Putative regulatory sites unraveled by network-embedded thermodynamic analysis of metabolome data

Metabolic Network Modeling of Microbial Interactions in Natural and Engineered Environmental Systems

We review approaches to characterize metabolic interactions within microbial communities using Stoichiometric Metabolic Network (SMN) models for applications in environmental and industrial biotechnology. SMN models are computational tools used to evaluate the metabolic engineering potential of various organisms. They have successfully been applied to design and optimize the microbial production of antibiotics, alcohols and amino acids by single strains. To date however, such models have been rarely applied to analyze and control the metabolism of more complex microbial communities. This is largely attributed to the diversity of microbial community functions, metabolisms, and interactions. Here, we firstly review different types of microbial interaction and describe their relevance for natural and engineered environmental processes. Next, we provide a general description of the essential methods of the SMN modeling workflow including the steps of network reconstruction, simulation through Flux Balance Analysis (FBA), experimental data gathering, and model calibration. Then we broadly describe and compare four approaches to model microbial interactions using metabolic networks, i.e., (i) lumped networks, (ii) compartment per guild networks, (iii) bi-level optimization simulations, and (iv) dynamic-SMN methods. These approaches can be used to integrate and analyze diverse microbial physiology, ecology and molecular community data. All of them (except the lumped approach) are suitable for incorporating species abundance data but so far they have been used only to model simple communities of two to eight different species. Interactions based on substrate exchange and competition can be directly modeled using the above approaches. However, interactions based on metabolic feedbacks, such as product inhibition and synthropy require extensions to current models, incorporating gene regulation and compounding accumulation mechanisms. SMN models of microbial interactions can be used to analyze complex “omics” data and to infer and optimize metabolic processes. Thereby, SMN models are suitable to capitalize on advances in high-throughput molecular and metabolic data generation. SMN models are starting to be applied to describe microbial interactions during wastewater treatment, in-situ bioremediation, microalgae blooms methanogenic fermentation, and bioplastic production. Despite their current challenges, we envisage that SMN models have future potential for the design and development of novel growth media, biochemical pathways and synthetic microbial associations.

Dynamic metabolic models in context: biomass backtracking

Mathematical modeling has proven to be a powerful tool to understand and predict functional and regulatory properties of metabolic processes. High accuracy dynamic modeling of individual pathways is thereby opposed by simplified but genome scale constraint based approaches. A method that links these two powerful techniques would greatly enhance predictive power but is so far lacking. We present biomass backtracking, a workflow that integrates the cellular context in existing dynamic metabolic models via stoichiometrically exact drain reactions based on a genome scale metabolic model. With comprehensive examples, for different species and environmental contexts, we show the importance and scope of applications and highlight the improvement compared to common boundary formulations in existing metabolic models. Our method allows for the contextualization of dynamic metabolic models based on all available information. We anticipate this to greatly increase their accuracy and predictive power for basic research and also for drug development and industrial applications.

Genome scale models of yeast: towards standardized evaluation and consistent omic integration

Genome scale models (GEMs) have enabled remarkable advances in systems biology, acting as functional databases of metabolism, and as scaffolds for the contextualization of high-throughput data. In the case of Saccharomyces cerevisiae (budding yeast), several GEMs have been published and are currently used for metabolic engineering and elucidating biological interactions. Here we review the history of yeast's GEMs, focusing on recent developments. We study how these models are typically evaluated, using both descriptive and predictive metrics. Additionally, we analyze the different ways in which all levels of omics data (from gene expression to flux) have been integrated in yeast GEMs. Relevant conclusions and current challenges for both GEM evaluation and omic integration are highlighted.

Metabolite concentrations, fluxes and free energies imply efficient enzyme usage

In metabolism, available free energy is limited and must be divided across pathway steps to maintain ΔG negative throughout. For each reaction, ΔG is log-proportional both to a concentration ratio (reaction quotient-to-equilibrium constant) and to a flux ratio (backward-to-forward flux). Here we use isotope labeling to measure absolute metabolite concentrations and fluxes in Escherichia coli, yeast, and a mammalian cell line. We then integrate this information to obtain a unified set of concentrations and ΔG for each organism. In glycolysis, we find that free energy is partitioned so as to mitigate unproductive backward fluxes associated with ΔG near zero. Across metabolism, we observe that absolute metabolite concentrations and ΔG are substantially conserved, and that most substrate (but not inhibitor) concentrations exceed the associated enzyme binding site affinity. The observed conservation of metabolite concentrations is consistent with an evolutionary drive to utilize enzymes efficiently given thermodynamic and osmotic constraints.

Metabolite Damage and Metabolite Damage Control in Plants

It is increasingly clear that (a) many metabolites undergo spontaneous or enzyme-catalyzed side reactions in vivo, (b) the damaged metabolites formed by these reactions can be harmful, and (c) organisms have biochemical systems that limit the buildup of damaged metabolites. These damage-control systems either return a damaged molecule to its pristine state (metabolite repair) or convert harmful molecules to harmless ones (damage preemption). Because all organisms share a core set of metabolites that suffer the same chemical and enzymatic damage reactions, certain damage-control systems are widely conserved across the kingdoms of life. Relatively few damage reactions and damage-control systems are well known. Uncovering new damage reactions and identifying the corresponding damaged metabolites, damage-control genes, and enzymes demands a coordinated mix of chemistry, metabolomics, cheminformatics, biochemistry, and comparative genomics. This review illustrates the above points using examples from plants, which are at least as prone to metabolite damage as other organisms.

Molecular thermodynamics of metabolism: quantum thermochemical calculations for key metabolites

The present work is the first of a series of papers aiming at a coherent and unified development of the thermodynamics of metabolism and the rationalization of feasibility analysis of metabolic pathways. The focus in this part is on high-level quantum chemical calculations of the thermochemical quantities of relatively heavy metabolites such as amino acids/oligopeptides, nucleosides, saccharides and their derivatives in the ideal gas state. The results of this study will be combined with the corresponding hydration/solvation results in subsequent parts of this work in order to derive the desired thermochemical quantities in aqueous solutions. The above metabolites exist in a vast conformational/isomerization space including rotational conformers, tautomers or anomers exhibiting often multiple or cooperative intramolecular hydrogen bonding. We examine the challenges posed by these features for the reliable estimation of thermochemical quantities. We discuss conformer search, conformer distribution and averaging processes. We further consider neutral metabolites as well as protonated and deprotonated metabolites. In addition to the traditional presentation of gas-phase acidities, basicities and proton affinities, we also examine heats and free energies of ionic species. We obtain simple linear relations between the thermochemical quantities of ions and the formation quantities of their neutral counterparts. Furthermore, we compare our calculations with reliable experimental measurements and predictive calculations from the literature, when available. Finally, we discuss the next steps and perspectives for this work.

Dynamics of benzoate metabolism in Pseudomonas putida KT2440

Soil microorganisms mineralize lignin-derived aromatic carbon sources using oxidative catabolic pathways, such as the β-ketoadipate pathway. Although this aromatic pathway is one of the best-studied pathways in biochemistry, the complete pathway, including its regulation by aromatic carbon sources, has not been integrated into the metabolic network. In particular, information about the in vivo operation (e.g., kinetics and flux capacity) of the pathway is lacking. In this contribution, we use kinetic modeling and thermodynamic analysis to evaluate the in vivo operation of this key aromatic multi-step pathway. The resulting ab initio deterministic model of benzoate degradation via the β-ketoadipate (ortho-cleavage) pathway in Pseudomonas putida KT2440 is presented. The kinetic model includes mechanistic rate expressions for the enzymes and transport processes. The design and experimental validation of the model are driven by data generated from short-term perturbation experiments in a benzoate-limited continuous culture. The results of rigorous modeling of the in vivo dynamics provide strong support for flux regulation by the benzoate transporter and the enzymes forming and cleaving catechol. Revisiting the β-ketoadipate pathway might be valuable for applications in different fields, such as biochemistry and metabolic engineering, that use lignin monomers as a carbon source.

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We describe a kinetic model for the β-ketoadipate pathway.

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Short term metabolic responses were tracked on metabolite level by rapid sampling.

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The model captures steady state and dynamic conditions of the β-ketoadipate pathway.

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Thermodynamic analysis revealed regulation points of the pathway.

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The results are discussed in the context of metabolic network operation.

Identification of metabolic engineering targets for the enhancement of 1,4-butanediol production in recombinant E. coli using large-scale kinetic models

Rational metabolic engineering methods are increasingly employed in designing the commercially viable processes for the production of chemicals relevant to pharmaceutical, biotechnology, and food and beverage industries. With the growing availability of omics data and of methodologies capable to integrate the available data into models, mathematical modeling and computational analysis are becoming important in designing recombinant cellular organisms and optimizing cell performance with respect to desired criteria. In this contribution, we used the computational framework ORACLE (Optimization and Risk Analysis of Complex Living Entities) to analyze the physiology of recombinant Escherichia coli producing 1,4-butanediol (BDO) and to identify potential strategies for improved production of BDO. The framework allowed us to integrate data across multiple levels and to construct a population of large-scale kinetic models despite the lack of available information about kinetic properties of every enzyme in the metabolic pathways. We analyzed these models and we found that the enzymes that primarily control the fluxes leading to BDO production are part of central glycolysis, the lower branch of tricarboxylic acid (TCA) cycle and the novel BDO production route. Interestingly, among the enzymes between the glucose uptake and the BDO pathway, the enzymes belonging to the lower branch of TCA cycle have been identified as the most important for improving BDO production and yield. We also quantified the effects of changes of the target enzymes on other intracellular states like energy charge, cofactor levels, redox state, cellular growth, and byproduct formation. Independent earlier experiments on this strain confirmed that the computationally obtained conclusions are consistent with the experimentally tested designs, and the findings of the present studies can provide guidance for future work on strain improvement. Overall, these studies demonstrate the potential and effectiveness of ORACLE for the accelerated design of microbial cell factories.

Quantifying NAD(P)H production in the upper Entner-Doudoroff pathway from Pseudomonas putida KT2440

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The first kinetic characterization of PputG6PDH-1 is presented.

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The relative production of NADH and NADPH by PputG6PDH-1 is quantified.

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The stoichiometric matrix of in silico metabolic models for Pseudomonas putida must be modified.

Despite the lack of biochemical information, all available in silico metabolic models of Pseudomonas putida KT2440 consider NADP as the only cofactor accepted by the glucose-6-phosphate dehydrogenases. Because the Entner–Doudoroff pathway is the main glycolytic route in this bacterium, determining how much NADH and NADPH are produced in the reaction catalyzed by these enzymes is very important for the correct interpretation of metabolic flux distributions. To determine the actual cofactor preference of the glucose-6-phosphate dehydrogenase encoded by the zwf-1 gene (PputG6PDH-1), the major isoform during growth on glucose, we purified this protein and studied its kinetic properties. Based on simple kinetic principles, we estimated the in vivo relative production of NADH and NADPH during the oxidation of glucose-6-phosphate (G6P). Contrary to the general assumption, our calculations showed that the reaction catalyzed by PputG6PDH-1 yields around 1/3 mol of NADPH and 2/3 mol of NADH per mol of oxidized G6P. Additionally, we obtained data suggesting that the reaction catalyzed by the 6-phosphogluconate dehydrogenase is active during growth on glucose, and it also produces NADH. These results indicate that the stoichiometric matrix of in silico models of P. putida KT2440 must be corrected and highlight the importance of considering the physiological concentrations of the involved metabolites to estimate the actual proportion of NADH and NADPH produced by a dehydrogenase.

Cell scale host-pathogen modeling: another branch in the evolution of constraint-based methods

Constraint-based models have become popular methods for systems biology as they enable the integration of complex, disparate datasets in a biologically cohesive framework that also supports the description of biological processes in terms of basic physicochemical constraints and relationships. The scope, scale, and application of genome scale models have grown from single cell bacteria to multi-cellular interaction modeling; host-pathogen modeling represents one of these examples at the current horizon of constraint-based methods. There are now a small number of examples of host-pathogen constraint-based models in the literature, however there has not yet been a definitive description of the methodology required for the functional integration of genome scale models in order to generate simulation capable host-pathogen models. Herein we outline a systematic procedure to produce functional host-pathogen models, highlighting steps which require debugging and iterative revisions in order to successfully build a functional model. The construction of such models will enable the exploration of host-pathogen interactions by leveraging the growing wealth of omic data in order to better understand mechanism of infection and identify novel therapeutic strategies.

Heading in the right direction: thermodynamics-based network analysis and pathway engineering

Thermodynamics-based network analysis through the introduction of thermodynamic constraints in metabolic models allows a deeper analysis of metabolism and guides pathway engineering. The number and the areas of applications of thermodynamics-based network analysis methods have been increasing in the last ten years. We review recent applications of these methods and we identify the areas that such analysis can contribute significantly, and the needs for future developments. We find that organisms with multiple compartments and extremophiles present challenges for modeling and thermodynamics-based flux analysis. The evolution of current and new methods must also address the issues of the multiple alternatives in flux directionalities and the uncertainties and partial information from analytical methods.

Network thermodynamic curation of human and yeast genome-scale metabolic models

Genome-scale models are used for an ever-widening range of applications. Although there has been much focus on specifying the stoichiometric matrix, the predictive power of genome-scale models equally depends on reaction directions. Two-thirds of reactions in the two eukaryotic reconstructions Homo sapiens Recon 1 and Yeast 5 are specified as irreversible. However, these specifications are mainly based on biochemical textbooks or on their similarity to other organisms and are rarely underpinned by detailed thermodynamic analysis. In this study, a to our knowledge new workflow combining network-embedded thermodynamic and flux variability analysis was used to evaluate existing irreversibility constraints in Recon 1 and Yeast 5 and to identify new ones. A total of 27 and 16 new irreversible reactions were identified in Recon 1 and Yeast 5, respectively, whereas only four reactions were found with directions incorrectly specified against thermodynamics (three in Yeast 5 and one in Recon 1). The workflow further identified for both models several isolated internal loops that require further curation. The framework also highlighted the need for substrate channeling (in human) and ATP hydrolysis (in yeast) for the essential reaction catalyzed by phosphoribosylaminoimidazole carboxylase in purine metabolism. Finally, the framework highlighted differences in proline metabolism between yeast (cytosolic anabolism and mitochondrial catabolism) and humans (exclusively mitochondrial metabolism). We conclude that network-embedded thermodynamics facilitates the specification and validation of irreversibility constraints in compartmentalized metabolic models, at the same time providing further insight into network properties.

Obstructions to Sampling Qualitative Properties

Background

Sampling methods have proven to be a very efficient and intuitive method to understand properties of complicated spaces that cannot easily be computed using deterministic methods. Therefore, sampling methods became a popular tool in the applied sciences.

Results

Here, we show that sampling methods are not an appropriate tool to analyze qualitative properties of complicated spaces unless RP = NP. We illustrate these results on the example of the thermodynamically feasible flux space of genome-scale metabolic networks and show that with artificial centering hit and run (ACHR) not all reactions that can have variable flux rates are sampled with variables flux rates. In particular a uniform sample of the flux space would not sample the flux variabilities completely.

Conclusion

We conclude that unless theoretical convergence results exist, qualitative results obtained from sampling methods should be considered with caution and if possible double checked using a deterministic method.

Improved metabolite profile smoothing for flux estimation

As genome-scale metabolic models become more sophisticated and dynamic, one significant challenge in using these models is to effectively integrate increasingly prevalent systems-scale metabolite profiling data into them. One common data processing step when integrating metabolite data is to smooth experimental time course measurements: the smoothed profiles can be used to estimate metabolite accumulation (derivatives), and thus the flux distribution of the metabolic model. However, this smoothing step is susceptible to the (often significant) noise in experimental measurements, limiting the accuracy of downstream model predictions. Here, we present several improvements to current approaches for smoothing metabolite time course data using defined functions. First, we use a biologically-inspired mathematical model function taken from transcriptional profiling and clustering literature that captures the dynamics of many biologically relevant transient processes. We demonstrate that it is competitive with, and often superior to, previously described fitting schemas, and may serve as an effective single option for data smoothing in metabolic flux applications. We also implement a resampling-based approach to buffer out sensitivity to specific data sets and allow for more accurate fitting of noisy data. We found that this method, as well as the addition of parameter space constraints, yielded improved estimates of concentrations and derivatives (fluxes) in previously described fitting functions. These methods have the potential to improve the accuracy of existing and future dynamic metabolic models by allowing for the more effective integration of metabolite profiling data.

Thermodynamics and H2 Transfer in a Methanogenic, Syntrophic Community

Microorganisms in nature do not exist in isolation but rather interact with other species in their environment. Some microbes interact via syntrophic associations, in which the metabolic by-products of one species serve as nutrients for another. These associations sustain a variety of natural communities, including those involved in methanogenesis. In anaerobic syntrophic communities, energy is transferred from one species to another, either through direct contact and exchange of electrons, or through small molecule diffusion. Thermodynamics plays an important role in governing these interactions, as the oxidation reactions carried out by the first community member are only possible because degradation products are consumed by the second community member. This work presents the development and analysis of genome-scale network reconstructions of the bacterium Syntrophobacter fumaroxidans and the methanogenic archaeon Methanospirillum hungatei. The models were used to verify proposed mechanisms of ATP production within each species. We then identified additional constraints and the cellular objective function required to match experimental observations. The thermodynamic S. fumaroxidans model could not explain why S. fumaroxidans does not produce H₂ in monoculture, indicating that current methods might not adequately estimate the thermodynamics, or that other cellular processes (e.g., regulation) play a role. We also developed a thermodynamic coculture model of the association between the organisms. The coculture model correctly predicted the exchange of both H₂ and formate between the two species and suggested conditions under which H₂ and formate produced by S. fumaroxidans would be fully consumed by M. hungatei.

Natural and engineered microbial communities can contain up to hundreds of interacting microbes. These interactions may be positive, negative, or neutral, as well as obligate or facultative. Syntrophy is an obligate, positive interaction, in which one species lives off the metabolic by-products of another. Syntrophic associations play an important role in sustaining a variety of natural communities, including those involved in the breakdown and conversion of short-chain fatty acids (e.g., propionate) to methane. In many syntrophic communities, electrons are transferred from one species to the other through small molecule diffusion. In this work, we expand the study of a two-member syntrophic, methanogenic community through the development and analysis of computational models for both species: the bacterium Syntrophobacter fumaroxidans and the methanogenic archaeon Methanospirillum hungatei. These models were used to analyze energy conservation mechanisms within each species, as well as small molecule exchange between the two organisms in coculture. The coculture model correctly predicted the exchange of both H₂ and formate between the two species and suggested conditions under which these molecules would be fully metabolized within the community.

Metabolic engineering of a tyrosine-overproducing yeast platform using targeted metabolomics

Background

L-tyrosine is a common precursor for a wide range of valuable secondary metabolites, including benzylisoquinoline alkaloids (BIAs) and many polyketides. An industrially tractable yeast strain optimized for production of L-tyrosine could serve as a platform for the development of BIA and polyketide cell factories. This study applied a targeted metabolomics approach to evaluate metabolic engineering strategies to increase the availability of intracellular L-tyrosine in the yeast Saccharomyces cerevisiae CEN.PK. Our engineering strategies combined localized pathway engineering with global engineering of central metabolism, facilitated by genome-scale steady-state modelling.

Results

Addition of a tyrosine feedback resistant version of 3-deoxy-D-arabino-heptulosonate-7-phosphate synthase Aro4 from S. cerevisiae was combined with overexpression of either a tyrosine feedback resistant yeast chorismate mutase Aro7, the native pentafunctional arom protein Aro1, native prephenate dehydrogenase Tyr1 or cyclohexadienyl dehydrogenase TyrC from Zymomonas mobilis. Loss of aromatic carbon was limited by eliminating phenylpyruvate decarboxylase Aro10. The TAL gene from Rhodobacter sphaeroides was used to produce coumarate as a simple test case of a heterologous by-product of tyrosine. Additionally, multiple strategies for engineering global metabolism to promote tyrosine production were evaluated using metabolic modelling. The T21E mutant of pyruvate kinase Cdc19 was hypothesized to slow the conversion of phosphoenolpyruvate to pyruvate and accumulate the former as precursor to the shikimate pathway. The ZWF1 gene coding for glucose-6-phosphate dehydrogenase was deleted to create an NADPH deficiency designed to force the cell to couple its growth to tyrosine production via overexpressed NADP⁺-dependent prephenate dehydrogenase Tyr1. Our engineered Zwf1⁻ strain expressing TYRC ARO4^FBR and grown in the presence of methionine achieved an intracellular L-tyrosine accumulation up to 520 μmol/g DCW or 192 mM in the cytosol, but sustained flux through this pathway was found to depend on the complete elimination of feedback inhibition and degradation pathways.

Conclusions

Our targeted metabolomics approach confirmed a likely regulatory site at DAHP synthase and identified another possible cofactor limitation at prephenate dehydrogenase. Additionally, the genome-scale metabolic model identified design strategies that have the potential to improve availability of erythrose 4-phosphate for DAHP synthase and cofactor availability for prephenate dehydrogenase. We evaluated these strategies and provide recommendations for further improvement of aromatic amino acid biosynthesis in S. cerevisiae.

Electronic supplementary material

The online version of this article (doi:10.1186/s12934-015-0252-2) contains supplementary material, which is available to authorized users.

NExT: integration of thermodynamic constraints and metabolomics data into a metabolic network

Thermodynamic constraints are widely used in metabolic modelling such that calculated flux phenotypes are closer to real cell behavior. If metabolic data is also included in the analysis, a check of the thermodynamic consistency of the data can be realized and subsequently use the metabolic data to further constrain the solution space, giving a more specific representation of the cell metabolism under the studied conditions. Here NExT, a software based on network-embedded thermodynamic analysis, is presented, to integrate thermodynamics constraints and metabolomics data in the estimation of intracellular fluxes. New irreversible reactions can be inferred by calculating the thermodynamically feasible range of metabolite concentrations and Gibbs energy of reactions.

Systems modeling approaches for microbial community studies: from metagenomics to inference of the community structure

Microbial communities play important roles in health, industrial applications and earth's ecosystems. With current molecular techniques we can characterize these systems in unprecedented detail. However, such methods provide little mechanistic insight into how the genetic properties and the dynamic couplings between individual microorganisms give rise to their dynamic activities. Neither do they give insight into what we call “the community state”, that is the fluxes and concentrations of nutrients within the community. This knowledge is a prerequisite for rational control and intervention in microbial communities. Therefore, the inference of the community structure from experimental data is a major current challenge. We will argue that this inference problem requires mathematical models that can integrate heterogeneous experimental data with existing knowledge. We propose that two types of models are needed. Firstly, mathematical models that integrate existing genomic, physiological, and physicochemical information with metagenomics data so as to maximize information content and predictive power. This can be achieved with the use of constraint-based genome-scale stoichiometric modeling of community metabolism which is ideally suited for this purpose. Next, we propose a simpler coarse-grained model, which is tailored to solve the inference problem from the experimental data. This model unambiguously relate to the more detailed genome-scale stoichiometric models which act as heterogeneous data integrators. The simpler inference models are, in our opinion, key to understanding microbial ecosystems, yet until now, have received remarkably little attention. This has led to the situation where the modeling of microbial communities, using only genome-scale models is currently more a computational, theoretical exercise than a method useful to the experimentalist.

Comparative metabolic analysis of CHO cell clones obtained through cell engineering, for IgG productivity, growth and cell longevity

Cell engineering has been used to improve animal cells’ central carbon metabolism. Due to the central carbon metabolism’s inefficiency and limiting input of carbons into the TCA cycle, key reactions belonging to these pathways have been targeted to improve cultures’ performance. Previous works have shown the positive effects of overexpressing PYC2, MDH II and fructose transporter. Since each of these modifications was performed in different cell lines and culture conditions, no comparisons between these modifications can be made. In this work we aim at contrasting the effect of each of the modifications by comparing pools of transfected IgG producing CHO cells cultivated in batch cultures. Results of the culture performance of engineered clones indicate that even though all studied clones had a more efficient metabolism, not all of them showed the expected improvement on cell proliferation and/or specific productivity. CHO cells overexpressing PYC2 were able to improve their exponential growth rate but IgG synthesis was decreased, MDH II overexpression lead to a reduction in cell growth and protein production, and cells transfected with the fructose transporter gene were able to increase cell density and reach the same volumetric protein production as parental CHO cells in glucose. We propose that a redox unbalance caused by the new metabolic flux distribution could affect IgG assembly and protein secretion. In addition to reaction dynamics, thermodynamic aspects of metabolism are also discussed to further understand the effect of these modifications over central carbon metabolism.

Metabolomics integrated elementary flux mode analysis in large metabolic networks

Elementary flux modes (EFMs) are non-decomposable steady-state pathways in metabolic networks. They characterize phenotypes, quantify robustness or identify engineering targets. An EFM analysis (EFMA) is currently restricted to medium-scale models, as the number of EFMs explodes with the network's size. However, many topologically feasible EFMs are biologically irrelevant. We present thermodynamic EFMA (tEFMA), which calculates only the small(er) subset of thermodynamically feasible EFMs. We integrate network embedded thermodynamics into EFMA and show that we can use the metabolome to identify and remove thermodynamically infeasible EFMs during an EFMA without losing biologically relevant EFMs. Calculating only the thermodynamically feasible EFMs strongly reduces memory consumption and program runtime, allowing the analysis of larger networks. We apply tEFMA to study the central carbon metabolism of E. coli and find that up to 80% of its EFMs are thermodynamically infeasible. Moreover, we identify glutamate dehydrogenase as a bottleneck, when E. coli is grown on glucose and explain its inactivity as a consequence of network embedded thermodynamics. We implemented tEFMA as a Java package which is available for download at https://github.com/mpgerstl/tEFMA.

tEFMA: computing thermodynamically feasible elementary flux modes in metabolic networks

: Elementary flux modes (EFMs) are important structural tools for the analysis of metabolic networks. It is known that many topologically feasible EFMs are biologically irrelevant. Therefore, tools are needed to find the relevant ones. We present thermodynamic tEFM analysis (tEFMA) which uses the cellular metabolome to avoid the enumeration of thermodynamically infeasible EFMs. Specifically, given a metabolic network and a not necessarily complete metabolome, tEFMA efficiently returns the full set of thermodynamically feasible EFMs consistent with the metabolome. Compared with standard approaches, tEFMA strongly reduces the memory consumption and the overall runtime. Thus tEFMA provides a new way to analyze unbiasedly hitherto inaccessible large-scale metabolic networks.

AVAILABILITY AND IMPLEMENTATION

https://github.com/mpgerstl/tEFMA CONTACT: : christian.jungreuthmayer@boku.ac.at or juergen.zanghellini@boku.ac.at

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Perturbation Experiments: Approaches for Metabolic Pathway Analysis in Bioreactors

In the last decades, targeted metabolic engineering of microbial cells has become one of the major tools in bioprocess design and optimization. For successful application, a detailed knowledge is necessary about the relevant metabolic pathways and their regulation inside the cells. Since in vitro experiments cannot display process conditions and behavior properly, process data about the cells' metabolic state have to be collected in vivo. For this purpose, special techniques and methods are necessary. Therefore, most techniques enabling in vivo characterization of metabolic pathways rely on perturbation experiments, which can be divided into dynamic and steady-state approaches. To avoid any process disturbance, approaches which enable perturbation of cell metabolism in parallel to the continuing production process are reasonable. Furthermore, the fast dynamics of microbial production processes amplifies the need of parallelized data generation. These points motivate the development of a parallelized approach for multiple metabolic perturbation experiments outside the operating production reactor. An appropriate approach for in vivo characterization of metabolic pathways is presented and applied exemplarily to a microbial L-phenylalanine production process on a 15 L-scale.

Concepts, challenges, and successes in modeling thermodynamics of metabolism

The modeling of the chemical reactions involved in metabolism is a daunting task. Ideally, the modeling of metabolism would use kinetic simulations, but these simulations require knowledge of the thousands of rate constants involved in the reactions. The measurement of rate constants is very labor intensive, and hence rate constants for most enzymatic reactions are not available. Consequently, constraint-based flux modeling has been the method of choice because it does not require the use of the rate constants of the law of mass action. However, this convenience also limits the predictive power of constraint-based approaches in that the law of mass action is used only as a constraint, making it difficult to predict metabolite levels or energy requirements of pathways. An alternative to both of these approaches is to model metabolism using simulations of states rather than simulations of reactions, in which the state is defined as the set of all metabolite counts or concentrations. While kinetic simulations model reactions based on the likelihood of the reaction derived from the law of mass action, states are modeled based on likelihood ratios of mass action. Both approaches provide information on the energy requirements of metabolic reactions and pathways. However, modeling states rather than reactions has the advantage that the parameters needed to model states (chemical potentials) are much easier to determine than the parameters needed to model reactions (rate constants). Herein, we discuss recent results, assumptions, and issues in using simulations of state to model metabolism.

Simulating metabolism with statistical thermodynamics

New methods are needed for large scale modeling of metabolism that predict metabolite levels and characterize the thermodynamics of individual reactions and pathways. Current approaches use either kinetic simulations, which are difficult to extend to large networks of reactions because of the need for rate constants, or flux-based methods, which have a large number of feasible solutions because they are unconstrained by the law of mass action. This report presents an alternative modeling approach based on statistical thermodynamics. The principles of this approach are demonstrated using a simple set of coupled reactions, and then the system is characterized with respect to the changes in energy, entropy, free energy, and entropy production. Finally, the physical and biochemical insights that this approach can provide for metabolism are demonstrated by application to the tricarboxylic acid (TCA) cycle of Escherichia coli. The reaction and pathway thermodynamics are evaluated and predictions are made regarding changes in concentration of TCA cycle intermediates due to 10- and 100-fold changes in the ratio of NAD⁺:NADH concentrations. Finally, the assumptions and caveats regarding the use of statistical thermodynamics to model non-equilibrium reactions are discussed.

Variability of metabolite levels is linked to differential metabolic pathways in Arabidopsis's responses to abiotic stresses

Constraint-based approaches have been used for integrating data in large-scale metabolic networks to obtain insights into metabolism of various organisms. Due to the underlying steady-state assumption, these approaches are usually not suited for making predictions about metabolite levels. Here, we ask whether we can make inferences about the variability of metabolite levels from a constraint-based analysis based on the integration of transcriptomics data. To this end, we analyze time-resolved transcriptomics and metabolomics data from Arabidopsis thaliana under a set of eight different light and temperature conditions. In a previous study, the gene expression data have already been integrated in a genome-scale metabolic network to predict pathways, termed modulators and sustainers, which are differentially regulated with respect to a biochemically meaningful data-driven null model. Here, we present a follow-up analysis which bridges the gap between flux- and metabolite-centric methods. One of our main findings demonstrates that under certain environmental conditions, the levels of metabolites acting as substrates in modulators or sustainers show significantly lower temporal variations with respect to the remaining measured metabolites. This observation is discussed within the context of a systems-view of plasticity and robustness of metabolite contents and pathway fluxes. Our study paves the way for investigating the existence of similar principles in other species for which both genome-scale networks and high-throughput metabolomics data of high quality are becoming increasingly available.

Quantitative Metabolomics and Instationary 13C-Metabolic Flux Analysis Reveals Impact of Recombinant Protein Production on Trehalose and Energy Metabolism in Pichia pastoris

Pichia pastoris has been recognized as an effective host for recombinant protein production. In this work, we combine metabolomics and instationary 13C metabolic flux analysis (INST 13C-MFA) using GC-MS and LC-MS/MS to evaluate the potential impact of the production of a Rhizopus oryzae lipase (Rol) on P. pastoris central carbon metabolism. Higher oxygen uptake and CO2 production rates and slightly reduced biomass yield suggest an increased energy demand for the producing strain. This observation is further confirmed by 13C-based metabolic flux analysis. In particular, the flux through the methanol oxidation pathway and the TCA cycle was increased in the Rol-producing strain compared to the reference strain. Next to changes in the flux distribution, significant variations in intracellular metabolite concentrations were observed. Most notably, the pools of trehalose, which is related to cellular stress response, and xylose, which is linked to methanol assimilation, were significantly increased in the recombinant strain.

A mathematical model of metabolism and regulation provides a systems-level view of how Escherichia coli responds to oxygen

The efficient redesign of bacteria for biotechnological purposes, such as biofuel production, waste disposal or specific biocatalytic functions, requires a quantitative systems-level understanding of energy supply, carbon, and redox metabolism. The measurement of transcript levels, metabolite concentrations and metabolic fluxes per se gives an incomplete picture. An appreciation of the interdependencies between the different measurement values is essential for systems-level understanding. Mathematical modeling has the potential to provide a coherent and quantitative description of the interplay between gene expression, metabolite concentrations, and metabolic fluxes. Escherichia coli undergoes major adaptations in central metabolism when the availability of oxygen changes. Thus, an integrated description of the oxygen response provides a benchmark of our understanding of carbon, energy, and redox metabolism. We present the first comprehensive model of the central metabolism of E. coli that describes steady-state metabolism at different levels of oxygen availability. Variables of the model are metabolite concentrations, gene expression levels, transcription factor activities, metabolic fluxes, and biomass concentration. We analyze the model with respect to the production capabilities of central metabolism of E. coli. In particular, we predict how precursor and biomass concentration are affected by product formation.

Pathway thermodynamics highlights kinetic obstacles in central metabolism

In metabolism research, thermodynamics is usually used to determine the directionality of a reaction or the feasibility of a pathway. However, the relationship between thermodynamic potentials and fluxes is not limited to questions of directionality: thermodynamics also affects the kinetics of reactions through the flux-force relationship, which states that the logarithm of the ratio between the forward and reverse fluxes is directly proportional to the change in Gibbs energy due to a reaction (Δ_rG′). Accordingly, if an enzyme catalyzes a reaction with a Δ_rG′ of -5.7 kJ/mol then the forward flux will be roughly ten times the reverse flux. As Δ_rG′ approaches equilibrium (Δ_rG′ = 0 kJ/mol), exponentially more enzyme counterproductively catalyzes the reverse reaction, reducing the net rate at which the reaction proceeds. Thus, the enzyme level required to achieve a given flux increases dramatically near equilibrium. Here, we develop a framework for quantifying the degree to which pathways suffer these thermodynamic limitations on flux. For each pathway, we calculate a single thermodynamically-derived metric (the Max-min Driving Force, MDF), which enables objective ranking of pathways by the degree to which their flux is constrained by low thermodynamic driving force. Our framework accounts for the effect of pH, ionic strength and metabolite concentration ranges and allows us to quantify how alterations to the pathway structure affect the pathway's thermodynamics. Applying this methodology to pathways of central metabolism sheds light on some of their features, including metabolic bypasses (e.g., fermentation pathways bypassing substrate-level phosphorylation), substrate channeling (e.g., of oxaloacetate from malate dehydrogenase to citrate synthase), and use of alternative cofactors (e.g., quinone as an electron acceptor instead of NAD). The methods presented here place another arrow in metabolic engineers' quiver, providing a simple means of evaluating the thermodynamic and kinetic quality of different pathway chemistries that produce the same molecules.

Given data about enzyme kinetics and reaction thermodynamics, traditional metabolic control analysis (MCA) can pinpoint the enzymes whose expression will have the largest effect on steady-state flux through the pathway. These analyses can aid experimentalists in tuning enzyme expression levels along a metabolic pathway. In this work, we offer a framework that is complementary to MCA. Rather than focusing on the relationship between enzyme levels and pathway flux, we examine a pathway's stoichiometry and thermodynamics and ask whether it is likely to support high flux in cellular conditions. Our framework calculates a single thermodynamically-derived metric (the MDF) for each pathway, which is convenient for selecting the promising pathways from a large collection. This approach has several advantages. First, enzyme kinetic properties are laborious to measure and differ between organisms and isozymes, but no kinetic data is required to calculate the MDF. Second, as our framework accounts for pH, ionic strength and allowed concentration ranges, it is simple to model the effect of these parameters on the MDF. Finally, as it can be difficult to control the exact expression level of enzymes within cells, the MDF helps identify alternative pathways that are less sensitive to the levels of their constituent enzymes.

Comparative evaluation of open source software for mapping between metabolite identifiers in metabolic network reconstructions: application to Recon 2

Background

An important step in the reconstruction of a metabolic network is annotation of metabolites. Metabolites are generally annotated with various database or structure based identifiers. Metabolite annotations in metabolic reconstructions may be incorrect or incomplete and thus need to be updated prior to their use. Genome-scale metabolic reconstructions generally include hundreds of metabolites. Manually updating annotations is therefore highly laborious. This prompted us to look for open-source software applications that could facilitate automatic updating of annotations by mapping between available metabolite identifiers. We identified three applications developed for the metabolomics and chemical informatics communities as potential solutions. The applications were MetMask, the Chemical Translation System, and UniChem. The first implements a “metabolite masking” strategy for mapping between identifiers whereas the latter two implement different versions of an InChI based strategy. Here we evaluated the suitability of these applications for the task of mapping between metabolite identifiers in genome-scale metabolic reconstructions. We applied the best suited application to updating identifiers in Recon 2, the latest reconstruction of human metabolism.

Results

All three applications enabled partially automatic updating of metabolite identifiers, but significant manual effort was still required to fully update identifiers. We were able to reduce this manual effort by searching for new identifiers using multiple types of information about metabolites. When multiple types of information were combined, the Chemical Translation System enabled us to update over 3,500 metabolite identifiers in Recon 2. All but approximately 200 identifiers were updated automatically.

Conclusions

We found that an InChI based application such as the Chemical Translation System was better suited to the task of mapping between metabolite identifiers in genome-scale metabolic reconstructions. We identified several features, however, that could be added to such an application in order to tailor it to this task.

Computational approaches for understanding energy metabolism

There has been a surge of interest in understanding the regulation of metabolic networks involved in disease in recent years. Quantitative models are increasingly being used to interrogate the metabolic pathways that are contained within this complex disease biology. At the core of this effort is the mathematical modeling of central carbon metabolism involving glycolysis and the citric acid cycle (referred to as energy metabolism). Here, we discuss several approaches used to quantitatively model metabolic pathways relating to energy metabolism and discuss their formalisms, successes, and limitations.

Steady-state metabolite concentrations reflect a balance between maximizing enzyme efficiency and minimizing total metabolite load

Steady-state metabolite concentrations in a microorganism typically span several orders of magnitude. The underlying principles governing these concentrations remain poorly understood. Here, we hypothesize that observed variation can be explained in terms of a compromise between factors that favor minimizing metabolite pool sizes (e.g. limited solvent capacity) and the need to effectively utilize existing enzymes. The latter requires adequate thermodynamic driving force in metabolic reactions so that forward flux substantially exceeds reverse flux. To test this hypothesis, we developed a method, metabolic tug-of-war (mTOW), which computes steady-state metabolite concentrations in microorganisms on a genome-scale. mTOW is shown to explain up to 55% of the observed variation in measured metabolite concentrations in E. coli and C. acetobutylicum across various growth media. Our approach, based strictly on first thermodynamic principles, is the first method that successfully predicts high-throughput metabolite concentration data in bacteria across conditions.

Temporal system-level organization of the switch from glycolytic to gluconeogenic operation in yeast

The diauxic shift in Saccharomyces cerevisiae is an ideal model to study how eukaryotic cells readjust their metabolism from glycolytic to gluconeogenic operation. In this work, we generated time-resolved physiological data, quantitative metabolome (69 intracellular metabolites) and proteome (72 enzymes) profiles. We found that the diauxic shift is accomplished by three key events that are temporally organized: (i) a reduction in the glycolytic flux and the production of storage compounds before glucose depletion, mediated by downregulation of phosphofructokinase and pyruvate kinase reactions; (ii) upon glucose exhaustion, the reversion of carbon flow through glycolysis and onset of the glyoxylate cycle operation triggered by an increased expression of the enzymes that catalyze the malate synthase and cytosolic citrate synthase reactions; and (iii) in the later stages of the adaptation, the shutting down of the pentose phosphate pathway with a change in NADPH regeneration. Moreover, we identified the transcription factors associated with the observed changes in protein abundances. Taken together, our results represent an important contribution toward a systems-level understanding of how this adaptation is realized.

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.

GIM3E: condition-specific models of cellular metabolism developed from metabolomics and expression data

MOTIVATION

Genome-scale metabolic models have been used extensively to investigate alterations in cellular metabolism. The accuracy of these models to represent cellular metabolism in specific conditions has been improved by constraining the model with omics data sources. However, few practical methods for integrating metabolomics data with other omics data sources into genome-scale models of metabolism have been developed.

RESULTS

GIM(3)E (Gene Inactivation Moderated by Metabolism, Metabolomics and Expression) is an algorithm that enables the development of condition-specific models based on an objective function, transcriptomics and cellular metabolomics data. GIM(3)E establishes metabolite use requirements with metabolomics data, uses model-paired transcriptomics data to find experimentally supported solutions and provides calculations of the turnover (production/consumption) flux of metabolites. GIM(3)E was used to investigate the effects of integrating additional omics datasets to create increasingly constrained solution spaces of Salmonella Typhimurium metabolism during growth in both rich and virulence media. This integration proved to be informative and resulted in a requirement of additional active reactions (12 in each case) or metabolites (26 or 29, respectively). The addition of constraints from transcriptomics also impacted the allowed solution space, and the cellular metabolites with turnover fluxes that were necessarily altered by the change in conditions increased from 118 to 271 of 1397.

AVAILABILITY

GIM(3)E has been implemented in Python and requires a COBRApy 0.2.x. The algorithm and sample data described here are freely available at: http://opencobra.sourceforge.net/

CONTACTS

brianjamesschmidt@gmail.com

Towards kinetic modeling of genome-scale metabolic networks without sacrificing stoichiometric, thermodynamic and physiological constraints

Mathematical modeling is an essential tool for the comprehensive understanding of cell metabolism and its interactions with the environmental and process conditions. Recent developments in the construction and analysis of stoichiometric models made it possible to define limits on steady-state metabolic behavior using flux balance analysis. However, detailed information on enzyme kinetics and enzyme regulation is needed to formulate kinetic models that can accurately capture the dynamic metabolic responses. The use of mechanistic enzyme kinetics is a difficult task due to uncertainty in the kinetic properties of enzymes. Therefore, the majority of recent works considered only mass action kinetics for reactions in metabolic networks. Herein, we applied the optimization and risk analysis of complex living entities (ORACLE) framework and constructed a large-scale mechanistic kinetic model of optimally grown Escherichia coli. We investigated the complex interplay between stoichiometry, thermodynamics, and kinetics in determining the flexibility and capabilities of metabolism. Our results indicate that enzyme saturation is a necessary consideration in modeling metabolic networks and it extends the feasible ranges of metabolic fluxes and metabolite concentrations. Our results further suggest that enzymes in metabolic networks have evolved to function at different saturation states to ensure greater flexibility and robustness of cellular metabolism.

Bridging the gap between gene expression and metabolic phenotype via kinetic models

Background

Despite the close association between gene expression and metabolism, experimental evidence shows that gene expression levels alone cannot predict metabolic phenotypes, indicating a knowledge gap in our understanding of how these processes are connected. Here, we present a method that integrates transcriptome, fluxome, and metabolome data using kinetic models to create a mechanistic link between gene expression and metabolism.

Results

We developed a modeling framework to construct kinetic models that connect the transcriptional and metabolic responses of a cell to exogenous perturbations. The framework allowed us to avoid extensive experimental characterization, literature mining, and optimization problems by estimating most model parameters directly from fluxome and transcriptome data. We applied the framework to investigate how gene expression changes led to observed phenotypic alterations of Saccharomyces cerevisiae treated with weak organic acids (i.e., acetate, benzoate, propionate, or sorbate) and the histidine synthesis inhibitor 3-aminotriazole under steady-state conditions. We found that the transcriptional response led to alterations in yeast metabolism that mimicked measured metabolic fluxes and concentration changes. Further analyses generated mechanistic insights of how S. cerevisiae responds to these stresses. In particular, these results suggest that S. cerevisiae uses different regulation strategies for responding to these insults: regulation of two reactions accounted for most of the tolerance to the four weak organic acids, whereas the response to 3-aminotriazole was distributed among multiple reactions. Moreover, we observed that the magnitude of the gene expression changes was not directly correlated with their effect on the ability of S. cerevisiae to grow under these treatments. In addition, we identified another potential mechanism of action of 3-aminotriazole associated with the depletion of tetrahydrofolate.

Conclusions

Our simulation results show that the modeling framework provided an accurate mechanistic link between gene expression and cellular metabolism. The proposed method allowed us to integrate transcriptome, fluxome, and metabolome data to determine and interpret important features of the physiological response of yeast to stresses. Importantly, given its flexibility and robustness, our approach can be applied to investigate the transcriptional-metabolic response in other cellular systems of medical and industrial relevance.

Quantitative assessment of thermodynamic constraints on the solution space of genome-scale metabolic models

Constraint-based methods provide powerful computational techniques to allow understanding and prediction of cellular behavior. These methods rely on physiochemical constraints to eliminate infeasible behaviors from the space of available behaviors. One such constraint is thermodynamic feasibility, the requirement that intracellular flux distributions obey the laws of thermodynamics. The past decade has seen several constraint-based methods that interpret this constraint in different ways, including those that are limited to small networks, rely on predefined reaction directions, and/or neglect the relationship between reaction free energies and metabolite concentrations. In this work, we utilize one such approach, thermodynamics-based metabolic flux analysis (TMFA), to make genome-scale, quantitative predictions about metabolite concentrations and reaction free energies in the absence of prior knowledge of reaction directions, while accounting for uncertainties in thermodynamic estimates. We applied TMFA to a genome-scale network reconstruction of Escherichia coli and examined the effect of thermodynamic constraints on the flux space. We also assessed the predictive performance of TMFA against gene essentiality and quantitative metabolomics data, under both aerobic and anaerobic, and optimal and suboptimal growth conditions. Based on these results, we propose that TMFA is a useful tool for validating phenotypes and generating hypotheses, and that additional types of data and constraints can improve predictions of metabolite concentrations.

Elementary flux modes in a nutshell: properties, calculation and applications

Elementary flux mode (EFM) analysis allows the unbiased decomposition of a metabolic network into minimal functional units, making it a powerful tool for metabolic engineering. While the use of EFM analysis (EFMA) is still limited by the size of the models it can handle, EFMA has been successfully applied to solve real-world metabolic engineering problems. Here we provide a user-oriented introduction to EFMA, provide examples of recent applications, analyze current research strategies to overcome the computational restrictions and give an overview over current approaches, which aim to identify and calculate only biologically relevant EFMs.

Glucose-methanol co-utilization in Pichia pastoris studied by metabolomics and instationary ¹³C flux analysis

Background

Several studies have shown that the utilization of mixed carbon feeds instead of methanol as sole carbon source is beneficial for protein production with the methylotrophic yeast Pichia pastoris. In particular, growth under mixed feed conditions appears to alleviate the metabolic burden related to stress responses triggered by protein overproduction and secretion. Yet, detailed analysis of the metabolome and fluxome under mixed carbon source metabolizing conditions are missing. To obtain a detailed flux distribution of central carbon metabolism, including the pentose phosphate pathway under methanol-glucose conditions, we have applied metabolomics and instationary ¹³C flux analysis in chemostat cultivations.

Results

Instationary ¹³C-based metabolic flux analysis using GC-MS and LC-MS measurements in time allowed for an accurate mapping of metabolic fluxes of glycolysis, pentose phosphate and methanol assimilation pathways. Compared to previous results from NMR-derived stationary state labelling data (proteinogenic amino acids, METAFoR) more fluxes could be determined with higher accuracy. Furthermore, using a thermodynamic metabolic network analysis the metabolite measurements and metabolic flux directions were validated. Notably, the concentration of several metabolites of the upper glycolysis and pentose phosphate pathway increased under glucose-methanol feeding compared to the reference glucose conditions, indicating a shift in the thermodynamic driving forces. Conversely, the extracellular concentrations of all measured metabolites were lower compared with the corresponding exometabolome of glucose-grown P. pastoris cells.

The instationary ¹³C flux analysis resulted in fluxes comparable to previously obtained from NMR datasets of proteinogenic amino acids, but allowed several additional insights. Specifically, i) in vivo metabolic flux estimations were expanded to a larger metabolic network e.g. by including trehalose recycling, which accounted for about 1.5% of the glucose uptake rate; ii) the reversibility of glycolytic/gluconeogenesis, TCA cycle and pentose phosphate pathways reactions was estimated, revealing a significant gluconeogenic flux from the dihydroxyacetone phosphate/glyceraldehydes phosphate pool to glucose-6P. The origin of this finding could be carbon recycling from the methanol assimilatory pathway to the pentose phosphate pool. Additionally, high exchange fluxes of oxaloacetate with aspartate as well as malate indicated amino acid pool buffering and the activity of the malate/Asp shuttle; iii) the ratio of methanol oxidation vs utilization appeared to be lower (54 vs 79% assimilated methanol directly oxidized to CO₂).

Conclusions

In summary, the application of instationary ¹³C-based metabolic flux analysis to P. pastoris provides an experimental framework with improved capabilities to explore the regulation of the carbon and energy metabolism of this yeast, particularly for the case of methanol and multicarbon source metabolism.

Fast thermodynamically constrained flux variability analysis

MOTIVATION

Flux variability analysis (FVA) is an important tool to further analyse the results obtained by flux balance analysis (FBA) on genome-scale metabolic networks. For many constraint-based models, FVA identifies unboundedness of the optimal flux space. This reveals that optimal flux solutions with net flux through internal biochemical loops are feasible, which violates the second law of thermodynamics. Such unbounded fluxes may be eliminated by extending FVA with thermodynamic constraints.

RESULTS

We present a new algorithm for efficient flux variability (and flux balance) analysis with thermodynamic constraints, suitable for analysing genome-scale metabolic networks. We first show that FBA with thermodynamic constraints is NP-hard. Then we derive a theoretical tractability result, which can be applied to metabolic networks in practice. We use this result to develop a new constraint programming algorithm Fast-tFVA for fast FVA with thermodynamic constraints (tFVA). Computational comparisons with previous methods demonstrate the efficiency of the new method. For tFVA, a speed-up of factor 30-300 is achieved. In an analysis of genome-scale metabolic networks in the BioModels database, we found that in 485 of 716 networks, additional irreversible or fixed reactions could be detected.

AVAILABILITY AND IMPLEMENTATION

Fast-tFVA is written in C++ and published under GPL. It uses the open source software SCIP and libSBML. There also exists a Matlab interface for easy integration into Matlab. Fast-tFVA is available from page.mi.fu-berlin.de/arnem/fast-tfva.html.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Application of Top-Down and Bottom-up Systems Approaches in Ruminant Physiology and Metabolism

Systems biology is a computational field that has been used for several years across different scientific areas of biological research to uncover the complex interactions occurring in living organisms. Applications of systems concepts at the mammalian genome level are quite challenging, and new complimentary computational/experimental techniques are being introduced. Most recent work applying modern systems biology techniques has been conducted on bacteria, yeast, mouse, and human genomes. However, these concepts and tools are equally applicable to other species including ruminants (e.g., livestock). In systems biology, both bottom-up and top-down approaches are central to assemble information from all levels of biological pathways that must coordinate physiological processes. A bottom-up approach encompasses draft reconstruction, manual curation, network reconstruction through mathematical methods, and validation of these models through literature analysis (i.e., bibliomics). Whereas top-down approach encompasses metabolic network reconstructions using ‘omics’ data (e.g., transcriptomics, proteomics) generated through DNA microarrays, RNA-Seq or other modern high-throughput genomic techniques using appropriate statistical and bioinformatics methodologies. In this review we focus on top-down approach as a means to improve our knowledge of underlying metabolic processes in ruminants in the context of nutrition. We also explore the usefulness of tissue specific reconstructions (e.g., liver and adipose tissue) in cattle as a means to enhance productive efficiency.

Analysis of omics data with genome-scale models of metabolism

Over the past decade a massive amount of research has been dedicated to generating omics data to gain insight into a variety of biological phenomena, including cancer, obesity, biofuel production, and infection. Although most of these omics data are available publicly, there is a growing concern that much of these data sit in databases without being used or fully analyzed. Statistical inference methods have been widely applied to gain insight into which genes may influence the activities of others in a given omics data set, however, they do not provide information on the underlying mechanisms or whether the interactions are direct or distal. Biochemically, genetically, and genomically consistent knowledge bases are increasingly being used to extract deeper biological knowledge and understanding from these data sets than possible by inferential methods. This improvement is largely due to knowledge bases providing a validated biological context for interpreting the data.