochemical, and genetic mechanisms that regulate the complex metabolic network of soybean seed development determine the ultimate balance of protein, lipid, and carbohydrate stored in the mature seed. Many of the genes and metabolites that participate in seed metabolism are unknown or poorly defined; even more remains to be understood about the regulation of their metabolic networks. A global omics analysis can provide insights into the regulation of seed metabolism, even without a priori assumptions about the structure of these networks.

RESULTS

With the future goal of predictive biology in mind, we have combined metabolomics, transcriptomics, and metabolic flux technologies to reveal the global developmental and metabolic networks that determine the structure and composition of the mature soybean seed. We have coupled this global approach with interactive bioinformatics and statistical analyses to gain insights into the biochemical programs that determine soybean seed composition. For this purpose, we used Plant/Eukaryotic and Microbial Metabolomics Systems Resource (PMR, http://www.metnetdb.org/pmr, a platform that incorporates metabolomics data to develop hypotheses concerning the organization and regulation of metabolic networks, and MetNet systems biology tools http://www.metnetdb.org for plant omics data, a framework to enable interactive visualization of metabolic and regulatory networks.

CONCLUSIONS

This combination of high-throughput experimental data and bioinformatics analyses has revealed sets of specific genes, genetic perturbations and mechanisms, and metabolic changes that are associated with the developmental variation in soybean seed composition. Researchers can explore these metabolomics and transcriptomics data interactively at PMR.

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.

Application of metabolic flux analysis to plants

This volume compiles a series of chapters that cover the major aspects of plant metabolic flux analysis, such as but not limited to labeling of plant material, acquisition of labeling data, mathematical modeling of metabolic network at the cell, tissue, and plant level. A short revue, including methodological points and applications of flux analysis to plants, is presented in this introductory chapter.

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.

SS-mPMG and SS-GA: tools for finding pathways and dynamic simulation of metabolic networks

Metabolomics analysis tools can provide quantitative information on the concentration of metabolites in an organism. In this paper, we propose the minimum pathway model generator tool for simulating the dynamics of metabolite concentrations (SS-mPMG) and a tool for parameter estimation by genetic algorithm (SS-GA). SS-mPMG can extract a subsystem of the metabolic network from the genome-scale pathway maps to reduce the complexity of the simulation model and automatically construct a dynamic simulator to evaluate the experimentally observed behavior of metabolites. Using this tool, we show that stochastic simulation can reproduce experimentally observed dynamics of amino acid biosynthesis in Arabidopsis thaliana. In this simulation, SS-mPMG extracts the metabolic network subsystem from published databases. The parameters needed for the simulation are determined using a genetic algorithm to fit the simulation results to the experimental data. We expect that SS-mPMG and SS-GA will help researchers to create relevant metabolic networks and carry out simulations of metabolic reactions derived from metabolomics data.

Network analysis: tackling complex data to study plant metabolism

Incomplete knowledge of biochemical pathways makes the holistic description of plant metabolism a non-trivial undertaking. Sensitive analytical platforms, which are capable of accurately quantifying the levels of the various molecular entities of the cell, can assist in tackling this task. However, the ever-increasing amount of high-throughput data, often from multiple technologies, requires significant computational efforts for integrative analysis. Here we introduce the application of network analysis to study plant metabolism and describe the construction and analysis of correlation-based networks from (time-resolved) metabolomics data. By investigating the interactions between metabolites, network analysis can help to interpret complex datasets through the identification of key network components. The relationship between structural and biological roles of network components can be evaluated and employed to aid metabolic engineering.

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.

Molecular modeling of metabolism for allergen-free low linoleic acid peanuts

It is necessary to eliminate linoleic acid and allergenic arachins from peanuts for good health reasons. Virginia-type peanuts, harvested from plots treated with mineral salts combinations that mimic the subunit compositions of glutamate dehydrogenase (GDH) were analyzed for fatty acid and arachin compositions by HPLC and polyacrylamide gel electrophoresis, respectively. Fatty acid desaturase and arachin encoding mRNAs were analyzed by Northern hybridization using the homologous RNAs synthesized by peanut GDH as probes. There were 70–80 % sequence similarities between the GDH-synthesized RNAs and the mRNAs encoding arachins, fatty acid desaturases, glutamate synthase, and nitrate reductase, which similarities induced permutation of the metabolic pathways at the mRNA level. Modeling of mRNAs showed there were 210, 3,150, 1,260, 2,520, and 4,200 metabolic permutations in the control, NPKS-, NS-, Pi-, NH₄Cl-, and PK-treated peanuts, respectively. The mRNA cross-talks decreased the arachin to almost zero percent in the NPKS- and PK-treated peanuts, and linoleate to ∼18 % in the PK-treated peanut. The mRNA cross-talks may account for the vastly reported environmentally induced variability in the linoleate contents of peanut genotypes. These results have quantitatively unified molecular biology and metabolic pathways into one simple biotechnology for optimizing peanut quality and may encourage small-scale industry to produce arachin-free low linoleate peanuts.

Elements of a dynamic systems model of canopy photosynthesis

Improving photosynthesis throughout the full canopy rather than photosynthesis of only the top leaves of the canopy is central to improving crop yields. Many canopy photosynthesis models have been developed from physiological and ecological perspectives, however most do not consider heterogeneities of microclimatic factors inside a canopy, canopy dynamics and associated energetics, or competition among different plants, and most models lack a direct linkage to molecular processes. Here we described the rationale, elements, and approaches necessary to build a dynamic systems model of canopy photosynthesis. A systems model should integrate metabolic processes including photosynthesis, respiration, nitrogen metabolism, resource re-mobilization and photosynthate partitioning with canopy level light, CO(2), water vapor distributions and heat exchange processes. In so doing a systems-based canopy photosynthesis model will enable studies of molecular ecology and dramatically improve our insight into engineering crops for improved canopy photosynthetic CO(2) uptake, resource use efficiencies and yields.

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.

A survey of carbon fixation pathways through a quantitative lens

While the reductive pentose phosphate cycle is responsible for the fixation of most of the carbon in the biosphere, it has several natural substitutes. In fact, due to the characterization of three new carbon fixation pathways in the last decade, the diversity of known metabolic solutions for autotrophic growth has doubled. In this review, the different pathways are analysed and compared according to various criteria, trying to connect each of the different metabolic alternatives to suitable environments or metabolic goals. The different roles of carbon fixation are discussed; in addition to sustaining autotrophic growth it can also be used for energy conservation and as an electron sink for the recycling of reduced electron carriers. Our main focus in this review is on thermodynamic and kinetic aspects, including thermodynamically challenging reactions, the ATP requirement of each pathway, energetic constraints on carbon fixation, and factors that are expected to limit the rate of the pathways. Finally, possible metabolic structures of yet unknown carbon fixation pathways are suggested and discussed.

Metabolomic approaches toward understanding nitrogen metabolism in plants

Plants can assimilate inorganic nitrogen (N) sources to organic N such as amino acids. N is the most important of the mineral nutrients required by plants and its metabolism is tightly coordinated with carbon (C) metabolism in the fundamental processes that permit plant growth. Increased understanding of N regulation may provide important insights for plant growth and improvement of quality of crops and vegetables because N as well as C metabolism are fundamental components of plant life. Metabolomics is a global biochemical approach useful to study N metabolism because metabolites not only reflect the ultimate phenotypes (traits), but can mediate transcript levels as well as protein levels directly and/or indirectly under different N conditions. This review outlines analytical and bioinformatic techniques particularly used to perform metabolomics for studying N metabolism in higher plants. Examples are used to illustrate the application of metabolomic techniques to the model plants Arabidopsis and rice, as well as other crops and vegetables.

A kinetic model describes metabolic response to perturbations and distribution of flux control in the benzenoid network of Petunia hybrida

In recent years there has been much interest in the genetic enhancement of plant metabolism; however, attempts at genetic modification are often unsuccessful due to an incomplete understanding of network dynamics and their regulatory properties. Kinetic modeling of plant metabolic networks can provide predictive information on network control and response to genetic perturbations, which allow estimation of flux at any concentration of intermediate or enzyme in the system. In this research, a kinetic model of the benzenoid network was developed to simulate whole network responses to different concentrations of supplied phenylalanine (Phe) in petunia flowers and capture flux redistributions caused by genetic manipulations. Kinetic parameters were obtained by network decomposition and non-linear least squares optimization of data from petunia flowers supplied with either 75 or 150 mm(2)H(5)-Phe. A single set of kinetic parameters simultaneously accommodated labeling and pool size data obtained for all endogenous and emitted volatiles at the two concentrations of supplied (2)H(5)-Phe. The generated kinetic model was validated using flowers from transgenic petunia plants in which benzyl CoA:benzyl alcohol/phenylethanol benzoyltransferase (BPBT) was down-regulated via RNAi. The determined in vivo kinetic parameters were used for metabolic control analysis, in which flux control coefficients were calculated for fluxes around the key branch point at Phe and revealed that phenylacetaldehyde synthase activity is the primary controlling factor for the phenylacetaldehyde branch of the benzenoid network. In contrast, control of flux through the beta-oxidative and non-beta-oxidative pathways is highly distributed.

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.

Flux balance analysis of barley seeds: a computational approach to study systemic properties of central metabolism

The accumulation of storage compounds is an important aspect of cereal seed metabolism. Due to the agronomical importance of the storage reserves of starch, protein, and oil, the understanding of storage metabolism is of scientific interest, with practical applications in agronomy and plant breeding. To get insight into storage patterning in developing cereal seed in response to environmental and genetic perturbation, a computational analysis of seed metabolism was performed. A metabolic network of primary metabolism in the developing endosperm of barley (Hordeum vulgare), a model plant for temperate cereals, was constructed that includes 257 biochemical and transport reactions across four different compartments. The model was subjected to flux balance analysis to study grain yield and metabolic flux distributions in response to oxygen depletion and enzyme deletion. In general, the simulation results were found to be in good agreement with the main biochemical properties of barley seed storage metabolism. The predicted growth rate and the active metabolic pathway patterns under anoxic, hypoxic, and aerobic conditions predicted by the model were in accordance with published experimental results. In addition, the model predictions gave insight into the potential role of inorganic pyrophosphate metabolism to maintain seed metabolism under oxygen deprivation.

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.

Metabolic flux analysis in plants: from intelligent design to rational engineering

Metabolic flux analysis (MFA) is a rapidly developing field concerned with the quantification and understanding of metabolism at the systems level. The application of MFA has produced detailed maps of flow through metabolic networks of a range of plant systems. These maps represent detailed metabolic phenotypes, contribute significantly to our understanding of metabolism in plants, and have led to the discovery of new metabolic routes. The presentation of thorough statistical evaluation with current flux maps has set a new standard for the quality of quantitative flux studies. In microbial systems, powerful methods have been developed for the reconstruction of metabolic networks from genomic and transcriptomic data, pathway analysis, and predictive modeling. This review brings together the recent developments in quantitative MFA and predictive modeling. The application of predictive tools to high quality flux maps in particular promises to be important in the rational metabolic engineering of plants.

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.

Determination of metabolic fluxes in a non-steady-state system

Estimation of fluxes through metabolic networks from redistribution patterns of (13)C has become a well developed technique in recent years. However, the approach is currently limited to systems at metabolic steady-state; dynamic changes in metabolic fluxes cannot be assessed. This is a major impediment to understanding the behaviour of metabolic networks, because steady-state is not always experimentally achievable and a great deal of information about the control hierarchy of the network can be derived from the analysis of flux dynamics. To address this issue, we have developed a method for estimating non-steady-state fluxes based on the mass-balance of mass isotopomers. This approach allows multiple mass-balance equations to be written for the change in labelling of a given metabolite pool and thereby permits over-determination of fluxes. We demonstrate how linear regression methods can be used to estimate non-steady-state fluxes from these mass balance equations. The approach can be used to calculate fluxes from both mass isotopomer and positional isotopomer labelling information and thus has general applicability to data generated from common spectrometry- or NMR-based analytical platforms. The approach is applied to a GC-MS time-series dataset of (13)C-labelling of metabolites in a heterotrophic Arabidopsis cell suspension culture. Threonine biosynthesis is used to demonstrate that non-steady-state fluxes can be successfully estimated from such data while organic acid metabolism is used to highlight some common issues that can complicate flux estimation. These include multiple pools of the same metabolite that label at different rates and carbon skeleton rearrangements.

Experimental and mathematical approaches to modeling plant metabolic networks

To support their sessile and autotrophic lifestyle higher plants have evolved elaborate networks of metabolic pathways. Dynamic changes in these metabolic networks are among the developmental forces underlying the functional differentiation of organs, tissues and specialized cell types. They are also important in the various interactions of a plant with its environment. Further complexity is added by the extensive compartmentation of the various interconnected metabolic pathways in plants. Thus, although being used widely for assessing the control of metabolic flux in microbes, mathematical modeling approaches that require steady-state approximations are of limited utility for understanding complex plant metabolic networks. However, considerable progress has been made when manageable metabolic subsystems were studied. In this article, we will explain in general terms and using simple examples the concepts underlying stoichiometric modeling (metabolic flux analysis and metabolic pathway analysis) and kinetic approaches to modeling (including metabolic control analysis as a special case). Selected studies demonstrating the prospects of these approaches, or combinations of them, for understanding the control of flux through particular plant pathways are discussed. We argue that iterative cycles of (dry) mathematical modeling and (wet) laboratory testing will become increasingly important for simulating the distribution of flux in plant metabolic networks and deriving rational experimental designs for metabolic engineering efforts.

A transient isotopic labeling methodology for 13C metabolic flux analysis of photoautotrophic microorganisms

Metabolic flux analysis is increasingly recognized as an integral component of systems biology. However, techniques for experimental measurement of system-wide metabolic fluxes in purely photoautotrophic systems (growing on CO(2) as the sole carbon source) have not yet been developed due to the unique problems posed by such systems. In this paper, we demonstrate that an approach that balances positional isotopic distributions transiently is the only route to obtaining system-wide metabolic flux maps for purely autotrophic metabolism. The outlined transient (13)C-MFA methodology enables measurement of fluxes at a metabolic steady-state, while following changes in (13)C-labeling patterns of metabolic intermediates as a function of time, in response to a step-change in (13)C-label input. We use mathematical modeling of the transient isotopic labeling patterns of central intermediates to assess various experimental requirements for photoautotrophic MFA. This includes the need for intracellular metabolite concentration measurements and isotopic labeling measurements as a function of time. We also discuss photobioreactor design and operation in order to measure fluxes under precise environmental conditions. The transient MFA technique can be used to measure and compare fluxes under different conditions of light intensity, nitrogen sources or compare strains with various mutations or gene deletions and additions.

Compartment-specific labeling information in 13C metabolic flux analysis of plants

Metabolic engineering of plants has great potential for the low cost production of chemical feedstocks and novel compounds, but to take full advantage of this potential a better understanding of plant central carbon metabolism is needed. Flux studies define the cellular phenotype of living systems and can facilitate rational metabolic engineering. However the measurements usually made in these analyses are often not sufficient to reliably determine many fluxes that are distributed between different subcellular compartments of eukaryotic cells. We have begun to address this shortcoming by increasing the number and quality of measurements that provide (13)C labeling information from specific compartments within the plant cell. The analysis of fatty acid groups, cell wall components, protein glycans, and starch, using both gas chromatography/mass spectrometry and nuclear magnetic resonance spectroscopy are presented here. Fatty acid labeling determinations are sometimes highly convoluted. Derivatization to butyl amides reduces the errors in isotopomer resolution and quantification, resulting in better determination of fluxes into seed lipid reserves, including both plastidic and cytosolic reactions. While cell walls can account for a third or more of biomass in many seeds, no quantitative cell wall labeling measurements have been reported for plant flux analysis. Hydrolyzing cell wall and derivatizing sugars to the alditol acetates, provides novel labeling information and thereby can improve identification of flux through upper glycolytic intermediates of the cytosol. These strategies improve the quantification of key carbon fluxes in the compartmentalized flux network of plant cells.

Production and engineering of terpenoids in plant cell culture

Terpenoids are a diverse class of natural products that have many functions in the plant kingdom and in human health and nutrition. Their chemical diversity has led to the discovery of over 40,000 different structures, with several classes serving as important pharmaceutical agents, including the anticancer agents paclitaxel (Taxol) and terpenoid-derived indole alkaloids. Many terpenoid compounds are found in low yield from natural sources, so plant cell cultures have been investigated as an alternate production strategy. Metabolic engineering of whole plants and plant cell cultures is an effective tool to both increase terpenoid yield and alter terpenoid distribution for desired properties such as enhanced flavor, fragrance or color. Recent advances in defining terpenoid metabolic pathways, particularly in secondary metabolism, enhanced knowledge concerning regulation of terpenoid accumulation, and application of emerging plant systems biology approaches, have enabled metabolic engineering of terpenoid production. This paper reviews the current state of knowledge of terpenoid metabolism, with a special focus on production of important pharmaceutically active secondary metabolic terpenoids in plant cell cultures. Strategies for defining pathways and uncovering rate-influencing steps in global metabolism, and applying this information for successful terpenoid metabolic engineering, are emphasized.

Phyllotaxis

Phyllotaxis, the regular arrangement of leaves or flowers around a plant stem, is an example of developmental pattern formation and organogenesis. Phyllotaxis is characterized by the divergence angles between the organs, the most common angle being 137.5 degrees , the golden angle. The quantitative aspects of phyllotaxis have stimulated research at the interface between molecular biology, physics and mathematics. This review documents the rich history of different approaches and conflicting hypotheses, and then focuses on recent molecular work that establishes a novel patterning mechanism based on active transport of the plant hormone auxin. Finally, it shows how computer simulations can help to formulate quantitative models that in turn can be tested by experiment. The accumulation of ever increasing amounts of experimental data makes quantitative modeling of interest for many developmental systems.

The metabolic response of heterotrophic Arabidopsis cells to oxidative stress

To cope with oxidative stress, the metabolic network of plant cells must be reconfigured either to bypass damaged enzymes or to support adaptive responses. To characterize the dynamics of metabolic change during oxidative stress, heterotrophic Arabidopsis (Arabidopsis thaliana) cells were treated with menadione and changes in metabolite abundance and (13)C-labeling kinetics were quantified in a time series of samples taken over a 6 h period. Oxidative stress had a profound effect on the central metabolic pathways with extensive metabolic inhibition radiating from the tricarboxylic acid cycle and including large sectors of amino acid metabolism. Sequential accumulation of metabolites in specific pathways indicated a subsequent backing up of glycolysis and a diversion of carbon into the oxidative pentose phosphate pathway. Microarray analysis revealed a coordinated transcriptomic response that represents an emergency coping strategy allowing the cell to survive the metabolic hiatus. Rather than attempt to replace inhibited enzymes, transcripts encoding these enzymes are in fact down-regulated while an antioxidant defense response is mounted. In addition, a major switch from anabolic to catabolic metabolism is signaled. Metabolism is also reconfigured to bypass damaged steps (e.g. induction of an external NADH dehydrogenase of the mitochondrial respiratory chain). The overall metabolic response of Arabidopsis cells to oxidative stress is remarkably similar to the superoxide and hydrogen peroxide stimulons of bacteria and yeast (Saccharomyces cerevisiae), suggesting that the stress regulatory and signaling pathways of plants and microbes may share common elements.