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

Coupling metabolic footprinting and flux balance analysis to predict how single gene knockouts perturb microbial metabolism

Tese de mestrado. Biologia (Bioinformática e Biologia Computacional). Universidade de Lisboa, Faculdade de Ciências, 2012The model organisms Caenorhabditis elegans and E. coli form one of the simplest gut microbe host interaction models. Interventions in the microbe that increase the host longevity including inhibition of folate synthesis have been reported previously. To find novel single gene knockouts with an effect on lifespan, a screen of the Keio collection of E. coli was undertaken, and some of the genes found are directly involved in metabolism. The next step in those specific cases is to understand how these mutations perturb metabolism systematically, so that hypotheses can be generated. For that, I employed dynamic Flux Balance Analysis (dFBA), a constraint-based modeling technique capable of simulating the dynamics of metabolism in a batch culture and making predictions about changes in intracellular flux distribution. Since the specificities of the C. elegans lifespan experiments demand us to culture microbes in conditions differing from most of the published literature on E. coli physiology, novel data must be acquired to characterize and make dFBA simulations as realistic as possible. To do this exchange fluxes were measured using quantitative H NMR Time-Resolved Metabolic Footprinting. Furthermore, I also investigate the combination of TReF and dFBA as a tool in microbial metabolism studies. These approaches were tested by comparing wild type E. coli with one of the knockout strains found, ΔmetL, a knockout of the metL gene which encodes a byfunctional enzyme involved in aspartate and threonine metabolism. I found that the strain exhibits a slower growth rate than the wild type. Model simulation results revealed that reduced homoserine and methionine synthesis, as well as impaired sulfur and folate metabolism are the main effects of this knockout and the reasons for the growth deficiency. These results indicate that there are common mechanisms of the lifespan extension between ΔmetL and inhibition of folate biosynthesis and that the flux balance analysis/metabolic footprinting approach can help us understand the nature of these mechanisms.Os organismos modelo Caenorhabditis elegans e E. coli formam um dos modelos mais simples de interacções entre micróbio do tracto digestivo e hospedeiro. Intervenções no micróbio capazes de aumentar a longevidade do hospedeiro, incluindo inibição de síntese de folatos, foram reportadas previamente. Para encontrar novas delecções génicas do micróbio capazes de aumentar a longevidade do hospedeiro, a colecção Keio de deleções génicas de E. coli foi rastreada. Alguns dos genes encontrados participam em processos metabólicos, e nesses casos, o próximpo passo é perceber como as deleções perturbam o metabolismo sistémicamente, para gerar hipóteses. Para isso, utilizo dynamic Flux Balance Analysis (dFBA), uma técnica de modelação metabólica capaz de fazer previsões sobre alterações na distribuição intracelular de fluxos. As especificidades das experiências de tempo de vida em C.elegans obrigam-nos a trabalhar em condições diferentes das usadas na maioria da literatura publicada em fisiologia de E. coli, e para dar o máximo realismo às simulações de dFBA novos dados foram adquiridos, utilizando H NMR Time-Resolved Metabolic Footprinting para medir fluxos de troca de metabolitos entre microorganismo e meio de cultura. A combinação de TReF e dFBA como ferramenta de estudo do metabolism microbiano é também investigada. Estas abordagens foram testadas ao comparar E. coli wild-type com uma das estirpes encontradas no rastreio, ΔmetL, knockout do gene metL, que codifica um enzima bifunctional participante no metabolismo de aspartato e treonina, e que exibe uma taxa de crescimento reduzida comparativamente ao wild-type. Os resultados das simulações revelaram que os principais efeitos da deleção deste gene, e as razões para a menor taxa de crescimento observada, são a produção reduzida de homoserina e metionina e os efeitos que provoca no metabolismo de folatos e enxofre. Estes resultados indicam que há mecanismos comuns na extensão da longevidade causada por esta deleção e inibição de síntese de folatos, e que a combinação metabolic footprinting/flux balance analysis pode ajudar-nos a compreender a natureza desses mecanismos

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

Elasticity sampling links thermodynamics to metabolic control

Metabolic networks can be turned into kinetic models in a predefined steady state by sampling the reaction elasticities in this state. Elasticities for many reversible rate laws can be computed from the reaction Gibbs free energies, which are determined by the state, and from physically unconstrained saturation values. Starting from a network structure with allosteric regulation and consistent metabolic fluxes and concentrations, one can sample the elasticities, compute the control coefficients, and reconstruct a kinetic model with consistent reversible rate laws. Some of the model variables are manually chosen, fitted to data, or optimised, while the others are computed from them. The resulting model ensemble allows for probabilistic predictions, for instance, about possible dynamic behaviour. By adding more data or tighter constraints, the predictions can be made more precise. Model variants differing in network structure, flux distributions, thermodynamic forces, regulation, or rate laws can be realised by different model ensembles and compared by significance tests. The thermodynamic forces have specific effects on flux control, on the synergisms between enzymes, and on the emergence and propagation of metabolite fluctuations. Large kinetic models could help to simulate global metabolic dynamics and to predict the effects of enzyme inhibition, differential expression, genetic modifications, and their combinations on metabolic fluxes. MATLAB code for elasticity sampling is freely available

Multiscale metabolic modeling of C4 plants: connecting nonlinear genome-scale models to leaf-scale metabolism in developing maize leaves

C4 plants, such as maize, concentrate carbon dioxide in a specialized compartment surrounding the veins of their leaves to improve the efficiency of carbon dioxide assimilation. Nonlinear relationships between carbon dioxide and oxygen levels and reaction rates are key to their physiology but cannot be handled with standard techniques of constraint-based metabolic modeling. We demonstrate that incorporating these relationships as constraints on reaction rates and solving the resulting nonlinear optimization problem yields realistic predictions of the response of C4 systems to environmental and biochemical perturbations. Using a new genome-scale reconstruction of maize metabolism, we build an 18000-reaction, nonlinearly constrained model describing mesophyll and bundle sheath cells in 15 segments of the developing maize leaf, interacting via metabolite exchange, and use RNA-seq and enzyme activity measurements to predict spatial variation in metabolic state by a novel method that optimizes correlation between fluxes and expression data. Though such correlations are known to be weak in general, here the predicted fluxes achieve high correlation with the data, successfully capture the experimentally observed base-to-tip transition between carbon-importing tissue and carbon-exporting tissue, and include a nonzero growth rate, in contrast to prior results from similar methods in other systems. We suggest that developmental gradients may be particularly suited to the inference of metabolic fluxes from expression data.Comment: 57 pages, 14 figures; submitted to PLoS Computational Biology; source code available at http://github.com/ebogart/fluxtools and http://github.com/ebogart/multiscale_c4_sourc

Improved Network Performance via Antagonism: From Synthetic Rescues to Multi-drug Combinations

Recent research shows that a faulty or sub-optimally operating metabolic network can often be rescued by the targeted removal of enzyme-coding genes--the exact opposite of what traditional gene therapy would suggest. Predictions go as far as to assert that certain gene knockouts can restore the growth of otherwise nonviable gene-deficient cells. Many questions follow from this discovery: What are the underlying mechanisms? How generalizable is this effect? What are the potential applications? Here, I will approach these questions from the perspective of compensatory perturbations on networks. Relations will be drawn between such synthetic rescues and naturally occurring cascades of reaction inactivation, as well as their analogues in physical and other biological networks. I will specially discuss how rescue interactions can lead to the rational design of antagonistic drug combinations that select against resistance and how they can illuminate medical research on cancer, antibiotics, and metabolic diseases.Comment: Online Open "Problems and Paradigms" articl

Metabolic modeling and analysis of the metabolic switch in Streptomyces coelicolor

Background The transition from exponential to stationary phase in Streptomyces coelicolor is accompanied by a major metabolic switch and results in a strong activation of secondary metabolism. Here we have explored the underlying reorganization of the metabolome by combining computational predictions based on constraint-based modeling and detailed transcriptomics time course observations. Results We reconstructed the stoichiometric matrix of S. coelicolor, including the major antibiotic biosynthesis pathways, and performed flux balance analysis to predict flux changes that occur when the cell switches from biomass to antibiotic production. We defined the model input based on observed fermenter culture data and used a dynamically varying objective function to represent the metabolic switch. The predicted fluxes of many genes show highly significant correlation to the time series of the corresponding gene expression data. Individual mispredictions identify novel links between antibiotic production and primary metabolism. Conclusion Our results show the usefulness of constraint-based modeling for providing a detailed interpretation of time course gene expression data

How enzyme economy shapes metabolic fluxes

Metabolic fluxes are governed by physical and economic principles. Stationarity constrains them to a subspace in flux space and thermodynamics makes them lead from higher to lower chemical potentials. At the same time, fluxes in cells represent a compromise between metabolic performance and enzyme cost. To capture this, some flux prediction methods penalise larger fluxes by heuristic cost terms. Economic flux analysis, in contrast, postulates a balance between enzyme costs and metabolic benefits as a necessary condition for fluxes to be realised by kinetic models with optimal enzyme levels. The constraints are formulated using economic potentials, state variables that capture the enzyme labour embodied in metabolites. Generally, fluxes must lead from lower to higher economic potentials. This principle, which resembles thermodynamic constraints, can complement stationarity and thermodynamic constraints in flux analysis. Futile modes, which would be incompatible with economic potentials, are defined algebraically and can be systematically removed from flux distributions. Enzymes that participate in potential futile modes are likely targets of regulation. Economic flux analysis can predict high-yield and low-yield strategies, and captures preemptive expression, multi-objective optimisation, and flux distributions across several cells living in symbiosis. Inspired by labour value theories in economics, it justifies and extends the principle of minimal fluxes and provides an intuitive framework to model the complex interplay of fluxes, metabolic control, and enzyme costs in cells