Using Topology of the Metabolic Network to Predict Viability of Mutant Strains

Background  

Understanding the relationships between the structure (topology) and function of biological networks is a central question of systems biology. The idea that topology is a major determinant of systems function has become an attractive and highly-disputed hypothesis. While the structural analysis of interaction networks demonstrates a correlation between the topological properties of a node (protein, gene) in the network and its functional essentiality, the analysis of metabolic networks fails to find such correlations. In contrast, approaches utilizing both the topology and biochemical parameters of metabolic networks, e.g. flux balance analysis (FBA), are more successful in predicting phenotypes of knock-out strains.     

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.     

Metabolic flux profiling of Escherichia coli mutants in central carbon metabolism using GC-MS.

We describe here a novel methodology for rapid diagnosis of metabolic changes, which is based on probabilistic equations that relate GC-MS-derived mass distributions in proteinogenic amino acids to in vivo enzyme activities. This metabolic flux ratio analysis by GC-MS provides a comprehensive perspective on central metabolism by quantifying 14 ratios of fluxes through converging pathways and reactions from [1-13C] and [U-13C]glucose experiments. Reliability and accuracy of this method were experimentally verified by successfully capturing expected flux responses of Escherichia coli to environmental modifications and seven knockout mutations in all major pathways of central metabolism. Furthermore, several mutants exhibited additional, unexpected flux responses that provide new insights into the behavior of the metabolic network in its entirety. Most prominently, the low in vivo activity of the Entner-Doudoroff pathway in wild-type E. coli increased up to a contribution of 30% to glucose catabolism in mutants of glycolysis and TCA cycle. Moreover, glucose 6-phosphate dehydrogenase mutants catabolized glucose not exclusively via glycolysis, suggesting a yet unidentified bypass of this reaction. Although strongly affected by environmental conditions, a stable balance between anaplerotic and TCA cycle flux was maintained by all mutants in the upper part of metabolism. Overall, our results provide quantitative insight into flux changes that bring about the resilience of metabolic networks to disruption.     

Responses of the central metabolism in Escherichia coli to phosphoglucose isomerase and glucose-6-phosphate dehydrogenase knockouts

The responses of Escherichia coli central carbon metabolism to knockout mutations in phosphoglucose isomerase and glucose-6-phosphate (G6P) dehydrogenase genes were investigated by using glucose- and ammonia-limited chemostats. The metabolic network structures and intracellular carbon fluxes in the wild type and in the knockout mutants were characterized by using the complementary methods of flux ratio analysis and metabolic flux analysis based on [U-(13)C]glucose labeling and two-dimensional nuclear magnetic resonance (NMR) spectroscopy of cellular amino acids, glycerol, and glucose. Disruption of phosphoglucose isomerase resulted in use of the pentose phosphate pathway as the primary route of glucose catabolism, while flux rerouting via the Embden-Meyerhof-Parnas pathway and the nonoxidative branch of the pentose phosphate pathway compensated for the G6P dehydrogenase deficiency. Furthermore, additional, unexpected flux responses to the knockout mutations were observed. Most prominently, the glyoxylate shunt was found to be active in phosphoglucose isomerase-deficient E. coli. The Entner-Doudoroff pathway also contributed to a minor fraction of the glucose catabolism in this mutant strain. Moreover, although knockout of G6P dehydrogenase had no significant influence on the central metabolism under glucose-limited conditions, this mutation resulted in extensive overflow metabolism and extremely low tricarboxylic acid cycle fluxes under ammonia limitation conditions.     

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.     

Analysis of metabolic and physiological responses to gnd knockout in Escherichia coli by using C-13 tracer experiment and enzyme activity measurement

The physiological and metabolic responses to gnd knockout in Escherichia coli K-12 was quantitatively investigated by using the (13)C tracer experiment (GC-MS/NMR) together with the enzyme activity analysis. It was shown that the general response to the gene knockout was the local flux rerouting via Entner-Doudoroff pathway and the direction reversing via non-oxidative pentose phosphate pathway (PPP). The mutant was found to direct higher flux to phosphoglucose isomerase reaction as compared to the wild-type, but the respiratory metabolism was comparable in both strains. The anaplerotic pathway catalyzed by malic enzyme was identified in the mutant, which was accompanied with an up-regulation of phosphoenolpyruvate carboxylase and down-regulation of phosphoenolpyruvate carboxykinase. The presented results provide first evidence that compensatory mechanism existed in PPP and anaplerotic pathway in response to the gnd deletion.     

Flux balance analysis of ammonia assimilation network in E. coli predicts preferred regulation point

Nitrogen assimilation is a critical biological process for the synthesis of biomolecules in Escherichia coli. The central ammonium assimilation network in E. coli converts carbon skeleton α-ketoglutarate and ammonium into glutamate and glutamine, which further serve as nitrogen donors for nitrogen metabolism in the cell. This reaction network involves three enzymes: glutamate dehydrogenase (GDH), glutamine synthetase (GS) and glutamate synthase (GOGAT). In minimal media, E. coli tries to maintain an optimal growth rate by regulating the activity of the enzymes to match the availability of the external ammonia. The molecular mechanism and the strategy of the regulation in this network have been the research topics for many investigators. In this paper, we develop a flux balance model for the nitrogen metabolism, taking into account of the cellular composition and biosynthetic requirements for nitrogen. The model agrees well with known experimental results. Specifically, it reproduces all the (15)N isotope labeling experiments in the wild type and the two mutant (ΔGDH and ΔGOGAT) strains of E. coli. Furthermore, the predicted catalytic activities of GDH, GS and GOGAT in different ammonium concentrations and growth rates for the wild type, ΔGDH and ΔGOGAT strains agree well with the enzyme concentrations obtained from western blots. Based on this flux balance model, we show that GS is the preferred regulation point among the three enzymes in the nitrogen assimilation network. Our analysis reveals the pattern of regulation in this central and highly regulated network, thus providing insights into the regulation strategy adopted by the bacteria. Our model and methods may also be useful in future investigations in this and other networks.     

Identifying gene targets for the metabolic engineering of lycopene biosynthesis in Escherichia coli

The identification of genetic targets that are effective in bringing about a desired phenotype change is still an open problem. While random gene knockouts have yielded improved strains in certain cases, it is also important to seek the guidance of cell-wide stoichiometric constraints in identifying promising gene knockout targets. To investigate these issues, we undertook a genome-wide stoichiometric flux balance analysis as an aid in discovering putative genes impacting network properties and cellular phenotype. Specifically, we calculated metabolic fluxes such as to optimize growth and then scanned the genome for single and multiple gene knockouts that yield improved product yield while maintaining acceptable overall growth rate. For the particular case of lycopene biosynthesis in Escherichia coli, we identified such targets that we subsequently tested experimentally by constructing the corresponding single, double and triple gene knockouts. While such strains are suggested (by the stoichiometric calculations) to increase precursor availability, this beneficial effect may be further impacted by kinetic and regulatory effects not captured by the stoichiometric model. For the case of lycopene biosynthesis, the so identified knockout targets yielded a triple knockout construct that exhibited a nearly 40% increase over an engineered, high producing parental strain.     

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.     

Prediction of dynamic behavior of mutant strains from limited wild-type data

Metabolic engineering is the field of introducing genetic changes in organisms so as to modify their function towards synthesizing new products of high impact to society. However, engineered cells frequently have impaired growth rates thus seriously limiting the rate at which such products are made. The problem is attributable to inadequate understanding of how a metabolic network functions in a dynamic sense. Predictions of mutant strain behavior in the past have been based on steady state theories such as flux balance analysis (FBA), minimization of metabolic adjustment (MOMA), and regulatory on/off minimization (ROOM). Such predictions are restricted to product yields and cannot address productivity, which is of focal interest to applications. We demonstrate that our framework ( [Song and Ramkrishna, 2010] and [Song and Ramkrishna, 2011]), based on a “cybernetic” view of metabolic systems, makes predictions of the dynamic behavior of mutant strains of Escherichia coli from a limited amount of data obtained from the wild-type. Dynamic frameworks must necessarily address the issue of metabolic regulation, which the cybernetic approach does by postulating that metabolism is an optimal dynamic response of the organism to the environment in driving reactions towards ensuring survival. The predictions made in this paper are without parallel in the literature and lay the foundation for rational metabolic engineering.     

Probing the performance limits of the Escherichia coli metabolic network subject to gene additions or deletions.

An optimization-based procedure for studying the response of metabolic networks after gene knockouts or additions is introduced and applied to a linear flux balance analysis (FBA) Escherichia coli model. Both the gene addition problem of optimally selecting which foreign genes to recombine into E. coli, as well as the gene deletion problem of removing a given number of existing ones, are formulated as mixed-integer optimization problems using binary 0-1 variables. The developed modeling and optimization framework is tested by investigating the effect of gene deletions on biomass production and addressing the maximum theoretical production of the 20 amino acids for aerobic growth on glucose and acetate substrates. In the gene deletion study, the smallest gene set necessary to achieve maximum biomass production in E. coli is determined for aerobic growth on glucose. The subsequent gene knockout analysis indicates that biomass production decreases monotonically, rendering the metabolic network incapable of growth after only 18 gene deletions. In the gene addition study, the E. coli flux balance model is augmented with 3,400 non-E. coli reactions from the KEGG database to form a multispecies model. This model is referred to as the Universal model. This study reveals that the maximum theoretical production of six amino acids could be improved by the addition of only one or two genes to the native amino acid production pathway of E. coli, even though the model could choose from 3,400 foreign reaction candidates. Specifically, manipulation of the arginine production pathway showed the most promise with 8.75% and 9.05% predicted increases with the addition of genes for growth on glucose and acetate, respectively. The mechanism of all suggested enhancements is either by: 1) improving the energy efficiency and/or 2) increasing the carbon conversion efficiency of the production route.     

Incorporating metabolic flux ratios into constraint-based flux analysis by using artificial metabolites and converging ratio determinants

One of the well-established approaches for the quantitative characterization of large-scale underdetermined metabolic network is constraint-based flux analysis, which quantifies intracellular metabolic fluxes to characterize the metabolic status. The system is typically underdetermined, and thus usually is solved by linear programming with the measured external fluxes as constraints. Thus, the intracellular flux distribution calculated may not represent the true values. (13)C-constrained flux analysis allows more accurate determination of internal fluxes, but is currently limited to relatively small metabolic networks due to the requirement of complicated mathematical formulation and limited parameters available. Here, we report a strategy of employing such partial information obtained from the (13)C-labeling experiments as additional constraints during the constraint-based flux analysis. A new methodology employing artificial metabolites and converging ratio determinants (CRDs) was developed for improving constraint-based flux analysis. The CRDs were determined based on the metabolic flux ratios obtained from (13)C-labeling experiments, and were incorporated into the mass balance equations for the artificial metabolites. These new mass balance equations were used as additional constraints during the constraint-based flux analysis with genome-scale E. coli metabolic model, which allowed more accurate determination of intracellular metabolic fluxes.     

Mass-balanced randomization of metabolic networks

MOTIVATION: Network-centered studies in systems biology attempt to integrate the topological properties of biological networks with experimental data in order to make predictions and posit hypotheses. For any topology-based prediction, it is necessary to first assess the significance of the analyzed property in a biologically meaningful context. Therefore, devising network null models, carefully tailored to the topological and biochemical constraints imposed on the network, remains an important computational problem. RESULTS: We first review the shortcomings of the existing generic sampling scheme-switch randomization-and explain its unsuitability for application to metabolic networks. We then devise a novel polynomial-time algorithm for randomizing metabolic networks under the (bio)chemical constraint of mass balance. The tractability of our method follows from the concept of mass equivalence classes, defined on the representation of compounds in the vector space over chemical elements. We finally demonstrate the uniformity of the proposed method on seven genome-scale metabolic networks, and empirically validate the theoretical findings. The proposed method allows a biologically meaningful estimation of significance for metabolic network properties.     

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。     

Minimal cut sets in biochemical reaction networks

MOTIVATION: Structural studies of metabolic networks yield deeper insight into topology, functionality and capabilities of the metabolisms of different organisms. Here, we address the analysis of potential failure modes in metabolic networks whose occurrence will render the network structurally incapable of performing certain functions. Such studies will help to identify crucial parts in the network structure and to find suitable targets for repressing undesired metabolic functions. RESULTS: We introduce the concept of minimal cut sets for biochemical networks. A minimal cut set (MCS) is a minimal (irreducible) set of reactions in the network whose inactivation will definitely lead to a failure in certain network functions. We present an algorithm which enables the computation of the MCSs in a given network related to user-defined objective reactions. This algorithm operates on elementary modes. A number of potential applications are outlined, including network verifications, phenotype predictions, assessing structural robustness and fragility, metabolic flux analysis and target identification in drug discovery. Applications are illustrated by the MCSs in the central metabolism of Escherichia coli for growth on different substrates. AVAILABILITY: Computation and analysis of MCSs is an additional feature of the FluxAnalyzer (freely available for academic users upon request, special contracts for industrial companies; see web page below). Supplementary information: http://www.mpi-magdeburg.mpg.de/projects/fluxanalyzer     

Basic concepts and principles of stoichiometric modeling of metabolic networks

Metabolic networks supply the energy and building blocks for cell growth and maintenance. Cells continuously rewire their metabolic networks in response to changes in environmental conditions to sustain fitness. Studies of the systemic properties of metabolic networks give insight into metabolic plasticity and robustness, and the ability of organisms to cope with different environments. Constraint-based stoichiometric modeling of metabolic networks has become an indispensable tool for such studies. Herein, we review the basic theoretical underpinnings of constraint-based stoichiometric modeling of metabolic networks. Basic concepts, such as stoichiometry, chemical moiety conservation, flux modes, flux balance analysis, and flux solution spaces, are explained with simple, illustrative examples. We emphasize the mathematical definitions and their network topological interpretations.     

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.     

Metabolic network analysis revealed distinct routes of deletion effects between essential and non-essential genes

Interest in essential genes has arisen recently given their importance in antimicrobial drug development. Although knockouts of essential genes are commonly known to cause lethal phenotypes, there is insufficient understanding on the intermediate changes followed by genetic perturbation and to what extent essential genes correlate to other genes. Here, we characterized the gene knockout effects by using a list of affected genes, termed as 'damage lists'. These damage lists were identified through a refined cascading failure approach that was based on a previous topological flux balance analysis. Using an Escherichia coli metabolic network, we incorporated essentiality information into damage lists and revealed that the knockout of an essential gene mainly affects a large range of other essential genes whereas knockout of a non-essential gene only interrupts other non-essential genes. Also, genes sharing common damage lists tend to have the same essentiality. We extracted 72 core functional modules from the common damage lists of essential genes and demonstrated their ability to halt essential metabolites production. Overall, our network analysis revealed that essential and non-essential genes propagated their deletion effects via distinct routes, conferring mechanistic explanation to the observed lethality phenotypes of essential genes.     

Effect of a single-gene knockout on the metabolic regulation in Escherichia coli for D-lactate production under microaerobic condition

The effects of several single-gene knockout mutants (pykF, ppc, pflA, pta, and adhE mutants) on the metabolic flux distribution in Escherichia coli were investigated under microaerobic condition. The intracellular metabolite concentrations and enzyme activities were measured, and the metabolic flux distribution was computed to study the metabolic regulation in the cell. The pflA, pta and ppc mutants produced large amount of lactate when using glucose as a carbon source under microaerobic condition. Comparing the flux distribution and the enzyme activities in the mutants, it was shown that the lactate production was promoted by the inactivation of pyruvate formate lyase and the resulting overexpression of lactate dehydrogenase. The flux through Pta-Ack pathways and the ethanol production were limited by the available acetyl coenzyme A. It was shown that the glycolysis was activated in pykF mutant in microaerobic culture. The glycolytic flux was related with Pyk activity except for pykF mutant. The cell growth rate was shown to be affected by the flux through phosphoenolpyruvate carboxylase. The quantitative regulation analysis was made based on the deviation indexes.     

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。