Detection of elementary flux modes in biochemical networks: a promising tool for pathway analysis and metabolic engineering

Rational metabolic engineering requires powerful theoretical methods such as pathway analysis, in which the topology of metabolic networks is considered. All metabolic capabilities in steady states are composed of elementary flux modes, which are minimal sets of enzymes that can each generate valid steady states. The modes of the fructose-2,6-bisphosphate cycle, the combined tricarboxylic-acid-glyoxylate-shunt system and tryptophan synthesis are used here for illustration. This approach can be used for many biotechnological applications such as increasing the yield of a product, channelling a product into desired pathways and in functional reconstruction from genomic data.     

Parametric sensitivity of stoichiometric flux balance models applied to wild-type Escherichia coli metabolism

The esterification of lauric acid with geraniol catalyzed by the commercially immobilized lipase preparation from Mucor miehei, Lipozyme(R), was studied in well-stirred flasks. The enzyme support was characterized in terms of its internal and external surface area, protein location, and protein content. It was found that the enzyme was mainly located on the external surface of the support, therefore, internal diffusional limitations were not important. It was also shown that the protein content of the support depends on the size of the particle, with smaller particles containing higher amounts of protein per unit weight. Under the conditions studied, the reaction was not under external mass transfer limitations, and the initial reaction rate depended on the size of the support particles. This was mainly due to the different protein contents on the support as a function of particle size and not to internal or external mass transfer limitations. Also, it was found that the inhibition exerted by water was predominantly a physical effect due to its accumulation around the enzyme. It was also found that the reaction was substrate inhibited by lauric acid, but not by geraniol. (c) 1995 John Wiley & Sons, Inc.     

Dynamic flux balance analysis of diauxic growth in Escherichia coli

Flux Balance Analysis (FBA) has been used in the past to analyze microbial metabolic networks. Typically, FBA is used to study the metabolic flux at a particular steady state of the system. However, there are many situations where the reprogramming of the metabolic network is important. Therefore, the dynamics of these metabolic networks have to be studied. In this paper, we have extended FBA to account for dynamics and present two different formulations for dynamic FBA. These two approaches were used in the analysis of diauxic growth in Escherichia coli. Dynamic FBA was used to simulate the batch growth of E. coli on glucose, and the predictions were found to qualitatively match experimental data. The dynamic FBA formalism was also used to study the sensitivity to the objective function. It was found that an instantaneous objective function resulted in better predictions than a terminal-type objective function. The constraints that govern the growth at different phases in the batch culture were also identified. Therefore, dynamic FBA provides a framework for analyzing the transience of metabolism due to metabolic reprogramming and for obtaining insights for the design of metabolic networks.     

一种基于代谢网络分析最小化基因组的方法及其在大肠杆菌中的应用

最小生命体的合成是合成生物学研究的重要方向。最小化基因组的同时而又不对细胞生长产生影响是代谢工程研究的一个重要目标。文中提出了一种从基因组尺度代谢网络模型出发,通过零通量反应删除及对非必需基因组合删除计算获得基因组最小化代谢网络模型的方法,利用该方法简化了大肠杆菌经典代谢网络模型iAF1260,由起始的1 260个基因简化得到了312个基因,而最优生物质生成速率保持不变。基因组最小化代谢网络模型预测了在细胞正常生长的前提下包含最少基因的代谢途径,为大肠杆菌获得最小基因组的湿实验设计提供了重要参考。     

System-level insights into yeast metabolism by thermodynamic analysis of elementary flux modes

One of the most obvious phenotypes of a cell is its metabolic activity, which is defined by the fluxes in the metabolic network. Although experimental methods to determine intracellular fluxes are well established, only a limited number of fluxes can be resolved. Especially in eukaryotes such as yeast, compartmentalization and the existence of many parallel routes render exact flux analysis impossible using current methods. To gain more insight into the metabolic operation of S. cerevisiae we developed a new computational approach where we characterize the flux solution space by determining elementary flux modes (EFMs) that are subsequently classified as thermodynamically feasible or infeasible on the basis of experimental metabolome data. This allows us to provably rule out the contribution of certain EFMs to the in vivo flux distribution. From the 71 million EFMs in a medium size metabolic network of S. cerevisiae, we classified 54% as thermodynamically feasible. By comparing the thermodynamically feasible and infeasible EFMs, we could identify reaction combinations that span the cytosol and mitochondrion and, as a system, cannot operate under the investigated glucose batch conditions. Besides conclusions on single reactions, we found that thermodynamic constraints prevent the import of redox cofactor equivalents into the mitochondrion due to limits on compartmental cofactor concentrations. Our novel approach of incorporating quantitative metabolite concentrations into the analysis of the space of all stoichiometrically feasible flux distributions allows generating new insights into the system-level operation of the intracellular fluxes without making assumptions on metabolic objectives of the cell.     

Application of dynamic flux balance analysis to an industrial Escherichia coli fermentation

We have developed a reactor-scale model of Escherichia coli metabolism and growth in a 1000L process for the production of a recombinant therapeutic protein. The model consists of two distinct parts: (1) a dynamic, process specific portion that describes the time evolution of 37 process variables of relevance and (2) a flux balance based, 123-reaction metabolic model of E. coli metabolism. This model combines several previously reported modeling approaches including a growth rate-dependent biomass composition, maximum growth rate objective function, and dynamic flux balancing. In addition, we introduce concentration-dependent boundary conditions of transport fluxes, dynamic maintenance demands, and a state-dependent cellular objective. This formulation was able to describe specific runs with high-fidelity over process conditions including rich media, simultaneous acetate and glucose consumption, glucose minimal media, and phosphate depleted media. Furthermore, the model accurately describes the effect of process perturbations—such as glucose overbatching and insufficient aeration—on growth, metabolism, and titer.     

Structural analysis of metabolic networks based on flux centrality

Metabolic reactions are fundamental to living organisms, and a large number of reactions simultaneously occur at a given time in living cells transforming diverse metabolites into each other. There has been an ongoing debate on how to classify metabolites with respect to their importance for metabolic performance, usually based on the analysis of topological properties of genome scale metabolic networks. However, none of these studies have accounted quantitatively for flux in metabolic networks, thus lacking an important component of a cell’s biochemistry.We therefore analyzed a genome scale metabolic network of Escherichia coli by comparing growth under 19 different growth conditions, using flux balance analysis and weighted network centrality investigation. With this novel concept of flux centrality we generated metabolite rankings for each particular growth condition. In contrast to the results of conventional analysis of genome scale metabolic networks, different metabolites were top-ranking dependent on the growth condition. At the same time, several metabolites were consistently among the high ranking ones. Those are associated with pathways that have been described by biochemists as the most central part of metabolism, such as glycolysis, tricarboxylic acid cycle and pentose phosphate pathway. The values for the average path length of the analyzed metabolite networks were between 10.5 and 12.6, supporting recent findings that the metabolic network of E. coli is not a small-world network.     

The fractional contributions of elementary modes to the metabolism of Escherichia coli and their estimation from reaction entropies

The metabolism of a cell can be viewed as a weighted sum of elementary modes. Due to the multiplicity of modes the identification of the individual weights represents a non-trivial problem. To enable the determination of weighting factors we have identified and implemented two gene deletions in combination with defined growth conditions that limit the metabolism from 4374 original elementary modes to 24 elementary modes for a non-PHB synthesizing control and 40 modes for a PHB synthesizing strain. These remaining modes can be further grouped into five families that have the same overall stoichiometry. Thus, the complexity of the problem is significantly reduced, and weighting factors for each family of modes could be determined from the measurement of accumulation rates of metabolites. Moreover, it is shown that individual weights are inversely correlated with the entropy generated by the operation of the used pathways defined in elementary modes. This suggests that evolution developed cellular regulatory patterns that permit diversity of pathways while favoring efficient pathways with low entropy generation. Furthermore, such correlation provides a rational way of estimating metabolic fluxes based on the thermodynamic properties of elementary modes. This is demonstrated with an example in which experimentally determined, intracellular fluxes are shown to be highly correlated with fluxes computed based on elementary modes and reaction entropies. The analysis suggests that the set of elementary modes can be interpreted analogous to a metabolic ensemble of quantum states of a macroscopic system.     

Including metabolite concentrations into flux balance analysis: thermodynamic realizability as a constraint on flux distributions in metabolic networks

Background  

In recent years, constrained optimization – usually referred to as flux balance analysis (FBA) – has become a widely applied method for the computation of stationary fluxes in large-scale metabolic networks. The striking advantage of FBA as compared to kinetic modeling is that it basically requires only knowledge of the stoichiometry of the network. On the other hand, results of FBA are to a large degree hypothetical because the method relies on plausible but hardly provable optimality principles that are thought to govern metabolic flux distributions.     

Batch culture characterization and metabolic flux analysis of succinate-producing Escherichia coli strains

This study presents an in-depth analysis of the anaerobic metabolic fluxes of various mutant strains of Escherichia coli overexpressing the Lactococcus lactis pyruvate carboxylase (PYC) for the production of succinate. Previously, a metabolic network design that includes an active glyoxylate pathway implemented in vivo increased succinate yield from glucose in an E. coli mutant to 1.6 mol/mol under fully anaerobic conditions. The design consists of a dual succinate synthesis route, which diverts required quantities of NADH through the traditional fermentative pathway and maximizes the carbon converted to succinate by balancing the carbon flux through the fermentative pathway and the glyoxylate pathway (which has a lower NADH requirement). Mutant strains previously constructed during the development of high-yield succinate-producing strains were selected for further characterization to understand their metabolic response as a result of several genetic manipulations and to determine the significance of the fermentative and the glyoxylate pathways in the production of succinate. Measured fluxes obtained under batch cultivation conditions were used to estimate intracellular fluxes and identify critical branch point flux split ratios. The comparison of changes in branch point flux split ratios to the glyoxylate pathway and the fermentative pathway at the oxaloacetate (OAA) node as a result of different mutations revealed the sensitivity of succinate yield to these manipulations. The most favorable split ratio to obtain the highest succinate yield was the fractional partition of OAA to glyoxylate of 0.32 and 0.68 to the fermentative pathway obtained in strains SBS550MG (pHL413) and SBS990MG (pHL413). The succinate yields achieved in these two strains were 1.6 and 1.7 mol/mol, respectively. In addition, an active glyoxylate pathway in an ldhA, adhE, ack-pta mutant strain is shown to be responsible for the high succinate yields achieved anaerobically. Furthermore, in vitro activity measurements of seven crucial enzymes involved in the pathways studied and intracellular measurements of key intermediate metabolite pools provided additional insights on the physiological perturbations caused by these mutations. The characterization of these recombinant mutant strains in terms of flux distribution pattern, in vitro enzyme activity and intracellular metabolite pools provides useful information for the rational modification of metabolic fluxes to improve succinate production.     

Comprehensive analysis of glucose and xylose metabolism in Escherichia coli under aerobic and anaerobic conditions by 13C metabolic flux analysis

Glucose and xylose are the two most abundant sugars derived from the breakdown of lignocellulosic biomass. While aerobic glucose metabolism is relatively well understood in E. coli, until now there have been only a handful of studies focused on anaerobic glucose metabolism and no ¹³C-flux studies on xylose metabolism. In the absence of experimentally validated flux maps, constraint-based approaches such as MOMA and RELATCH cannot be used to guide new metabolic engineering designs. In this work, we have addressed this critical gap in current understanding by performing comprehensive characterizations of glucose and xylose metabolism under aerobic and anaerobic conditions, using recent state-of-the-art techniques in ¹³C metabolic flux analysis (¹³C-MFA). Specifically, we quantified precise metabolic fluxes for each condition by performing parallel labeling experiments and analyzing the data through integrated ¹³C-MFA using the optimal tracers [1,2-¹³C]glucose, [1,6-¹³C]glucose, [1,2-¹³C]xylose and [5-¹³C]xylose. We also quantified changes in biomass composition and confirmed turnover of macromolecules by applying [U-¹³C]glucose and [U-¹³C]xylose tracers. We demonstrated that under anaerobic growth conditions there is significant turnover of lipids and that a significant portion of CO₂ originates from biomass turnover. Using knockout strains, we also demonstrated that β-oxidation is critical for anaerobic growth on xylose. Quantitative analysis of co-factor balances (NADH/FADH₂, NADPH, and ATP) for different growth conditions provided new insights regarding the interplay of energy and redox metabolism and the impact on E. coli cell physiology.     

基于代谢流量分布信息理解大肠杆菌中异柠檬酸裂解酶调节因子的代谢调控作用

基因的表达受不同的转录调节因子调节。大肠杆菌中的异柠檬酸裂解酶调节因子(IclR)能够抑制编码乙醛酸支路酶的aceBAK操纵子的表达。本研究基于代谢物的13C同位体物质分布来定量解析代谢反应,主要研究了iclR基因在大肠杆菌生理和代谢中的作用。大肠杆菌iclR基因缺失突变株的生长速率、糖耗速率和乙酸的产量相对于原始菌株都有所降低,但菌体得率略有增加。通过代谢途径的流量比率分析发现基因缺失株的乙醛酸支路得到了激活,33%的异柠檬酸流经了乙醛酸支路;戊糖磷酸途径的流量变小,使得CO2的生成量减少。同时,乙醛酸支路激活,但草酰乙酸形成磷酸烯醇式丙酮酸的流量基本不变,说明磷酸烯醇式丙酮酸-乙醛酸循环没有激活,没有过多的碳原子在磷酸烯醇式丙酮酸羧化激酶反应中以CO2形式排出,从而确保了菌体得率。葡萄糖利用速率的降低、乙酰辅酶A的代谢效率提高等使得iclR基因敲除菌的乙酸分泌较原始菌株有所降低。     

Effect of the global redox sensing/regulation networks on Escherichia coli and metabolic flux distribution based on C-13 labeling experiments

Escherichia coli has several elaborate sensing mechanisms for response to the availability of oxygen and the presence of other electron acceptors. Among them, the one component Fnr protein and the two-component Arc system coordinate the adaptive responses to oxygen availability. To systematically investigate the contribution of Arc- and Fnr-dependent regulation in catabolism, glucose-limited chemostat cultures were conducted on wild-type E. coli, an arcA mutant, an fnr mutant, and an arcAfnr double mutant strains under a well-defined semi-aerobic condition. The metabolic flux distributions of the cultures of these strains were estimated based on C-13 labeling experiments. It was shown that the oxidative pentose phosphate (PP) pathway was functioning at low level under semi-aerobic condition. The fluxes through pyruvate dehydrogenase (PDH) and tricarboxylic acid (TCA) cycle were found to be lower in the arcA mutant and the arcAfnr double mutant strains than that in the wild-type strain, although the expression of the genes involved in these pathways have been proved to be derepressed in the mutant strains ([Shalel-Levanon, S., San, K.Y., Bennett, G.N., 2005a. Effect of ArcA and FNR on the expression of genes related to the oxygen regulation and the glycolysis pathway in Escherichia coli under microaerobic growth conditions. Biotechnol. Bioeng. 92, 147-159; Shalel-Levanon, S., San, K.Y., Bennett, G.N., 2005c. Effect of oxygen, and ArcA and FNR regulators on the expression of genes related to the electron transfer chain and the TCA cycle in Escherichia coli. Metab. Eng. 7, 364-374]). The significantly higher lactate production in the arcAfnr double mutant strain was shown to be an indirect effect caused by the reduced pyruvate formate-lyase (PFL) and PDH fluxes as well as the intracellular redox state.