Integrating cybernetic modeling with pathway analysis provides a dynamic, systems-level description of metabolic control

Cybernetic modeling strives to uncover the inbuilt regulatory programs of biological systems and leverage them toward computational prediction of metabolic dynamics. Because of its focus on incorporating the global aims of metabolism, cybernetic modeling provides a systems-oriented approach for describing regulatory inputs and inferring the impact of regulation within biochemical networks. Combining cybernetic control laws with concepts from metabolic pathway analysis has culminated in a systematic strategy for constructing cybernetic models, which was previously lacking. The newly devised framework relies upon the simultaneous application of local controls that maximize the net flux through each elementary flux mode and global controls that modulate the activities of these modes to optimize the overall nutritional state of the cell. The modeling concepts are illustrated using a simple linear pathway and a larger network representing anaerobic E. coli central metabolism. The E. coli model successfully describes the metabolic shift that occurs upon deleting the pta-ackA operon that is responsible for fermentative acetate production. The model also furnishes predictions that are consistent with experimental results obtained from additional knockout strains as well as strains expressing heterologous genes. Because of the stabilizing influence of the included control variables, the resulting cybernetic models are more robust and reliable than their predecessors in simulating the network response to imposed genetic and environmental perturbations.     

代谢流量比率分析及其在代谢工程中的应用

细胞内代谢反应流量在系统理解细胞代谢特性和指导代谢工程改造等方面都起着重要的作用。由于代谢流量难以直接测量得到,在很多情况下通过跟踪稳定同位素在代谢网络中的转移并进行相应的模型计算能有效地定量代谢流量。代谢流量比率分析法能够高度体现系统的生物化学真实性、辨别细胞代谢网络的拓扑结构,并且能够相对简单快速地定量反应速率等,因此受到代谢工程研究者越来越多的重视。以下着重介绍并讨论了利用代谢物同位体分布信息分析关键代谢节点合成途径的流量比率、基于流量比率的代谢流量解析、以及应用于代谢工程等的相关原理、实验测量、数据分析、使用条件等,以期充分发挥代谢流量比率分析法的优势,并将其拓展推广至更多细胞体系的代谢特性阐明和代谢工程改造中去。     

Using isotopomer path tracing to quantify metabolic fluxes in pathway models containing reversible reactions

As a more complete picture of the genetic and enzymatic composition of cells becomes available, there is a growing need to describe how cellular regulatory elements interact with the cellular environment to affect cell physiology. One means for describing intracellular regulatory mechanisms is concurrent measurement of multiple metabolic pathways and their interactions by metabolic flux analysis. Flux of carbon through a metabolic pathway responds to all cellular regulatory systems, including changes in enzyme and substrate concentrations, enzyme activation or inhibition, and ultimately genetic control. The extent to which metabolic flux analysis can describe cellular physiology depends on the number of pathways in the model and the quality of the data. Intracellular information is obtainable from isotopic tracer experiments, the most extensive being the determination of the isotopomer distribution, or specific labeling pattern, of intracellular metabolites. We present a rapid and novel solution method that determines the flux of carbon through complex pathway models using isotopomer data. This time-consuming problem was solved with the introduction of isotopomer path tracing, which drastically reduces the number of isotopomer variables to the number of isotopomers observed experimentally. We propose a partitioned solution method that takes advantage of the nearly linear relationship between fluxes and isotopomers. Whereas the stoichiometric matrix and the isotopomer matrix are invertible, simulated annealing and the Newton-Raphson method are used for the nonlinear components. Reversible reactions are described by a new parameter, the association factor, which scales hyperbolically with the rate of metabolite exchange. Automating the solution method permits a variety of models to be compared, thus enhancing the accuracy of results. A simplified example that contains all of the complexities of a comprehensive pathway model is presented. Copyright John Wiley & Sons, Inc.     

代谢网络定量分析研究进展

综述了代谢工程中代谢控制分析、代谢通量分析、生化系统理论、途径分析、控制论模型等定量分析方法的基本理论,以实例说明了这些方法的应用,并对代谢分析方法的发展进行了展望。     

13C代谢流量分析发展30年

13C代谢流量分析(13C metabolic flux analysis,13C-MFA),是通过标记实验分析蛋白氨基酸或胞内代谢物同位素标记异构体的分布情况,从而准确定量胞内反应速率.该技术在系统理解细胞代谢特性、指导代谢工程改造和揭示病理生理学等方面起着重要作用,引起研究者的广泛重视.文中重点综述了代谢流分析30...     

Metabolic flux analysis with a comprehensive isotopomer model in Bacillus subtilis

Fluxes in central carbon metabolism of a genetically engineered, riboflavin-producing Bacillus subtilis strain were investigated in glucose-limited chemostat cultures at low (0.11 h(-1)) and high (0.44 h(-1)) dilution rates. Using a mixture of 10% [U-(13)C] and 90% glucose labeled at natural abundance, (13)C-labeling experiments were carried out to provide additional information for metabolic flux balancing. The resulting labeling pattern in the proteinogenic amino acids were analyzed by two-dimensional [(13)C, (1)H] nuclear magnetic resonance (NMR) spectroscopy. To account rigorously for all available data from these experiments, we developed a comprehensive isotopomer model of B. subtilis central metabolism. Using this model, intracellular carbon net and exchange fluxes were estimated on the basis of validated physiological data and biomass composition in combination with 2D NMR data from 45 individual carbon atom spectra in the amino acids. Glucose catabolism proceeded primarily via glycolysis but pentose phosphate pathway fluxes increased with increasing growth rate. Moreover, significant back fluxes from the TCA cycle to the lower part of glycolysis via the gluconeogenic PEP carboxykinase were detected. The malic enzyme reaction, in contrast, was found to be inactive. A thorough statistical analysis was performed to prove the reliability of the isotopomer balance model and the obtained results. Specifically, a chi(2) test was applied to validate the model and the chi-square criterion was used to explore the sensitivity of model predictions to the experimental data.     

Combinatorial complexity of pathway analysis in metabolic networks

Elementary flux mode analysis is a promising approach for a pathway-oriented perspective of metabolic networks. However, in larger networks it is hampered by the combinatorial explosion of possible routes. In this work we give some estimations on the combinatorial complexity including theoretical upper bounds for the number of elementary flux modes in a network of a given size. In a case study, we computed the elementary modes in the central metabolism of Escherichia coli while utilizing four different substrates. Interestingly, although the number of modes occurring in this complex network can exceed half a million, it is still far below the upper bound. Hence, to a certain extent, pathway analysis of central catabolism is feasible to assess network properties such as flexibility and functionality.     

Optimization-based metabolic control analysis

In this work, a novel optimization-based metabolic control analysis (OMCA) method is introduced for reducing data requirement for metabolic control analysis (MCA). It is postulated that using the optimal control approach, the fluxes in a metabolic network are correlated to metabolite concentrations and enzyme activities as a state-feedback control system that is optimal with respect to a homeostasis objective. It is then shown that the optimal feedback gains are directly related to the elasticity coefficients (ECs) of MCA. This approach requires determination of the relative "importance" of metabolites and fluxes for the system, which is possible with significantly reduced experimental data, as compared with typical MCA requirements. The OMCA approach is applied to a top-down control model of glycolysis in hepatocytes. It is statistically demonstrated that the OMCA model is capable of predicting the ECs observed experimentally with few exceptions. Further, an OMCA-based model reconciliation study shows that the modification of four assumed stoichiometric coefficients in the model can explain most of the discrepancies, with the exception of elasticities with respect to the NADH/NAD ratio.     

A stoichiometric model of Acidithiobacillus ferrooxidans ATCC 23270 for metabolic flux analysis

A stoichiometric model of Acidithiobacillus ferrooxidans based on the sequenced genome from strain ATCC 23270 is derived and parameterized using genome/pathway databases. The model describes the main aspects of catabolism and anabolism. By the construction and utilization of the mathematical determination of the network, metabolic flux analysis is performed for such a bacterium for the first time and results are successfully verified by comparison to literature values. This first metabolic model of A. ferrooxidans is able to simulate the main aspects of metabolism and will be useful for further investigation and improvement of bioleaching procedures. Biotechnol. Bioeng. 2009;102: 1448–1459. © 2008 Wiley Periodicals, Inc.     

Estimation of metabolic fluxes, expression levels and metabolite dynamics of a secondary metabolic pathway in potato using label pulse-feeding experiments combined with kinetic network modelling and simulation

In this paper we present a method that allows dynamic flux analysis without a priori kinetic knowledge. This method was developed and validated using the pulse-feeding experimental data obtained in our previous study (Matsuda et al., 2005), in which incorporation of exogenously applied l-phenylalanine-d(5) into seven phenylpropanoid metabolites in potato tubers was determined. After identification of the topology of the metabolic network of these biosynthetic pathways, the system was described by dynamic mass balances in combination with power-law kinetics. After the first simulations, some reactions were removed from the network because they were not contributing significantly to network behaviour. As a next step, the exponents of the power-law kinetics were identified and then kept at fixed values during further analysis. The model was tested for statistical reliability using Monte Carlo simulations. Most fluxes could be identified with high accuracy. The two test cases, control and after elicitation, were clearly distinguished, and with elicitation fluxes to N-p-coumaroyloctopamine (pCO) and N-p-coumaroyltyramine (pCT) increased significantly, whereas those for chlorogenic acid (CGA) and p-coumaroylshikimate decreased significantly. According to the model, increases in the first two fluxes were caused by induction/derepression mechanisms. The decreases in the latter two fluxes were caused by decreased concentrations of their substrates, which in turn were caused by increased activity of the pCO- and pCT-producing enzymes. Flux-control analysis showed that, in most cases, flux control was changed after application of elicitor. Thus the results revealed potential targets for improving actions against tissue wounding and pathogen attack.     

Physiology of microbial cells and metabolic engineering

This review is devoted to the problems of the physiology and cell biology of microorganisms in relation to metabolic engineering. The latter is considered as a branch of fundamental and applied biotechnology aimed at controlling microbial metabolism by methods of genetic engineering and classical genetics and based on intimate knowledge of cell metabolism. Attention is also given to the problems associated with the metabolic limitation of microbial biosyntheses, analysis and control of metabolic fluxes, rigidity of metabolic pathways, the role of pleiotropic (global) regulatory systems in the control of metabolic fluxes, and prospects of physiological and evolutionary approaches in metabolic engineering.     

代谢工程发展20年

代谢工程从上世纪90年代初期发展至今已有20年历史,对微生物发酵工业的发展起到了极大的推动作用。以下回顾了代谢工程发展至今的三个重要阶段,讨论了各阶段中代谢工程在技术方面的进展及其对微生物发酵工业的促进作用。最后还讨论了代谢工程将来发展中的关键问题及解决策略。     

Optimal tracers for parallel labeling experiments and 13C metabolic flux analysis: A new precision and synergy scoring system

¹³C-Metabolic flux analysis (¹³C-MFA) is a widely used approach in metabolic engineering for quantifying intracellular metabolic fluxes. The precision of fluxes determined by ¹³C-MFA depends largely on the choice of isotopic tracers and the specific set of labeling measurements. A recent advance in the field is the use of parallel labeling experiments for improved flux precision and accuracy. However, as of today, no systemic methods exist for identifying optimal tracers for parallel labeling experiments. In this contribution, we have addressed this problem by introducing a new scoring system and evaluating thousands of different isotopic tracer schemes. Based on this extensive analysis we have identified optimal tracers for ¹³C-MFA. The best single tracers were doubly ¹³C-labeled glucose tracers, including [1,6-¹³C]glucose, [5,6-¹³C]glucose and [1,2-¹³C]glucose, which consistently produced the highest flux precision independent of the metabolic flux map (here, 100 random flux maps were evaluated). Moreover, we demonstrate that pure glucose tracers perform better overall than mixtures of glucose tracers. For parallel labeling experiments the optimal isotopic tracers were [1,6-¹³C]glucose and [1,2-¹³C]glucose. Combined analysis of [1,6-¹³C]glucose and [1,2-¹³C]glucose labeling data improved the flux precision score by nearly 20-fold compared to widely use tracer mixture 80% [1-¹³C]glucose +20% [U-¹³C]glucose.     

Rapid media transition: An experimental approach for steady state analysis of metabolic pathways

Commonly steady state analysis of microbial metabolism is performed under well defined physiological conditions in continuous cultures with fixed external rates. However, most industrial bioprocesses are operated in fed‐batch mode under non‐stationary conditions, which cannot be realized in chemostat cultures. A novel experimental setup—rapid media transition—enables steady state perturbation of metabolism on a time scale of several minutes in parallel to operating bioprocesses. For this purpose, cells are separated from the production process and transferred into a lab‐scale stirred‐tank reactor with modified environmental conditions. This new approach was evaluated experimentally in four rapid media transition experiments with Escherichia coli from a fed‐batch process. We tested the reaction to different carbon sources entering at various points of central metabolism. In all cases, the applied substrates (glucose, succinate, acetate, and pyruvate) were immediately utilized by the cells. Extracellular rates and metabolome data indicate a metabolic steady state during the short‐term cultivation. Stoichiometric analysis revealed distribution of intracellular fluxes, which differs drastically subject to the applied carbon source. For some reactions, the variation of flux could be correlated to changes of metabolite concentrations. © 2009 American Institute of Chemical Engineers Biotechnol. Prog., 2010     

13C标记代谢流分析中天然稳定性同位素修正矩阵构建方法及应用

稳定性同位素¹³C标记实验是分析细胞代谢流的一种重要手段,主要通过质谱检测胞内代谢物中¹³C标记的同位素分布,并作为胞内代谢流计算时的约束条件,进而通过代谢流分析算法得到相应代谢网络中的通量分布。然而在自然界中,并非只有C元素存在天然稳定性同位素¹³C,其他元素如O元素也有其天然稳定性同位素¹⁷O、¹⁸O等,这使得质谱方法所测得的同位素分布中会夹杂除¹³C标记之外的其他元素的同位素信息,特别是分子中含有较多其他元素的分子,这将导致很大的实验误差,因此需要在进行代谢流计算前进行质谱数据的矫正。本研究提出了一种基于Python语言的天然同位素修正矩阵的构建方法,用于修正同位素分布测量值中由于天然同位素分布引起的测定误差。文中提出的基本修正矩阵幂方法用于构建各元素修正矩阵,结构简单、易于编码实现,可直接应用于¹³C代谢流分析软件数据前处理。将该修正方法应用于¹³C标记的黑曲霉（Aspergillus niger）胞内代谢流分析,结果表明本研究提出的方法准确有效,为准确获取微生物胞内代谢流分析提供了可靠的数据修正方法。     

Metabolic flux analysis in Escherichia coli by integrating isotopic dynamic and isotopic stationary 13C labeling data

The novel concept of isotopic dynamic 13C metabolic flux analysis (ID-13C MFA) enables integrated analysis of isotopomer data from isotopic transient and/or isotopic stationary phase of a 13C labeling experiment, short-time experiments, and an extended range of applications of 13C MFA. In the presented work, an experimental and computational framework consisting of short-time 13C labeling, an integrated rapid sampling procedure, a LC-MS analytical method, numerical integration of the system of isotopomer differential equations, and estimation of metabolic fluxes was developed and applied to determine intracellular fluxes in glycolysis, pentose phosphate pathway (PPP), and citric acid cycle (TCA) in Escherichia coli grown in aerobic, glucose-limited chemostat culture at a dilution rate of D = 0.10 h(-1). Intracellular steady state concentrations were quantified for 12 metabolic intermediates. A total of 90 LC-MS mass isotopomers were quantified at sampling times t = 0, 91, 226, 346, 589 s and at isotopic stationary conditions. Isotopic stationarity was reached within 10 min in glycolytic and PPP metabolites. Consistent flux solutions were obtained by ID-13C MFA using isotopic dynamic and isotopic stationary 13C labeling data and by isotopic stationary 13C MFA (IS-13C MFA) using solely isotopic stationary data. It is demonstrated that integration of dynamic 13C labeling data increases the sensitivity of flux estimation, particularly at the glucose-6-phosphate branch point. The identified split ratio between glycolysis and PPP was 55%:44%. These results were confirmed by IS-13C MFA additionally using labeling data in proteinogenic amino acids (GC-MS) obtained after 5 h from sampled biomass.     

Revealing metabolic mechanisms of interaction in the anaerobic digestion microbiome by flux balance analysis

Anaerobic digestion is a key biological process for renewable energy, yet the mechanistic knowledge on its hidden microbial dynamics is still limited. The present work charted the interaction network in the anaerobic digestion microbiome via the full characterization of pairwise interactions and the associated metabolite exchanges. To this goal, a novel collection of 836 genome-scale metabolic models was built to represent the functional capabilities of bacteria and archaea species derived from genome-centric metagenomics. Dominant microbes were shown to prefer mutualistic, parasitic and commensalistic interactions over neutralism, amensalism and competition, and are more likely to behave as metabolite importers and profiteers of the coexistence. Additionally, external hydrogen injection positively influences microbiome dynamics by promoting commensalism over amensalism. Finally, exchanges of glucogenic amino acids were shown to overcome auxotrophies caused by an incomplete tricarboxylic acid cycle. Our novel strategy predicted the most favourable growth conditions for the microbes, overall suggesting strategies to increasing the biogas production efficiency. In principle, this approach could also be applied to microbial populations of biomedical importance, such as the gut microbiome, to allow a broad inspection of the microbial interplays.