Determination of the fluxes in the central metabolism of Corynebacterium glutamicum by nuclear magnetic resonance spectroscopy combined with metabolite balancing

To determine the in vivo fluxes of the central metabolism we have developed a comprehensive approach exclusively based on the fundamental enzyme reactions known to be present, the fate of the carbon atoms of individual reactions, and the metabolite balance of the culture. No information on the energy balance is required, nor information on enzyme activities, or the directionalities of reactions. Our approach combines the power of (1)H-detected (13)C nuclear magnetic resonance spectroscopy to follow individual carbons with the simplicity of establishing carbon balances of bacterial cultures. We grew a lysine-producing strain of Corynebacterium glutamicum to the metabolic and isotopic steady state with [1-(13)C]glucose and determined the fractional enrichments in 27 carbon atoms of 11 amino acids isolated from the cell. Since precursor metabolites of the central metabolism are incorporated in an exactly defined manner in the carbon skeleton of amino acids, the fractional enrichments in carbons of precursor metabolites (oxaloacetate, glyceraldehyde 3-phosphate, erythrose 4-phosphate, etc.) became directly accessible. A concise and generally applicable mathematical model was established using matrix calculus to express all metabolite mass and carbon labeling balances. An appropriate all-purpose software for the iterative solution of the equations is supplied. Applying this comprehensive methodology to C. glutamicum, all major fluxes within the central metabolism were determined. The result is that the flux through the pentose phosphate pathway is 66.4% (relative to the glucose input flux of 1.49 mmol/g dry weight h), that of entry into the tricarboxylic acid cycle 62.2%, and the contribution of the succinylase pathway of lysine synthesis 13.7%. Due to the large amount and high quality of measured data in vivo exchange reactions could also be quantitated with particularly high exchange rates within the pentose phosphate pathway for the ribose 5-phosphate transketolase reaction. Moreover, the total net flux of the anaplerotic reactions was quantitated as 38.0%. Most importantly, we found that in vivo one component within these anaplerotic reactions is a back flux from the carbon 4 units of the tricarboxylic acid cycle to the carbon 3 units of glycolysis of 30.6%. (c) 1996 John Wiley & Sons, Inc.

influx_s: increasing numerical stability and precision for metabolic flux analysis in isotope labelling experiments

MOTIVATION

The problem of stationary metabolic flux analysis based on isotope labelling experiments first appeared in the early 1950s and was basically solved in early 2000s. Several algorithms and software packages are available for this problem. However, the generic stochastic algorithms (simulated annealing or evolution algorithms) currently used in these software require a lot of time to achieve acceptable precision. For deterministic algorithms, a common drawback is the lack of convergence stability for ill-conditioned systems or when started from a random point.

RESULTS

In this article, we present a new deterministic algorithm with significantly increased numerical stability and accuracy of flux estimation compared with commonly used algorithms. It requires relatively short CPU time (from several seconds to several minutes with a standard PC architecture) to estimate fluxes in the central carbon metabolism network of Escherichia coli.

AVAILABILITY

The software package influx_s implementing this algorithm is distributed under an OpenSource licence at http://metasys.insa-toulouse.fr/software/influx/.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

New time-scale criteria for model simplification of bio-reaction systems

Background

Quasi-steady state approximation (QSSA) based on time-scale analysis is known to be an effective method for simplifying metabolic reaction system, but the conventional analysis becomes time-consuming and tedious when the system is large. Although there are automatic methods, they are based on eigenvalue calculations of the Jacobian matrix and on linear transformations, which have a high computation cost. A more efficient estimation approach is necessary for complex systems.

Results

This work derived new time-scale factor by focusing on the problem structure. By mathematically reasoning the balancing behavior of fast species, new time-scale criteria were derived with a simple expression that uses the Jacobian matrix directly. The algorithm requires no linear transformation or decomposition of the Jacobian matrix, which has been an essential part for previous automatic time-scaling methods. Furthermore, the proposed scale factor is estimated locally. Therefore, an iterative procedure was also developed to find the possible multiple boundary layers and to derive an appropriate reduced model.

Conclusion

By successive calculation of the newly derived time-scale criteria, it was possible to detect multiple boundary layers of full ordinary differential equation (ODE) models. Besides, the iterative procedure could derive the appropriate reduced differential algebraic equation (DAE) model with consistent initial values, which was tested with simple examples and a practical example.

The thermodynamic meaning of metabolic exchange fluxes

Metabolic flux analysis (MFA) deals with the experimental determination of steady-state fluxes in metabolic networks. An important feature of the (13)C MFA method is its capability to generate information on both directions of bidirectional reaction steps given by exchange fluxes. The biological interpretation of these exchange fluxes and their relation to thermodynamic properties of the respective reaction steps has never been systematically investigated. As a central result, it is shown here that for a general class of enzyme reaction mechanisms the quotients of net and exchange fluxes measured by (13)C MFA are coupled to Gibbs energies of the reaction steps. To establish this relation the concept of apparent flux ratios of enzymatic isotope-labeling networks is introduced and some computing rules for these flux ratios are given. Application of these rules reveals a conceptional pitfall of (13)C MFA, which is the inherent dependency of measured exchange fluxes on the chosen tracer atom. However, it is shown that this effect can be neglected for typical biochemical reaction steps under physiological conditions. In this situation, the central result can be formulated as a two-sided inequality relating fluxes, pool sizes, and standard Gibbs energies. This relation has far-reaching consequences for metabolic flux analysis, quantitative metabolomics, and network thermodynamics.

Carbohydrate cycling in micro-organisms: what can (13)C-NMR tell us?

The extension of (13)C-nuclear magnetic resonance (NMR) techniques to study cellular metabolism over recent years has provided valuable data supporting the occurrence, diversity and extent of carbon cycling in the carbohydrate metabolism of micro-organisms. The occurrence of such cycles, resulting from the simultaneous operation of different and sometimes opposite individual steps, is inherently related to the network organisation of cellular metabolism. These cycles are tentatively classified here as 'reversibility', 'metabolic' and 'substrate' cycles on the basis of their balance in carbon and cofactors. Current hypotheses concerning the physiological relevance of carbohydrate cycles are discussed in light of the (13)C-NMR data. They most likely represent system-level mechanisms for coherent and timely partitioning of carbon resources to fit with the various biosynthetic, energetic or redox needs of cells and/or additional strategies in the adaptive capacity of micro-organisms to face variation in environmental conditions.

Relevance and isotopic assessment of hexose-6-phosphate recycling in micro-organisms

Some pathways of hexose-6-phosphate recycling--those involving a breakdown of the hexose skeleton--through carbohydrate metabolism of micro-organisms were analyzed for both metabolic and isotopic effects. Two modes of recycling were proposed based on the degree of alteration of the hexose molecule through the catabolic part of the cycle. Simulated operation of most of these pathways resulted in increased synthesis of hexose-6-phosphate and NADPH, and reduced the NADH and moreover the ATP synthesis within the carbohydrate metabolism. A basic model for the quantitative assessment by means of isotopic studies of the processes of hexose-6-phosphate recycling is presented. The model was initially designed for the study of micro-organisms producing polysaccharides, but it can be extended to other situations.

Cyclic organization of the carbohydrate metabolism in Sinorhizobium meliloti

The pathways of polysaccharide biosynthesis were investigated in cells of Sinorhizobium meliloti (strain Su47) using a stable isotope approach. The isotopic labeling of the periplasmic beta-1,2-glucans synthesized from glucose labeled at various positions evidenced the involvement of catabolic pathways, namely the pentose-phosphate and Entner-Doudoroff pathways, into the early steps of polysaccharide synthesis. The exopolysaccharides produced at the same time had a labeling pattern similar to that of the beta-glucans, indicating similar early steps for both polysaccharides. The results emphasized a cyclic organization of the carbohydrate metabolism in S. meliloti, in which the carbons of the initial hexose were allowed to re-enter the catabolic pathways many times. The metabolic incidences of such metabolic topology are discussed.

In vivo stationary flux analysis by 13C labeling experiments

Stationary flux analysis is an invaluable tool for metabolic engineering. In the last years the metabolite balancing technique has become well established in the bioengineering community. On the other hand metabolic tracer experiments using 13C isotopes have long been used for intracellular flux determination. Only recently have both techniques been fully combined to form a considerably more powerful flux analysis method. This paper concentrates on modeling and data analysis for the evaluation of such stationary 13C labeling experiments. After reviewing recent experimental developments, the basic equations for modeling carbon labeling in metabolic systems, i.e. metabolite, carbon label and isotopomer balances, are introduced and discussed in some detail. Then the basics of flux estimation from measured extracellular fluxes combined with carbon labeling data are presented and, finally, this method is illustrated by using an example from C. glutamicum. The main emphasis is on the investigation of the extra information that can be obtained with tracer experiments compared with the metabolite balancing technique alone. As a principal result it is shown that the combined flux analysis method can dispense with some rather doubtful assumptions on energy balancing and that the forward and backward flux rates of bidirectional reaction steps can be simultaneously determined in certain situations. Finally, it is demonstrated that the variant of fractional isotopomer measurement is even more powerful than fractional labeling measurement but requires much higher numerical effort to solve the balance equations.

Metabolic flux determination in C6 glioma cells using carbon-13 distribution upon [1-13C]glucose incubation

A mathematical model of mammalian cell intermediary metabolism is presented. It describes the distribution of the carbon-13 isotope (13C) at the different carbon positions of metabolites in cells fed with 13C-enriched substrates. The model allows the determination of fluxes through different metabolic pathways from 13C- and 1H-NMR spectroscopy and mass spectrometry data. The considered metabolic network includes glycolysis, gluconeogenesis, the citric acid cycle and a number of reactions corresponding to protein or fatty acid metabolism. The model was used for calculating metabolic fluxes in a rat tumor cell line, the C6 glioma, incubated with [1-13C]glucose. After evolution to metabolic and isotopic steady states, the intracellular metabolites were extracted with perchloric acid. The specific enrichments of glutamate, aspartate and alanine carbons were determined from 13C-, 1H-NMR spectroscopy, or mass spectrometry data. Taking into account the rate of glucose consumption and of lactate formation, determined from the evolution of glucose and lactate contents in the cell medium, and knowing the activity of the hexose monophosphate shunt, it was possible to estimate the absolute values of all the considered fluxes. From the analysis the following results were obtained. (a) Glucose accounts for about 78% of the pyruvate and 57% of the CoASAc. (b) A metabolic channelling occurs at the citric acid cycle level; it favours the conversion of carbons 2, 3, 4, and 5 of 2-oxoglutarate into carbons 1, 2, 3, and 4 of oxaloacetate, respectively. The percentage of channelled metabolites amounts to 39%. (c) The pyruvate carboxylase activity and the efflux from the citric acid cycle are estimated to be very low, suggesting a lack of glutamine production in C6 cells. The results emphasize different metabolic characteristics of C6 cells when compared to astrocytes, their normal counterpart.