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.     

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.     

Towards kinetic modeling of genome-scale metabolic networks without sacrificing stoichiometric,thermodynamic and physiological constraints

Mathematical modeling is an essential tool for the comprehensive understanding of cell metabolism and its interactions with the environmental and process conditions. Recent developments in the construction and analysis of stoichiometric models made it possible to define limits on steady-state metabolic behavior using flux balance analysis. However, detailed information on enzyme kinetics and enzyme regulation is needed to formulate kinetic models that can accurately capture the dynamic metabolic responses. The use of mechanistic enzyme kinetics is a difficult task due to uncertainty in the kinetic properties of enzymes. Therefore, the majority of recent works considered only mass action kinetics for reactions in metabolic networks. Herein, we applied the optimization and risk analysis of complex living entities (ORACLE) framework and constructed a large-scale mechanistic kinetic model of optimally grown Escherichia coli. We investigated the complex interplay between stoichiometry, thermodynamics, and kinetics in determining the flexibility and capabilities of metabolism. Our results indicate that enzyme saturation is a necessary consideration in modeling metabolic networks and it extends the feasible ranges of metabolic fluxes and metabolite concentrations. Our results further suggest that enzymes in metabolic networks have evolved to function at different saturation states to ensure greater flexibility and robustness of cellular metabolism.     

Prediction of microbial growth rate versus biomass yield by a metabolic network with kinetic parameters

Identifying the factors that determine microbial growth rate under various environmental and genetic conditions is a major challenge of systems biology. While current genome-scale metabolic modeling approaches enable us to successfully predict a variety of metabolic phenotypes, including maximal biomass yield, the prediction of actual growth rate is a long standing goal. This gap stems from strictly relying on data regarding reaction stoichiometry and directionality, without accounting for enzyme kinetic considerations. Here we present a novel metabolic network-based approach, MetabOlic Modeling with ENzyme kineTics (MOMENT), which predicts metabolic flux rate and growth rate by utilizing prior data on enzyme turnover rates and enzyme molecular weights, without requiring measurements of nutrient uptake rates. The method is based on an identified design principle of metabolism in which enzymes catalyzing high flux reactions across different media tend to be more efficient in terms of having higher turnover numbers. Extending upon previous attempts to utilize kinetic data in genome-scale metabolic modeling, our approach takes into account the requirement for specific enzyme concentrations for catalyzing predicted metabolic flux rates, considering isozymes, protein complexes, and multi-functional enzymes. MOMENT is shown to significantly improve the prediction accuracy of various metabolic phenotypes in E. coli, including intracellular flux rates and changes in gene expression levels under different growth rates. Most importantly, MOMENT is shown to predict growth rates of E. coli under a diverse set of media that are correlated with experimental measurements, markedly improving upon existing state-of-the art stoichiometric modeling approaches. These results support the view that a physiological bound on cellular enzyme concentrations is a key factor that determines microbial growth rate.     

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 ²H₅‐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 ²H₅‐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 β‐oxidative and non‐β‐oxidative pathways is highly distributed.     

Kinetic isotope effects significantly influence intracellular metabolite 13C labeling patterns and flux determination

Rigorous mathematical modeling of carbon-labeling experiments allows estimation of fluxes through the pathways of central carbon metabolism, yielding powerful information for basic scientific studies as well as for a wide range of applications. However, the mathematical models that have been developed for flux determination from ¹³C labeling data have commonly neglected the influence of kinetic isotope effects on the distribution of ¹³C label in intracellular metabolites, as these effects have often been assumed to be inconsequential. We have used measurements of the ¹³C isotope effects on the pyruvate dehydrogenase enzyme from the literature to model isotopic fractionation at the pyruvate node and quantify the modeling errors expected to result from the assumption that isotope effects are negligible. We show that under some conditions kinetic isotope effects have a significant impact on the ¹³C labeling patterns of intracellular metabolites, and the errors associated with neglecting isotope effects in ¹³C-metabolic flux analysis models can be comparable in size to measurement errors associated with GC–MS. Thus, kinetic isotope effects must be considered in any rigorous assessment of errors in ¹³C labeling data, goodness-of-fit between model and data, confidence intervals of estimated metabolic fluxes, and statistical significance of differences between estimated metabolic flux distributions.     

Towards model-driven characterization and manipulation of plant lipid metabolism

Plant lipids have versatile applications and provide essential fatty acids in human diet. Therefore, there has been a growing interest to better characterize the genetic basis, regulatory networks, and metabolic pathways that shape lipid quantity and composition. Addressing these issues is challenging due to context-specificity of lipid metabolism integrating environmental, developmental, and tissue-specific cues. Here we systematically review the known metabolic pathways and regulatory interactions that modulate the levels of storage lipids in oilseeds. We argue that the current understanding of lipid metabolism provides the basis for its study in the context of genome-wide plant metabolic networks with the help of approaches from constraint-based modeling and metabolic flux analysis. The focus is on providing a comprehensive summary of the state-of-the-art of modeling plant lipid metabolic pathways, which we then contrast with the existing modeling efforts in yeast and microalgae. We then point out the gaps in knowledge of lipid metabolism, and enumerate the recent advances of using genome-wide association and quantitative trait loci mapping studies to unravel the genetic regulations of lipid metabolism. Finally, we offer a perspective on how advances in the constraint-based modeling framework can propel further characterization of plant lipid metabolism and its rational manipulation.     

基于酶约束的代谢网络模型研究进展及其应用

基因组尺度代谢网络模型已经成功地应用于指导代谢工程改造,但由于传统通量平衡分析法仅考虑化学计量学和反应方向约束,模拟得到的是理论最优结果,对一些现象如代谢溢流、底物层级利用等无法准确描述。近年来人们通过在代谢网络模型中引入新的蛋白量、热力学等约束发展了新的约束优化计算方法,可以更准确真实地模拟细胞在不同条件下的代谢行为。文中主要对近年来提出的多种酶约束模型进行评述,对酶约束引入的基本思路、酶约束的数学方程表示及优化目标设定、引入酶约束后对代谢通量计算结果的影响及酶约束模型在代谢工程菌种改造中的应用等进行了全面深入的介绍,并提出了已有各种方法存在的主要问题,展望了相关方法的未来发展方向。通过引入新的约束,代谢网络模型能够更精确模拟和预测细胞在环境和基因扰动下的代谢行为,为代谢工程菌种改造提供更准确可靠的指导。     

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.     

iSCHRUNK – In Silico Approach to Characterization and Reduction of Uncertainty in the Kinetic Models of Genome-scale Metabolic Networks

Accurate determination of physiological states of cellular metabolism requires detailed information about metabolic fluxes, metabolite concentrations and distribution of enzyme states. Integration of fluxomics and metabolomics data, and thermodynamics-based metabolic flux analysis contribute to improved understanding of steady-state properties of metabolism. However, knowledge about kinetics and enzyme activities though essential for quantitative understanding of metabolic dynamics remains scarce and involves uncertainty. Here, we present a computational methodology that allow us to determine and quantify the kinetic parameters that correspond to a certain physiology as it is described by a given metabolic flux profile and a given metabolite concentration vector. Though we initially determine kinetic parameters that involve a high degree of uncertainty, through the use of kinetic modeling and machine learning principles we are able to obtain more accurate ranges of kinetic parameters, and hence we are able to reduce the uncertainty in the model analysis. We computed the distribution of kinetic parameters for glucose-fed E. coli producing 1,4-butanediol and we discovered that the observed physiological state corresponds to a narrow range of kinetic parameters of only a few enzymes, whereas the kinetic parameters of other enzymes can vary widely. Furthermore, this analysis suggests which are the enzymes that should be manipulated in order to engineer the reference state of the cell in a desired way. The proposed approach also sets up the foundations of a novel type of approaches for efficient, non-asymptotic, uniform sampling of solution spaces.     

Green pathways: Metabolic network analysis of plant systems

Metabolic engineering of plants with enhanced crop yield and value-added compositional traits is particularly challenging as they probably exhibit the highest metabolic network complexity of all living organisms. Therefore, approaches of plant metabolic network analysis, which can provide systems-level understanding of plant physiology, appear valuable as guidance for plant metabolic engineers. Strongly supported by the sequencing of plant genomes, a number of different experimental and computational methods have emerged in recent years to study plant systems at various levels: from heterotrophic cell cultures to autotrophic entire plants. The present review presents a state-of-the-art toolbox for plant metabolic network analysis. Among the described approaches are different in silico modeling techniques, including flux balance analysis, elementary flux mode analysis and kinetic flux profiling, as well as different variants of experiments with plant systems which use radioactive and stable isotopes to determine in vivo plant metabolic fluxes. The fundamental principles of these techniques, the required data input and the obtained flux information are enriched by technical advices, specific to plants. In addition, pioneering and high-impacting findings of plant metabolic network analysis highlight the potential of the field.     

Metabolic cartography: experimental quantification of metabolic fluxes from isotopic labelling studies

For the past decade, flux maps have provided researchers with an in-depth perspective on plant metabolism. As a rapidly developing field, significant headway has been made recently in computation, experimentation, and overall understanding of metabolic flux analysis. These advances are particularly applicable to the study of plant metabolism. New dynamic computational methods such as non-stationary metabolic flux analysis are finding their place in the toolbox of metabolic engineering, allowing more organisms to be studied and decreasing the time necessary for experimentation, thereby opening new avenues by which to explore the vast diversity of plant metabolism. Also, improved methods of metabolite detection and measurement have been developed, enabling increasingly greater resolution of flux measurements and the analysis of a greater number of the multitude of plant metabolic pathways. Methods to deconvolute organelle-specific metabolism are employed with increasing effectiveness, elucidating the compartmental specificity inherent in plant metabolism. Advances in metabolite measurements have also enabled new types of experiments, such as the calculation of metabolic fluxes based on (13)CO(2) dynamic labelling data, and will continue to direct plant metabolic engineering. Newly calculated metabolic flux maps reveal surprising and useful information about plant metabolism, guiding future genetic engineering of crops to higher yields. Due to the significant level of complexity in plants, these methods in combination with other systems biology measurements are necessary to guide plant metabolic engineering in the future.     

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.     

Edelfosine-induced metabolic changes in cancer cells that precede the overproduction of reactive oxygen species and apoptosis

Background  

Metabolic flux profiling based on the analysis of distribution of stable isotope tracer in metabolites is an important method widely used in cancer research to understand the regulation of cell metabolism and elaborate new therapeutic strategies. Recently, we developed software Isodyn, which extends the methodology of kinetic modeling to the analysis of isotopic isomer distribution for the evaluation of cellular metabolic flux profile under relevant conditions. This tool can be applied to reveal the metabolic effect of proapoptotic drug edelfosine in leukemia Jurkat cell line, uncovering the mechanisms of induction of apoptosis in cancer cells.     

植物次生代谢基因工程研究进展

随着对植物代谢网络日渐全面的认识,应用基因工程技术对植物次生代谢途径进行遗传改良已取得了可喜的进展.对次生代谢途径进行基因修饰的策略包括:导入单个、多个靶基因或一个完整的代谢途径,使宿主植物合成新的目标物质;通过反义RNA和RNA干涉等技术降低靶基因的表达水平,从而抑制竞争性代谢途径,改变代谢流和增加目标物质的含量;对控制多个生物合成基因的转录因子进行修饰,更有效地调控植物次生代谢以提高特定化合物的积累.作者结合对大豆种子异黄酮类代谢调控和基因工程改良的研究,着重介绍了花青素和黄酮类物质、生物碱、萜类化合物和安息香酸衍生物等次生代谢产物生物合成的基因工程研究进展.     

Metabolic control analysis under uncertainty: framework development and case studies

Information about the enzyme kinetics in a metabolic network will enable understanding of the function of the network and quantitative prediction of the network responses to genetic and environmental perturbations. Despite recent advances in experimental techniques, such information is limited and existing experimental data show extensive variation and they are based on in vitro experiments. In this article, we present a computational framework based on the well-established (log)linear formalism of metabolic control analysis. The framework employs a Monte Carlo sampling procedure to simulate the uncertainty in the kinetic data and applies statistical tools for the identification of the rate-limiting steps in metabolic networks. We applied the proposed framework to a branched biosynthetic pathway and the yeast glycolysis pathway. Analysis of the results allowed us to interpret and predict the responses of metabolic networks to genetic and environmental changes, and to gain insights on how uncertainty in the kinetic mechanisms and kinetic parameters propagate into the uncertainty in predicting network responses. Some of the practical applications of the proposed approach include the identification of drug targets for metabolic diseases and the guidance for design strategies in metabolic engineering for the purposeful manipulation of the metabolism of industrial organisms.     

Plant Metabolic Modeling: Achieving New Insight into Metabolism and Metabolic Engineering

Models are used to represent aspects of the real world for specific purposes, and mathematical models have opened up new approaches in studying the behavior and complexity of biological systems. However, modeling is often time-consuming and requires significant computational resources for data development, data analysis, and simulation. Computational modeling has been successfully applied as an aid for metabolic engineering in microorganisms. But such model-based approaches have only recently been extended to plant metabolic engineering, mainly due to greater pathway complexity in plants and their highly compartmentalized cellular structure. Recent progress in plant systems biology and bioinformatics has begun to disentangle this complexity and facilitate the creation of efficient plant metabolic models. This review highlights several aspects of plant metabolic modeling in the context of understanding, predicting and modifying complex plant metabolism. We discuss opportunities for engineering photosynthetic carbon metabolism, sucrose synthesis, and the tricarboxylic acid cycle in leaves and oil synthesis in seeds and the application of metabolic modeling to the study of plant acclimation to the environment. The aim of the review is to offer a current perspective for plant biologists without requiring specialized knowledge of bioinformatics or systems biology.     

Insights into metabolic efficiency from flux analysis

The efficiency of carbon and energy flows throughout metabolism defines the potential for growth and reproductive success of plants. Understanding the basis for metabolic efficiency requires relevant definitions of efficiency as well as measurements of biochemical functions through metabolism. Here insights into the basis of efficiency provided by (13)C-based metabolic flux analysis (MFA) as well as the uses and limitations of efficiency in predictive flux balance analysis (FBA) are highlighted. (13)C-MFA studies have revealed unusual features of central metabolism in developing green seeds for the efficient use of light to conserve carbon and identified metabolic inefficiencies in plant metabolism due to dissipation of ATP by substrate cycling. Constraints-based FBA has used efficiency to guide the prediction of the growth and actual internal flux distribution of plant systems. Comparisons in a few cases have been made between flux maps measured by (13)C-based MFA and those predicted by FBA assuming one or more maximal efficiency parameters. These studies suggest that developing plant seeds and photoautotrophic microorganisms may indeed have patterns of metabolic flux that maximize efficiency. MFA and FBA are synergistic toolsets for uncovering and explaining the metabolic basis of efficiencies and inefficiencies in plant systems.     

Optimization-driven identification of genetic perturbations accelerates the convergence of model parameters in ensemble modeling of metabolic networks

The ensemble modeling (EM) approach has shown promise in capturing kinetic and regulatory effects in the modeling of metabolic networks. Efficacy of the EM procedure relies on the identification of model parameterizations that adequately describe all observed metabolic phenotypes upon perturbation. In this study, we propose an optimization-based algorithm for the systematic identification of genetic/enzyme perturbations to maximally reduce the number of models retained in the ensemble after each round of model screening. The key premise here is to design perturbations that will maximally scatter the predicted steady-state fluxes over the ensemble parameterizations. We demonstrate the applicability of this procedure for an Escherichia coli metabolic model of central metabolism by successively identifying single, double, and triple enzyme perturbations that cause the maximum degree of flux separation between models in the ensemble. Results revealed that optimal perturbations are not always located close to reaction(s) whose fluxes are measured, especially when multiple perturbations are considered. In addition, there appears to be a maximum number of simultaneous perturbations beyond which no appreciable increase in the divergence of flux predictions is achieved. Overall, this study provides a systematic way of optimally designing genetic perturbations for populating the ensemble of models with relevant model parameterizations.