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

Microbial carbon use efficiency predicted from genome-scale metabolic models

Respiration by soil bacteria and fungi is one of the largest fluxes of carbon (C) from the land surface. Although this flux is a direct product of microbial metabolism, controls over metabolism and their responses to global change are a major uncertainty in the global C cycle. Here, we explore an in silico approach to predict bacterial C-use efficiency (CUE) for over 200 species using genome-specific constraint-based metabolic modeling. We find that potential CUE averages 0.62 ± 0.17 with a range of 0.22 to 0.98 across taxa and phylogenetic structuring at the subphylum levels. Potential CUE is negatively correlated with genome size, while taxa with larger genomes are able to access a wider variety of C substrates. Incorporating the range of CUE values reported here into a next-generation model of soil biogeochemistry suggests that these differences in physiology across microbial taxa can feed back on soil-C cycling.Published versio

A robust and efficient method for estimating enzyme complex abundance and metabolic flux from expression data

A major theme in constraint-based modeling is unifying experimental data, such as biochemical information about the reactions that can occur in a system or the composition and localization of enzyme complexes, with highthroughput data including expression data, metabolomics, or DNA sequencing. The desired result is to increase predictive capability resulting in improved understanding of metabolism. The approach typically employed when only gene (or protein) intensities are available is the creation of tissue-specific models, which reduces the available reactions in an organism model, and does not provide an objective function for the estimation of fluxes, which is an important limitation in many modeling applications. We develop a method, flux assignment with LAD (least absolute deviation) convex objectives and normalization (FALCON), that employs metabolic network reconstructions along with expression data to estimate fluxes. In order to use such a method, accurate measures of enzyme complex abundance are needed, so we first present a new algorithm that addresses quantification of complex abundance. Our extensions to prior techniques include the capability to work with large models and significantly improved run-time performance even for smaller models, an improved analysis of enzyme complex formation logic, the ability to handle very large enzyme complex rules that may incorporate multiple isoforms, and depending on the model constraints, either maintained or significantly improved correlation with experimentally measured fluxes. FALCON has been implemented in MATLAB and ATS, and can be downloaded from: https://github.com/bbarker/FALCON. ATS is not required to compile the software, as intermediate C source code is available, and binaries are provided for Linux x86-64 systems. FALCON requires use of the COBRA Toolbox, also implemented in MATLAB.Comment: 30 pages, 12 figures, 4 table

Dispensability of Escherichia coli's latent pathways

Gene-knockout experiments on single-cell organisms have established that expression of a substantial fraction of genes is not needed for optimal growth. This problem acquired a new dimension with the recent discovery that environmental and genetic perturbations of the bacterium Escherichia coli are followed by the temporary activation of a large number of latent metabolic pathways, which suggests the hypothesis that temporarily activated reactions impact growth and hence facilitate adaptation in the presence of perturbations. Here we test this hypothesis computationally and find, surprisingly, that the availability of latent pathways consistently offers no growth advantage, and tends in fact to inhibit growth after genetic perturbations. This is shown to be true even for latent pathways with a known function in alternate conditions, thus extending the significance of this adverse effect beyond apparently nonessential genes. These findings raise the possibility that latent pathway activation is in fact derivative of another, potentially suboptimal, adaptive response

Metabolomics methods for the synthetic biology of secondary metabolism

Many microbial secondary metabolites are of high biotechnological value for medicine, agriculture, and the food industry. Bacterial genome mining has revealed numerous novel secondary metabolite biosynthetic gene clusters, which encode the potential to synthesize a large diversity of compounds that have never been observed before. The stimulation or “awakening” of this cryptic microbial secondary metabolism has naturally attracted the attention of synthetic microbiologists, who exploit recent advances in DNA sequencing and synthesis to achieve unprecedented control over metabolic pathways. One of the indispensable tools in the synthetic biology toolbox is metabolomics, the global quantification of small biomolecules. This review illustrates the pivotal role of metabolomics for the synthetic microbiology of secondary metabolism, including its crucial role in novel compound discovery in microbes, the examination of side products of engineered metabolic pathways, as well as the identification of major bottlenecks for the overproduction of compounds of interest, especially in combination with metabolic modeling. We conclude by highlighting remaining challenges and recent technological advances that will drive metabolomics towards fulfilling its potential as a cornerstone technology of synthetic microbiology

Systems biology analysis of drivers underlying hallmarks of cancer cell metabolism.

Malignant transformation is often accompanied by significant metabolic changes. To identify drivers underlying these changes, we calculated metabolic flux states for the NCI60 cell line collection and correlated the variance between metabolic states of these lines with their other properties. The analysis revealed a remarkably consistent structure underlying high flux metabolism. The three primary uptake pathways, glucose, glutamine and serine, are each characterized by three features: (1) metabolite uptake sufficient for the stoichiometric requirement to sustain observed growth, (2) overflow metabolism, which scales with excess nutrient uptake over the basal growth requirement, and (3) redox production, which also scales with nutrient uptake but greatly exceeds the requirement for growth. We discovered that resistance to chemotherapeutic drugs in these lines broadly correlates with the amount of glucose uptake. These results support an interpretation of the Warburg effect and glutamine addiction as features of a growth state that provides resistance to metabolic stress through excess redox and energy production. Furthermore, overflow metabolism observed may indicate that mitochondrial catabolic capacity is a key constraint setting an upper limit on the rate of cofactor production possible. These results provide a greater context within which the metabolic alterations in cancer can be understood

Volume of the steady-state space of financial flows in a monetary stock-flow-consistent model

We show that a steady-state stock-flow consistent macro-economic model can be represented as a Constraint Satisfaction Problem (CSP).The set of solutions is a polytope, which volume depends on the constraintsapplied and reveals the potential fragility of the economic circuit,with no need to study the dynamics. Several methods to compute the volume are compared, inspired by operations research methods and theanalysis of metabolic networks, both exact and approximate.We also introduce a random transaction matrix, and study the particularcase of linear flows with respect to money stocks

Design of stable metabolic networks

In this work, we propose eigenvalue optimization combined with Lyapunov theory concepts to ensure stability of the Embden—Meyerhof–Parnas pathway, the pentosephosphate pathway, the phosphotransferase system and fermentation reactions of Escherichia coli. We address the design of a metabolic network for the maximization of different metabolite production rates. The first case study focuses on serine production, based on a model that consists of 18 differential equations corresponding to dynamic mass balances for extracellular glucose and intracellular metabolites, and thirty kinetic rate expressions. A second case study addresses the design problem to maximize ethanol production, based on a dynamic model that involves mass balancesfor 25 metabolites and 38 kinetic rate equations. The nonlinear optimization problem including stability constraints has been solved with reduced space Successive Quadratic Programming techniques. Numerical results provide useful insights on the stability properties of the studied kinetic models.Fil: Di Maggio, Jimena Andrea. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Planta Piloto de Ingeniería Química. Universidad Nacional del Sur. Planta Piloto de Ingeniería Química; ArgentinaFil: Blanco, Anibal Manuel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Planta Piloto de Ingeniería Química. Universidad Nacional del Sur. Planta Piloto de Ingeniería Química; ArgentinaFil: Bandoni, Jose Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Planta Piloto de Ingeniería Química. Universidad Nacional del Sur. Planta Piloto de Ingeniería Química; ArgentinaFil: Diaz Ricci, Juan Carlos. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Tucumán. Instituto Superior de Investigaciones Biológicas. Universidad Nacional de Tucumán. Instituto Superior de Investigaciones Biológicas; ArgentinaFil: Díaz, María Soledad. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Planta Piloto de Ingeniería Química. Universidad Nacional del Sur. Planta Piloto de Ingeniería Química; Argentin

Data-driven modelling of biological multi-scale processes

Biological processes involve a variety of spatial and temporal scales. A holistic understanding of many biological processes therefore requires multi-scale models which capture the relevant properties on all these scales. In this manuscript we review mathematical modelling approaches used to describe the individual spatial scales and how they are integrated into holistic models. We discuss the relation between spatial and temporal scales and the implication of that on multi-scale modelling. Based upon this overview over state-of-the-art modelling approaches, we formulate key challenges in mathematical and computational modelling of biological multi-scale and multi-physics processes. In particular, we considered the availability of analysis tools for multi-scale models and model-based multi-scale data integration. We provide a compact review of methods for model-based data integration and model-based hypothesis testing. Furthermore, novel approaches and recent trends are discussed, including computation time reduction using reduced order and surrogate models, which contribute to the solution of inference problems. We conclude the manuscript by providing a few ideas for the development of tailored multi-scale inference methods.Comment: This manuscript will appear in the Journal of Coupled Systems and Multiscale Dynamics (American Scientific Publishers