Flux imbalance analysis and the sensitivity of cellular growth to changes in metabolite pools

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

MetaboTools: A comprehensive toolbox for analysis of genome-scale metabolic models

Metabolomic data sets provide a direct read-out of cellular phenotypes and are increasingly generated to study biological questions. Our previous work revealed the potential of analyzing extracellular metabolomic data in the context of the metabolic model using constraint-based modeling. Through this work, which consists of a protocol, a toolbox, and tutorials of two use cases, we make our methods available to the broader scientific community. The protocol describes, in a step-wise manner, the workflow of data integration and computational analysis. The MetaboTools comprise the Matlab code required to complete the workflow described in the protocol. Tutorials explain the computational steps for integration of two different data sets and demonstrate a comprehensive set of methods for the computational analysis of metabolic models and stratification thereof into different phenotypes. The presented workflow supports integrative analysis of multiple omics data sets. Importantly, all analysis tools can be applied to metabolic models without performing the entire workflow. Taken together, this protocol constitutes a comprehensive guide to the intra-model analysis of extracellular metabolomic data and a resource offering a broad set of computational analysis tools for a wide biomedical and non-biomedical research community

Impact of stoichiometry representation on simulation of genotype-phenotype relationships in metabolic networks.

<div><p>Genome-scale metabolic networks provide a comprehensive structural framework for modeling genotype-phenotype relationships through flux simulations. The solution space for the metabolic flux state of the cell is typically very large and optimization-based approaches are often necessary for predicting the active metabolic state under specific environmental conditions. The objective function to be used in such optimization algorithms is directly linked with the biological hypothesis underlying the model and therefore it is one of the most relevant parameters for successful modeling. Although linear combination of selected fluxes is widely used for formulating metabolic objective functions, we show that the resulting optimization problem is sensitive towards stoichiometry representation of the metabolic network. This undesirable sensitivity leads to different simulation results when using numerically different but biochemically equivalent stoichiometry representations and thereby makes biological interpretation intrinsically subjective and ambiguous. We hereby propose a new method, Minimization of Metabolites Balance (MiMBl), which decouples the artifacts of stoichiometry representation from the formulation of the desired objective functions, by casting objective functions using metabolite turnovers rather than fluxes. By simulating perturbed metabolic networks, we demonstrate that the use of stoichiometry representation independent algorithms is fundamental for unambiguously linking modeling results with biological interpretation. For example, MiMBl allowed us to expand the scope of metabolic modeling in elucidating the mechanistic basis of several genetic interactions in <em>Saccharomyces cerevisiae</em>.</p> </div

Machine learning applied to enzyme turnover numbers reveals protein structural correlates and improves metabolic models.

Knowing the catalytic turnover numbers of enzymes is essential for understanding the growth rate, proteome composition, and physiology of organisms, but experimental data on enzyme turnover numbers is sparse and noisy. Here, we demonstrate that machine learning can successfully predict catalytic turnover numbers in Escherichia coli based on integrated data on enzyme biochemistry, protein structure, and network context. We identify a diverse set of features that are consistently predictive for both in vivo and in vitro enzyme turnover rates, revealing novel protein structural correlates of catalytic turnover. We use our predictions to parameterize two mechanistic genome-scale modelling frameworks for proteome-limited metabolism, leading to significantly higher accuracy in the prediction of quantitative proteome data than previous approaches. The presented machine learning models thus provide a valuable tool for understanding metabolism and the proteome at the genome scale, and elucidate structural, biochemical, and network properties that underlie enzyme kinetics

Why Optimal States Recruit Fewer Reactions in Metabolic Networks

The metabolic network of a living cell involves several hundreds or thousands of interconnected biochemical reactions. Previous research has shown that under realistic conditions only a fraction of these reactions is concurrently active in any given cell. This is partially determined by nutrient availability, but is also strongly dependent on the metabolic function and network structure. Here, we establish rigorous bounds showing that the fraction of active reactions is smaller (rather than larger) in metabolic networks evolved or engineered to optimize a specific metabolic task, and we show that this is largely determined by the presence of thermodynamically irreversible reactions in the network. We also show that the inactivation of a certain number of reactions determined by irreversibility can generate a cascade of secondary reaction inactivations that propagates through the network. The mathematical results are complemented with numerical simulations of the metabolic networks of the bacterium Escherichia coli and of human cells, which show, counterintuitively, that even the maximization of the total reaction flux in the network leads to a reduced number of active reactions.Comment: Contribution to the special issue in honor of John Guckenheimer on the occasion of his 65th birthda

Signatures of arithmetic simplicity in metabolic network architecture

Metabolic networks perform some of the most fundamental functions in living cells, including energy transduction and building block biosynthesis. While these are the best characterized networks in living systems, understanding their evolutionary history and complex wiring constitutes one of the most fascinating open questions in biology, intimately related to the enigma of life's origin itself. Is the evolution of metabolism subject to general principles, beyond the unpredictable accumulation of multiple historical accidents? Here we search for such principles by applying to an artificial chemical universe some of the methodologies developed for the study of genome scale models of cellular metabolism. In particular, we use metabolic flux constraint-based models to exhaustively search for artificial chemistry pathways that can optimally perform an array of elementary metabolic functions. Despite the simplicity of the model employed, we find that the ensuing pathways display a surprisingly rich set of properties, including the existence of autocatalytic cycles and hierarchical modules, the appearance of universally preferable metabolites and reactions, and a logarithmic trend of pathway length as a function of input/output molecule size. Some of these properties can be derived analytically, borrowing methods previously used in cryptography. In addition, by mapping biochemical networks onto a simplified carbon atom reaction backbone, we find that several of the properties predicted by the artificial chemistry model hold for real metabolic networks. These findings suggest that optimality principles and arithmetic simplicity might lie beneath some aspects of biochemical complexity

Decoding Complexity in Metabolic Networks using Integrated Mechanistic and Machine Learning Approaches

How can we get living cells to do what we want? What do they actually ‘want’? What ‘rules’ do they observe? How can we better understand and manipulate them? Answers to fundamental research questions like these are critical to overcoming bottlenecks in metabolic engineering and optimizing heterologous pathways for synthetic biology applications. Unfortunately, biological systems are too complex to be completely described by physicochemical modeling alone. In this research, I developed and applied integrated mechanistic and data-driven frameworks to help uncover the mysteries of cellular regulation and control. These tools provide a computational framework for seeking answers to pertinent biological questions. Four major tasks were accomplished. First, I developed innovative tools for key areas in the genome-to-phenome mapping pipeline. An efficient gap filling algorithm (called BoostGAPFILL) that integrates mechanistic and machine learning techniques was developed for the refinement of genome-scale metabolic network reconstructions. Genome-scale metabolic network reconstructions are finding ever increasing applications in metabolic engineering for industrial, medical and environmental purposes. Second, I designed a thermodynamics-based framework (called REMEP) for mutant phenotype prediction (integrating metabolomics, fluxomics and thermodynamics data). These tools will go a long way in improving the fidelity of model predictions of microbial cell factories. Third, I designed a data-driven framework for characterizing and predicting the effectiveness of metabolic engineering strategies. This involved building a knowledgebase of historical microbial cell factory performance from published literature. Advanced machine learning concepts, such as ensemble learning and data augmentation, were employed in combination with standard mechanistic models to develop a predictive platform for important industrial biotechnology metrics such as yield, titer, and productivity. Fourth, my modeling tools and skills have been used for case studies on fungal lipid metabolism analyses, E. coli resource allocation balances, reconstruction of the genome-scale metabolic network for a non-model species, R. opacus, as well as the rapid prediction of bacterial heterotrophic fluxomics. In the long run, this integrated modeling approach will significantly shorten the “design-build-test-learn” cycle of metabolic engineering, as well as provide a platform for biological discovery

Modeling metabolism of Mycobacterium tuberculosis

Approximately one-fourth of the Mycobacterium tuberculosis (Mtb) genome contains genes that encode enzymes directly involved in its metabolism. These enzymes represent potential drug targets that can be systematically probed with constraint based (CB) models through the prediction of genes essential (or the combination thereof) for the pathogen to grow. However, gene essentiality depends on the growth conditions and, so far, no in vitro model precisely mimics the host at the different stages of mycobacterial infection, limiting model predictions. A first step in creating such a model is a thoroughly curated and extended genome-scale CB metabolic model of Mtb metabolism. The history of genome-scale CB models of Mtb metabolism up to model sMtb are discussed and sMtb is quantitatively validated using 13C measurements. The human pathogen Mtb has the capacity to escape eradication by professional phagocytes. During infection, Mtb resists the harsh environment of phagosomes and actively manipulates macrophages and dendritic cells to ensure prolonged intracellular survival. In contrast to many other intracellular pathogens, it has remained difficult to capture the transcriptome of mycobacteria during infection due to an unfavorable host-to-pathogen ratio. The human macrophage-like cell line THP-1 was infected with the attenuated Mtb surrogate Mycobacterium bovis Bacillus Calmette–Guérin (M. bovis BCG). Mycobacterial RNA was up to 1000-fold underrepresented in total RNA preparations of infected host cells. By combining microbial enrichment with specific ribosomal RNA depletion the transcriptional responses of host and pathogen during infection were simultaneously analyzed using dual RNA sequencing. Mycobacterial pathways for cholesterol degradation and iron acquisition are upregulated during infection. In addition, genes involved in the methylcitrate cycle, aspartate metabolism and recycling of mycolic acids are induced. In response to M. bovis BCG infection, host cells upregulate de novo cholesterol biosynthesis presumably to compensate for the loss of this metabolite by bacterial catabolism. By systematically probing the metabolic network underpinning sMtb, the reactions that are essential for Mtb are identified. A majority of these reactions are catalyzed by enzymes and thus represent candidate drug targets to fight an Mtb infection. Modeling the behavior of the bacteria during infection requires knowledge of the so-called biomass reaction that represents bacterial biomass composition. This composition varies in different environments or bacterial growth phases. Accurate modeling of all fluxes through metabolism under a given condition at a moment in time, the so called metabolic state, requires a precise description of the biomass reaction for the described condition. The transcript abundance data obtained by dual RNA sequencing was used to develop a straightforward and systematic method to obtain a condition-specific biomass reaction for Mtb during in vitro growth and during infection of its host. The method described herein is virtually free of any pre-set assumptions on uptake rates of nutrients, making it suitable for exploring environments with limited accessibility. The condition-specific biomass reaction represents the 'metabolic objective' of Mtb in a given environment (in-host growth and growth on defined medium) at a specific time point, and as such allows modeling the bacterial metabolic state in these environments. Five different biomass reactions were used predict nutrient uptake rates and gene essentiality. Predictions were subsequently compared to available experimental data. Nutrient uptake can accurately be predicted, but accurate gene essentiality predictions remain difficult to obtain. By combining sMtb and a model of human metabolism, model sMtb-RECON was developed and used to predict the metabolic state of Mtb during infection of the host. Amino acids are predicted to be used for energy production as well as biomass formation. Subsequently the effect of increasing dosages of drugs, targeting metabolism, on the metabolic state of the pathogen was assessed and resulting metabolic adaptations and flux rerouting through various pathways is predicted. In particular, the TCA cycle becomes more important upon drug application, as well as alanine, aspartate, glutamate, proline, arginine and porphyrin metabolism, while glycine, serine and threonine metabolism become less important for survival. Notably, an effect of eight out of eleven metabolically active drugs could be recreated and two major profiles of the metabolic state were predicted. The profiles of the metabolic states of Mtb affected by the drugs BTZ043, cycloserine and its derivative terizidone, ethambutol, ethionamide, propionamide, and isoniazid were very similar, while TMC207 is predicted to have quite a different effect on metabolism as it inhibits ATP synthase and therefore indirectly interferes with a multitude of metabolic pathways.</p