Bidirectional reaction steps in metabolic networks: I. Modeling and simulation of carbon isotope labeling experiments

The extension of metabolite balancing with carbon labeling experiments, as described by Marx et al. (Biotechnol. Bioeng. 49: 11-29), results in a much more detailed stationary metabolic flux analysis. As opposed to basic metabolite flux balancing alone, this method enables both flux directions of bidirectional reaction steps to be quantitated. However, the mathematical treatment of carbon labeling systems is much more complicated, because it requires the solution of numerous balance equations that are bilinear with respect to fluxes and fractional labeling. In this study, a universal modeling framework is presented for describing the metabolite and carbon atom flux in a metabolic network. Bidirectional reaction steps are extensively treated and their impact on the system's labeling state is investigated. Various kinds of modeling assumptions, as usually made for metabolic fluxes, are expressed by linear constraint equations. A numerical algorithm for the solution of the resulting linear constrained set of nonlinear equations is developed. The numerical stability problems caused by large bidirectional fluxes are solved by a specially developed transformation method. Finally, the simulation of carbon labeling experiments is facilitated by a flexible software tool for network synthesis. An illustrative simulation study on flux identifiability from available flux and labeling measurements in the cyclic pentose phosphate pathway of a recombinant strain of Zymomonas mobilis concludes this contribution. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 55: 101-117, 1997.     

Strategies for measuring and modelling carbon dioxide and water vapour fluxes over terrestrial ecosystems

Continuous and direct measurements of ecosystem carbon dioxide and water vapour fluxes can improve our ability to close regional and global carbon and hydrological budgets. On this behalf, an international and multidisciplinary group of scientists (micrometeorologists, ecophysiologists and biogeochemists) assembled at La Thuile, Italy to convene a workshop on ‘Strategies for Monitoring and Modelling CO₂ and Water Vapour Fluxes over Terrestrial Ecosystems’. Over the course of the week talks and discussions focused on: (i) the results from recent field studies on the annual cycle of carbon dioxide and water vapour fluxes over terrestrial ecosystems; (ii) the problems and pitfalls associated with making long-term flux measurements; (iii) alternative methods for assessing ecosystem carbon dioxide and water vapour fluxes; (iv) how direct and continuous carbon dioxide and water vapour flux measurements could be used by the ecological and biogeochemical modelling communities; and (v) if, how and where to proceed with establishing a network of long-term flux measurement sites. This report discusses the purpose of the meeting and summarizes the conclusions drawn from the discussions by the attending scientists. There was a consensus that recent advances in instrumentation and software make possible long-term measurements of carbon dioxide and water vapour fluxes over terrestrial ecosystems. At this writing, eight research teams have conducted long-term carbon dioxide and water vapour flux experiments and more long-term studies are anticipated. The participants advocated an experimental design that would make long-term flux measurement valuable to a wider community of modelers, biogeochemists and ecologists. A network of carbon dioxide and water vapour flux measurement stations should include ancillary measurements of meteorological, ecological and biological variables. To assess spatial representativeness of the long term and tower-based flux measurements, periodic aircraft-based flux experiments and satellite-based assessments of land cover were recommended. Occasional cuvette-based measurements of leaf-level carbon dioxide and water vapour fluxes were endorsed to provide information on the biological control of surface fluxes. They can also provide data to parameterize ecophysiological models. Flask sampling of stable carbon isotopes was advocated to extend the flux measurements to the global scale.     

Bidirectional reaction steps in metabolic networks: II. Flux estimation and statistical analysis

Metabolic carbon labelling experiments enable a large amount of extracellular fluxes and intracellular carbon isotope enrichments to be measured. Since the relation between the measured quantities and the unknown intracellular metabolic fluxes is given by bilinear balance equations, flux determination from this data set requires the numerical solution of a nonlinear inverse problem. To this end, a general algorithm for flux estimation from metabolic carbon labelling experiments based on the least squares approach is developed in this contribution and complemented by appropriate tools for statistical analysis. The linearization technique usually applied for the computation of nonlinear confidence regions is shown to be inappropriate in the case of large exchange fluxes. For this reason a sophisticated compactification transformation technique for nonlinear statistical analysis is developed. Statistical analysis is then performed by computing appropriate statistical quality measures like output sensitivities, parameter sensitivities and the parameter covariance matrix. This allows one to determine the order of magnitude of exchange fluxes in most practical situations. An application study with a large data set from lysine-producing Corynebacterium glutamicum demonstrates the power and limitations of the carbon-labelling technique. It is shown that all intracellular fluxes in central metabolism can be quantitated without assumptions on intracellular energy yields. At the same time several exchange fluxes are determined which is invaluable information for metabolic engineering. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 55: 118-135, 1997.     

Integrating aquatic and terrestrial components to construct a complete carbon budget for a north temperate lake district

The development of complete regional carbon (C) budgets for different biomes is an integral step in the effort to predict global response and potential feedbacks to a changing climate regime. Wetland and lake contributions to regional C cycling remain relatively uncertain despite recent research highlighting their importance. Using a combination of field surveys and tower‐based carbon dioxide (CO₂) flux measurements, modeling, and published literature, we constructed a complete C budget for the Northern Highlands Lake District in northern Wisconsin/Michigan, a ～6400 km² region rich in lakes and wetlands. This is one of the first regional C budgets to incorporate aquatic and terrestrial C cycling under the same framework. We divided the landscape into three major compartments (forests, wetlands, and surface waters) and quantified all major C fluxes into and out of those compartments, with a particular focus on atmospheric exchange but also including sedimentation in lakes and hydrologic fluxes. Landscape C storage was dominated by peat‐containing wetlands and lake sediments, which make up only 20% and 13% of the landscape area, respectively, but contain >80% of the total fixed C pool (ca. 400 Tg). We estimated a current regional C accumulation of 1.1±0.1 Tg yr^?1, and the largest regional flux was forest net ecosystem exchange (NEE) into aggrading forests for a total of 1.0±0.1 Tg yr^?1. Mean wetland NEE (0.12±0.06 Tg yr^?1 into wetlands), lake CO₂ emissions and riverine efflux (each ca. 0.03±0.01 Tg yr^?1) were smaller but of consequence to the overall budget. Hydrologic transport from uplands/wetlands to surface waters within the region was an important vector of terrestrial C. Regional C fluxes and pools would be misrepresented without inclusion of surface waters and wetlands, and C budgets in heterogeneous landscapes open opportunities to examine the sensitivities of important fluxes to changes in climate and land use/land cover.     

Boundary layer budgets for regional estimates of scalar fluxes

The paper considers the theory and application of budget techniques for regional scalar flux estimation using the daytime convective boundary layer (CBL) and the nocturnal boundary layer (NBL). CBL techniques treat the well mixed layer of air between heights of, say, 100 m and 1000 m as an integrator of surface fluxes along the path of a column of air moving over the landscape. They calculate the average surface flux from the scalar concentration in and above the mixed layer, and the CBL height. The flux estimates are averaged over regions of 10–10⁴ km² extending 10 to 100 km upwind. An integral form of the CBL budget is used to estimate daily regional rates of CO₂ uptake and evaporation from three data sets. There was plausible agreement between the estimates and locally measured fluxes. CBL budgets have great potential for estimating regional scalar fluxes, but there is an urgent need for validation through direct measurements of fluxes and budget parameters. NBL budgets are useful when low-level, radiative inversions inhibit vertical mixing. Surface scalar fluxes can then be estimated from the rate of concentration change below the inversion. An example application for estimating the nocturnal CO₂ flux is given. While simple in concept, NBL budgets are more difficult to apply in practice because of the unpredictability of the depth of the layer and sometimes, its absence altogether. On the other hand, the depth of the atmospheric mixing chamber is better defined, few assumptions are required and the concentration changes usually will be larger and hence more easily detectable than in CBL budgetting.     

Proximate biochemical composition and caloric content calculated from elemental CHN analysis: a stoichiometric concept

Summary Carbohydrate, lipid, and protein compositions are stoichiometrically related to organic CHN (carbon, hydrogen, nitrogen) contents. Elemental CHN analyses of total biomass and ash, therefore, provide a basis for the calculation of proximate biochemical composition and bomb caloric value. The classical nitrogen to protein conversion factor (6.25) should be replaced by 5.8±0.13. A linear relation exists between the mass fraction of non-protein carbon and the carbohydrate and lipid content. Residual water in dry organic matter can be estimated with the additional information derived from hydrogen measurements.The stoichiometric CHN method and direct biochemical analysis agreed within 10% of ash-free dry biomass (for muscle, liver and fat tissue of silver carp; gut contents composed of detritus and algae; commercial fish food). The detrital material, however, had to be corrected for non-protein nitrogen.A linear relationship between bomb caloric value and organic carbon fractions was derived on the basis of thermodynamic and stoichiometric principles, in agreement with experimental data published for bacteria, algae, protozoa and invertebrates. The highly automatic stoichiometric CHN method for the separation of nutrient contents in biomass extends existing ecophysiological concepts for the construction of balanced carbon and nitrogen, as well as biochemical and energy budgets. Offprint requests to: Institut für Zoologie, Abt. Zoophysiologie, Universität Innsbruck, Peter-Mayr-Str. 1A, A-6020 Innsbruck, Austria     

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.     

Metabolic isotopomer labeling systems. Part II: structural flux identifiability analysis

Metabolic flux analysis using carbon labeling experiments (CLEs) is an important tool in metabolic engineering where the intracellular fluxes have to be computed from the measured extracellular fluxes and the partially measured distribution of 13C labeling within the intracellular metabolite pools. The relation between unknown fluxes and measurements is described by an isotopomer labeling system (ILS) (see Part I [Math. Biosci. 169 (2001) 173]). Part II deals with the structural flux identifiability of measured ILSs in the steady state. The central question is whether the measured data contains sufficient information to determine the unknown intracellular fluxes. This question has to be decided a priori, i.e. before the CLE is carried out. In structural identifiability analysis the measurements are assumed to be noise-free. A general theory of structural flux identifiability for measured ILSs is presented and several algorithms are developed to solve the identifiability problem. In the particular case of maximal measurement information, a symbolical algorithm is presented that decides the identifiability question by means of linear methods. Several upper bounds of the number of identifiable fluxes are derived, and the influence of the chosen inputs is evaluated. By introducing integer arithmetic this algorithm can even be applied to large networks. For the general case of arbitrary measurement information, identifiability is decided by a local criterion. A new algorithm based on integer arithmetic enables an a priori local identifiability analysis to be performed for networks of arbitrary size. All algorithms have been implemented and flux identifiability is investigated for the network of the central metabolic pathways of a microorganism. Moreover, several small examples are worked out to illustrate the influence of input metabolite labeling and the paradox of information loss due to network simplification.     

Budgets of organic and inorganic carbon in a Mediterranean coastal lagoon dominated by submerged vegetation

In this article, we studied the fluxes of organic and inorganic (DIC) carbon in a coastal lagoon dominated by highly productive macrophyte meadows (Albufera des Grau, Balearic Islands). Seasonal and annual carbon budgets were performed from estimates of whole-system fluxes, and the fate of organic matter production was evaluated through a stable isotope exploration of the food web. The results showed an extremely intense cycling of DIC, with a turnover between 65 and 13 times faster than water turnover. The metabolic fluxes were the main contributors to the seasonal and annual DIC budgets, which were secondarily affected by calcite precipitation, atmospheric exchange and hydrological fluxes. The inorganic carbon dynamics was strongly determined by the seasonal cycle of the meadows. Accordingly the air?Cwater CO₂ flux shifted seasonally, and the lagoon was a sink of atmospheric CO₂ during the vegetated period and a source during the period without macrophytes. The high macrophytic production played a minor role in the lagoon food web, which apparently relied on phytoplanktonic or allochthonous organic matter. A fast decomposition of macrophytic biomass appeared to be the main destiny of the annual macrophytic production, which was only secondarily buried in the sediments.     

Glucose metabolism in the antibiotic producing actinomycete Nonomuraea sp. ATCC 39727

The actinomycete Nonomuraea sp. ATCC 39727, producer of the glycopeptide A40926 that is used as precursor for the novel antibiotic dalbavancin, has an unusual carbon metabolism. Glucose is primarily metabolized via the Entner-Doudoroff (ED) pathway, although the energetically more favorable Embden-Meyerhof-Parnas (EMP) pathway is present in this organism. Moreover, Nonomuraea utilizes a PPi-dependent phosphofructokinase, an enzyme that has been connected with anaerobic metabolism in eukaryotes and higher plants, but recently has been recognized in several actinomycetes. In order to study its primary carbon metabolism in further detail, Nonomuraea was cultivated with [1-13C] glucose as the only carbon source and the 13C-labeling patterns of proteinogenic amino acids were determined by GC-MS analysis. Through this method, the fluxes in the central carbon metabolism during balanced growth were estimated. Moreover, a shift in the label incorporation pattern was observed in connection with phosphate limitation and increased antibiotic productivity in Nonomuraea. The shift indicated an increased flux through the EMP pathway at the expense of the flux through the ED pathway, a suggestion that was supported by alterations in intracellular metabolite levels during phosphate limitation. In contrast, expression levels of genes encoding enzymes in the ED and EMP pathways were not affected by phosphate limitation.     

An improved algorithm for stoichiometric network analysis: theory and applications

MOTIVATION: Genome scale analysis of the metabolic network of a microorganism is a major challenge in bioinformatics. The combinatorial explosion, which occurs during the construction of elementary fluxes (non-redundant pathways) requires sophisticated and efficient algorithms to tackle the problem. RESULTS: Mathematically, the calculation of elementary fluxes amounts to characterizing the space of solutions to a mixed system of linear equalities, given by the stoichiometry matrix, and linear inequalities, arising from the irreversibility of some or all of the reactions in the network. Previous approaches to this problem have iteratively solved for the equalities while satisfying the inequalities throughout the process. In an extension of previous work, here we consider the complementary approach and derive an algorithm which satisfies the inequalities one by one while staying in the space of solution of the equality constraints. Benchmarks on different subnetworks of the central carbon metabolism of Escherichia coli show that this new approach yields a significant reduction in the execution time of the calculation. This reduction arises since the odds that an intermediate elementary flux already fulfills an additional inequality are larger than when having to satisfy an additional equality constraint.     

Diagenetic stoichiometry and benthic nutrient fluxes at the sediment–water interface of Lake Illawarra, Australia

Benthic flux measurements of O₂, TCO₂ and inorganic nutrients were made at three stations (seagrass beds, shallow bare sand and deep mud) in Lake Illawarra (Australia) to compare the characteristics of diagenesis and benthic biogeochemical processes for different primary producers (seagrass or microphytobenthos, (MPB)) and/or sediment types (sand or mud).Seagrass beds exhibited the highest gross primary productivity while the lowest rates occurred at the deep mud station. At the shallow bare sand station only, the gross primary production (GPP) and respiration (R) were balanced, while at the other two stations, R exceeded GPP by as much as 2 fold, indicating more organic carbon was decomposed than produced at the time of sampling. In general, nutrient fluxes displayed typical diurnal variation.Organic carbon oxidation scenarios, evaluated by either calcium carbonate dissolution or sulfate reduction models, indicated that both models can represent organic matter mineralization. The difference of estimated total carbon oxidized in this lake using the two models was small, ranging from 0.2% at deep mud station to maximum of 21% at seagrass station. In addition, N₂ flux rates (net denitrification), estimated using carbon and nitrogen stoichiometry, were of similar magnitude as the rates estimated using LOICZ budget modeling or measured using the N₂/Ar technique.Finally, a comparison of calculated diffusive fluxes and measured fluxes using incubation cores indicated that the results were of similar magnitude at the deep mud station, but the incubation cores fluxes were much higher than the calculated diffusive fluxes at the other two stations. This may have been caused by bioturbation or bioirrigation.     

Improvements in metabolic flux analysis using carbon bond labeling experiments: bondomer balancing and Boolean function mapping

The biosynthetically directed fractional (13)C labeling method for metabolic flux evaluation relies on performing a 2-D [(13)C, (1)H] NMR experiment on extracts from organisms cultured on a uniformly labeled carbon substrate. This article focuses on improvements in the interpretation of data obtained from such an experiment by employing the concept of bondomers. Bondomers take into account the natural abundance of (13)C; therefore many bondomers in a real network are zero, and can be precluded a priori--thus resulting in fewer balances. Using this method, we obtained a set of linear equations which can be solved to obtain analytical formulas for NMR-measurable quantities in terms of fluxes in glycolysis and the pentose phosphate pathways. For a specific case of this network with four degrees of freedom, a priori identifiability of the fluxes was shown possible for any set of fluxes. For a more general case with five degrees of freedom, the fluxes were shown identifiable for a representative set of fluxes. Minimal sets of measurements which best identify the fluxes are listed. Furthermore, we have delineated Boolean function mapping, a new method to iteratively simulate bondomer abundances or efficiently convert carbon skeleton rearrangement information to mapping matrices. The efficiency of this method is expected to be valuable while analyzing metabolic networks which are not completely known (such as in plant metabolism) or while implementing iterative bondomer balancing methods.     

Protistan grazing and viral lysis losses of bacterial carbon production in a large mesotrophic lake (Lake Biwa)

The grazing and lysis mortalities of planktonic bacteria were estimated using the modified dilution method and respiratory quinone (RQ) analysis in mesotrophic Lake Biwa, Japan. The planktonic bacterial assemblages in the lake consisted of various RQ subgroups with different growth and mortality rates. The sum of total bacterial mortalities due to protistan grazing and viral lysis accounted for 96.6 % (range 89.0–107.2 %) of daily total bacterial production. This is the first report that successfully demonstrates a balanced relationship between bacterial production and losses using the modified dilution method in a lake. The growth rates of ubiquinone (UQ)-containing bacteria were faster than those of menaquinone-containing bacteria. Especially the dominant and fastest growing bacterial groups in the present study were the bacterial groups containing UQ-8 or UQ-10. The sum of their production and loss accounted for 60 % of carbon fluxes within the microbial loop. Thus, a large portion of the carbon cycling through the bacterial community in Lake Biwa can be explained by the carbon fluxes through dominant bacterial groups.     

Carbon allocation in forest ecosystems

Carbon allocation plays a critical role in forest ecosystem carbon cycling. We reviewed existing literature and compiled annual carbon budgets for forest ecosystems to test a series of hypotheses addressing the patterns, plasticity, and limits of three components of allocation: biomass, the amount of material present; flux, the flow of carbon to a component per unit time; and partitioning, the fraction of gross primary productivity (GPP) used by a component. Can annual carbon flux and partitioning be inferred from biomass? Our survey revealed that biomass was poorly related to carbon flux and to partitioning of photosynthetically derived carbon, and should not be used to infer either. Are component fluxes correlated? Carbon fluxes to foliage, wood, and belowground production and respiration all increased linearly with increasing GPP (a rising tide lifts all boats). Autotrophic respiration was strongly linked to production for foliage, wood and roots, and aboveground net primary productivity and total belowground carbon flux (TBCF) were positively correlated across a broad productivity gradient. How does carbon partitioning respond to variability in resources and environment? Within sites, partitioning to aboveground wood production and TBCF responded to changes in stand age and resource availability, but not to competition (tree density). Increasing resource supply and stand age, with one exception, resulted in increased partitioning to aboveground wood production and decreased partitioning to TBCF. Partitioning to foliage production was much less sensitive to changes in resources and environment. Overall, changes in partitioning within a site in response to resource supply and age were small (<15% of GPP), but much greater than those inferred from global relationships. Across all sites, foliage production plus respiration, and total autotrophic respiration appear to use relatively constant fractions of GPP – partitioning to both was conservative across a broad range of GPP – but values did vary across sites. Partitioning to aboveground wood production and to TBCF were the most variable – conditions that favored high GPP increased partitioning to aboveground wood production and decreased partitioning to TBCF. Do priorities exist for the products of photosynthesis? The available data do not support the concept of priorities for the products of photosynthesis, because increasing GPP increased all fluxes. All facets of carbon allocation are important to understanding carbon cycling in forest ecosystems. Terrestrial ecosystem models require information on partitioning, yet we found few studies that measured all components of the carbon budget to allow estimation of partitioning coefficients. Future studies that measure complete annual carbon budgets contribute the most to understanding carbon allocation.     

The relationships between the metabolic fluxes and 13C-labeled isotopomer distribution for the flux analysis of the main metabolic pathways

It has been known that ¹³C-labeling technique is quite useful in estimating the metabolic fluxes. Although the program-based flux analysis is powerful, it is not easy to be confident with the result obtained without experiences and exhaustive trial and errors based on statistical analysis for the confidence intervals in practice. It is, therefore, quite important to grasp the relationship between the fluxes and the ¹³C-labeled isotopomer distribution to get deeper insight into the metabolic flux analysis. In the present research, it was shown explicitly how the isotopomer distribution changes with respect to the fluxes in relation to the labeling patterns of the substrate, where either labeled glucose, acetate, or pyruvate was used as a carbon source. Some of the analytical expressions were derived based on the matrix representation, and they were utilized for analysis. It was shown that the isotopomer pattern does not necessarily change uniformly with respect to fluxes, but changes in a complicated way in particular for the case of using pyruvate as a carbon source where some isotopomers do not necessarily change monotonically. It was shown to be quite important to grasp how the isotopomer pattern changes with respect to fluxes and the labeling pattern of the substrate for flux determination and the experimental design. It was also shown that the mixture of [1-¹³C] acetate and [2-¹³C] acetate should not be used from the information index point of view. Some of the experimental data were evaluated from the present approach. It was also shown that the isotopomer distribution is less sensitive to the bidirectional fluxes in the reversible pathway.     

Optimal selection of metabolic fluxes for in vivo measurement. I. Development of mathematical methods.

The measurement of uptake and secretion rates is often not sufficient to allow the calculation of all internal metabolic fluxes. Measurements of internal fluxes are needed and these additional measurements are used in conjunction with mass-balance equations to calculate the complete metabolic flux map. A method is presented that identifies the fluxes that should be selected for experimental measurement, and the fluxes that can be computed using the mass-balance equations. The criterion for selecting internal metabolic fluxes for measurement is that the values of the computed fluxes should have low sensitivity to experimental error in the measured fluxes. A condition number indicating the upper bound on this sensitivity, is calculated based on stoichiometry alone. The actual sensitivity is dependent on both the flux measurements and the error in flux measurements, as well as the stoichiometry. If approximate physiologic ranges of fluxes are known a realistic sensitivity can be computed. The exact sensitivity cannot be calculated since the experimental error is usually unknown. The most probable value of the actual sensitivity for a given selection of measured fluxes is estimated by selecting a large number of representative error vectors and calculating the actual sensitivity for each of these. A frequency distribution of actual sensitivities is thus obtained giving a representative range of actual sensitivities for a particular experimental situation.     

Spatial and temporal variability of net ecosystem production in a tropical forest: testing the hypothesis of a significant carbon sink

Tropical forest ecosystems play an important role in the global carbon balance. Depending on age and land use, they can act as carbon sources, sinks, or be in approximate balance, but it is uncertain if global environmental changes are forcing these ecosystems outside their natural range of variation. We asked the question of whether or not the net carbon flux of a tropical primary forest, which should be in balance over the long term, is within the expected range of natural variation. A simple Bayesian hypothesis testing method was used to address this question for primary forests in the Porce region of Colombia. Net ecosystem production (NEP) was measured in this forest in a set of 33 permanent plots from 2000 to 2002 in 2, 1‐year intervals. Our estimate of NEP ranged between −4.03 and 2.22 Mg C ha⁻¹ yr⁻¹ for the two intervals. This range was compared with a priori defined range of natural variation estimated from the ecosystem model STANDCARB, which estimated spatial and temporal variation due to gap dynamics. The prior range of variation was estimated between −1.5 and 1.5 Mg C ha⁻¹ yr⁻¹. The observed data on NEP did not provide sufficient evidence to reject the null hypothesis that these forests are in C balance. We concluded that the ecosystem is likely behaving within its range of natural variation, but measurement uncertainties were a major limitation to finding evidence to reject the null hypothesis. A literature review of C flux studies in the tropics revealed that about half of the observations could be explained by gap dynamics alone, while significant C sinks have only been observed during La Niña years, with contrasting results in other tropical forests. In conclusion, observational data of carbon fluxes do not appear to provide direct evidence for a significant carbon sink in some sites in the tropics.     

The principle of flux minimization and its application to estimate stationary fluxes in metabolic networks.

Cellular functions are ultimately linked to metabolic fluxes brought about by thousands of chemical reactions and transport processes. The synthesis of the underlying enzymes and membrane transporters causes the cell a certain 'effort' of energy and external resources. Considering that those cells should have had a selection advantage during natural evolution that enabled them to fulfil vital functions (such as growth, defence against toxic compounds, repair of DNA alterations, etc.) with minimal effort, one may postulate the principle of flux minimization, as follows: given the available external substrates and given a set of functionally important 'target' fluxes required to accomplish a specific pattern of cellular functions, the stationary metabolic fluxes have to become a minimum. To convert this principle into a mathematical method enabling the prediction of stationary metabolic fluxes, the total flux in the network is measured by a weighted linear combination of all individual fluxes whereby the thermodynamic equilibrium constants are used as weighting factors, i.e. the more the thermodynamic equilibrium lies on the right-hand side of the reaction, the larger the weighting factor for the backward reaction. A linear programming technique is applied to minimize the total flux at fixed values of the target fluxes and under the constraint of flux balance (= steady-state conditions) with respect to all metabolites. The theoretical concept is applied to two metabolic schemes: the energy and redox metabolism of erythrocytes, and the central metabolism of Methylobacterium extorquens AM1. The flux rates predicted by the flux-minimization method exhibit significant correlations with flux rates obtained by either kinetic modelling or direct experimental determination. Larger deviations occur for segments of the network composed of redundant branches where the flux-minimization method always attributes the total flux to the thermodynamically most favourable branch. Nevertheless, compared with existing methods of structural modelling, the principle of flux minimization appears to be a promising theoretical approach to assess stationary flux rates in metabolic systems in cases where a detailed kinetic model is not yet available.     

Terrestrial fluxes of carbon in GCP carbon budgets

The Global Carbon Project (GCP) has published global carbon budgets annually since 2007 (Canadell et al. [2007], Proc Natl Acad Sci USA, 104, 18866–18870; Raupach et al. [2007], Proc Natl Acad Sci USA, 104, 10288–10293). There are many scientists involved, but the terrestrial fluxes that appear in the budgets are not well understood by ecologists and biogeochemists outside of that community. The purpose of this paper is to make the terrestrial fluxes of carbon in those budgets more accessible to a broader community. The GCP budget is composed of annual perturbations from pre‐industrial conditions, driven by addition of carbon to the system from combustion of fossil fuels and by transfers of carbon from land to the atmosphere as a result of land use. The budget includes a term for each of the major fluxes of carbon (fossil fuels, oceans, land) as well as the rate of carbon accumulation in the atmosphere. Land is represented by two terms: one resulting from direct anthropogenic effects (Land Use, Land‐Use Change, and Forestry or land management) and one resulting from indirect anthropogenic (e.g., CO₂, climate change) and natural effects. Each of these two net terrestrial fluxes of carbon, in turn, is composed of opposing gross emissions and removals (e.g., deforestation and forest regrowth). Although the GCP budgets have focused on the two net terrestrial fluxes, they have paid little attention to the gross components, which are important for a number of reasons, including understanding the potential for land management to remove CO₂ from the atmosphere and understanding the processes responsible for the sink for carbon on land. In contrast to the net fluxes of carbon, which are constrained by the global carbon budget, the gross fluxes are largely unconstrained, suggesting that there is more uncertainty than commonly believed about how terrestrial carbon emissions will respond to future fossil fuel emissions and a changing climate.