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.     

Effect of amino acid supplementation on titer and glycosylation distribution in hybridoma cell cultures—Systems biology‐based interpretation using genome‐scale metabolic flux balance model and multivariate data analysis

Genome‐scale flux balance analysis (FBA) is a powerful systems biology tool to characterize intracellular reaction fluxes during cell cultures. FBA estimates intracellular reaction rates by optimizing an objective function, subject to the constraints of a metabolic model and media uptake/excretion rates. A dynamic extension to FBA, dynamic flux balance analysis (DFBA), can calculate intracellular reaction fluxes as they change during cell cultures. In a previous study by Read et al. (2013), a series of informed amino acid supplementation experiments were performed on twelve parallel murine hybridoma cell cultures, and this data was leveraged for further analysis (Read et al., Biotechnol Prog. 2013;29:745–753). In order to understand the effects of media changes on the model murine hybridoma cell line, a systems biology approach is applied in the current study. Dynamic flux balance analysis was performed using a genome‐scale mouse metabolic model, and multivariate data analysis was used for interpretation. The calculated reaction fluxes were examined using partial least squares and partial least squares discriminant analysis. The results indicate media supplementation increases product yield because it raises nutrient levels extending the growth phase, and the increased cell density allows for greater culture performance. At the same time, the directed supplementation does not change the overall metabolism of the cells. This supports the conclusion that product quality, as measured by glycoform assays, remains unchanged because the metabolism remains in a similar state. Additionally, the DFBA shows that metabolic state varies more at the beginning of the culture but less by the middle of the growth phase, possibly due to stress on the cells during inoculation. © 2016 American Institute of Chemical Engineers Biotechnol. Prog., 32:1163–1173, 2016     

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.     

Flux-balance analysis of mitochondrial energy metabolism: consequences of systemic stoichiometric constraints

Mitochondrial metabolism is a critical component in the functioning and maintenance of cellular organs. The stoichiometry of biochemical reaction networks imposes constraints on mitochondrial function. A modeling framework, flux-balance analysis (FBA), was used to characterize the optimal flux distributions for maximal ATP production in the mitochondrion. The model predicted the expected ATP yields for glucose, lactate, and palmitate. Genetic defects that affect mitochondrial functions have been implicated in several human diseases. FBA can characterize the metabolic behavior due to genetic deletions at the metabolic level, and the effect of mutations in the tricarboxylic acid (TCA) cycle on mitochondrial ATP production was simulated. The mitochondrial ATP production is severely affected by TCA-cycle mutations. In addition, the model predicts the secretion of TCA-cycle intermediates, which is observed in clinical studies of mitochondriopathies such as those associated with fumarase deficiency. The model provides a systemic perspective to characterize the effect of stoichiometric constraints and specific metabolic fluxes on mitochondrial function.     

Predictive Potential of Flux Balance Analysis of Saccharomyces cerevisiae Using as Optimization Function Combinations of Cell Compartmental Objectives

Background

The main objective of flux balance analysis (FBA) is to obtain quantitative predictions of metabolic fluxes of an organism, and it is necessary to use an appropriate objective function to guarantee a good estimation of those fluxes.

Methodology

In this study, the predictive performance of FBA was evaluated, using objective functions arising from the linear combination of different cellular objectives. This approach is most suitable for eukaryotic cells, owing to their multiplicity of cellular compartments. For this reason, Saccharomyces cerevisiae was used as model organism, and its metabolic network was represented using the genome-scale metabolic model iMM904. As the objective was to evaluate the predictive performance from the FBA using the kind of objective function previously described, substrate uptake and oxygen consumption were the only input data used for the FBA. Experimental information about microbial growth and exchange of metabolites with the environment was used to assess the quality of the predictions.

Conclusions

The quality of the predictions obtained with the FBA depends greatly on the knowledge of the oxygen uptake rate. For the most of studied classifications, the best predictions were obtained with “maximization of growth”, and with some combinations that include this objective. However, in the case of exponential growth with unknown oxygen exchange flux, the objective function “maximization of growth, plus minimization of NADH production in cytosol, plus minimization of NAD(P)H consumption in mitochondrion” gave much more accurate estimations of fluxes than the obtained with any other objective function explored in this study.     

Improving the accuracy of flux balance analysis through the implementation of carbon availability constraints for intracellular reactions

Constraint-based modeling methods, such as Flux Balance Analysis (FBA), have been extensively used to decipher complex, information rich -omics datasets to elicit system-wide behavioral patterns of cellular metabolism. FBA has been successfully used to gain insight in a wide range of applications, such as range of substrate utilization, product yields and to design metabolic engineering strategies to improve bioprocess performance. A well-known challenge associated with large genome-scale metabolic networks is that they result in underdetermined problem formulations. Consequently, rather than unique solutions, FBA and related methods examine ranges of reaction flux values that are consistent with the studied physiological conditions. The wider the reported flux ranges, the higher the uncertainty in the determination of basic reaction properties, limiting interpretability of and confidence in the results. Herein, we propose a new, computationally efficient approach that refines flux range predictions by constraining reaction fluxes on the basis of the elemental balance of carbon. We compared carbon constraint FBA (ccFBA) against experimentally-measured intracellular fluxes using the latest CHO GEM (iCHO1766) and were able to substantially improve the accuracy of predicted flux values compared with FBA. ccFBA can be used as a stand-alone method but is also compatible with and complimentary to other constraint-based approaches.     

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.     

Metabolic flux analysis and visualization

One of the ultimate goals of systems biology research is to obtain a comprehensive understanding of the control mechanisms of complex cellular metabolisms. Metabolic Flux Analysis (MFA) is a important method for the quantitative estimation of intracellular metabolic flows through metabolic pathways and the elucidation of cellular physiology. The primary challenge in the use of MFA is that many biological networks are underdetermined systems; it is therefore difficult to narrow down the solution space from the stoichiometric constraints alone. In this tutorial, we present an overview of Flux Balance Analysis (FBA) and (13)C-Metabolic Flux Analysis ((13)C-MFA), both of which are frequently used to solve such underdetermined systems, and we demonstrate FBA and (13)C-MFA using the genome-scale model and the central carbon metabolism model, respectively. Furthermore, because such comprehensive study of intracellular fluxes is inherently complex, we subsequently introduce various pathway mapping and visualization tools to facilitate understanding of these data in the context of the pathways. Specific visualization of MFA results using the BioCyc Omics Viewer and Pathway Projector are shown as illustrative examples.     

Characterizing the metabolic phenotype: a phenotype phase plane analysis.

Genome-scale metabolic maps can be reconstructed from annotated genome sequence data, biochemical literature, bioinformatic analysis, and strain-specific information. Flux-balance analysis has been useful for qualitative and quantitative analysis of metabolic reconstructions. In the past, FBA has typically been performed in one growth condition at a time, thus giving a limited view of the metabolic capabilities of a metabolic network. We have broadened the use of FBA to map the optimal metabolic flux distribution onto a single plane, which is defined by the availability of two key substrates. A finite number of qualitatively distinct patterns of metabolic pathway utilization were identified in this plane, dividing it into discrete phases. The characteristics of these distinct phases are interpreted using ratios of shadow prices in the form of isoclines. The isoclines can be used to classify the state of the metabolic network. This methodology gives rise to a "phase plane" analysis of the metabolic genotype-phenotype relation relevant for a range of growth conditions. Phenotype phase planes (PhPPs) were generated for Escherichia coli growth on two carbon sources (acetate and glucose) at all levels of oxygenation, and the resulting optimal metabolic phenotypes were studied. Supplementary information can be downloaded from our website (http://epicurus.che.udel.edu).     

Insights into metabolic efficiency from flux analysis

The efficiency of carbon and energy flows throughout metabolism defines the potential for growth and reproductive success of plants. Understanding the basis for metabolic efficiency requires relevant definitions of efficiency as well as measurements of biochemical functions through metabolism. Here insights into the basis of efficiency provided by (13)C-based metabolic flux analysis (MFA) as well as the uses and limitations of efficiency in predictive flux balance analysis (FBA) are highlighted. (13)C-MFA studies have revealed unusual features of central metabolism in developing green seeds for the efficient use of light to conserve carbon and identified metabolic inefficiencies in plant metabolism due to dissipation of ATP by substrate cycling. Constraints-based FBA has used efficiency to guide the prediction of the growth and actual internal flux distribution of plant systems. Comparisons in a few cases have been made between flux maps measured by (13)C-based MFA and those predicted by FBA assuming one or more maximal efficiency parameters. These studies suggest that developing plant seeds and photoautotrophic microorganisms may indeed have patterns of metabolic flux that maximize efficiency. MFA and FBA are synergistic toolsets for uncovering and explaining the metabolic basis of efficiencies and inefficiencies in plant systems.     

A hybrid kinetic and constraint-based model of leaf metabolism allows predictions of metabolic fluxes in different environments

While flux balance analysis (FBA) provides a framework for predicting steady-state leaf metabolic network fluxes, it does not readily capture the response to environmental variables without being coupled to other modelling formulations. To address this, we coupled an FBA model of 903 reactions of soybean (Glycine max) leaf metabolism with e-photosynthesis, a dynamic model that captures the kinetics of 126 reactions of photosynthesis and associated chloroplast carbon metabolism. Successful coupling was achieved in an iterative formulation in which fluxes from e-photosynthesis were used to constrain the FBA model and then, in turn, fluxes computed from the FBA model used to update parameters in e-photosynthesis. This process was repeated until common fluxes in the two models converged. Coupling did not hamper the ability of the kinetic module to accurately predict the carbon assimilation rate, photosystem II electron flux, and starch accumulation of field-grown soybean at two CO₂ concentrations. The coupled model also allowed accurate predictions of additional parameters such as nocturnal respiration, as well as analysis of the effect of light intensity and elevated CO₂ on leaf metabolism. Predictions included an unexpected decrease in the rate of export of sucrose from the leaf at high light, due to altered starch–sucrose partitioning, and altered daytime flux modes in the tricarboxylic acid cycle at elevated CO₂. Mitochondrial fluxes were notably different between growing and mature leaves, with greater anaplerotic, tricarboxylic acid cycle and mitochondrial ATP synthase fluxes predicted in the former, primarily to provide carbon skeletons and energy for protein synthesis.     

Systems-level analysis of genome-scalein silico metabolic models using MetaFluxNet

The systems-level analysis of microbes with myriad of heterologous data generated by omics technologies has been applied to improve our understanding of cellular function and physiology and consequently to enhance production of various bioproducts. At the heart of this revolution residesin silico genome-scale metabolic model. In order to fully exploit the power of genome-scale model, a systematic approach employing user-friendly software is required. Metabolic flux analysis of genome-scale metabolic network is becoming widely employed to quantify the flux distribution and validate model-driven hypotheses. Here we describe the development of an upgraded MetaFluxNet which allows (1) construction of metabolic models connected to metabolic databases, (2) calculation of fluxes by metabolic flux analysis, (3) comparative flux analysis with flux-profile visualization, (4) the use of metabolic flux analysis markup language to enable models to be exchanged efficiently, and (5) the exporting of data from constraints-based flux analysis into various formats. MetaFluxNet also allows cellular physiology to be predicted and strategies for strain improvement to be developed from genome-based information on flux distributions. This integrated software environment promises to enhance our understanding on metabolic network at a whole organism level and to establish novel strategies for improving the properties of organisms for various biotechnological applications.     

Flux analysis and metabolomics for systematic metabolic engineering of microorganisms

Rational engineering of metabolism is important for bio-production using microorganisms. Metabolic design based on in silico simulations and experimental validation of the metabolic state in the engineered strain helps in accomplishing systematic metabolic engineering. Flux balance analysis (FBA) is a method for the prediction of metabolic phenotype, and many applications have been developed using FBA to design metabolic networks. Elementary mode analysis (EMA) and ensemble modeling techniques are also useful tools for in silico strain design. The metabolome and flux distribution of the metabolic pathways enable us to evaluate the metabolic state and provide useful clues to improve target productivity. Here, we reviewed several computational applications for metabolic engineering by using genome-scale metabolic models of microorganisms. We also discussed the recent progress made in the field of metabolomics and ¹³C-metabolic flux analysis techniques, and reviewed these applications pertaining to bio-production development. Because these in silico or experimental approaches have their respective advantages and disadvantages, the combined usage of these methods is complementary and effective for metabolic engineering.     

Stoichiometric model and flux balance analysis for a mixed culture of Leptospirillum ferriphilum and Ferroplasma acidiphilum

The oxidation process of sulfide minerals in natural environments is achieved by microbial communities from the Archaea and Bacteria domains. A metabolic reconstruction of two dominant species, Leptospirillum ferriphilum and Ferroplasma acidiphilum, which are always found together as a mixed culture in this natural environments, was made. The metabolic model, composed of 152 internal reactions and 29 transport reactions, describes the main interactions between these species, assuming that both use ferrous iron as energy source, and F. acidiphilum takes advantage of the organic compounds secreted by L. ferriphilum for chemomixotrophic growth. A first metabolic model for a mixed culture used in bacterial leaching is proposed in this article, which pretends to represent the characteristics of the mixed culture in a simplified manner. It was evaluated with experimental data through flux balance analysis (FBA) using as objective function the maximization of biomass. The growth yields on ferrous iron obtained for each microorganism are consistent with experimental data, and the flux distribution obtained allows understanding of the metabolic capabilities of both microorganisms growing together in a bioleaching process. The model was used to simulate the growth of F. acidiphilum on different substrates, to determine in silico which compounds maximize cell growth, and which are essential. Knockout simulations were carried out for L. ferriphilum and F. acidiphilum metabolic models, predicting key enzymes of central metabolism. The results of this analysis are consistent with experimental data from literature, showing a robust behavior of the metabolic model. © 2014 American Institute of Chemical Engineers Biotechnol. Prog., 31:307–315, 2015     

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.     

Understanding flux in plant metabolic networks

The revolutionary growth in our ability to identify the 'parts list' of cellular infrastructure in plants in detail, and to alter it with precision, challenges us to develop methods to quantify how these parts function. For components of metabolism, this means mapping fluxes at the level of metabolic networks. Advances in experimental, analytical and software tools for metabolic flux analysis now allow maps of the fluxes through central metabolism to be obtained from the results of stable-isotope-labeling experiments. Such maps have led to notable successes in understanding and engineering metabolic function in microorganisms. Recent studies in plants are giving insight into particular fluxes, such as those of the pentose phosphate pathway, and into general phenomena, such as substrate- or futile-cycles and compartmentation. The importance of experimental design and statistical analysis have been illustrated, and analyses of fluxes in heterotrophic plant tissues have been carried out recently.     

The generalized flux-minimization method and its application to metabolic networks affected by enzyme deficiencies

The flux-minimization method [Holzhütter, H.G., 2004. The principle of flux-minimization and its application to calculate stationary fluxes in metabolic networks. Eur. J. Biochem. 271, 2905-2922] has been proposed as an alternative to kinetic modeling to calculate stationary fluxes in metabolic networks. Here a generalization of this method is proposed that takes into account possible limitations of internal fluxes, e.g. due to enzyme defects or partial inhibition of enzyme activities by drugs. The generalized method consists in the minimization of an objective function which expresses the compromise that has to be made between minimization of internal fluxes on one hand and maintenance of the metabolic output required for various cellular functions on the other. Fulfillment of the latter condition is measured through a fitness function, which evaluates the relative deviation of the output fluxes from demanded target values. The method is applied to assess the metabolic consequences caused by a deficiency of enzymes involved in the metabolism of erythrocytes. The obtained results are in good agreement with those obtained on the basis of a comprehensive kinetic model.     

Structural Control of Metabolic Flux

Organisms have to continuously adapt to changing environmental conditions or undergo developmental transitions. To meet the accompanying change in metabolic demands, the molecular mechanisms of adaptation involve concerted interactions which ultimately induce a modification of the metabolic state, which is characterized by reaction fluxes and metabolite concentrations. These state transitions are the effect of simultaneously manipulating fluxes through several reactions. While metabolic control analysis has provided a powerful framework for elucidating the principles governing this orchestrated action to understand metabolic control, its applications are restricted by the limited availability of kinetic information. Here, we introduce structural metabolic control as a framework to examine individual reactions'' potential to control metabolic functions, such as biomass production, based on structural modeling. The capability to carry out a metabolic function is determined using flux balance analysis (FBA). We examine structural metabolic control on the example of the central carbon metabolism of Escherichia coli by the recently introduced framework of functional centrality (FC). This framework is based on the Shapley value from cooperative game theory and FBA, and we demonstrate its superior ability to assign “share of control” to individual reactions with respect to metabolic functions and environmental conditions. A comparative analysis of various scenarios illustrates the usefulness of FC and its relations to other structural approaches pertaining to metabolic control. We propose a Monte Carlo algorithm to estimate FCs for large networks, based on the enumeration of elementary flux modes. We further give detailed biological interpretation of FCs for production of lactate and ATP under various respiratory conditions.