Combining pathway analysis with flux balance analysis for the comprehensive study of metabolic systems

The elucidation of organism-scale metabolic networks necessitates the development of integrative methods to analyze and interpret the systemic properties of cellular metabolism. A shift in emphasis from single metabolic reactions to systemically defined pathways is one consequence of such an integrative analysis of metabolic systems. The constraints of systemic stoichiometry, and limited thermodynamics have led to the definition of the flux space within the context of convex analysis. The flux space of the metabolic system, containing all allowable flux distributions, is constrained to a convex polyhedral cone in a high-dimensional space. From metabolic pathway analysis, the edges of the high-dimensional flux cone are vectors that correspond to systemically defined "extreme pathways" spanning the capabilities of the system. The addition of maximum flux capacities of individual metabolic reactions serves to further constrain the flux space and has led to the development of flux balance analysis using linear optimization to calculate optimal flux distributions. Here we provide the precise theoretical connections between pathway analysis and flux balance analysis allowing for their combined application to study integrated metabolic function. Shifts in metabolic behavior are calculated using linear optimization and are then interpreted using the extreme pathways to demonstrate the concept of pathway utilization. Changes to the reaction network, such as the removal of a reaction, can lead to the generation of suboptimal phenotypes that can be directly attributed to the loss of pathway function and capabilities. Optimal growth phenotypes are calculated as a function of environmental variables, such as the availability of substrate and oxygen, leading to the definition of phenotypic phase planes. It is illustrated how optimality properties of the computed flux distributions can be interpreted in terms of the extreme pathways. Together these developments are applied to an example network and to core metabolism of Escherichia coli demonstrating the connections between the extreme pathways, optimal flux distributions, and phenotypic phase planes. The consequences of changing environmental and internal conditions of the network are examined for growth on glucose and succinate in the face of a variety of gene deletions. The convergence of the calculation of optimal phenotypes through linear programming and the definition of extreme pathways establishes a different perspective for the understanding of how a defined metabolic network is best used under different environmental and internal conditions or, in other words, a pathway basis for the interpretation of the metabolic reaction norm.     

Theory for the systemic definition of metabolic pathways and their use in interpreting metabolic function from a pathway-oriented perspective

Cellular metabolism is most often described and interpreted in terms of the biochemical reactions that make up the metabolic network. Genomics is providing near complete information regarding the genes/gene products participating in cellular metabolism for a growing number of organisms. As the true functional units of metabolic systems are its pathways, the time has arrived to define metabolic pathways in the context of whole-cell metabolism for the analysis of the structural design and capabilities of the metabolic network. In this study, we present the theoretical foundations for the identification of the unique set of systemically independent biochemical pathways, termed extreme pathways, based on system stochiometry and limited thermodynamics. These pathways represent the edges of the steady-state flux cone derived from convex analysis, and they can be used to represent any flux distribution achievable by the metabolic network. An algorithm is presented to determine the set of extreme pathways for a system of any complexity and a classification scheme is introduced for the characterization of these pathways. The property of systemic independence is discussed along with its implications for issues related to metabolic regulation and the evolution of cellular metabolic networks. The underlying pathway structure that is determined from the set of extreme pathways now provides us with the ability to analyse, interpret, and perhaps predict metabolic function from a pathway-based perspective in addition to the traditional reaction-based perspective. The algorithm and classification scheme developed can be used to describe the pathway structure in annotated genomes to explore the capabilities of an organism.     

Extreme pathway analysis of human red blood cell metabolism

The development of high-throughput technologies and the resulting large-scale data sets have necessitated a systems approach to the analysis of metabolic networks. One way to approach the issue of complex metabolic function is through the calculation and interpretation of extreme pathways. Extreme pathways are a mathematically defined set of generating vectors that describe the conical steady-state solution space for flux distributions through an entire metabolic network. Herein, the extreme pathways of the well-characterized human red blood cell metabolic network were calculated and interpreted in a biochemical and physiological context. These extreme pathways were divided into groups based on such criteria as their cofactor and by-product production, and carbon inputs including those that 1) convert glucose to pyruvate; 2) interchange pyruvate and lactate; 3) produce 2,3-diphosphoglycerate that binds to hemoglobin; 4) convert inosine to pyruvate; 5) induce a change in the total adenosine pool; and 6) dissipate ATP. Additionally, results from a full kinetic model of red blood cell metabolism were predicted based solely on an interpretation of the extreme pathway structure. The extreme pathways for the red blood cell thus give a concise representation of red blood cell metabolism and a way to interpret its metabolic physiology.     

Constraints-based models: regulation of gene expression reduces the steady-state solution space

Constraints-based models have been effectively used to analyse, interpret, and predict the function of reconstructed genome-scale metabolic models. The first generation of these models used "hard" non-adjustable constraints associated with network connectivity, irreversibility of metabolic reactions, and maximal flux capacities. These constraints restrict the allowable behaviors of a network to a convex mathematical solution space whose edges are extreme pathways that can be used to characterize the optimal performance of a network under a stated performance criterion. The development of a second generation of constraints-based models by incorporating constraints associated with regulation of gene expression was described in a companion paper published in this journal, using flux-balance analysis to generate time courses of growth and by-product secretion using a skeleton representation of core metabolism. The imposition of these additional restrictions prevents the use of a subset of the extreme pathways that are derived from the "hard" constraints, thus reducing the solution space and restricting allowable network functions. Here, we examine the reduction of the solution space due to regulatory constraints using extreme pathway analysis. The imposition of environmental conditions and regulatory mechanisms sharply reduces the number of active extreme pathways. This approach is demonstrated for the skeleton system mentioned above, which has 80 extreme pathways. As regulatory constraints are applied to the system, the number of feasible extreme pathways is reduced to between 26 and 2 extreme pathways, a reduction of between 67.5 and 97.5%. The method developed here provides a way to interpret how regulatory mechanisms are used to constrain network functions and produce a small range of physiologically meaningful behaviors from all allowable network functions.     

基于转录组分析铜绿假单胞菌DN1降解荧蒽特性

[背景]铜绿假单胞菌DN1是一株从石油污染土壤中分离筛选到的具有广谱降解功能的菌株。[目的]深入了解荧蒽胁迫条件下铜绿假单胞菌DN1降解污染物过程中重要的降解相关基因信息。[方法]通过高通量测序技术对铜绿假单胞菌DN1进行转录组测序,对其所有的转录本进行KEGG (kyoto encyclopedia of genes and genomes)分类和Pathway注释、GO (gene ontology)分类和富集分析。[结果]转录组测序显示:与对照组相比,荧蒽诱导组检测到6 189个基因,其中1 919个基因上调表达,1 603个基因下调表达。KEGG注释分析显示差异上调表达基因匹配到了112个KEGG代谢途径,注释到"代谢途径"的1 408个基因(约占总差异基因的73.4%)中有317个基因参与了碳氢化合物代谢及含有苯环结构的异源生物质的生物降解,占"代谢途径"的16.53%,暗示了菌株DN1降解荧蒽可能与这些途径有密切关系。另外,主要代谢途径中的差异表达基因主要集中在ABC转运系统、氨基酸生物合成、双组分系统及碳代谢,这些途径大多数参与了底物的识别转运、信号转导及基因表达调控。[结论]进一步拓展了铜绿假单胞菌DN1在荧蒽胁迫条件下的代谢途径和逆境反应,也为微生物修复环境污染物研究夯实了理论基础。     

Network reduction in metabolic pathway analysis: elucidation of the key pathways involved in the photoautotrophic growth of the green alga Chlamydomonas reinhardtii

Metabolic pathway analysis aims at discovering and analyzing meaningful routes and their interactions in metabolic networks. A major difficulty in applying this technique lies in the decomposition of metabolic flux distributions into elementary mode or extreme pathway activity patterns, which in general is not unique. We propose a network reduction approach based on the decomposition of a set of flux vectors representing adaptive microbial metabolic behavior in bioreactors into a minimal set of shared pathways. Several optimality criteria from the literature were compared in order to select the most appropriate objective function. We further analyze photoautotrophic metabolism of the green alga Chlamydomonas reinhardtii growing in a photobioreactor under maximal growth rate conditions. Key pathways involved in its adaptive metabolic response to changes in light influx are identified and discussed using an energetic approach.     

Two approaches for metabolic pathway analysis?

Metabolic pathway analysis is becoming increasingly important for assessing inherent network properties in (reconstructed) biochemical reaction networks. Of the two most promising concepts for pathway analysis, one relies on elementary flux modes and the other on extreme pathways. These concepts are closely related because extreme pathways are a subset of elementary modes. Here, the common features, differences and applicability of these concepts are discussed. Assessing metabolic systems by the set of extreme pathways can, in general, give misleading results owing to the exclusion of possibly important routes. However, in certain network topologies, the sets of elementary modes and extreme pathways coincide. This is quite often the case in realistic applications. In our opinion, the unification of both approaches into one common framework for metabolic pathway analysis is necessary and achievable.     

Assessment of the metabolic capabilities of Haemophilus influenzae Rd through a genome-scale pathway analysis

The annotated full DNA sequence is becoming available for a growing number of organisms. This information along with additional biochemical and strain-specific data can be used to define metabolic genotypes and reconstruct cellular metabolic networks. The first free-living organism for which the entire genomic sequence was established was Haemophilus influenzae. Its metabolic network is reconstructed herein and contains 461 reactions operating on 367 intracellular and 84 extracellular metabolites. With the metabolic reaction network established, it becomes necessary to determine its underlying pathway structure as defined by the set of extreme pathways. The H. influenzae metabolic network was subdivided into six subsystems and the extreme pathways determined for each subsystem based on stoichiometric, thermodynamic, and systems-specific constraints. Positive linear combinations of these pathways can be taken to determine the extreme pathways for the complete system. Since these pathways span the capabilities of the full system, they could be used to address a number of important physiological questions. First, they were used to reconcile and curate the sequence annotation by identifying reactions whose function was not supported in any of the extreme pathways. Second, they were used to predict gene products that should be co-regulated and perhaps co-expressed. Third, they were used to determine the composition of the minimal substrate requirements needed to support the production of 51 required metabolic products such as amino acids, nucleotides, phospholipids, etc. Fourth, sets of critical gene deletions from core metabolism were determined in the presence of the minimal substrate conditions and in more complete conditions reflecting the environmental niche of H. influenzae in the human host. In the former case, 11 genes were determined to be critical while six remained critical under the latter conditions. This study represents an important milestone in theoretical biology, namely the establishment of the first extreme pathway structure of a whole genome.     

基于UPLC-Q-TOF/MS代谢组学探究虹鳟鳃对热应激的生理反应

全球气温日趋升高导致的水温上升可引起虹鳟(Oncorhynchus mykiss)代谢紊乱,为解析其在热应激下的代谢变化特征,研究基于UPLC-Q-TOF/MS代谢组学技术,探究了虹鳟鳃靶器官在高温暴露(20℃和24℃)及恢复到初始温度(14℃)下的代谢生理反应。研究结果表明,与对照组相比,在20℃、24℃高温组和14℃恢复组中分别鉴定出128、130和108种差异显著代谢物。在高温暴露下,亚油酸、花生四烯酸等与脂质代谢相关的代谢物及还原型辅酶Ⅱ(NADPH)、谷胱甘肽(GSH)、谷胱甘肽二硫化物(GSSG)等与细胞氧化还原状态相关的代谢物均发生显著改变。富集分析表明这些代谢物主要涉及虹鳟鳃的甘油磷脂代谢、鞘脂代谢、亚油酸代谢、花生四烯酸代谢、磷酸戊糖途径和谷胱甘肽代谢等代谢通路,但在温度恢复到14℃后,除鞘脂代谢外,其他代谢途径均未恢复至正常状态。上述结果表明,热激导致了虹鳟鳃靶器官的脂质代谢紊乱,可能导致鳃细胞膜的结构和功能的损伤,诱使鳃细胞出现炎症反应,并产生免疫应答。同时,虹鳟鳃细胞通过磷酸戊糖途径产生的NADPH来调节谷胱甘肽代谢中GSH/GSSG比值以提高细胞的抗氧化能力来...     

Fumarate mitigates disruption induced by fenpropathrin in the silkworm Bombyx mori (Lepidoptera): A metabolomics study

The silkworm Bombyx mori L. is a model organism of the order Lepidoptera. Understanding the mechanism of pesticide resistance in silkworms is valuable for Lepidopteran pest control. In this study, comparative metabolomics was used to analyze the metabolites of 2 silkworm strains with different pesticide resistance levels at 6, 12, and 24 h after feeding with fenpropathrin. Twenty-six of 27 metabolites showed significant differences after fenpropathrin treatment and were classified into 6 metabolic pathways: glycerophospholipid metabolism, sulfur metabolism, glycolysis, amino acid metabolism, the urea cycle, and the tricarboxylic acid (TCA) cycle. After analyzing the percentage changes in the metabolic pathways at the 3 time points, sulfur metabolism, glycolysis, and the TCA cycle showed significant responses to fenpropathrin. Confirmatory experiments were performed by feeding silkworms with key metabolites of the 3 pathways. The combination of iron(II) fumarate + folic acid (IF-FA) enhanced fenpropathrin resistance in silkworms 6.38 fold, indicating that the TCA cycle is the core pathway associated with resistance. Furthermore, the disruption of several energy-related metabolic pathways caused by fenpropathrin was shown to be recovered by IF-FA in vitro. Therefore, IF-FA may have a role in boosting silkworm pesticide resistance by modulating the equilibrium between the TCA cycle and its related metabolic pathways.     

Modeling with a view to target identification in metabolic engineering: A critical evaluation of the available tools

The state of the art tools for modeling metabolism, typically used in the domain of metabolic engineering, were reviewed. The tools considered are stoichiometric network analysis (elementary modes and extreme pathways), stoichiometric modeling (metabolic flux analysis, flux balance analysis, and carbon modeling), mechanistic and approximative modeling, cybernetic modeling, and multivariate statistics. In the context of metabolic engineering, one should be aware that the usefulness of these tools to optimize microbial metabolism for overproducing a target compound depends predominantly on the characteristic properties of that compound. Because of their shortcomings not all tools are suitable for every kind of optimization; issues like the dependence of the target compound's synthesis on severe (redox) constraints, the characteristics of its formation pathway, and the achievable/desired flux towards the target compound should play a role when choosing the optimization strategy. © 2010 American Institute of Chemical Engineers Biotechnol. Prog., 2010     

The genome-scale metabolic extreme pathway structure in Haemophilus influenzae shows significant network redundancy

Genome-scale metabolic networks can be characterized by a set of systemically independent and unique extreme pathways. These extreme pathways span a convex, high-dimensional space that circumscribes all potential steady-state flux distributions achievable by the defined metabolic network. Genome-scale extreme pathways associated with the production of non-essential amino acids in Haemophilus influenzae were computed. They offer valuable insight into the functioning of its metabolic network. Three key results were obtained. First, there were multiple internal flux maps corresponding to externally indistinguishable states. It was shown that there was an average of 37 internal states per unique exchange flux vector in H. influenzae when the network was used to produce a single amino acid while allowing carbon dioxide and acetate as carbon sinks. With the inclusion of succinate as an additional output, this ratio increased to 52, a 40% increase. Second, an analysis of the carbon fates illustrated that the extreme pathways were non-uniformly distributed across the carbon fate spectrum. In the detailed case study, 45% of the distinct carbon fate values associated with lysine production represented 85% of the extreme pathways. Third, this distribution fell between distinct systemic constraints. For lysine production, the carbon fate values that represented 85% of the pathways described above corresponded to only 2 distinct ratios of 1:1 and 4:1 between carbon dioxide and acetate. The present study analysed single outputs from one organism, and provides a start to genome-scale extreme pathways studies. These emergent system-level characterizations show the significance of metabolic extreme pathway analysis at the genome-scale.     

An algorithm for linear metabolic pathway alignment

Metabolic pathway alignment represents one of the most powerful tools for comparative analysis of metabolism. It involves recognition of metabolites common to a set of functionally-related metabolic pathways, interpretation of biological evolution processes and determination of alternative metabolic pathways. Moreover, it is of assistance in function prediction and metabolism modeling. Although research on genomic sequence alignment is extensive, the problem of aligning metabolic pathways has received less attention. We are motivated to develop an algorithm of metabolic pathway alignment to reveal the similarities between metabolic pathways. A new definition of the metabolic pathway is introduced. The algorithm has been implemented into the PathAligner system; its web-based interface is available at http://bibiserv.techfak.uni-bielefeld.de/pathaligner/.     

Effects of aeration on metabolic profiles of <Emphasis Type="Italic">Mortierella alpina</Emphasis> during the production of arachidonic acid

To investigate the metabolic regulation against oxygen supply, comparative metabolomics was performed to explore the metabolic responses of Mortierella alpina in the process of arachidonic acid (ARA) production. More than 110 metabolites involved in Embden–Meyerhof–Parnas pathway, pentose phosphate pathway, tricarboxylic acid cycle, inositol phosphate metabolism, fatty acid biosynthesis, and amino acid metabolism were identified by gas chromatography–mass spectrometry. Samples at different aeration rates were clearly distinguished by principal components analysis and partial least squares analysis, indicating that oxygen supply had a profound effect on the metabolism of M. alpina. Eleven major metabolites were identified as potential biomarkers to be primarily responsible for the difference of metabolism. Further study of metabolic changes with the relevant pathways demonstrated that the levels of several intermediate metabolites in relation to central carbon metabolism changed remarkably via both processes and citrate and malate was supposed to play vital roles in polyunsaturated acid (PUFA) synthesis. Increase of myo-inositol and sorbitol were probably for osmo-regulation and redox balance, while enhanced phosphoric acid and pyroglutamic acid were supposed to have function in the activation of signal transduction pathway for stress resistance. The present study provides a novel insight into the metabolic responses of M. alpina to aeration rates and the metabolic characteristics during the ARA fermentation.     

Proteome analysis of Pseudomonas sp. K82 biodegradation pathways

Pseudomonas sp. K82 is a soil bacterium that can degrade and use monocyclic aromatic compounds including aniline, 3-methylaniline, 4-methylaniline, benzoate and p-hydroxybenzoate as its sole carbon and energy sources. In order to understand the impact of these aromatic compounds on metabolic pathways in Pseudomonas sp. K82, proteomes obtained from cultures exposed to different substrates were displayed by two-dimensional gel electrophoresis and were compared to search for differentially induced metabolic enzymes. Column separations of active fractions were performed to identify major biodegradation enzymes. More than thirty proteins involved in biodegradation and other types of metabolism were identified by electrospray ionization-quadrupole time of flight mass spectrometry. The proteome analysis suggested that Pseudomonas sp. K82 has three main metabolic pathways to degrade these aromatic compounds and induces specific metabolic pathways for each compound. The catechol 2,3-dioxygenase (CD2,3) pathway was the major pathway and the catechol 1,2-dioxygenase (beta-ketoadipate) pathway was the secondary pathway induced by aniline (aniline analogues) exposure. On the other hand, the catechol 1,2-dioxygenase pathway was the major pathway induced by benzoate exposure. For the degradation of p-hydroxybenzoate, the protocatechuate 4,5-dioxygenase pathway was the major degradation pathway induced. The nuclear magnetic resonance analysis of substrates demonstrated that Pseudomonas sp. K82 metabolizes some aromatic compounds more rapidly than others (benzoate > p-hydroxybenzoate > aniline) and that when combined, p-hydroxybenzoate metabolism is repressed by the presence of benzoate or aniline. These results suggest that proteome analysis can be useful in the high throughput study of bacterial metabolic pathways, including that of biodegradation, and that inter-relationships exist with respect to the metabolic pathways of aromatic compounds in Pseudomonas sp. K82.     

Elucidating and reprogramming Escherichia coli metabolisms for obligate anaerobic n-butanol and isobutanol production

Elementary mode (EM) analysis based on the constraint-based metabolic network modeling was applied to elucidate and compare complex fermentative metabolisms of Escherichia coli for obligate anaerobic production of n-butanol and isobutanol. The result shows that the n-butanol fermentative metabolism was NADH-deficient, while the isobutanol fermentative metabolism was NADH redundant. E. coli could grow and produce n-butanol anaerobically as the sole fermentative product but not achieve the maximum theoretical n-butanol yield. In contrast, for the isobutanol fermentative metabolism, E. coli was required to couple with either ethanol- or succinate-producing pathway to recycle NADH. To overcome these "defective" metabolisms, EM analysis was implemented to reprogram the native fermentative metabolism of E. coli for optimized anaerobic production of n-butanol and isobutanol through multiple gene deletion (~8-9 genes), addition (~6-7 genes), up- and downexpression (~6-7 genes), and cofactor engineering (e.g., NADH, NADPH). The designed strains were forced to couple both growth and anaerobic production of n-butanol and isobutanol, which is a useful characteristic to enhance biofuel production and tolerance through metabolic pathway evolution. Even though the n-butanol and isobutanol fermentative metabolisms were quite different, the designed strains could be engineered to have identical metabolic flux distribution in "core" metabolic pathways mainly supporting cell growth and maintenance. Finally, the model prediction in elucidating and reprogramming the native fermentative metabolism of E. coli for obligate anaerobic production of n-butanol and isobutanol was validated with published experimental data.