Flux Imbalance Analysis and the Sensitivity of Cellular Growth to Changes in Metabolite Pools

Stoichiometric models of metabolism, such as flux balance analysis (FBA), are classically applied to predicting steady state rates - or fluxes - of metabolic reactions in genome-scale metabolic networks. Here we revisit the central assumption of FBA, i.e. that intracellular metabolites are at steady state, and show that deviations from flux balance (i.e. flux imbalances) are informative of some features of in vivo metabolite concentrations. Mathematically, the sensitivity of FBA to these flux imbalances is captured by a native feature of linear optimization, the dual problem, and its corresponding variables, known as shadow prices. First, using recently published data on chemostat growth of Saccharomyces cerevisae under different nutrient limitations, we show that shadow prices anticorrelate with experimentally measured degrees of growth limitation of intracellular metabolites. We next hypothesize that metabolites which are limiting for growth (and thus have very negative shadow price) cannot vary dramatically in an uncontrolled way, and must respond rapidly to perturbations. Using a collection of published datasets monitoring the time-dependent metabolomic response of Escherichia coli to carbon and nitrogen perturbations, we test this hypothesis and find that metabolites with negative shadow price indeed show lower temporal variation following a perturbation than metabolites with zero shadow price. Finally, we illustrate the broader applicability of flux imbalance analysis to other constraint-based methods. In particular, we explore the biological significance of shadow prices in a constraint-based method for integrating gene expression data with a stoichiometric model. In this case, shadow prices point to metabolites that should rise or drop in concentration in order to increase consistency between flux predictions and gene expression data. In general, these results suggest that the sensitivity of metabolic optima to violations of the steady state constraints carries biologically significant information on the processes that control intracellular metabolites in the cell.     

Conservation of high-flux backbone in alternate optimal and near-optimal flux distributions of metabolic networks

Constraint-based flux balance analysis (FBA) has proven successful in predicting the flux distribution of metabolic networks in diverse environmental conditions. FBA finds one of the alternate optimal solutions that maximizes the biomass production rate. Almaas et al. have shown that the flux distribution follows a power law, and it is possible to associate with most metabolites two reactions which maximally produce and consume a given metabolite, respectively. This observation led to the concept of high-flux backbone (HFB) in metabolic networks. In previous work, the HFB has been computed using a particular optima obtained using FBA. In this paper, we investigate the conservation of HFB of a particular solution for a given medium across different alternate optima and near-optima in metabolic networks of E. coli and S. cerevisiae. Using flux variability analysis (FVA), we propose a method to determine reactions that are guaranteed to be in HFB regardless of alternate solutions. We find that the HFB of a particular optima is largely conserved across alternate optima in E. coli, while it is only moderately conserved in S. cerevisiae. However, the HFB of a particular near-optima shows a large variation across alternate near-optima in both organisms. We show that the conserved set of reactions in HFB across alternate near-optima has a large overlap with essential reactions and reactions which are both uniquely consuming (UC) and uniquely producing (UP). Our findings suggest that the structure of the metabolic network admits a high degree of redundancy and plasticity in near-optimal flow patterns enhancing system robustness for a given environmental condition.     

Dynamic control over feedback regulatory mechanisms improves NADPH flux and xylitol biosynthesis in engineered E. coli

We report improved NADPH flux and xylitol biosynthesis in engineered E. coli. Xylitol is produced from xylose via an NADPH dependent reductase. We utilize 2-stage dynamic metabolic control to compare two approaches to optimize xylitol biosynthesis, a stoichiometric approach, wherein competitive fluxes are decreased, and a regulatory approach wherein the levels of key regulatory metabolites are reduced. The stoichiometric and regulatory approaches lead to a 20-fold and 90-fold improvement in xylitol production, respectively. Strains with reduced levels of enoyl-ACP reductase and glucose-6-phosphate dehydrogenase, led to altered metabolite pools resulting in the activation of the membrane bound transhydrogenase and an NADPH generation pathway, consisting of pyruvate ferredoxin oxidoreductase coupled with NADPH dependent ferredoxin reductase, leading to increased NADPH fluxes, despite a reduction in NADPH pools. These strains produced titers of 200 g/L of xylitol from xylose at 86% of theoretical yield in instrumented bioreactors. We expect dynamic control over the regulation of the membrane bound transhydrogenase as well as NADPH production through pyruvate ferredoxin oxidoreductase to broadly enable improved NADPH dependent bioconversions or production via NADPH dependent metabolic pathways.     

ΔFBA—Predicting metabolic flux alterations using genome-scale metabolic models and differential transcriptomic data

Genome-scale metabolic models (GEMs) provide a powerful framework for simulating the entire set of biochemical reactions in a cell using a constraint-based modeling strategy called flux balance analysis (FBA). FBA relies on an assumed metabolic objective for generating metabolic fluxes using GEMs. But, the most appropriate metabolic objective is not always obvious for a given condition and is likely context-specific, which often complicate the estimation of metabolic flux alterations between conditions. Here, we propose a new method, called ΔFBA (deltaFBA), that integrates differential gene expression data to evaluate directly metabolic flux differences between two conditions. Notably, ΔFBA does not require specifying the cellular objective. Rather, ΔFBA seeks to maximize the consistency and minimize inconsistency between the predicted flux differences and differential gene expression. We showcased the performance of ΔFBA through several case studies involving the prediction of metabolic alterations caused by genetic and environmental perturbations in Escherichia coli and caused by Type-2 diabetes in human muscle. Importantly, in comparison to existing methods, ΔFBA gives a more accurate prediction of flux differences.     

Metabolic flux balance analysis and the in silicoanalysis of Escherichia coliK-12 gene deletions

Background

Genome sequencing and bioinformatics are producing detailed lists of the molecular components contained in many prokaryotic organisms. From this 'parts catalogue' of a microbial cell, in silicorepresentations of integrated metabolic functions can be constructed and analyzed using flux balance analysis (FBA). FBA is particularly well-suited to study metabolic networks based on genomic, biochemical, and strain specific information.

Results

Herein, we have utilized FBA to interpret and analyze the metabolic capabilities of Escherichia coli. We have computationally mapped the metabolic capabilities of E. coliusing FBA and examined the optimal utilization of the E. colimetabolic pathways as a function of environmental variables. We have used an in silicoanalysis to identify seven gene products of central metabolism (glycolysis, pentose phosphate pathway, TCA cycle, electron transport system) essential for aerobic growth of E. colion glucose minimal media, and 15 gene products essential for anaerobic growth on glucose minimal media. The in silico tpi ^-, zwf, and pta ^-mutant strains were examined in more detail by mapping the capabilities of these in silicoisogenic strains.

Conclusions

We found that computational models of E. colimetabolism based on physicochemical constraints can be used to interpret mutant behavior. These in silicaresults lead to a further understanding of the complex genotype-phenotype relation. Supplementary information: 10.1186/1471-2105-1-1     

MapMaker and PathTracer for tracking carbon in genome‐scale metabolic models

Constraint‐based reconstruction and analysis (COBRA) modeling results can be difficult to interpret given the large numbers of reactions in genome‐scale models. While paths in metabolic networks can be found, existing methods are not easily combined with constraint‐based approaches. To address this limitation, two tools (MapMaker and PathTracer) were developed to find paths (including cycles) between metabolites, where each step transfers carbon from reactant to product. MapMaker predicts carbon transfer maps (CTMs) between metabolites using only information on molecular formulae and reaction stoichiometry, effectively determining which reactants and products share carbon atoms. MapMaker correctly assigned CTMs for over 97% of the 2,251 reactions in an Escherichia coli metabolic model (iJO1366). Using CTMs as inputs, PathTracer finds paths between two metabolites. PathTracer was applied to iJO1366 to investigate the importance of using CTMs and COBRA constraints when enumerating paths, to find active and high flux paths in flux balance analysis (FBA) solutions, to identify paths for putrescine utilization, and to elucidate a potential CO₂ fixation pathway in E. coli. These results illustrate how MapMaker and PathTracer can be used in combination with constraint‐based models to identify feasible, active, and high flux paths between metabolites.     

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.     

Genome-Scale Metabolic Network Validation of Shewanella oneidensis Using Transposon Insertion Frequency Analysis

Transposon mutagenesis, in combination with parallel sequencing, is becoming a powerful tool for en-masse mutant analysis. A probability generating function was used to explain observed miniHimar transposon insertion patterns, and gene essentiality calls were made by transposon insertion frequency analysis (TIFA). TIFA incorporated the observed genome and sequence motif bias of the miniHimar transposon. The gene essentiality calls were compared to: 1) previous genome-wide direct gene-essentiality assignments; and, 2) flux balance analysis (FBA) predictions from an existing genome-scale metabolic model of Shewanella oneidensis MR-1. A three-way comparison between FBA, TIFA, and the direct essentiality calls was made to validate the TIFA approach. The refinement in the interpretation of observed transposon insertions demonstrated that genes without insertions are not necessarily essential, and that genes that contain insertions are not always nonessential. The TIFA calls were in reasonable agreement with direct essentiality calls for S. oneidensis, but agreed more closely with E. coli essentiality calls for orthologs. The TIFA gene essentiality calls were in good agreement with the MR-1 FBA essentiality predictions, and the agreement between TIFA and FBA predictions was substantially better than between the FBA and the direct gene essentiality predictions.     

Simulating Serial-Target Antibacterial Drug Synergies Using Flux Balance Analysis

Flux balance analysis (FBA) is an increasingly useful approach for modeling the behavior of metabolic systems. However, standard FBA modeling of genetic knockouts cannot predict drug combination synergies observed between serial metabolic targets, even though such synergies give rise to some of the most widely used antibiotic treatments. Here we extend FBA modeling to simulate responses to chemical inhibitors at varying concentrations, by diverting enzymatic flux to a waste reaction. This flux diversion yields very similar qualitative predictions to prior methods for single target activity. However, we find very different predictions for combinations, where flux diversion, which mimics the kinetics of competitive metabolic inhibitors, can explain serial target synergies between metabolic enzyme inhibitors that we confirmed in Escherichia coli cultures. FBA flux diversion opens the possibility for more accurate genome-scale predictions of drug synergies, which can be used to suggest treatments for infections and other diseases.     

Comparative study on central metabolic fluxes of <Emphasis Type="Italic">Bacillus megaterium</Emphasis> strains in continuous culture using <Superscript>13</Superscript>C labelled substrates

Fluxes of central carbon metabolism [glycolysis, pentose phosphate pathway (PPP), tricarboxylic acid cycle (TCA cycle), biomass formation] were determined for several Bacillus megaterium strains (DSM319, WH320, WH323, MS941) in C- and N-limited chemostat cultures by ¹³C labelling experiments. The labelling patterns of proteinogenic amino acids were analysed by GC/MS and therefrom flux ratios at important nodes within the metabolic network could be calculated. On the basis of a stoichiometric metabolic model flux distributions were estimated for the different B. megaterium strains used at various cultivation conditions. Generally all strains exhibited similar metabolic flux distributions, however, several significant changes were found in (1) the glucose flux entering the PPP via the oxidative branch, (2) the reversibilities within the PPP, (3) the relative fluxes of pyruvate and acetyl-CoA fed to the TCA cycle, (4) the fluxes around the pyruvate node involving a futile cycle.     

The Ability of Flux Balance Analysis to Predict Evolution of Central Metabolism Scales with the Initial Distance to the Optimum

The most powerful genome-scale framework to model metabolism, flux balance analysis (FBA), is an evolutionary optimality model. It hypothesizes selection upon a proposed optimality criterion in order to predict the set of internal fluxes that would maximize fitness. Here we present a direct test of the optimality assumption underlying FBA by comparing the central metabolic fluxes predicted by multiple criteria to changes measurable by a ¹³C-labeling method for experimentally-evolved strains. We considered datasets for three Escherichia coli evolution experiments that varied in their length, consistency of environment, and initial optimality. For ten populations that were evolved for 50,000 generations in glucose minimal medium, we observed modest changes in relative fluxes that led to small, but significant decreases in optimality and increased the distance to the predicted optimal flux distribution. In contrast, seven populations evolved on the poor substrate lactate for 900 generations collectively became more optimal and had flux distributions that moved toward predictions. For three pairs of central metabolic knockouts evolved on glucose for 600–800 generations, there was a balance between cases where optimality and flux patterns moved toward or away from FBA predictions. Despite this variation in predictability of changes in central metabolism, two generalities emerged. First, improved growth largely derived from evolved increases in the rate of substrate use. Second, FBA predictions bore out well for the two experiments initiated with ancestors with relatively sub-optimal yield, whereas those begun already quite optimal tended to move somewhat away from predictions. These findings suggest that the tradeoff between rate and yield is surprisingly modest. The observed positive correlation between rate and yield when adaptation initiated further from the optimum resulted in the ability of FBA to use stoichiometric constraints to predict the evolution of metabolism despite selection for rate.     

Estimating Metabolic Fluxes Using a Maximum Network Flexibility Paradigm

MotivationGenome-scale metabolic networks can be modeled in a constraint-based fashion. Reaction stoichiometry combined with flux capacity constraints determine the space of allowable reaction rates. This space is often large and a central challenge in metabolic modeling is finding the biologically most relevant flux distributions. A widely used method is flux balance analysis (FBA), which optimizes a biologically relevant objective such as growth or ATP production. Although FBA has proven to be highly useful for predicting growth and byproduct secretion, it cannot predict the intracellular fluxes under all environmental conditions. Therefore, alternative strategies have been developed to select flux distributions that are in agreement with experimental “omics” data, or by incorporating experimental flux measurements. The latter, unfortunately can only be applied to a limited set of reactions and is currently not feasible at the genome-scale. On the other hand, it has been observed that micro-organisms favor a suboptimal growth rate, possibly in exchange for a more “flexible” metabolic network. Instead of dedicating the internal network state to an optimal growth rate in one condition, a suboptimal growth rate is used, that allows for an easier switch to other nutrient sources. A small decrease in growth rate is exchanged for a relatively large gain in metabolic capability to adapt to changing environmental conditions.ResultsHere, we propose Maximum Metabolic Flexibility (MMF) a computational method that utilizes this observation to find the most probable intracellular flux distributions. By mapping measured flux data from central metabolism to the genome-scale models of Escherichia coli and Saccharomyces cerevisiae we show that i) indeed, most of the measured fluxes agree with a high adaptability of the network, ii) this result can be used to further reduce the space of feasible solutions iii) this reduced space improves the quantitative predictions made by FBA and contains a significantly larger fraction of the measured fluxes compared to the flux space that was reduced by a uniform sampling approach and iv) MMF can be used to select reactions in the network that contribute most to the steady-state flux space. Constraining the selected reactions improves the quantitative predictions of FBA considerably more than adding an equal amount of flux constraints, selected using a more naïve approach. Our method can be applied to any cell type without requiring prior information.AvailabilityMMF is freely available as a MATLAB plugin at: http://cs.ru.nl/~wmegchel/mmf.     

Flux analysis of recombinant Saccharomyces cerevisiae YPB-G utilizing starch for optimal ethanol production

Genetically modified Saccharomyces cerevisiae strain (YPB-G) which secretes a bifunctional fusion protein that contains both Bacillus subtilis -amylase and Aspergillus awamori glucoamylase activities was used for the direct conversion of starch into ethanol. Starch was either supplied initially to different nutrient media or added instantaneously to the reactor at various discrete time instants (pulse feeding). Stoichiometric modeling was used to investigate the effects of initial substrate concentration and growth rate of the recombinant yeast culture on ethanol production. Reaction stoichiometries describing both the anabolism and catabolism of the microorganism were used as an input to flux balance analysis (FBA), the preferred metabolic modeling approach since the constructed stoichiometric network was underdetermined. Experiments for batch and fed-batch systems at different substrate concentrations were analyzed theoretically in terms of flux distributions using ethanol production rate as the maximization criteria. Calculated ethanol rates were in agreement with experimental measurements, suggesting that this recombinant microorganism is sufficiently evolved to optimize its ethanol production. The function of the main pathways of yeast metabolism (PPP, EMP, TCA) are discussed together with the node analyses of glucose-6-P and pyruvate branch points. Theoretical node analysis revealed that if the split ratio in G6P branch point is changed by genetic manipulations, the ethanol yield would be affected considerably.     

Thermodynamics-based Metabolite Sensitivity Analysis in metabolic networks

The increasing availability of large metabolomics datasets enhances the need for computational methodologies that can organize the data in a way that can lead to the inference of meaningful relationships. Knowledge of the metabolic state of a cell and how it responds to various stimuli and extracellular conditions can offer significant insight in the regulatory functions and how to manipulate them. Constraint based methods, such as Flux Balance Analysis (FBA) and Thermodynamics-based flux analysis (TFA), are commonly used to estimate the flow of metabolites through genome-wide metabolic networks, making it possible to identify the ranges of flux values that are consistent with the studied physiological and thermodynamic conditions. However, unless key intracellular fluxes and metabolite concentrations are known, constraint-based models lead to underdetermined problem formulations. This lack of information propagates as uncertainty in the estimation of fluxes and basic reaction properties such as the determination of reaction directionalities. Therefore, knowledge of which metabolites, if measured, would contribute the most to reducing this uncertainty can significantly improve our ability to define the internal state of the cell. In the present work we combine constraint based modeling, Design of Experiments (DoE) and Global Sensitivity Analysis (GSA) into the Thermodynamics-based Metabolite Sensitivity Analysis (TMSA) method. TMSA ranks metabolites comprising a metabolic network based on their ability to constrain the gamut of possible solutions to a limited, thermodynamically consistent set of internal states. TMSA is modular and can be applied to a single reaction, a metabolic pathway or an entire metabolic network. This is, to our knowledge, the first attempt to use metabolic modeling in order to provide a significance ranking of metabolites to guide experimental measurements.     

Metabolic transistor strategy for controlling electron transfer chain activity in Escherichia coli

A novel strategy to finely control a large metabolic flux by using a “metabolic transistor” approach was established. In this approach a small change in the level or availability of an essential component for the process is controlled by adding a competitive reaction that affects a precursor or an intermediate in its biosynthetic pathway. The change of the basal level of the essential component, considered as a base current in a transistor, has a large effect on the flux through the major pathway. In this way, the fine-tuning of a large flux can be accomplished. The “metabolic transistor” strategy was applied to control electron transfer chain function by manipulation of the quinone synthesis pathway in Escherichia coli. The achievement of a theoretical yield of lactate production under aerobic conditions via this strategy upon manipulation of the biosynthetic pathway of the key participant, ubiquinone-8 (Q8), in an E. coli strain provides an in vivo, genetically tunable means to control the activity of the electron transfer chain and manipulate the production of reduced products while limiting consumption of oxygen to a defined amount.     

Optimal cofactor swapping can increase the theoretical yield for chemical production in Escherichia coli and Saccharomyces cerevisiae

Maintaining cofactor balance is a critical function in microorganisms, but often the native cofactor balance does not match the needs of an engineered metabolic flux state. Here, an optimization procedure is utilized to identify optimal cofactor-specificity “swaps” for oxidoreductase enzymes utilizing NAD(H) or NADP(H) in the genome-scale metabolic models of Escherichia coli and Saccharomyces cerevisiae. The theoretical yields of all native carbon-containing molecules are considered, as well as theoretical yields of twelve heterologous production pathways in E. coli. Swapping the cofactor specificity of central metabolic enzymes (especially GAPD and ALCD2x) is shown to increase NADPH production and increase theoretical yields for native products in E. coli and yeast—including l-aspartate, l-lysine, l-isoleucine, l-proline, l-serine, and putrescine—and non-native products in E. coli—including 1,3-propanediol, 3-hydroxybutyrate, 3-hydroxypropanoate, 3-hydroxyvalerate, and styrene.     

A guide to metabolic flux analysis in metabolic engineering: Methods,tools and applications

The field of metabolic engineering is primarily concerned with improving the biological production of value-added chemicals, fuels and pharmaceuticals through the design, construction and optimization of metabolic pathways, redirection of intracellular fluxes, and refinement of cellular properties relevant for industrial bioprocess implementation. Metabolic network models and metabolic fluxes are central concepts in metabolic engineering, as was emphasized in the first paper published in this journal, “Metabolic fluxes and metabolic engineering” (Metabolic Engineering, 1: 1–11, 1999). In the past two decades, a wide range of computational, analytical and experimental approaches have been developed to interrogate the capabilities of biological systems through analysis of metabolic network models using techniques such as flux balance analysis (FBA), and quantify metabolic fluxes using constrained-based modeling approaches such as metabolic flux analysis (MFA) and more advanced experimental techniques based on the use of stable-isotope tracers, i.e. ¹³C-metabolic flux analysis (¹³C-MFA). In this review, we describe the basic principles of metabolic flux analysis, discuss current best practices in flux quantification, highlight potential pitfalls and alternative approaches in the application of these tools, and give a broad overview of pragmatic applications of flux analysis in metabolic engineering practice.     

Integrated knowledge mining,genome-scale modeling,and machine learning for predicting Yarrowia lipolytica bioproduction

Predicting bioproduction titers from microbial hosts has been challenging due to complex interactions between microbial regulatory networks, stress responses, and suboptimal cultivation conditions. This study integrated knowledge mining, feature extraction, genome-scale modeling (GSM), and machine learning (ML) to develop a model for predicting Yarrowia lipolytica chemical titers (i.e., organic acids, terpenoids, etc.). First, Y. lipolytica production data, including cultivation conditions, genetic engineering strategies, and product information, was manually collected from literature (~100 papers) and stored as either numerical (e.g., substrate concentrations) or categorical (e.g., bioreactor modes) variables. For each case recorded, central pathway fluxes were estimated using GSMs and flux balance analysis (FBA) to provide metabolic features. Second, a ML ensemble learner was trained to predict strain production titers. Accurate predictions on the test data were obtained for instances with production titers >1 g/L (R² = 0.87). However, the model had reduced predictability for low performance strains (0.01–1 g/L, R² = 0.29) potentially due to biosynthesis bottlenecks not captured in the features. Feature ranking indicated that the FBA fluxes, the number of enzyme steps, the substrate inputs, and thermodynamic barriers (i.e., Gibbs free energy of reaction) were the most influential factors. Third, the model was evaluated on other oleaginous yeasts and indicated there were conserved features for some hosts that can be potentially exploited by transfer learning. The platform was also designed to assist computational strain design tools (such as OptKnock) to screen genetic targets for improved microbial production in light of experimental conditions.     

Identifying All Moiety Conservation Laws in Genome-Scale Metabolic Networks

The stoichiometry of a metabolic network gives rise to a set of conservation laws for the aggregate level of specific pools of metabolites, which, on one hand, pose dynamical constraints that cross-link the variations of metabolite concentrations and, on the other, provide key insight into a cell''s metabolic production capabilities. When the conserved quantity identifies with a chemical moiety, extracting all such conservation laws from the stoichiometry amounts to finding all non-negative integer solutions of a linear system, a programming problem known to be NP-hard. We present an efficient strategy to compute the complete set of integer conservation laws of a genome-scale stoichiometric matrix, also providing a certificate for correctness and maximality of the solution. Our method is deployed for the analysis of moiety conservation relationships in two large-scale reconstructions of the metabolism of the bacterium E. coli, in six tissue-specific human metabolic networks, and, finally, in the human reactome as a whole, revealing that bacterial metabolism could be evolutionarily designed to cover broader production spectra than human metabolism. Convergence to the full set of moiety conservation laws in each case is achieved in extremely reduced computing times. In addition, we uncover a scaling relation that links the size of the independent pool basis to the number of metabolites, for which we present an analytical explanation.