Monte Carlo sampling can be used to determine the size and shape of the steady-state flux space

NEXT-FBA: A hybrid stoichiometric/data-driven approach to improve intracellular flux predictions

Genome-scale metabolic models (GEMs) have been widely utilized to understand cellular metabolism. The application of GEMs has been advanced by computational methods that enable the prediction and analysis of intracellular metabolic states. However, the accuracy and biological relevance of these predictions often suffer from the many degrees of freedom and scarcity of available data to constrain the models adequately. Here, we introduce Neural-net EXtracellular Trained Flux Balance Analysis, (NEXT-FBA), a novel computational methodology that addresses these limitations by utilizing exometabolomic data to derive biologically relevant constraints for intracellular fluxes in GEMs. We achieve this by training artificial neural networks (ANNs) with exometabolomic data from Chinese hamster ovary (CHO) cells and correlating it with 13C-labeled intracellular fluxomic data. By capturing the underlying relationships between exometabolomics and cell metabolism, NEXT-FBA predicts upper and lower bounds for intracellular reaction fluxes to constrain GEMs. We demonstrate the efficacy of NEXT-FBA across several validation experiments, where it outperforms existing methods in predicting intracellular flux distributions that align closely with experimental observations. Furthermore, a case study demonstrates how NEXT-FBA can guide bioprocess optimization by identifying key metabolic shifts and refining flux predictions to yield actionable process and metabolic engineering targets. Overall, NEXT-FBA aims to improve the accuracy and biological relevance of intracellular flux predictions in metabolic modelling, with minimal input data requirements for pre-trained models.

CFSA: Comparative flux sampling analysis as a guide for strain design

Genome-scale metabolic models of microbial metabolism have extensively been used to guide the design of microbial cell factories, still, many of the available strain design algorithms often fail to produce a reduced list of targets for improved performance that can be implemented and validated in a step-wise manner. We present Comparative Flux Sampling Analysis (CFSA), a strain design method based on the extensive comparison of complete metabolic spaces corresponding to maximal or near-maximal growth and production phenotypes. The comparison is complemented by statistical analysis to identify reactions with altered flux that are suggested as targets for genetic interventions including up-regulations, down-regulations and gene deletions. We applied CFSA to the production of lipids by Cutaneotrichosporon oleaginosus and naringenin by Saccharomyces cerevisiae identifying engineering targets in agreement with previous studies as well as new interventions. CFSA is an easy-to-use, robust method that suggests potential metabolic engineering targets for growth-uncoupled production that can be applied to the design of microbial cell factories.

Machine learning predicts system-wide metabolic flux control in cyanobacteria

Metabolic fluxes and their control mechanisms are fundamental in cellular metabolism, offering insights for the study of biological systems and biotechnological applications. However, quantitative and predictive understanding of controlling biochemical reactions in microbial cell factories, especially at the system level, is limited. In this work, we present ARCTICA, a computational framework that integrates constraint-based modelling with machine learning tools to address this challenge. Using the model cyanobacterium Synechocystis sp. PCC 6803 as chassis, we demonstrate that ARCTICA effectively simulates global-scale metabolic flux control. Key findings are that (i) the photosynthetic bioproduction is mainly governed by enzymes within the Calvin-Benson-Bassham (CBB) cycle, rather than by those involve in the biosynthesis of the end-product, (ii) the catalytic capacity of the CBB cycle limits the photosynthetic activity and downstream pathways and (iii) ribulose-1,5-bisphosphate carboxylase/oxygenase (RuBisCO) is a major, but not the most, limiting step within the CBB cycle. Predicted metabolic reactions qualitatively align with prior experimental observations, validating our modelling approach. ARCTICA serves as a valuable pipeline for understanding cellular physiology and predicting rate-limiting steps in genome-scale metabolic networks, and thus provides guidance for bioengineering of cyanobacteria.

A structured evaluation of genome-scale constraint-based modeling tools for microbial consortia

Harnessing the power of microbial consortia is integral to a diverse range of sectors, from healthcare to biotechnology to environmental remediation. To fully realize this potential, it is critical to understand the mechanisms behind the interactions that structure microbial consortia and determine their functions. Constraint-based reconstruction and analysis (COBRA) approaches, employing genome-scale metabolic models (GEMs), have emerged as the state-of-the-art tool to simulate the behavior of microbial communities from their constituent genomes. In the last decade, many tools have been developed that use COBRA approaches to simulate multi-species consortia, under either steady-state, dynamic, or spatiotemporally varying scenarios. Yet, these tools have not been systematically evaluated regarding their software quality, most suitable application, and predictive power. Hence, it is uncertain which tools users should apply to their system and what are the most urgent directions that developers should take in the future to improve existing capacities. This study conducted a systematic evaluation of COBRA-based tools for microbial communities using datasets from two-member communities as test cases. First, we performed a qualitative assessment in which we evaluated 24 published tools based on a list of FAIR (Findability, Accessibility, Interoperability, and Reusability) features essential for software quality. Next, we quantitatively tested the predictions in a subset of 14 of these tools against experimental data from three different case studies: a) syngas fermentation by C. autoethanogenum and C. kluyveri for the static tools, b) glucose/xylose fermentation with engineered E. coli and S. cerevisiae for the dynamic tools, and c) a Petri dish of E. coli and S. enterica for tools incorporating spatiotemporal variation. Our results show varying performance levels of the best qualitatively assessed tools when examining the different categories of tools. The differences in the mathematical formulation of the approaches and their relation to the results were also discussed. Ultimately, we provide recommendations for refining future GEM microbial modeling tools.

Practical sampling of constraint-based models: Optimized thinning boosts CHRR performance

Thinning is a sub-sampling technique to reduce the memory footprint of Markov chain Monte Carlo. Despite being commonly used, thinning is rarely considered efficient. For sampling constraint-based models, a highly relevant use-case in systems biology, we here demonstrate that thinning boosts computational and, thereby, sampling efficiencies of the widely used Coordinate Hit-and-Run with Rounding (CHRR) algorithm. By benchmarking CHRR with thinning with simplices and genome-scale metabolic networks of up to thousands of dimensions, we find a substantial increase in computational efficiency compared to unthinned CHRR, in our examples by orders of magnitude, as measured by the effective sample size per time (ESS/t), with performance gains growing with polytope (effective network) dimension. Using a set of benchmark models we derive a ready-to-apply guideline for tuning thinning to efficient and effective use of compute resources without requiring additional coding effort. Our guideline is validated using three (out-of-sample) large-scale networks and we show that it allows sampling convex polytopes uniformly to convergence in a fraction of time, thereby unlocking the rigorous investigation of hitherto intractable models. The derivation of our guideline is explained in detail, allowing future researchers to update it as needed as new model classes and more training data becomes available. CHRR with deliberate utilization of thinning thereby paves the way to keep pace with progressing model sizes derived with the constraint-based reconstruction and analysis (COBRA) tool set. Sampling and evaluation pipelines are available at https://jugit.fz-juelich.de/IBG-1/ModSim/fluxomics/chrrt.

A Path Planning Method with a Bidirectional Potential Field Probabilistic Step Size RRT for a Dual Manipulator

The search efficiency of a rapidly exploring random tree (RRT) can be improved by introducing a high-probability goal bias strategy. In the case of multiple complex obstacles, the high-probability goal bias strategy with a fixed step size will fall into a local optimum, which reduces search efficiency. Herein, a bidirectional potential field probabilistic step size rapidly exploring random tree (BPFPS-RRT) was proposed for the path planning of a dual manipulator by introducing a search strategy of a step size with a target angle and random value. The artificial potential field method was introduced, combining the search features with the bidirectional goal bias and the concept of greedy path optimization. According to simulations, taking the main manipulator as an example, compared with goal bias RRT, variable step size RRT, and goal bias bidirectional RRT, the proposed algorithm reduces the search time by 23.53%, 15.45%, and 43.78% and decreases the path length by 19.35%, 18.83%, and 21.38%, respectively. Moreover, taking the slave manipulator as another example, the proposed algorithm reduces the search time by 6.71%, 1.49%, and 46.88% and decreases the path length by 19.88%, 19.39%, and 20.83%, respectively. The proposed algorithm can be adopted to effectively achieve path planning for the dual manipulator.

Understanding Antimicrobial Resistance Using Genome-Scale Metabolic Modeling

The urgent necessity to fight antimicrobial resistance is universally recognized. In the search of new targets and strategies to face this global challenge, a promising approach resides in the study of the cellular response to antimicrobial exposure and on the impact of global cellular reprogramming on antimicrobial drugs' efficacy. The metabolic state of microbial cells has been shown to undergo several antimicrobial-induced modifications and, at the same time, to be a good predictor of the outcome of an antimicrobial treatment. Metabolism is a promising reservoir of potential drug targets/adjuvants that has not been fully exploited to date. One of the main problems in unraveling the metabolic response of cells to the environment resides in the complexity of such metabolic networks. To solve this problem, modeling approaches have been developed, and they are progressively gaining in popularity due to the huge availability of genomic information and the ease at which a genome sequence can be converted into models to run basic phenotype predictions. Here, we review the use of computational modeling to study the relationship between microbial metabolism and antimicrobials and the recent advances in the application of genome-scale metabolic modeling to the study of microbial responses to antimicrobial exposure.

Phenotypic response of yeast metabolic network to availability of proteinogenic amino acids

Genome-scale metabolism can best be described as a highly interconnected network of biochemical reactions and metabolites. The flow of metabolites, i.e., flux, throughout these networks can be predicted and analyzed using approaches such as flux balance analysis (FBA). By knowing the network topology and employing only a few simple assumptions, FBA can efficiently predict metabolic functions at the genome scale as well as microbial phenotypes. The network topology is represented in the form of genome-scale metabolic models (GEMs), which provide a direct mapping between network structure and function via the enzyme-coding genes and corresponding metabolic capacity. Recently, the role of protein limitations in shaping metabolic phenotypes have been extensively studied following the reconstruction of enzyme-constrained GEMs. This framework has been shown to significantly improve the accuracy of predicting microbial phenotypes, and it has demonstrated that a global limitation in protein availability can prompt the ubiquitous metabolic strategy of overflow metabolism. Being one of the most abundant and differentially expressed proteome sectors, metabolic proteins constitute a major cellular demand on proteinogenic amino acids. However, little is known about the impact and sensitivity of amino acid availability with regards to genome-scale metabolism. Here, we explore these aspects by extending on the enzyme-constrained GEM framework by also accounting for the usage of amino acids in expressing the metabolic proteome. Including amino acids in an enzyme-constrained GEM of Saccharomyces cerevisiae, we demonstrate that the expanded model is capable of accurately reproducing experimental amino acid levels. We further show that the metabolic proteome exerts variable demands on amino acid supplies in a condition-dependent manner, suggesting that S. cerevisiae must have evolved to efficiently fine-tune the synthesis of amino acids for expressing its metabolic proteins in response to changes in the external environment. Finally, our results demonstrate how the metabolic network of S. cerevisiae is robust towards perturbations of individual amino acids, while simultaneously being highly sensitive when the relative amino acid availability is set to mimic a priori distributions of both yeast and non-yeast origins.

Comparison of metabolic states using genome-scale metabolic models

Genome-scale metabolic models (GEMs) are comprehensive knowledge bases of cellular metabolism and serve as mathematical tools for studying biological phenotypes and metabolic states or conditions in various organisms and cell types. Given the sheer size and complexity of human metabolism, selecting parameters for existing analysis methods such as metabolic objective functions and model constraints is not straightforward in human GEMs. In particular, comparing several conditions in large GEMs to identify condition- or disease-specific metabolic features is challenging. In this study, we showcase a scalable, model-driven approach for an in-depth investigation and comparison of metabolic states in large GEMs which enables identifying the underlying functional differences. Using a combination of flux space sampling and network analysis, our approach enables extraction and visualisation of metabolically distinct network modules. Importantly, it does not rely on known or assumed objective functions. We apply this novel approach to extract the biochemical differences in adipocytes arising due to unlimited vs blocked uptake of branched-chain amino acids (BCAAs, considered as biomarkers in obesity) using a human adipocyte GEM (iAdipocytes1809). The biological significance of our approach is corroborated by literature reports confirming our identified metabolic processes (TCA cycle and Fatty acid metabolism) to be functionally related to BCAA metabolism. Additionally, our analysis predicts a specific altered uptake and secretion profile indicating a compensation for the unavailability of BCAAs. Taken together, our approach facilitates determining functional differences between any metabolic conditions of interest by offering a versatile platform for analysing and comparing flux spaces of large metabolic networks.

Cellular metabolism is a highly complex and interconnected system. As many lifestyle diseases in humans have a strong metabolic component, it is important to understand metabolic differences between healthy and diseased states. In systems biology, metabolic behaviours are investigated using genome-scale metabolic models. In addition to the sheer size and complexity of the genome-scale metabolic models of human systems, using existing analysis methods is challenging and the parameter selection is not straightforward. Therefore, novel methodological frameworks are necessary for analysing metabolic conditions despite the challenges posed by human models. Particularly, an ongoing challenge has been that of comparing several phenotypes for identifying condition- or disease-specific metabolic signatures. We address this significant challenge by developing a scalable and model-driven approach, ComMet (Comparison of Metabolic states). ComMet enables an in-depth investigation and comparison of metabolic phenotypes in large models while also identifying the underlying functional differences. Novel hypotheses can be generated using ComMet for not only understanding known metabolic phenotypes better but also for guiding the design of new experiments to validate the processes predicted by ComMet.

Towards a deeper understanding of microbial communities: integrating experimental data with dynamic models

Microbial communities and their functions are shaped by complex networks of interactions among microbes and with their environment. While the critical roles microbial communities play in numerous environments have become increasingly appreciated, we have a very limited understanding of their interactions and how these interactions combine to generate community-level behaviors. This knowledge gap hinders our ability to predict community responses to perturbations and to design interventions that manipulate these communities to our benefit. Dynamic models are promising tools to address these questions. We review existing modeling techniques to construct dynamic models of microbial communities at different scales and suggest ways to leverage multiple types of models and data to facilitate our understanding and engineering of microbial communities.

Addressing uncertainty in genome-scale metabolic model reconstruction and analysis

The reconstruction and analysis of genome-scale metabolic models constitutes a powerful systems biology approach, with applications ranging from basic understanding of genotype-phenotype mapping to solving biomedical and environmental problems. However, the biological insight obtained from these models is limited by multiple heterogeneous sources of uncertainty, which are often difficult to quantify. Here we review the major sources of uncertainty and survey existing approaches developed for representing and addressing them. A unified formal characterization of these uncertainties through probabilistic approaches and ensemble modeling will facilitate convergence towards consistent reconstruction pipelines, improved data integration algorithms, and more accurate assessment of predictive capacity.

Opportunities at the Interface of Network Science and Metabolic Modeling

Metabolism plays a central role in cell physiology because it provides the molecular machinery for growth. At the genome-scale, metabolism is made up of thousands of reactions interacting with one another. Untangling this complexity is key to understand how cells respond to genetic, environmental, or therapeutic perturbations. Here we discuss the roles of two complementary strategies for the analysis of genome-scale metabolic models: Flux Balance Analysis (FBA) and network science. While FBA estimates metabolic flux on the basis of an optimization principle, network approaches reveal emergent properties of the global metabolic connectivity. We highlight how the integration of both approaches promises to deliver insights on the structure and function of metabolic systems with wide-ranging implications in discovery science, precision medicine and industrial biotechnology.

A comparison of Monte Carlo sampling methods for metabolic network models

Reaction rates (fluxes) in a metabolic network can be analyzed using constraint-based modeling which imposes a steady state assumption on the system. In a deterministic formulation of the problem the steady state assumption has to be fulfilled exactly, and the observed fluxes are included in the model without accounting for experimental noise. One can relax the steady state constraint, and also include experimental noise in the model, through a stochastic formulation of the problem. Uniform sampling of fluxes, feasible in both the deterministic and stochastic formulation, can provide us with statistical properties of the metabolic network, such as marginal flux probability distributions. In this study we give an overview of both the deterministic and stochastic formulation of the problem, and of available Monte Carlo sampling methods for sampling the corresponding solution space. We apply the ACHR, OPTGP, CHRR and Gibbs sampling algorithms to ten metabolic networks and evaluate their convergence, consistency and efficiency. The coordinate hit-and-run with rounding (CHRR) is found to perform best among the algorithms suitable for the deterministic formulation. A desirable property of CHRR is its guaranteed distributional convergence. Among the three other algorithms, ACHR has the largest consistency with CHRR for genome scale models. For the stochastic formulation, the Gibbs sampler is the only method appropriate for sampling at genome scale. However, our analysis ranks it as less efficient than the samplers used for the deterministic formulation.

Statistical mechanics of interacting metabolic networks

We cast the metabolism of interacting cells within a statistical mechanics framework considering both the actual phenotypic capacities of each cell and its interaction with its neighbors. Reaction fluxes will be the components of high-dimensional spin vectors, whose values will be constrained by the stochiometry and the energy requirements of the metabolism. Within this picture, finding the phenotypic states of the population turns out to be equivalent to searching for the equilibrium states of a disordered spin model. We provide a general solution of this problem for arbitrary metabolic networks and interactions. We apply this solution to a simplified model of metabolism and to a complex metabolic network, the central core of Escherichia coli, and demonstrate that the combination of selective pressure and interactions defines a complex phenotypic space. We also present numerical results for cells fixed in a grid. These results reproduce the qualitative picture discussed for the mean-field model. Cells may specialize in producing or consuming metabolites complementing each other, and this is described by an equilibrium phase space with multiple minima, like in a spin-glass model.

Flux sampling is a powerful tool to study metabolism under changing environmental conditions

The development of high-throughput 'omic techniques has sparked a rising interest in genome-scale metabolic models, with applications ranging from disease diagnostics to crop adaptation. Efficient and accurate methods are required to analyze large metabolic networks. Flux sampling can be used to explore the feasible flux solutions in metabolic networks by generating probability distributions of steady-state reaction fluxes. Unlike other methods, flux sampling can be used without assuming a particular cellular objective. We have undertaken a rigorous comparison of several sampling algorithms and concluded that the coordinate hit-and-run with rounding (CHRR) algorithm is the most efficient based on both run-time and multiple convergence diagnostics. We demonstrate the power of CHRR by using it to study the metabolic changes that underlie photosynthetic acclimation to cold of Arabidopsis thaliana plant leaves. In combination with experimental measurements, we show how the regulated interplay between diurnal starch and organic acid accumulation defines the plant acclimation process. We confirm fumarate accumulation as a requirement for cold acclimation and further predict γ-aminobutyric acid to have a key role in metabolic signaling under cold conditions. These results demonstrate how flux sampling can be used to analyze the feasible flux solutions across changing environmental conditions, whereas eliminating the need to make assumptions which introduce observer bias.

Modelling and mathematical analysis of the M$_{2}$ receptor-dependent joint signalling and secondary messenger network in CHO cells

The muscarinic M$_{2}$ receptor is a prominent member of the GPCR family and strongly involved in heart diseases. Recently published experimental work explored the cellular response to iperoxo-induced M$_{2}$ receptor stimulation in Chinese hamster ovary (CHO) cells. To better understand these responses, we modelled and analysed the muscarinic M$_{2}$ receptor-dependent signalling pathway combined with relevant secondary messenger molecules using mass action. In our literature-based joint signalling and secondary messenger model, all binding and phosphorylation events are explicitly taken into account in order to enable subsequent stoichiometric matrix analysis. We propose constraint flux sampling (CFS) as a method to characterize the expected shift of the steady state reaction flux distribution due to the known amount of cAMP production and PDE4 activation. CFS correctly predicts an experimentally observable influence on the cytoskeleton structure (marked by actin and tubulin) and in consequence a change of the optical density of cells. In a second step, we use CFS to simulate the effect of knock-out experiments within our biological system, and thus to rank the influence of individual molecules on the observed change of the optical cell density. In particular, we confirm the relevance of the protein RGS14, which is supported by current literature. A combination of CFS with Elementary Flux Mode analysis enabled us to determine the possible underlying mechanism. Our analysis suggests that mathematical tools developed for metabolic network analysis can also be applied to mixed secondary messenger and signalling models. This could be very helpful to perform model checking with little effort and to generate hypotheses for further research if parameters are not known.

Sequence Specific Modeling of E. coli Cell-Free Protein Synthesis

Cell-free protein synthesis (CFPS) is a widely used research tool in systems and synthetic biology. However, if CFPS is to become a mainstream technology for applications such as point of care manufacturing, we must understand the performance limits and costs of these systems. Toward this question, we used sequence specific constraint based modeling to evaluate the performance of E. coli cell-free protein synthesis. A core E. coli metabolic network, describing glycolysis, the pentose phosphate pathway, energy metabolism, amino acid biosynthesis, and degradation was augmented with sequence specific descriptions of transcription and translation and effective models of promoter function. Model parameters were largely taken from literature; thus the constraint based approach coupled the transcription and translation of the protein product, and the regulation of gene expression, with the availability of metabolic resources using only a limited number of adjustable model parameters. We tested this approach by simulating the expression of two model proteins: chloramphenicol acetyltransferase and dual emission green fluorescent protein, for which we have data sets; we then expanded the simulations to a range of additional proteins. Protein expression simulations were consistent with measurements for a variety of cases. The constraint based simulations confirmed that oxidative phosphorylation was active in the CAT cell-free extract, as without it there was no feasible solution within the experimental constraints of the system. We then compared the metabolism of theoretically optimal and experimentally constrained CFPS reactions, and developed parameter free correlations which could be used to estimate productivity as a function of carbon number and promoter type. Lastly, global sensitivity analysis identified the key metabolic processes that controlled CFPS productivity and energy efficiency. In summary, sequence specific constraint based modeling of CFPS offered a novel means to a priori estimate the performance of a cell-free system, using only a limited number of adjustable parameters. While we modeled the production of a single protein in this study, the approach could easily be extended to multiprotein synthetic circuits, RNA circuits, or the cell-free production of small molecule products.

Insights into metabolic osmoadaptation of the ectoines-producer bacterium Chromohalobacter salexigens through a high-quality genome scale metabolic model

Background

The halophilic bacterium Chromohalobacter salexigens is a natural producer of ectoines, compatible solutes with current and potential biotechnological applications. As production of ectoines is an osmoregulated process that draws away TCA intermediates, bacterial metabolism needs to be adapted to cope with salinity changes. To explore and use C. salexigens as cell factory for ectoine(s) production, a comprehensive knowledge at the systems level of its metabolism is essential. For this purpose, the construction of a robust and high-quality genome-based metabolic model of C. salexigens was approached.

Results

We generated and validated a high quality genome-based C. salexigens metabolic model (iFP764). This comprised an exhaustive reconstruction process based on experimental information, analysis of genome sequence, manual re-annotation of metabolic genes, and in-depth refinement. The model included three compartments (periplasmic, cytoplasmic and external medium), and two salinity-specific biomass compositions, partially based on experimental results from C. salexigens. Using previous metabolic data as constraints, the metabolic model allowed us to simulate and analyse the metabolic osmoadaptation of C. salexigens under conditions for low and high production of ectoines. The iFP764 model was able to reproduce the major metabolic features of C. salexigens. Flux Balance Analysis (FBA) and Monte Carlo Random sampling analysis showed salinity-specific essential metabolic genes and different distribution of fluxes and variation in the patterns of correlation of reaction sets belonging to central C and N metabolism, in response to salinity. Some of them were related to bioenergetics or production of reducing equivalents, and probably related to demand for ectoines. Ectoines metabolic reactions were distributed according to its correlation in four modules. Interestingly, the four modules were independent both at low and high salinity conditions, as they did not correlate to each other, and they were not correlated with other subsystems.

Conclusions

Our validated model is one of the most complete curated networks of halophilic bacteria. It is a powerful tool to simulate and explore C. salexigens metabolism at low and high salinity conditions, driving to low and high production of ectoines. In addition, it can be useful to optimize the metabolism of other halophilic bacteria for metabolite production.

Electronic supplementary material

The online version of this article (10.1186/s12934-017-0852-0) contains supplementary material, which is available to authorized users.

An analytic approximation of the feasible space of metabolic networks

Assuming a steady-state condition within a cell, metabolic fluxes satisfy an underdetermined linear system of stoichiometric equations. Characterizing the space of fluxes that satisfy such equations along with given bounds (and possibly additional relevant constraints) is considered of utmost importance for the understanding of cellular metabolism. Extreme values for each individual flux can be computed with linear programming (as flux balance analysis), and their marginal distributions can be approximately computed with Monte Carlo sampling. Here we present an approximate analytic method for the latter task based on expectation propagation equations that does not involve sampling and can achieve much better predictions than other existing analytic methods. The method is iterative, and its computation time is dominated by one matrix inversion per iteration. With respect to sampling, we show through extensive simulation that it has some advantages including computation time, and the ability to efficiently fix empirically estimated distributions of fluxes.

Large-scale metabolic models of organisms from microbes to mammals can provide great insight into cellular function, but their analysis remains challenging. Here, the authors provide an approximate analytic method to estimate the feasible solution space for the flux vectors of metabolic networks, enabling more accurate analysis under a wide range of conditions of interest.

Genome-Scale Reconstruction of the Human Astrocyte Metabolic Network

Astrocytes are the most abundant cells of the central nervous system; they have a predominant role in maintaining brain metabolism. In this sense, abnormal metabolic states have been found in different neuropathological diseases. Determination of metabolic states of astrocytes is difficult to model using current experimental approaches given the high number of reactions and metabolites present. Thus, genome-scale metabolic networks derived from transcriptomic data can be used as a framework to elucidate how astrocytes modulate human brain metabolic states during normal conditions and in neurodegenerative diseases. We performed a Genome-Scale Reconstruction of the Human Astrocyte Metabolic Network with the purpose of elucidating a significant portion of the metabolic map of the astrocyte. This is the first global high-quality, manually curated metabolic reconstruction network of a human astrocyte. It includes 5,007 metabolites and 5,659 reactions distributed among 8 cell compartments, (extracellular, cytoplasm, mitochondria, endoplasmic reticle, Golgi apparatus, lysosome, peroxisome and nucleus). Using the reconstructed network, the metabolic capabilities of human astrocytes were calculated and compared both in normal and ischemic conditions. We identified reactions activated in these two states, which can be useful for understanding the astrocytic pathways that are affected during brain disease. Additionally, we also showed that the obtained flux distributions in the model, are in accordance with literature-based findings. Up to date, this is the most complete representation of the human astrocyte in terms of inclusion of genes, proteins, reactions and metabolic pathways, being a useful guide for in-silico analysis of several metabolic behaviors of the astrocyte during normal and pathologic states.

Decoding how a soil bacterium extracts building blocks and metabolic energy from ligninolysis provides road map for lignin valorization

Sphingobium sp. SYK-6 is a soil bacterium boasting a well-studied ligninolytic pathway and the potential for development into a microbial chassis for lignin valorization. An improved understanding of its metabolism will help researchers in the engineering of SYK-6 for the production of value-added chemicals through lignin valorization. We used ¹³C-fingerprinting, ¹³C metabolic flux analysis (¹³C-MFA), and RNA-sequencing differential expression analysis to uncover the following metabolic traits: (i) SYK-6 prefers alkaline conditions, making it an efficient host for the consolidated bioprocessing of lignin, and it also lacks the ability to metabolize sugars or organic acids; (ii) the CO₂ release (i.e., carbon loss) from the ligninolysis-based metabolism of SYK-6 is significantly greater than the CO₂ release from the sugar-based metabolism of Escherichia coli; (iii) the vanillin catabolic pathway (which is the converging point of majority of the lignin catabolic pathways) is coupled with the tetrahydrofolate-dependent C1 pathway that is essential for the biosynthesis of serine, histidine, and methionine; (iv) catabolic end products of lignin (pyruvate and oxaloacetate) must enter the tricarboxylic acid (TCA) cycle first and then use phosphoenolpyruvate carboxykinase to initiate gluconeogenesis; and (v) ¹³C-MFA together with RNA-sequencing differential expression analysis establishes the vanillin catabolic pathway as the major contributor of NAD(P)H synthesis. Therefore, the vanillin catabolic pathway is essential for SYK-6 to obtain sufficient reducing equivalents for its healthy growth; cosubstrate experiments support this finding. This unique energy feature of SYK-6 is particularly interesting because most heterotrophs rely on the transhydrogenase, the TCA cycle, and the oxidative pentose phosphate pathway to obtain NADPH.

ll-ACHRB: a scalable algorithm for sampling the feasible solution space of metabolic networks

MOTIVATION

Random sampling of the solution space has emerged as a popular tool to explore and infer properties of large metabolic networks. However, conventional sampling approaches commonly used do not eliminate thermodynamically unfeasible loops.

RESULTS

In order to overcome this limitation, we developed an efficient sampling algorithm called loopless Artificially Centered Hit-and-Run on a Box (ll-ACHRB). This algorithm is inspired by the Hit-and-Run on a Box algorithm for uniform sampling from general regions, but employs the directions of choice approach of Artificially Centered Hit-and-Run. A novel strategy for generating feasible warmup points improved both sampling efficiency and mixing. ll-ACHRB shows overall better performance than current strategies to generate feasible flux samples across several models. Furthermore, we demonstrate that a failure to eliminate unfeasible loops greatly affects sample statistics, in particular the correlation structure. Finally, we discuss recommendations for the interpretation of sampling results and possible algorithmic improvements.

AVAILABILITY AND IMPLEMENTATION

Source code for MATLAB and OCTAVE including examples are freely available for download at http://www.aibn.uq.edu.au/cssb-resources under Software. Optimization runs can use Gurobi Optimizer (by default if available) or GLPK (included with the algorithm).

CONTACT

lars.nielsen@uq.edu.au

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Reconstruction of Tissue-Specific Metabolic Networks Using CORDA

Human metabolism involves thousands of reactions and metabolites. To interpret this complexity, computational modeling becomes an essential experimental tool. One of the most popular techniques to study human metabolism as a whole is genome scale modeling. A key challenge to applying genome scale modeling is identifying critical metabolic reactions across diverse human tissues. Here we introduce a novel algorithm called Cost Optimization Reaction Dependency Assessment (CORDA) to build genome scale models in a tissue-specific manner. CORDA performs more efficiently computationally, shows better agreement to experimental data, and displays better model functionality and capacity when compared to previous algorithms. CORDA also returns reaction associations that can greatly assist in any manual curation to be performed following the automated reconstruction process. Using CORDA, we developed a library of 76 healthy and 20 cancer tissue-specific reconstructions. These reconstructions identified which metabolic pathways are shared across diverse human tissues. Moreover, we identified changes in reactions and pathways that are differentially included and present different capacity profiles in cancer compared to healthy tissues, including up-regulation of folate metabolism, the down-regulation of thiamine metabolism, and tight regulation of oxidative phosphorylation.

Genome-scale estimate of the metabolic turnover of E. coli from the energy balance analysis

In this article the notion of metabolic turnover is revisited in the light of recent results of out-of-equilibrium thermodynamics. By means of Monte Carlo methods we perform an exact sampling of the enzymatic fluxes in a genome scale metabolic network of E. coli in stationary growth conditions from which we infer the metabolites turnover times. However the latter are inferred from net fluxes, and we argue that this approximation is not valid for enzymes working nearby thermodynamic equilibrium. We recalculate turnover times from total fluxes by performing an energy balance analysis of the network and recurring to the fluctuation theorem. We find in many cases values one of order of magnitude lower, implying a faster picture of intermediate metabolism.

Characterizing the optimal flux space of genome-scale metabolic reconstructions through modified latin-hypercube sampling

Sampling of the optimal flux space using modified LHS gives a more uniform coverage than Monte-Carlo Sampling. Analysis of the flux data shows that majority of variation in the flux distribution pattern within the space arises due to the presence of few alternate pathways.

Mapping high-growth phenotypes in the flux space of microbial metabolism

Experimental and empirical observations on cell metabolism cannot be understood as a whole without their integration into a consistent systematic framework. However, the characterization of metabolic flux phenotypes is typically reduced to the study of a single optimal state, such as maximum biomass yield that is by far the most common assumption. Here, we confront optimal growth solutions to the whole set of feasible flux phenotypes (FFPs), which provides a benchmark to assess the likelihood of optimal and high-growth states and their agreement with experimental results. In addition, FFP maps are able to uncover metabolic behaviours, such as aerobic fermentation accompanying exponential growth on sugars at nutrient excess conditions, that are unreachable using standard models based on optimality principles. The information content of the full FFP space provides us with a map to explore and evaluate metabolic behaviour and capabilities, and so it opens new avenues for biotechnological and biomedical applications.

Interplay between constraints, objectives, and optimality for genome-scale stoichiometric models

High-throughput data generation and genome-scale stoichiometric models have greatly facilitated the comprehensive study of metabolic networks. The computation of all feasible metabolic routes with these models, given stoichiometric, thermodynamic, and steady-state constraints, provides important insights into the metabolic capacities of a cell. How the feasible metabolic routes emerge from the interplay between flux constraints, optimality objectives, and the entire metabolic network of a cell is, however, only partially understood. We show how optimal metabolic routes, resulting from flux balance analysis computations, arise out of elementary flux modes, constraints, and optimization objectives. We illustrate our findings with a genome-scale stoichiometric model of Escherichia coli metabolism. In the case of one flux constraint, all feasible optimal flux routes can be derived from elementary flux modes alone. We found up to 120 million of such optimal elementary flux modes. We introduce a new computational method to compute the corner points of the optimal solution space fast and efficiently. Optimal flux routes no longer depend exclusively on elementary flux modes when we impose additional constraints; new optimal metabolic routes arise out of combinations of elementary flux modes. The solution space of feasible metabolic routes shrinks enormously when additional objectives---e.g. those related to pathway expression costs or pathway length---are introduced. In many cases, only a single metabolic route remains that is both feasible and optimal. This paper contributes to reaching a complete topological understanding of the metabolic capacity of organisms in terms of metabolic flux routes, one that is most natural to biochemists and biotechnologists studying and engineering metabolism.

Sampling with poling-based flux balance analysis: optimal versus sub-optimal flux space analysis of Actinobacillus succinogenes

BACKGROUND

Flux balance analysis is traditionally implemented to identify the maximum theoretical flux for some specified reaction and a single distribution of flux values for all the reactions present which achieve this maximum value. However it is well known that the uncertainty in reaction networks due to branches, cycles and experimental errors results in a large number of combinations of internal reaction fluxes which can achieve the same optimal flux value.

RESULTS

In this work, we have modified the applied linear objective of flux balance analysis to include a poling penalty function, which pushes each new set of reaction fluxes away from previous solutions generated. Repeated poling-based flux balance analysis generates a sample of different solutions (a characteristic set), which represents all the possible functionality of the reaction network. Compared to existing sampling methods, for the purpose of generating a relatively "small" characteristic set, our new method is shown to obtain a higher coverage than competing methods under most conditions. The influence of the linear objective function on the sampling (the linear bias) constrains optimisation results to a subspace of optimal solutions all producing the same maximal fluxes. Visualisation of reaction fluxes plotted against each other in 2 dimensions with and without the linear bias indicates the existence of correlations between fluxes. This method of sampling is applied to the organism Actinobacillus succinogenes for the production of succinic acid from glycerol.

CONCLUSIONS

A new method of sampling for the generation of different flux distributions (sets of individual fluxes satisfying constraints on the steady-state mass balances of intermediates) has been developed using a relatively simple modification of flux balance analysis to include a poling penalty function inside the resulting optimisation objective function. This new methodology can achieve a high coverage of the possible flux space and can be used with and without linear bias to show optimal versus sub-optimal solution spaces. Basic analysis of the Actinobacillus succinogenes system using sampling shows that in order to achieve the maximal succinic acid production CO₂ must be taken into the system. Solutions involving release of CO₂ all give sub-optimal succinic acid production.

An integrated network visualization framework towards metabolic engineering applications

Background

Over the last years, several methods for the phenotype simulation of microorganisms, under specified genetic and environmental conditions have been proposed, in the context of Metabolic Engineering (ME). These methods provided insight on the functioning of microbial metabolism and played a key role in the design of genetic modifications that can lead to strains of industrial interest. On the other hand, in the context of Systems Biology research, biological network visualization has reinforced its role as a core tool in understanding biological processes. However, it has been scarcely used to foster ME related methods, in spite of the acknowledged potential.

Results

In this work, an open-source software that aims to fill the gap between ME and metabolic network visualization is proposed, in the form of a plugin to the OptFlux ME platform. The framework is based on an abstract layer, where the network is represented as a bipartite graph containing minimal information about the underlying entities and their desired relative placement. The framework provides input/output support for networks specified in standard formats, such as XGMML, SBGN or SBML, providing a connection to genome-scale metabolic models. An user-interface makes it possible to edit, manipulate and query nodes in the network, providing tools to visualize diverse effects, including visual filters and aspect changing (e.g. colors, shapes and sizes). These tools are particularly interesting for ME, since they allow overlaying phenotype simulation results or elementary flux modes over the networks.

Conclusions

The framework and its source code are freely available, together with documentation and other resources, being illustrated with well documented case studies.

Electronic supplementary material

The online version of this article (doi:10.1186/s12859-014-0420-0) contains supplementary material, which is available to authorized users.

A peptide-based method for 13C Metabolic Flux Analysis in microbial communities

The study of intracellular metabolic fluxes and inter-species metabolite exchange for microbial communities is of crucial importance to understand and predict their behaviour. The most authoritative method of measuring intracellular fluxes, ¹³C Metabolic Flux Analysis (¹³C MFA), uses the labeling pattern obtained from metabolites (typically amino acids) during ¹³C labeling experiments to derive intracellular fluxes. However, these metabolite labeling patterns cannot easily be obtained for each of the members of the community. Here we propose a new type of ¹³C MFA that infers fluxes based on peptide labeling, instead of amino acid labeling. The advantage of this method resides in the fact that the peptide sequence can be used to identify the microbial species it originates from and, simultaneously, the peptide labeling can be used to infer intracellular metabolic fluxes. Peptide identity and labeling patterns can be obtained in a high-throughput manner from modern proteomics techniques. We show that, using this method, it is theoretically possible to recover intracellular metabolic fluxes in the same way as through the standard amino acid based ¹³C MFA, and quantify the amount of information lost as a consequence of using peptides instead of amino acids. We show that by using a relatively small number of peptides we can counter this information loss. We computationally tested this method with a well-characterized simple microbial community consisting of two species.

Microbial communities underlie a variety of important biochemical processes ranging from underground cave formation to gold mining or the onset of obesity. Metabolic fluxes describe how carbon and energy flow through the microbial community and therefore provide insights that are rarely captured by other techniques, such as metatranscriptomics or metaproteomics. The most authoritative method to measure fluxes for pure cultures consists of feeding the cells a labeled carbon source and deriving the fluxes from the ensuing metabolite labeling pattern (typically amino acids). Since we cannot easily separate cells of metabolite for each species in a community, this approach is not generally applicable to microbial communities. Here we present a method to derive fluxes from the labeling of peptides, instead of amino acids. This approach has the advantage that peptides can be assigned to each species in a community in a high-throughput fashion through modern proteomic methods. We show that, by using this method, it is theoretically possible to recover the same amount of information as through the standard approach, if enough peptides are used. We computationally tested this method with a well-characterized simple microbial community consisting of two species.

Identifying all moiety conservation laws in genome-scale metabolic networks

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

optGpSampler: an improved tool for uniformly sampling the solution-space of genome-scale metabolic networks

Constraint-based models of metabolic networks are typically underdetermined, because they contain more reactions than metabolites. Therefore the solutions to this system do not consist of unique flux rates for each reaction, but rather a space of possible flux rates. By uniformly sampling this space, an estimated probability distribution for each reaction’s flux in the network can be obtained. However, sampling a high dimensional network is time-consuming. Furthermore, the constraints imposed on the network give rise to an irregularly shaped solution space. Therefore more tailored, efficient sampling methods are needed. We propose an efficient sampling algorithm (called optGpSampler), which implements the Artificial Centering Hit-and-Run algorithm in a different manner than the sampling algorithm implemented in the COBRA Toolbox for metabolic network analysis, here called gpSampler. Results of extensive experiments on different genome-scale metabolic networks show that optGpSampler is up to 40 times faster than gpSampler. Application of existing convergence diagnostics on small network reconstructions indicate that optGpSampler converges roughly ten times faster than gpSampler towards similar sampling distributions. For networks of higher dimension (i.e. containing more than 500 reactions), we observed significantly better convergence of optGpSampler and a large deviation between the samples generated by the two algorithms. Availability:optGpSampler for Matlab and Python is available for non-commercial use at: http://cs.ru.nl/~wmegchel/optGpSampler/.

Integration of a constraint-based metabolic model of Brassica napus developing seeds with (13)C-metabolic flux analysis

The use of large-scale or genome-scale metabolic reconstructions for modeling and simulation of plant metabolism and integration of those models with large-scale omics and experimental flux data is becoming increasingly important in plant metabolic research. Here we report an updated version of bna572, a bottom-up reconstruction of oilseed rape (Brassica napus L.; Brassicaceae) developing seeds with emphasis on representation of biomass-component biosynthesis. New features include additional seed-relevant pathways for isoprenoid, sterol, phenylpropanoid, flavonoid, and choline biosynthesis. Being now based on standardized data formats and procedures for model reconstruction, bna572+ is available as a COBRA-compliant Systems Biology Markup Language (SBML) model and conforms to the Minimum Information Requested in the Annotation of Biochemical Models (MIRIAM) standards for annotation of external data resources. Bna572+ contains 966 genes, 671 reactions, and 666 metabolites distributed among 11 subcellular compartments. It is referenced to the Arabidopsis thaliana genome, with gene-protein-reaction (GPR) associations resolving subcellular localization. Detailed mass and charge balancing and confidence scoring were applied to all reactions. Using B. napus seed specific transcriptome data, expression was verified for 78% of bna572+ genes and 97% of reactions. Alongside bna572+ we also present a revised carbon centric model for (13)C-Metabolic Flux Analysis ((13)C-MFA) with all its reactions being referenced to bna572+ based on linear projections. By integration of flux ratio constraints obtained from (13)C-MFA and by elimination of infinite flux bounds around thermodynamically infeasible loops based on COBRA loopless methods, we demonstrate improvements in predictive power of Flux Variability Analysis (FVA). Using this combined approach we characterize the difference in metabolic flux of developing seeds of two B. napus genotypes contrasting in starch and oil content.

Dynamics of growth and metabolism controlled by glutamine availability in Chinese hamster ovary cells

The physiology of animal cells is characterized by constantly changing environmental conditions and adapting cellular responses. Applied dynamic metabolic flux analysis captures metabolic dynamics and can be applied to industrially relevant cultivation conditions. We investigated the impact of glutamine availability or limitation on the physiology of CHO K1 cells in eight different batch and fed-batch cultivations. Varying glutamine availability resulted in global metabolic changes. We observed dose-dependent effects of glutamine in batch cultivation. Identifying metabolic links from the glutamine metabolism to specific metabolic pathways, we show that glutamine feeding results in its coupling to tricarboxylic acid cycle fluxes and in its decoupling from metabolic waste production. We provide a mechanistic explanation of the cellular responses upon mild or severe glutamine limitation and ammonia stress. The growth rate of CHO K1 decreased with increasing ammonia levels in the supernatant. On the other hand, growth, especially culture longevity, was stimulated at mild glutamine-limiting conditions. Flux rearrangements in the pyruvate and amino acid metabolism compensate glutamine limitation by consumption of alternative carbon sources and facilitating glutamine synthesis and mitigate ammonia stress as result of glutamine abundance.

ReacKnock: identifying reaction deletion strategies for microbial strain optimization based on genome-scale metabolic network

Gene knockout has been used as a common strategy to improve microbial strains for producing chemicals. Several algorithms are available to predict the target reactions to be deleted. Most of them apply mixed integer bi-level linear programming (MIBLP) based on metabolic networks, and use duality theory to transform bi-level optimization problem of large-scale MIBLP to single-level programming. However, the validity of the transformation was not proved. Solution of MIBLP depends on the structure of inner problem. If the inner problem is continuous, Karush-Kuhn-Tucker (KKT) method can be used to reformulate the MIBLP to a single-level one. We adopt KKT technique in our algorithm ReacKnock to attack the intractable problem of the solution of MIBLP, demonstrated with the genome-scale metabolic network model of E. coli for producing various chemicals such as succinate, ethanol, threonine and etc. Compared to the previous methods, our algorithm is fast, stable and reliable to find the optimal solutions for all the chemical products tested, and able to provide all the alternative deletion strategies which lead to the same industrial objective.

Counting and correcting thermodynamically infeasible flux cycles in genome-scale metabolic networks

Thermodynamics constrains the flow of matter in a reaction network to occur through routes along which the Gibbs energy decreases, implying that viable steady-state flux patterns should be void of closed reaction cycles. Identifying and removing cycles in large reaction networks can unfortunately be a highly challenging task from a computational viewpoint. We propose here a method that accomplishes it by combining a relaxation algorithm and a Monte Carlo procedure to detect loops, with ad hoc rules (discussed in detail) to eliminate them. As test cases, we tackle (a) the problem of identifying infeasible cycles in the E. coli metabolic network and (b) the problem of correcting thermodynamic infeasibilities in the Flux-Balance-Analysis solutions for 15 human cell-type-specific metabolic networks. Results for (a) are compared with previous analyses of the same issue, while results for (b) are weighed against alternative methods to retrieve thermodynamically viable flux patterns based on minimizing specific global quantities. Our method, on the one hand, outperforms previous techniques and, on the other, corrects loopy solutions to Flux Balance Analysis. As a byproduct, it also turns out to be able to reveal possible inconsistencies in model reconstructions.

An objective function exploiting suboptimal solutions in metabolic networks

Background

Flux Balance Analysis is a theoretically elegant, computationally efficient, genome-scale approach to predicting biochemical reaction fluxes. Yet FBA models exhibit persistent mathematical degeneracy that generally limits their predictive power.

Results

We propose a novel objective function for cellular metabolism that accounts for and exploits degeneracy in the metabolic network to improve flux predictions. In our model, regulation drives metabolism toward a region of flux space that allows nearly optimal growth. Metabolic mutants deviate minimally from this region, a function represented mathematically as a convex cone. Near-optimal flux configurations within this region are considered equally plausible and not subject to further optimizing regulation. Consistent with relaxed regulation near optimality, we find that the size of the near-optimal region predicts flux variability under experimental perturbation.

Conclusion

Accounting for suboptimal solutions can improve the predictive power of metabolic FBA models. Because fluctuations of enzyme and metabolite levels are inevitable, tolerance for suboptimality may support a functionally robust metabolic network.

A novel methodology to estimate metabolic flux distributions in constraint-based models

Quite generally, constraint-based metabolic flux analysis describes the space of viable flux configurations for a metabolic network as a high-dimensional polytope defined by the linear constraints that enforce the balancing of production and consumption fluxes for each chemical species in the system. In some cases, the complexity of the solution space can be reduced by performing an additional optimization, while in other cases, knowing the range of variability of fluxes over the polytope provides a sufficient characterization of the allowed configurations. There are cases, however, in which the thorough information encoded in the individual distributions of viable fluxes over the polytope is required. Obtaining such distributions is known to be a highly challenging computational task when the dimensionality of the polytope is sufficiently large, and the problem of developing cost-effective ad hoc algorithms has recently seen a major surge of interest. Here, we propose a method that allows us to perform the required computation heuristically in a time scaling linearly with the number of reactions in the network, overcoming some limitations of similar techniques employed in recent years. As a case study, we apply it to the analysis of the human red blood cell metabolic network, whose solution space can be sampled by different exact techniques, like Hit-and-Run Monte Carlo (scaling roughly like the third power of the system size). Remarkably accurate estimates for the true distributions of viable reaction fluxes are obtained, suggesting that, although further improvements are desirable, our method enhances our ability to analyze the space of allowed configurations for large biochemical reaction networks.

Decomposition of flux distributions into metabolic pathways

Genome-scale reconstructions are often used for studying relationships between fundamental components of a metabolic system. In this study, we develop a novel computational method for analyzing predicted flux distributions for metabolic reconstructions. Because chemical reactions may have multiple reactants and products, a directed hypergraph where hyperarcs may have multiple tail vertices and head vertices is a more appropriate representation of the metabolic network than a conventional network. We use this view to represent predicted flux distributions by maximum generalized flows on hypergraphs. We then demonstrate that the generalized hyperflow problem may be transformed to an equivalent network flow problem with side constraints. This transformation allows a flux to be decomposed into chains of reactions. Subsequent analysis of these chains helps to characterize active pathways in a flux distribution. Such characterizations facilitate comparisons of flux distributions for different environmental conditions. The proposed method is applied to compare predicted flux distributions for Salmonella typhimurium to study changes in metabolism that cause enhanced virulence during a space flight. The differences between flux distributions corresponding to normal and enhanced virulence states confirm previous observations concerning infection mechanisms and suggest new pathways for exploration.

Identification of metabolic engineering targets through analysis of optimal and sub-optimal routes

Identification of optimal genetic manipulation strategies for redirecting substrate uptake towards a desired product is a challenging task owing to the complexity of metabolic networks, esp. in terms of large number of routes leading to the desired product. Algorithms that can exploit the whole range of optimal and suboptimal routes for product formation while respecting the biological objective of the cell are therefore much needed. Towards addressing this need, we here introduce the notion of structural flux, which is derived from the enumeration of all pathways in the metabolic network in question and accounts for the contribution towards a given biological objective function. We show that the theoretically estimated structural fluxes are good predictors of experimentally measured intra-cellular fluxes in two model organisms, namely, Escherichia coli and Saccharomyces cerevisiae. For a small number of fluxes for which the predictions were poor, the corresponding enzyme-coding transcripts were also found to be distinctly regulated, showing the ability of structural fluxes in capturing the underlying regulatory principles. Exploiting the observed correspondence between in vivo fluxes and structural fluxes, we propose an in silico metabolic engineering approach, iStruF, which enables the identification of gene deletion strategies that couple the cellular biological objective with the product flux while considering optimal as well as sub-optimal routes and their efficiency.

Quantitative in silico Analysis of Neurotransmitter Pathways Under Steady State Conditions

The modeling of glutamate/GABA-glutamine cycling in the brain tissue involving astrocytes, glutamatergic and GABAergic neurons leads to a complex compartmentalized metabolic network that comprises neurotransmitter synthesis, shuttling, and degradation. Without advanced computational tools, it is difficult to quantitatively track possible scenarios and identify viable ones. In this article, we follow a sampling-based computational paradigm to analyze the biochemical network in a multi-compartment system modeling astrocytes, glutamatergic, and GABAergic neurons, and address some questions about the details of transmitter cycling, with particular emphasis on the ammonia shuttling between astrocytes and neurons, and the synthesis of transmitter GABA. More specifically, we consider the joint action of the alanine-lactate shuttle, the branched chain amino acid shuttle, and the glutamine-glutamate cycle, as well as the role of glutamate dehydrogenase (GDH) activity. When imposing a minimal amount of bound constraints on reaction and transport fluxes, a preferred stoichiometric steady state equilibrium requires an unrealistically high reductive GDH activity in neurons, indicating the need for additional bound constants which were included in subsequent computer simulations. The statistical flux balance analysis also suggests a stoichiometrically viable role for leucine transport as an alternative to glutamine for replenishing the glutamate pool in neurons.

Integrating cellular metabolism into a multiscale whole-body model

Cellular metabolism continuously processes an enormous range of external compounds into endogenous metabolites and is as such a key element in human physiology. The multifaceted physiological role of the metabolic network fulfilling the catalytic conversions can only be fully understood from a whole-body perspective where the causal interplay of the metabolic states of individual cells, the surrounding tissue and the whole organism are simultaneously considered. We here present an approach relying on dynamic flux balance analysis that allows the integration of metabolic networks at the cellular scale into standardized physiologically-based pharmacokinetic models at the whole-body level. To evaluate our approach we integrated a genome-scale network reconstruction of a human hepatocyte into the liver tissue of a physiologically-based pharmacokinetic model of a human adult. The resulting multiscale model was used to investigate hyperuricemia therapy, ammonia detoxification and paracetamol-induced toxication at a systems level. The specific models simultaneously integrate multiple layers of biological organization and offer mechanistic insights into pathology and medication. The approach presented may in future support a mechanistic understanding in diagnostics and drug development.

Cellular metabolism is a key element in human physiology. Ideally the metabolic network needs to be considered within the context of the surrounding tissue and organism since the various levels of biological organization are mutually influencing each other. To mechanistically describe the interplay between intracellular space and extracellular environment, we here integrate the genome-scale metabolic network model HepatoNet1 at the cellular scale into physiologically-based pharmacokinetic models at the whole-body level. The resulting multiscale model allows the quantitative description of metabolic behavior in the context of time-resolved metabolite concentration profiles in the body and the surrounding liver tissue. The model has been applied to three case studies covering fundamental aspects of medicine and pharmacology: drug administration, biomarker identification and drug-induced toxication. Most notably, our multiscale approach fosters an improved quantitative understanding of drug action and the impact of metabolic disorders at an organism level, based on a genome-scale representation of cellular metabolism. Computational models such as the one presented include various aspects of human physiology and may therefore significantly support rational approaches in medical diagnostics and pharmaceutical drug development in the future.

Probabilistic approach for predicting periodic orbits in piecewise affine differential models

Piecewise affine models provide a qualitative description of the dynamics of a system, and are often used to study genetic regulatory networks. The state space of a piecewise affine system is partitioned into hyperrectangles, which can be represented as nodes in a directed graph, so that the system's trajectories follow a path in a transition graph. This paper proposes and compares two definitions of probability of transition between two nodes A and B of the graph, based on the volume of the initial conditions on the hyperrectangle A whose trajectories cross to B. The parameters of the system can thus be compared to the observed transitions between two hyperrectangles. This property may become useful to identify sets of parameters for which the system yields a desired periodic orbit with a high probability, or to predict the most likely periodic orbit given a set of parameters, as illustrated by a gene regulatory system composed of two intertwined negative loops.

Optimal flux spaces of genome-scale stoichiometric models are determined by a few subnetworks

The metabolism of organisms can be studied with comprehensive stoichiometric models of their metabolic networks. Flux balance analysis (FBA) calculates optimal metabolic performance of stoichiometric models. However, detailed biological interpretation of FBA is limited because, in general, a huge number of flux patterns give rise to the same optimal performance. The complete description of the resulting optimal solution spaces was thus far a computationally intractable problem. Here we present CoPE-FBA: Comprehensive Polyhedra Enumeration Flux Balance Analysis, a computational method that solves this problem. CoPE-FBA indicates that the thousands to millions of optimal flux patterns result from a combinatorial explosion of flux patterns in just a few metabolic sub-networks. The entire optimal solution space can now be compactly described in terms of the topology of these sub-networks. CoPE-FBA simplifies the biological interpretation of stoichiometric models of metabolism, and provides a profound understanding of metabolic flexibility in optimal states.

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.

Advanced stoichiometric analysis of metabolic networks of mammalian systems

Metabolic engineering tools have been widely applied to living organisms to gain a comprehensive understanding about cellular networks and to improve cellular properties. Metabolic flux analysis (MFA), flux balance analysis (FBA), and metabolic pathway analysis (MPA) are among the most popular tools in stoichiometric network analysis. Although application of these tools into well-known microbial systems is extensive in the literature, various barriers prevent them from being utilized in mammalian cells. Limited experimental data, complex regulatory mechanisms, and the requirement of more complex nutrient media are some major obstacles in mammalian cell systems. However, mammalian cells have been used to produce therapeutic proteins, to characterize disease states or related abnormal metabolic conditions, and to analyze the toxicological effects of some medicinally important drugs. Therefore, there is a growing need for extending metabolic engineering principles to mammalian cells in order to understand their underlying metabolic functions. In this review article, advanced metabolic engineering tools developed for stoichiometric analysis including MFA, FBA, and MPA are described. Applications of these tools in mammalian cells are discussed in detail, and the challenges and opportunities are highlighted.

Exploring the gap between dynamic and constraint-based models of metabolism

Systems biology provides new approaches for metabolic engineering through the development of models and methods for simulation and optimization of microbial metabolism. Here we explore the relationship between two modeling frameworks in common use namely, dynamic models with kinetic rate laws and constraint-based flux models. We compare and analyze dynamic and constraint-based formulations of the same model of the central carbon metabolism of Escherichia coli. Our results show that, if unconstrained, the space of steady states described by both formulations is the same. However, the imposition of parameter-range constraints can be mapped into kinetically feasible regions of the solution space for the dynamic formulation that is not readily transferable to the constraint-based formulation. Therefore, with partial kinetic parameter knowledge, dynamic models can be used to generate constraints that reduce the solution space below that identified by constraint-based models, eliminating infeasible solutions and increasing the accuracy of simulation and optimization methods.