Dynamic metabolic flux analysis (DMFA): a framework for determining fluxes at metabolic non-steady state

Metabolic flux analysis (MFA) is a key tool for measuring in vivo metabolic fluxes in systems at metabolic steady state. Here, we present a new method for dynamic metabolic flux analysis (DMFA) of systems that are not at metabolic steady state. The advantages of our DMFA method are: (1) time-series of metabolite concentration data can be applied directly for estimating dynamic fluxes, making data smoothing and estimation of average extracellular rates unnecessary; (2) flux estimation is achieved without integration of ODEs, or iterations; (3) characteristic metabolic phases in the fermentation data are identified automatically by the algorithm, rather than selected manually/arbitrarily. We demonstrate the application of the new DMFA framework in three example systems. First, we evaluated the performance of DMFA in a simple three-reaction model in terms of accuracy, precision and flux observability. Next, we analyzed a commercial glucose-limited fed-batch process for 1,3-propanediol production. The DMFA method accurately captured the dynamic behavior of the fed-batch fermentation and identified characteristic metabolic phases. Lastly, we demonstrate that DMFA can be used without any assumed metabolic network model for data reconciliation and detection of gross measurement errors using carbon and electron balances as constraints.     

Determination of metabolic fluxes in a non-steady-state system

Estimation of fluxes through metabolic networks from redistribution patterns of (13)C has become a well developed technique in recent years. However, the approach is currently limited to systems at metabolic steady-state; dynamic changes in metabolic fluxes cannot be assessed. This is a major impediment to understanding the behaviour of metabolic networks, because steady-state is not always experimentally achievable and a great deal of information about the control hierarchy of the network can be derived from the analysis of flux dynamics. To address this issue, we have developed a method for estimating non-steady-state fluxes based on the mass-balance of mass isotopomers. This approach allows multiple mass-balance equations to be written for the change in labelling of a given metabolite pool and thereby permits over-determination of fluxes. We demonstrate how linear regression methods can be used to estimate non-steady-state fluxes from these mass balance equations. The approach can be used to calculate fluxes from both mass isotopomer and positional isotopomer labelling information and thus has general applicability to data generated from common spectrometry- or NMR-based analytical platforms. The approach is applied to a GC-MS time-series dataset of (13)C-labelling of metabolites in a heterotrophic Arabidopsis cell suspension culture. Threonine biosynthesis is used to demonstrate that non-steady-state fluxes can be successfully estimated from such data while organic acid metabolism is used to highlight some common issues that can complicate flux estimation. These include multiple pools of the same metabolite that label at different rates and carbon skeleton rearrangements.     

Relations between carbon dioxide fluxes and environmental factors of Kobresia humilis meadows and Potentilla fruticosa meadows

Carbon dioxide fluxes of Kobresia humilis and Potentillafruticosa shrub meadows,two typical ecosystems in the Qinghai-Tibet Plateau,were measured by eddy covariance technology and the data collected in August 2003 were employed to analyze the relations between carbon dioxide fluxes and environmental factors of the ecosystems.August is the time when the two ecosystems reach their peak leaf area indexes and stay stable,and also the period when the net carbon absorptions of Kobresia humilis and Potentilla photo flux densities (PPFD),the carbon dioxide-uptake rate of the Kobresia humilis meadow is higher than that of the Potentilla fruticosa shrub meadow;where the PPFD are rates of the two ecosystems declined as air temperature increased,but the carbon dioxide uptake rate of the Kobresia humilis meadow decreased more quickly (-0.086) than that of the Potentilla fruticosa shrub meadow (-0.016).Soil moistures exert influence on the soil respirations and this varies with the vegetation type.The daily carbon dioxide absorptions of the ecosystems increase with increased diurnal temperature differences and higher diurnal temperature differences result in higher carbon dioxide exchanges.There exists a negative correlation between the vegetation albedos and the carbon dioxide fluxes.     

Quantification of proteome dynamics in Corynebacterium glutamicum by (15)N-labeling and selected reaction monitoring

Selected reaction monitoring allows quantitative measurements of proteins over several orders of magnitude in complex biological samples. Here we present a targeted approach for quantification of 19 enzymes from Corynebacterium glutamicum applying isotope dilution mass spectrometry coupled to high performance liquid chromatography (IDMS-LC-MS/MS). Investigations of protein dynamics upon growth on acetate and glucose as sole carbon source shows highly stable peptide amounts for enzymes of the central carbon metabolism during the transition phase and after substrate depletion. However significant adaptations of protein amounts are observed between both growth conditions well agreeing with known changes in metabolic fluxes. Time-resolved measurements of protein expression after metabolic switch from glycolytic to gluconeogenetic conditions reveal fast responses in protein synthesis rates for glyoxylate shunt enzymes.     

Scaling of respiration to nitrogen in leaves, stems and roots of higher land plants

Using a database of 2510 measurements from 287 species, we assessed whether general relationships exist between mass-based dark respiration rate and nitrogen concentration for stems and roots, and if they do, whether they are similar to those for leaves. The results demonstrate strong respiration–nitrogen scaling relationships for all observations and for data averaged by species; for roots, stems and leaves examined separately; and for life-forms (woody, herbaceous plants) and phylogenetic groups (angiosperms, gymnosperms) considered separately. No consistent differences in the slopes of these log–log scaling relations were observed among organs or among plant groups, but respiration rates at any common nitrogen concentration were consistently lower on average in leaves than in stems or roots, indicating that organ-specific relationships should be used in models that simulate respiration based on tissue nitrogen concentrations. The results demonstrate both common and divergent aspects of tissue-level respiration–nitrogen scaling for leaves, stems and roots across higher land plants, which are important in their own right and for their utility in modelling carbon fluxes at local to global scales.     

Testing metabolic ecology theory for allometric scaling of tree size, growth and mortality in tropical forests

The theory of metabolic ecology predicts specific relationships among tree stem diameter, biomass, height, growth and mortality. As demographic rates are important to estimates of carbon fluxes in forests, this theory might offer important insights into the global carbon budget, and deserves careful assessment. We assembled data from 10 old-growth tropical forests encompassing censuses of 367 ha and > 1.7 million trees to test the theory's predictions. We also developed a set of alternative predictions that retained some assumptions of metabolic ecology while also considering how availability of a key limiting resource, light, changes with tree size. Our results show that there are no universal scaling relationships of growth or mortality with size among trees in tropical forests. Observed patterns were consistent with our alternative model in the one site where we had the data necessary to evaluate it, and were inconsistent with the predictions of metabolic ecology in all forests.     

Quantitative analysis of metabolic fluxes in Escherichia coli, using two-dimensional NMR spectroscopy and complete isotopomer models.

Complete isotopomer models that simulate distribution of label in 13C tracer experiments are applied to the quantification of metabolic fluxes in the primary carbon metabolism of E. coli under aerobic and anaerobic conditions. The concept of isotopomer mapping matrices (IMMs) is used to simplify the formulation of isotopomer mass balances by expressing all isotopomer mass balances of a metabolite pool in a single matrix equation. A numerically stable method to calculate the steady-state isotopomer distribution in metabolic networks in introduced. Net values of intracellular fluxes and the degree of reversibility of enzymatic steps are estimated by minimization of the deviations between experimental and simulated measurements. The metabolic model applied includes the Embden-Meyerhof-Parnas and the pentose phosphate pathway, the tricarboxylic acid cycle, anaplerotic reaction sequences and pathways involved in amino acid synthesis. The study clearly demonstrates the value of complete isotopomer models for maximizing the information obtainable from 13C tracer experiments. The approach applied here offers a completely general and comprehensive analysis of carbon tracer experiments where any set of experimental data on the labeling state and extracellular fluxes can be used for the quantification of metabolic fluxes in complex metabolic networks.     

Hybrid metabolic flux analysis and recombinant protein prediction in <Emphasis Type="Italic">Pichia pastoris</Emphasis> X-33 cultures expressing a single-chain antibody fragment

Despite the growing importance of the Pichia pastoris expression system as industrial workhorse, the literature is almost absent in systematic studies on how culture medium composition affects central carbon fluxes and heterologous protein expression. In this study we investigate how 26 variations of the BSM+PTM1 medium impact central carbon fluxes and protein expression in a P. pastoris X-33 strain expressing a single-chain antibody fragment. To achieve this goal, we adopted a hybrid metabolic flux analysis (MFA) methodology, which is a modification of standard MFA to predict the rate of synthesis of recombinant proteins. Hybrid MFA combines the traditional parametric estimation of central carbon fluxes with non-parametric statistical modeling of product-related quantitative or qualitative measurements as a function of central carbon fluxes. It was observed that protein yield variability was 53.6 % (relative standard deviation) among the different experiments. Protein yield is much more sensitive to medium composition than biomass growth, which is mainly determined by the carbon source availability and main salts. Hybrid MFA was able to describe accurately the protein yield with normalized RMSE of 6.3 % over 5 independent experiments. The metabolic state that promotes high protein yields is characterized by high overall metabolic rates through main central carbon pathways concomitantly with a relative shift of carbon flux from biosynthetic towards energy generating pathways.     

Understanding fatty acid synthesis in developing maize embryos using metabolic flux analysis

The efficiency with which developing maize embryos convert substrates into seed storage reserves was determined to be 57–71%, by incubating developing maize embryos with uniformly labeled ¹⁴C substrates and measuring their conversion to CO₂ and biomass products. To map the pattern of metabolic fluxes underlying this efficiency, maize embryos were labeled to isotopic steady state using a combination of labeled ¹³C-substrates. Intermediary metabolic fluxes were estimated by computer-aided modeling of the central metabolic network using the labeling data collected by NMR and GC-MS and the biomass composition. The resultant flux map reveals that even though 36% of the entering carbon goes through the oxidative pentose-phosphate pathway, this does not fully meet the NADPH demands for fatty acid synthesis. Metabolic flux analysis and enzyme activities highlight the importance of plastidic NADP-dependent malic enzyme, which provides one-third of the carbon and NADPH required for fatty acid synthesis in developing maize embryos.     

Dew water isotopic ratios and their relationships to ecosystem water pools and fluxes in a cropland and a grassland in China

Dew formation has the potential to modulate the spatial and temporal variations of isotopic contents of atmospheric water vapor, oxygen and carbon dioxide. The goal of this paper is to improve our understanding of the isotopic interactions between dew water and ecosystem water pools and fluxes through two field experiments in a wheat/maize cropland and in a short steppe grassland in China. Measurements were made during 94 dew events of the D and ¹⁸O compositions of dew, atmospheric vapor, leaf, xylem and soil water, and the whole ecosystem water flux. Our results demonstrate that the equilibrium fractionation played a dominant role over the kinetic fractionation in controlling the dew water isotopic compositions. A significant correlation between the isotopic compositions of leaf water and dew water suggests a large role of top-down exchange with atmospheric vapor controlling the leaf water turnover at night. According to the isotopic labeling, dew water consisted of a downward flux of water vapor from above the canopy (98%) and upward fluxes originated from soil evaporation and transpiration of the leaves in the lower canopy (2%).     

INCA 2.0: A tool for integrated,dynamic modeling of NMR- and MS-based isotopomer measurements and rigorous metabolic flux analysis

Metabolic flux analysis (MFA) combines experimental measurements and computational modeling to determine biochemical reaction rates in live biological systems. Advancements in analytical instrumentation, such as nuclear magnetic resonance (NMR) spectroscopy and mass spectrometry (MS), have facilitated chemical separation and quantification of isotopically enriched metabolites. However, no software packages have been previously described that can integrate isotopomer measurements from both MS and NMR analytical platforms and have the flexibility to estimate metabolic fluxes from either isotopic steady-state or dynamic labeling experiments. By applying physiologically relevant cardiac and hepatic metabolic models to assess NMR isotopomer measurements, we herein test and validate new modeling capabilities of our enhanced flux analysis software tool, INCA 2.0. We demonstrate that INCA 2.0 can simulate and regress steady-state ¹³C NMR datasets from perfused hearts with an accuracy comparable to other established flux assessment tools. Furthermore, by simulating the infusion of three different ¹³C acetate tracers, we show that MFA based on dynamic ¹³C NMR measurements can more precisely resolve cardiac fluxes compared to isotopically steady-state flux analysis. Finally, we show that estimation of hepatic fluxes using combined ¹³C NMR and MS datasets improves the precision of estimated fluxes by up to 50%. Overall, our results illustrate how the recently added NMR data modeling capabilities of INCA 2.0 can enable entirely new experimental designs that lead to improved flux resolution and can be applied to a wide range of biological systems and measurement time courses.     

A Method to Constrain Genome-Scale Models with 13C Labeling Data

Current limitations in quantitatively predicting biological behavior hinder our efforts to engineer biological systems to produce biofuels and other desired chemicals. Here, we present a new method for calculating metabolic fluxes, key targets in metabolic engineering, that incorporates data from ¹³C labeling experiments and genome-scale models. The data from ¹³C labeling experiments provide strong flux constraints that eliminate the need to assume an evolutionary optimization principle such as the growth rate optimization assumption used in Flux Balance Analysis (FBA). This effective constraining is achieved by making the simple but biologically relevant assumption that flux flows from core to peripheral metabolism and does not flow back. The new method is significantly more robust than FBA with respect to errors in genome-scale model reconstruction. Furthermore, it can provide a comprehensive picture of metabolite balancing and predictions for unmeasured extracellular fluxes as constrained by ¹³C labeling data. A comparison shows that the results of this new method are similar to those found through ¹³C Metabolic Flux Analysis (¹³C MFA) for central carbon metabolism but, additionally, it provides flux estimates for peripheral metabolism. The extra validation gained by matching 48 relative labeling measurements is used to identify where and why several existing COnstraint Based Reconstruction and Analysis (COBRA) flux prediction algorithms fail. We demonstrate how to use this knowledge to refine these methods and improve their predictive capabilities. This method provides a reliable base upon which to improve the design of biological systems.     

Insect eggs exert rapid control over an oxygen-water tradeoff

In terrestrial environments, the exchange of respiratory gases exacts a water cost: obtaining oxygen or carbon dioxide requires losing water. Insect eggs should be especially sensitive to this tradeoff-because they are unable to forage for water, have high surface area-to-volume ratios, and experience large temperature-driven changes in oxygen demand. Previous work from our laboratory, on eggs of a common hawk-moth, Manduca sexta, has shown that, during development, metabolic rate and water loss rates rise in parallel. These correlative data suggest that eggshell conductance increases to accommodate increasing metabolic demand. Here, we test this idea experimentally by subjecting eggs of M. sexta to 15, 21 (normoxia) and 35% oxygen for 24h, while measuring rates of metabolism (as carbon dioxide emission) and water loss. Hypoxia depressed egg metabolic rates, but led to pronounced, rapid increases in water loss. By contrast, hyperoxia had no significant effect on metabolism or water loss. These data demonstrate that insect eggs actively participate in balancing oxygen gain and water loss, and that they use tissue oxygen status, or some correlate of it, as a cue for increasing eggshell conductance. Rapid control over conductance may allow eggs to conserve water during an initial period of low metabolic demand, thereby deferring water costs of respiratory gas exchange until late in development.     

A transient isotopic labeling methodology for 13C metabolic flux analysis of photoautotrophic microorganisms

Metabolic flux analysis is increasingly recognized as an integral component of systems biology. However, techniques for experimental measurement of system-wide metabolic fluxes in purely photoautotrophic systems (growing on CO(2) as the sole carbon source) have not yet been developed due to the unique problems posed by such systems. In this paper, we demonstrate that an approach that balances positional isotopic distributions transiently is the only route to obtaining system-wide metabolic flux maps for purely autotrophic metabolism. The outlined transient (13)C-MFA methodology enables measurement of fluxes at a metabolic steady-state, while following changes in (13)C-labeling patterns of metabolic intermediates as a function of time, in response to a step-change in (13)C-label input. We use mathematical modeling of the transient isotopic labeling patterns of central intermediates to assess various experimental requirements for photoautotrophic MFA. This includes the need for intracellular metabolite concentration measurements and isotopic labeling measurements as a function of time. We also discuss photobioreactor design and operation in order to measure fluxes under precise environmental conditions. The transient MFA technique can be used to measure and compare fluxes under different conditions of light intensity, nitrogen sources or compare strains with various mutations or gene deletions and additions.     

METABOLIC FLUX IS A DETERMINANT OF THE EVOLUTIONARY RATES OF ENZYME‐ENCODING GENES

Relationships between evolutionary rates and gene properties on a genomic, functional, pathway, or system level are being explored to unravel the principles of the evolutionary process. In particular, functional network properties have been analyzed to recognize the constraints they may impose on the evolutionary fate of genes. Here we took as a case study the core metabolic network in human erythrocytes and we analyzed the relationship between the evolutionary rates of its genes and the metabolic flux distribution throughout it. We found that metabolic flux correlates with the ratio of nonsynonymous to synonymous substitution rates. Genes encoding enzymes that carry high fluxes have been more constrained in their evolution, while purifying selection is more relaxed in genes encoding enzymes carrying low metabolic fluxes. These results demonstrate the importance of considering the dynamical functioning of gene networks when assessing the action of selection on system‐level properties.