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

Substrate Utilisation and Energy Metabolism in Non-Growing Campylobacter jejuni M1cam

Campylobacter jejuni, the major cause of bacterial foodborne illness, is also a fastidious organism that requires strict growth requirements in the laboratory. Our aim was to study substrate utilisation and energy metabolism in non-growing C. jejuni to investigate the ability of these bacteria to survive so effectively in the food chain. We integrated phenotypic microarrays and genome-scale metabolic modelling (GSM) to investigate the survival of C. jejuni on 95 substrates. We further investigated the underlying metabolic re-adjustment associated with varying energy demands on each substrate. We identified amino acids, organic acids and H2, as single substrates supporting survival without growth. We identified several different mechanisms, which were used alone or in combination, for ATP production: substrate-level phosphorylation via acetate kinase, the TCA cycle, and oxidative phosphorylation via the electron transport chain that utilised alternative electron donors and acceptors. The benefit of ATP production through each of these mechanisms was associated with the cost of enzyme investment, nutrient availability and/or O2 utilisation. C. jejuni can utilise a wide range of substrates as energy sources, including organic acids commonly used for marination or preservation of ingredients, which might contribute to the success of their survival in changing environments.

Genome-Scale Metabolic Modelling Approach to Understand the Metabolism of the Opportunistic Human Pathogen Staphylococcus epidermidis RP62A

Staphylococcus epidermidis is a common commensal of collagen-rich regions of the body, such as the skin, but also represents a threat to patients with medical implants (joints and heart), and to preterm babies. Far less studied than Staphylococcus aureus, the mechanisms behind this increasingly recognised pathogenicity are yet to be fully understood. Improving our knowledge of the metabolic processes that allow S. epidermidis to colonise different body sites is key to defining its pathogenic potential. Thus, we have constructed a fully curated, genome-scale metabolic model for S. epidermidis RP62A, and investigated its metabolic properties with a focus on substrate auxotrophies and its utilisation for energy and biomass production. Our results show that, although glucose is available in the medium, only a small portion of it enters the glycolytic pathways, whils most is utilised for the production of biofilm, storage and the structural components of biomass. Amino acids, proline, valine, alanine, glutamate and arginine, are preferred sources of energy and biomass production. In contrast to previous studies, we have shown that this strain has no real substrate auxotrophies, although removal of proline from the media has the highest impact on the model and the experimental growth characteristics. Further study is needed to determine the significance of proline, an abundant amino acid in collagen, in S. epidermidis colonisation.

Boosting Biomass Quantity and Quality by Improved Mixotrophic Culture of the Diatom Phaeodactylum tricornutum

Diatoms are photoautotrophic unicellular algae and are among the most abundant, adaptable, and diverse marine phytoplankton. They are extremely interesting not only for their ecological role but also as potential feedstocks for sustainable biofuels and high-value commodities such as omega fatty acids, because of their capacity to accumulate lipids. However, the cultivation of microalgae on an industrial scale requires higher cell densities and lipid accumulation than those found in nature to make the process economically viable. One of the known ways to induce lipid accumulation in Phaeodactylum tricornutum is nitrogen deprivation, which comes at the expense of growth inhibition and lower cell density. Thus, alternative ways need to be explored to enhance the lipid production as well as biomass density to make them sustainable at industrial scale. In this study, we have used experimental and metabolic modeling approaches to optimize the media composition, in terms of elemental composition, organic and inorganic carbon sources, and light intensity, that boost both biomass quality and quantity of P. tricornutum. Eventually, the optimized conditions were scaled-up to 2 L photobioreactors, where a better system control (temperature, pH, light, aeration/mixing) allowed a further improvement of the biomass capacity of P. tricornutum to 12 g/L.

Gsmodutils: a python based framework for test-driven genome scale metabolic model development

MOTIVATION

Genome scale metabolic models (GSMMs) are increasingly important for systems biology and metabolic engineering research as they are capable of simulating complex steady-state behaviour. Constraints based models of this form can include thousands of reactions and metabolites, with many crucial pathways that only become activated in specific simulation settings. However, despite their widespread use, power and the availability of tools to aid with the construction and analysis of large scale models, little methodology is suggested for their continued management. For example, when genome annotations are updated or new understanding regarding behaviour is discovered, models often need to be altered to reflect this. This is quickly becoming an issue for industrial systems and synthetic biotechnology applications, which require good quality reusable models integral to the design, build, test and learn cycle.

RESULTS

As part of an ongoing effort to improve genome scale metabolic analysis, we have developed a test-driven development methodology for the continuous integration of validation data from different sources. Contributing to the open source technology based around COBRApy, we have developed the gsmodutils modelling framework placing an emphasis on test-driven design of models through defined test cases. Crucially, different conditions are configurable allowing users to examine how different designs or curation impact a wide range of system behaviours, minimizing error between model versions.

AVAILABILITY AND IMPLEMENTATION

The software framework described within this paper is open source and freely available from http://github.com/SBRCNottingham/gsmodutils.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

A systems-wide understanding of photosynthetic acclimation in algae and higher plants

The ability of phototrophs to colonise different environments relies on robust protection against oxidative stress, a critical requirement for the successful evolutionary transition from water to land. Photosynthetic organisms have developed numerous strategies to adapt their photosynthetic apparatus to changing light conditions in order to optimise their photosynthetic yield, which is crucial for life on Earth to exist. Photosynthetic acclimation is an excellent example of the complexity of biological systems, where highly diverse processes, ranging from electron excitation over protein protonation to enzymatic processes coupling ion gradients with biosynthetic activity, interact on drastically different timescales from picoseconds to hours. Efficient functioning of the photosynthetic apparatus and its protection is paramount for efficient downstream processes, including metabolism and growth. Modern experimental techniques can be successfully integrated with theoretical and mathematical models to promote our understanding of underlying mechanisms and principles. This review aims to provide a retrospective analysis of multidisciplinary photosynthetic acclimation research carried out by members of the Marie Curie Initial Training Project, AccliPhot, placing the results in a wider context. The review also highlights the applicability of photosynthetic organisms for industry, particularly with regards to the cultivation of microalgae. It intends to demonstrate how theoretical concepts can successfully complement experimental studies broadening our knowledge of common principles in acclimation processes in photosynthetic organisms, as well as in the field of applied microalgal biotechnology.

Modelling metabolism of the diatom Phaeodactylum tricornutum

Marine diatoms have potential as a biotechnological production platform, especially for lipid-derived products, including biofuels. Here we introduce some features of diatom metabolism, particularly with respect to photosynthesis, photorespiration and lipid synthesis and their differences relative to other photosynthetic eukaryotes. Since structural metabolic modelling of other photosynthetic organisms has been shown to be capable of representing their metabolic capabilities realistically, we briefly review the main approaches to this type of modelling. We then propose that genome-scale modelling of the diatom Phaeodactylum tricornutum, in response to varying light intensity, could uncover the novel aspects of the metabolic potential of this organism.

Promise and reality in the expanding field of network interaction analysis: metabolic networks

In the last few decades, metabolic networks revealed their capabilities as powerful tools to analyze the cellular metabolism. Many research fields (eg, metabolic engineering, diagnostic medicine, pharmacology, biochemistry, biology and physiology) improved the understanding of the cell combining experimental assays and metabolic network-based computations. This process led to the rise of the “systems biology” approach, where the theory meets experiments and where two complementary perspectives cooperate in the study of biological phenomena. Here, the reconstruction of metabolic networks is presented, along with established and new algorithms to improve the description of cellular metabolism. Then, advantages and limitations of modeling algorithms and network reconstruction are discussed.

Identification of potential drug targets in Salmonella enterica sv. Typhimurium using metabolic modelling and experimental validation

Salmonella enterica sv. Typhimurium is an established model organism for Gram-negative, intracellular pathogens. Owing to the rapid spread of resistance to antibiotics among this group of pathogens, new approaches to identify suitable target proteins are required. Based on the genome sequence of S. Typhimurium and associated databases, a genome-scale metabolic model was constructed. Output was based on an experimental determination of the biomass of Salmonella when growing in glucose minimal medium. Linear programming was used to simulate variations in the energy demand while growing in glucose minimal medium. By grouping reactions with similar flux responses, a subnetwork of 34 reactions responding to this variation was identified (the catabolic core). This network was used to identify sets of one and two reactions that when removed from the genome-scale model interfered with energy and biomass generation. Eleven such sets were found to be essential for the production of biomass precursors. Experimental investigation of seven of these showed that knockouts of the associated genes resulted in attenuated growth for four pairs of reactions, whilst three single reactions were shown to be essential for growth.

Partial inhibition and bilevel optimization in flux balance analysis

MOTIVATION

Within Flux Balance Analysis, the investigation of complex subtasks, such as finding the optimal perturbation of the network or finding an optimal combination of drugs, often requires to set up a bilevel optimization problem. In order to keep the linearity and convexity of these nested optimization problems, an ON/OFF description of the effect of the perturbation (i.e. Boolean variable) is normally used. This restriction may not be realistic when one wants, for instance, to describe the partial inhibition of a reaction induced by a drug.

RESULTS

In this paper we present a formulation of the bilevel optimization which overcomes the oversimplified ON/OFF modeling while preserving the linear nature of the problem. A case study is considered: the search of the best multi-drug treatment which modulates an objective reaction and has the minimal perturbation on the whole network. The drug inhibition is described and modulated through a convex combination of a fixed number of Boolean variables. The results obtained from the application of the algorithm to the core metabolism of E.coli highlight the possibility of finding a broader spectrum of drug combinations compared to a simple ON/OFF modeling.

CONCLUSIONS

The method we have presented is capable of treating partial inhibition inside a bilevel optimization, without loosing the linearity property, and with reasonable computational performances also on large metabolic networks. The more fine-graded representation of the perturbation allows to enlarge the repertoire of synergistic combination of drugs for tasks such as selective perturbation of cellular metabolism. This may encourage the use of the approach also for other cases in which a more realistic modeling is required.

Network-based assessment of the selectivity of metabolic drug targets in Plasmodium falciparum with respect to human liver metabolism

Background

The search for new drug targets for antibiotics against Plasmodium falciparum, a major cause of human deaths, is a pressing scientific issue, as multiple resistance strains spread rapidly. Metabolic network-based analyses may help to identify those parasite’s essential enzymes whose homologous counterparts in the human host cells are either absent, non-essential or relatively less essential.

Results

Using the well-curated metabolic networks PlasmoNet of the parasite Plasmodium falciparum and HepatoNet1 of the human hepatocyte, the selectivity of 48 experimental antimalarial drug targets was analyzed. Applying in silico gene deletions, 24 of these drug targets were found to be perfectly selective, in that they were essential for the parasite but non-essential for the human cell. The selectivity of a subset of enzymes, that were essential in both models, was evaluated with the reduced fitness concept. It was, then, possible to quantify the reduction in functional fitness of the two networks under the progressive inhibition of the same enzymatic activity. Overall, this in silico analysis provided a selectivity ranking that was in line with numerous in vivo and in vitro observations.

Conclusions

Genome-scale models can be useful to depict and quantify the effects of enzymatic inhibitions on the impaired production of biomass components. From the perspective of a host-pathogen metabolic interaction, an estimation of the drug targets-induced consequences can be beneficial for the development of a selective anti-parasitic drug.

Optimality principles in the regulation of metabolic networks

One of the challenging tasks in systems biology is to understand how molecular networks give rise to emergent functionality and whether universal design principles apply to molecular networks. To achieve this, the biophysical, evolutionary and physiological constraints that act on those networks need to be identified in addition to the characterisation of the molecular components and interactions. Then, the cellular "task" of the network-its function-should be identified. A network contributes to organismal fitness through its function. The premise is that the same functions are often implemented in different organisms by the same type of network; hence, the concept of design principles. In biology, due to the strong forces of selective pressure and natural selection, network functions can often be understood as the outcome of fitness optimisation. The hypothesis of fitness optimisation to understand the design of a network has proven to be a powerful strategy. Here, we outline the use of several optimisation principles applied to biological networks, with an emphasis on metabolic regulatory networks. We discuss the different objective functions and constraints that are considered and the kind of understanding that they provide.

Genome-scale metabolic flux analysis of Streptomyces lividans growing on a complex medium

Constraint-based metabolic modeling comprises various excellent tools to assess experimentally observed phenotypic behavior of micro-organisms in terms of intracellular metabolic fluxes. In combination with genome-scale metabolic networks, micro-organisms can be investigated in much more detail and under more complex environmental conditions. Although complex media are ubiquitously applied in industrial fermentations and are often a prerequisite for high protein secretion yields, such multi-component conditions are seldom investigated using genome-scale flux analysis. In this paper, a systematic and integrative approach is presented to determine metabolic fluxes in Streptomyces lividans TK24 grown on a nutritious and complex medium. Genome-scale flux balance analysis and randomized sampling of the solution space are combined to extract maximum information from exometabolome profiles. It is shown that biomass maximization cannot predict the observed metabolite production pattern as such. Although this cellular objective commonly applies to batch fermentation data, both input and output constraints are required to reproduce the measured biomass production rate. Rich media hence not necessarily lead to maximum biomass growth. To eventually identify a unique intracellular flux vector, a hierarchical optimization of cellular objectives is adopted. Out of various tested secondary objectives, maximization of the ATP yield per flux unit returns the closest agreement with the maximum frequency in flux histograms. This unique flux estimation is hence considered as a reasonable approximation for the biological fluxes. Flux maps for different growth phases show no active oxidative part of the pentose phosphate pathway, but NADPH generation in the TCA cycle and NADPH transdehydrogenase activity are most important in fulfilling the NADPH balance. Amino acids contribute to biomass growth by augmenting the pool of available amino acids and by boosting the TCA cycle, particularly when using glutamate and aspartate. Depletion of glutamate and aspartate causes a distinct shift in fluxes of the central carbon and nitrogen metabolism. In the current work, hurdles encountered in flux analysis at a genome-scale level are addressed using hierarchical flux balance analysis and uniform sampling of the constrained solution space. This general framework can now be adopted in further studies of S. lividans, e.g., as a host for heterologous protein production.

FASIMU: flexible software for flux-balance computation series in large metabolic networks

Background

Flux-balance analysis based on linear optimization is widely used to compute metabolic fluxes in large metabolic networks and gains increasingly importance in network curation and structural analysis. Thus, a computational tool flexible enough to realize a wide variety of FBA algorithms and able to handle batch series of flux-balance optimizations is of great benefit.

Results

We present FASIMU, a command line oriented software for the computation of flux distributions using a variety of the most common FBA algorithms, including the first available implementation of (i) weighted flux minimization, (ii) fitness maximization for partially inhibited enzymes, and (iii) of the concentration-based thermodynamic feasibility constraint. It allows batch computation with varying objectives and constraints suited for network pruning, leak analysis, flux-variability analysis, and systematic probing of metabolic objectives for network curation. Input and output supports SBML. FASIMU can work with free (lp_solve and GLPK) or commercial solvers (CPLEX, LINDO). A new plugin (faBiNA) for BiNA allows to conveniently visualize calculated flux distributions. The platform-independent program is an open-source project, freely available under GNU public license at http://www.bioinformatics.org/fasimu including manual, tutorial, and plugins.

Conclusions

We present a flux-balance optimization program whose main merits are the implementation of thermodynamics as a constraint, batch series of computations, free availability of sources, choice on various external solvers, and the flexibility on metabolic objectives and constraints.

HepatoNet1: a comprehensive metabolic reconstruction of the human hepatocyte for the analysis of liver physiology

We present HepatoNet1, the first reconstruction of a comprehensive metabolic network of the human hepatocyte that is shown to accomplish a large canon of known metabolic liver functions. The network comprises 777 metabolites in six intracellular and two extracellular compartments and 2539 reactions, including 1466 transport reactions. It is based on the manual evaluation of >1500 original scientific research publications to warrant a high-quality evidence-based model. The final network is the result of an iterative process of data compilation and rigorous computational testing of network functionality by means of constraint-based modeling techniques. Taking the hepatic detoxification of ammonia as an example, we show how the availability of nutrients and oxygen may modulate the interplay of various metabolic pathways to allow an efficient response of the liver to perturbations of the homeostasis of blood compounds.

Querying metabolism under different physiological constraints

Metabolism is a representation of the biochemical principles that govern the production, consumption, degradation, and biosynthesis of metabolites in living cells. Organisms respond to changes in their physiological conditions or environmental perturbations (i.e. constraints) via cooperative implementation of such principles. Querying inner working principles of metabolism under different constraints provides invaluable insights for both researchers and educators. In this paper, we propose a metabolism query language (MQL) and discuss its query processing. MQL enables researchers to explore the behavior of the metabolism with a wide-range of predicates including dietary and physiological condition specifications. The query results of MQL are enriched with both textual and visual representations, and its query processing is completely tailored based on the underlying metabolic principles.

Metabolic network model of a human oral pathogen

The microbial community present in the human mouth is engaged in a complex network of diverse metabolic activities. In addition to serving as energy and building-block sources, metabolites are key players in interspecies and host-pathogen interactions. Metabolites are also implicated in triggering the local inflammatory response, which can affect systemic conditions such as atherosclerosis, obesity, and diabetes. While the genome of several oral pathogens has been sequenced, quantitative understanding of the metabolic functions of any oral pathogen at the system level has not been explored yet. Here we pursue the computational construction and analysis of the genome-scale metabolic network of Porphyromonas gingivalis, a gram-negative anaerobe that is endemic in the human population and largely responsible for adult periodontitis. Integrating information from the genome, online databases, and literature screening, we built a stoichiometric model that encompasses 679 metabolic reactions. By using flux balance approaches and automated network visualization, we analyze the growth capacity under amino-acid-rich medium and provide evidence that amino acid preference and cytotoxic by-product secretion rates are suitably reproduced by the model. To provide further insight into the basic metabolic functions of P. gingivalis and suggest potential drug targets, we study systematically how the network responds to any reaction knockout. We focus specifically on the lipopolysaccharide biosynthesis pathway and identify eight putative targets, one of which has been recently verified experimentally. The current model, which is amenable to further experimental testing and refinements, could prove useful in evaluating the oral microbiome dynamics and in the development of novel biomedical applications.

Model-driven analysis of experimentally determined growth phenotypes for 465 yeast gene deletion mutants under 16 different conditions

An iterative approach that integrates high-throughput measurements of yeast deletion mutants and flux balance model predictions improves understanding of both experimental and computational results.

Background

Understanding the response of complex biochemical networks to genetic perturbations and environmental variability is a fundamental challenge in biology. Integration of high-throughput experimental assays and genome-scale computational methods is likely to produce insight otherwise unreachable, but specific examples of such integration have only begun to be explored.

Results

In this study, we measured growth phenotypes of 465 Saccharomyces cerevisiae gene deletion mutants under 16 metabolically relevant conditions and integrated them with the corresponding flux balance model predictions. We first used discordance between experimental results and model predictions to guide a stage of experimental refinement, which resulted in a significant improvement in the quality of the experimental data. Next, we used discordance still present in the refined experimental data to assess the reliability of yeast metabolism models under different conditions. In addition to estimating predictive capacity based on growth phenotypes, we sought to explain these discordances by examining predicted flux distributions visualized through a new, freely available platform. This analysis led to insight into the glycerol utilization pathway and the potential effects of metabolic shortcuts on model results. Finally, we used model predictions and experimental data to discriminate between alternative raffinose catabolism routes.

Conclusions

Our study demonstrates how a new level of integration between high throughput measurements and flux balance model predictions can improve understanding of both experimental and computational results. The added value of a joint analysis is a more reliable platform for specific testing of biological hypotheses, such as the catabolic routes of different carbon sources.

Top-down analysis of temporal hierarchy in biochemical reaction networks

The study of dynamic functions of large-scale biological networks has intensified in recent years. A critical component in developing an understanding of such dynamics involves the study of their hierarchical organization. We investigate the temporal hierarchy in biochemical reaction networks focusing on: (1) the elucidation of the existence of “pools” (i.e., aggregate variables) formed from component concentrations and (2) the determination of their composition and interactions over different time scales. To date the identification of such pools without prior knowledge of their composition has been a challenge. A new approach is developed for the algorithmic identification of pool formation using correlations between elements of the modal matrix that correspond to a pair of concentrations and how such correlations form over the hierarchy of time scales. The analysis elucidates a temporal hierarchy of events that range from chemical equilibration events to the formation of physiologically meaningful pools, culminating in a network-scale (dynamic) structure–(physiological) function relationship. This method is validated on a model of human red blood cell metabolism and further applied to kinetic models of yeast glycolysis and human folate metabolism, enabling the simplification of these models. The understanding of temporal hierarchy and the formation of dynamic aggregates on different time scales is foundational to the study of network dynamics and has relevance in multiple areas ranging from bacterial strain design and metabolic engineering to the understanding of disease processes in humans.

Cellular metabolism describes the complex web of biochemical transformations that are necessary to build the structural components, to convert nutrients into “usable energy” by the cell, and to degrade or excrete the by-products. A critical aspect toward understanding metabolism is the set of dynamic interactions between metabolites, some of which occur very quickly while others occur more slowly. To develop a “systems” understanding of how networks operate dynamically we need to identify the different processes that occur on different time scales. When one moves from very fast time scales to slower ones, certain components in the network move in concert and pool together. We develop a method to elucidate the time scale hierarchy of a network and to simplify its structure by identifying these pools. This is applied to dynamic models of metabolism for the human red blood cell, human folate metabolism, and yeast glycolysis. It was possible to simplify the structure of these networks into biologically meaningful groups of variables. Because dynamics play important roles in normal and abnormal function in biology, it is expected that this work will contribute to an area of great relevance for human disease and engineering applications.

Is maximization of molar yield in metabolic networks favoured by evolution?

Stoichiometric analysis of metabolic networks allows the calculation of possible metabolic flux distributions in the absence of kinetic data. In order to predict which of the possible fluxes are present under certain conditions, additional constraints and optimization principles can be applied. One approach of calculating unknown fluxes (frequently called flux balance analysis) is based on the optimality principle of maximizing the molar yield of biotransformations. Here, the relevance and applicability of that approach are examined, and it is compared with the principle of maximizing pathway flux. We discuss diverse experimental evidence showing that, often, those biochemical pathways are operative that allow fast but low-yield synthesis of important products, such as fermentation in Saccharomyces cerevisiae and several other yeast species. Together with arguments based on evolutionary game theory, this leads us to the conclusion that maximization of molar yield is by no means a universal principle.

Reconstruction and flux analysis of coupling between metabolic pathways of astrocytes and neurons: application to cerebral hypoxia

BACKGROUND

It is a daunting task to identify all the metabolic pathways of brain energy metabolism and develop a dynamic simulation environment that will cover a time scale ranging from seconds to hours. To simplify this task and make it more practicable, we undertook stoichiometric modeling of brain energy metabolism with the major aim of including the main interacting pathways in and between astrocytes and neurons.

MODEL

The constructed model includes central metabolism (glycolysis, pentose phosphate pathway, TCA cycle), lipid metabolism, reactive oxygen species (ROS) detoxification, amino acid metabolism (synthesis and catabolism), the well-known glutamate-glutamine cycle, other coupling reactions between astrocytes and neurons, and neurotransmitter metabolism. This is, to our knowledge, the most comprehensive attempt at stoichiometric modeling of brain metabolism to date in terms of its coverage of a wide range of metabolic pathways. We then attempted to model the basal physiological behaviour and hypoxic behaviour of the brain cells where astrocytes and neurons are tightly coupled.

RESULTS

The reconstructed stoichiometric reaction model included 217 reactions (184 internal, 33 exchange) and 216 metabolites (183 internal, 33 external) distributed in and between astrocytes and neurons. Flux balance analysis (FBA) techniques were applied to the reconstructed model to elucidate the underlying cellular principles of neuron-astrocyte coupling. Simulation of resting conditions under the constraints of maximization of glutamate/glutamine/GABA cycle fluxes between the two cell types with subsequent minimization of Euclidean norm of fluxes resulted in a flux distribution in accordance with literature-based findings. As a further validation of our model, the effect of oxygen deprivation (hypoxia) on fluxes was simulated using an FBA-derivative approach, known as minimization of metabolic adjustment (MOMA). The results show the power of the constructed model to simulate disease behaviour on the flux level, and its potential to analyze cellular metabolic behaviour in silico.

CONCLUSION

The predictive power of the constructed model for the key flux distributions, especially central carbon metabolism and glutamate-glutamine cycle fluxes, and its application to hypoxia is promising. The resultant acceptable predictions strengthen the power of such stoichiometric models in the analysis of mammalian cell metabolism.

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

BACKGROUND

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

RESULTS

To augment the reliability of FBA-based flux calculations we propose an additional side constraint which assures thermodynamic realizability, i.e. that the flux directions are consistent with the corresponding changes of Gibb's free energies. The latter depend on metabolite levels for which plausible ranges can be inferred from experimental data. Computationally, our method results in the solution of a mixed integer linear optimization problem with quadratic scoring function. An optimal flux distribution together with a metabolite profile is determined which assures thermodynamic realizability with minimal deviations of metabolite levels from their expected values. We applied our novel approach to two exemplary metabolic networks of different complexity, the metabolic core network of erythrocytes (30 reactions) and the metabolic network iJR904 of Escherichia coli (931 reactions). Our calculations show that increasing network complexity entails increasing sensitivity of predicted flux distributions to variations of standard Gibb's free energy changes and metabolite concentration ranges. We demonstrate the usefulness of our method for assessing critical concentrations of external metabolites preventing attainment of a metabolic steady state.

CONCLUSION

Our method incorporates the thermodynamic link between flux directions and metabolite concentrations into a practical computational algorithm. The weakness of conventional FBA to rely on intuitive assumptions about the reversibility of biochemical reactions is overcome. This enables the computation of reliable flux distributions even under extreme conditions of the network (e.g. enzyme inhibition, depletion of substrates or accumulation of end products) where metabolite concentrations may be drastically altered.