SYNTAX: a rule-based stochastic simulation of the time-varying concentrations of positional isotopomers of metabolic intermediates

A mathematical model of compartmentalized neurotransmitter metabolism in the human brain

After administration of enriched [1-13C]glucose, the rate of 13C label incorporation into glutamate C4, C3, and C2, glutamine C4, C3, and C2, and aspartate C2 and C3 was simultaneously measured in six normal subjects by 13C NMR at 4 Tesla in 45-ml volumes encompassing the visual cortex. The resulting eight time courses were simultaneously fitted to a mathematical model. The rate of (neuronal) tricarboxylic acid cycle flux (V(PDH)), 0.57 +/- 0.06 micromol. g(-1). min(-1), was comparable to the exchange rate between (mitochondrial) 2-oxoglutarate and (cytosolic) glutamate (Vx), 0.57 +/- 0.19 micromol. g(-1). min(-1)), which may reflect to a large extent malate-aspartate shuttle activity. At rest, oxidative glucose consumption [CMR(Glc(ox))] was 0.41 +/- 0.03 miccromol. g(-1). min(-1), and (glial) pyruvate carboxylation (VPC) was 0.09 +/- 0.02 micromol. g(-1). min(-1). The flux through glutamine synthetase (Vsyn) was 0.26 +/- 0.06 micromol. g(-1). min(-1). A fraction of Vsyn was attributed to be from (neuronal) glutamate, and the corresponding rate of apparent glutamatergic neurotransmission (VNT) was 0.17 +/- 0.05 micromol. g(-1). min(-1). The ratio [VNT/CMR(Glcox)] was 0.41 +/- 0.14 and thus clearly different from a 1:1 stoichiometry, consistent with a significant fraction (approximately 90%) of ATP generated in astrocytes being oxidative. The study underlines the importance of assumptions made in modeling 13C labeling data in brain.

Methodology for measuring in vitro/ex vivo cardiac energy metabolism

The high energy demands of the heart are met primarily by the metabolism of fatty acids and carbohydrates. These energy substrates are efficiently and rapidly metabolized in order to produce the high levels of adenosine triphosphate (ATP) necessary to sustain both contractile activity and other cellular functions. Alterations in energy metabolism contribute to abnormal heart function in many cardiac diseases. As a result, a number of techniques have been developed to directly measure energy metabolism in the heart in order to study energy metabolism. Two important variables that must be considered when making these measurements are energy substrate supply to the heart and the metabolic demand of the heart (i.e. contractile function). The use of the in vitro/ex vivo heart, perfused with relevant energy substrates, is a useful experimental approach that accounts for these variables. This paper overviews a number of the techniques that are used to measure energy substrate metabolism in the isolated perfused heart. Recently developed technology that allows for the direct measurement of energy metabolism in an isolated working mouse heart preparation are also described.

Metabolic flux analysis: a powerful tool for monitoring tissue function

In recent years, metabolic flux analysis has been widely used in bioprocess engineering to monitor cell viability and improve strain activity. Metabolic flux analysis refers to a methodology for investigating cellular metabolism whereby intracellular fluxes are calculated using a stoichiometric model for the major intracellular reactions and applying mass balances around intracellular metabolites. A powerful feature of this methodology is its ability to consider cellular biochemistry in terms of reaction networks. By considering the stoichiometry of biochemical reactions, it is possible to estimate the degree of engagement of each pathway participating in overall cellular activity, and hence obtain a comprehensive view of a cell s metabolic state. Given the potential impact of cellular energy metabolism on the function of engineered tissues, such comprehensive analysis of metabolic activity can be an extremely useful tool for tissue engineers. Estimates of intracellular fluxes under various environmental conditions could be used to optimize function in vivo as well as culture conditions in vitro. In this review, we provide a brief theoretical background of metabolic flux analysis and summarize the most widely used experimental approaches to obtain flux data. This review is intended as an overview of the field and as a starting point for tissue engineers wishing to learn about and eventually employ this methodology.

Computation with the KEGG pathway database

We introduce and discuss a new computational approach towards prediction and inference of biological functions from genomic sequences by making use of the pathway data in KEGG. Due to its piecewise nature, the current approach of predicting each gene function based on sequence similarity searches often fails to reconstruct cellular functions with all necessary components. The pathway diagram in KEGG, which may be considered a wiring diagram of molecules in biological systems, can be utilised as a reference for functional reconstruction. KEGG also contains binary relations that represent molecular interactions and relations and that can be utilised for computing and comparing pathways.

Improved estimation of anaplerosis in heart using 13C NMR

Anaplerotic enzymes, such as pyruvate carboxylase or malic enzyme, catalyze reactions that fill up the pools of the citric acid cycle (CAC), thereby increasing the total mass of CAC intermediates. Relative anaplerosis (y) denotes the ratio of anaplerotic flux to the flux catalyzed by citrate synthase. We examine conventional methods [C. R. Malloy, A. D. Sherry, and F. M. H. Jeffrey. J. Biol. Chem. 263:6964-6971, 1988; C. R. Malloy, A. D. Sherry, and F. M. H. Jeffrey. Am. J. Physiol. 259 (Heart Circ. Physiol. 28): H987-H995, 1990] of measurement of y using 13C-labeled precursors and analysis of [13C]glutamate labeling by nuclear magnetic resonance (NMR) spectroscopy. Through mathematical analysis and computer simulation, we show that isotopic enrichment of the pool of pyruvate that is substrate for anaplerosis will severely decrease the accuracy of estimates of y made with conventional methods no matter how small the mass of the pool of pyruvate. Suppose that the recycling parameter R denotes the fraction of molecules of pyruvate that contain carbons derived from intermediates of the CAC. Each means of estimation of relative anaplerosis in the peer-reviewed literature assumes that R = O, although this assumption has not been confirmed by experiment. We show that conventional formulas, using either fractional enrichments of carbons or isotopomer analysis, actually estimate at most y.(1 - R) instead of y during administration of [2-13C]acetate and unlabeled pyruvate. Using a new formula for estimation of y, we recalculate values of y from the literature and find them approximately 50% too low. We assume that all anaplerosis is via pyruvate and that the difference in isotopic enrichment between cytosolic and mitochondrial malate is negligible.

Numerical isotopomer analysis: estimation of metabolic activity

The use of stable isotopes to analyze intracellular metabolism is a powerful technique because of the wealth of information contained in the distribution of isotopes in key metabolites. We present a new numerical method of using measurements of isotope isomer (isotopomer) distributions to calculate the fluxes through a biochemical reaction network. Nuclear magnetic resonance (NMR) and/or mass spectroscopy can quantify the isotopomers which result from the metabolism of an isotopically enriched substrate. These data can be analyzed via a numerical model of the metabolic network which uses atom-mapping matrices to simplify model construction. The atom-mapping matrices describe the transfer of atoms from reactant to product and the resulting isoopomer balance equations are compact and intuitive. These equations are solved iteratively to determine the unknown intracellular fluxes. Results from the numerical method agreed with an analytical solution developed for the analysis of the tricarboxylic acid cycle in perfused hearts.

Calculation of absolute metabolic flux and the elucidation of the pathways of glutamate labeling in perfused rat heart by 13C NMR spectroscopy and nonlinear least squares analysis

Absolute metabolic fluxes in isolated perfused hearts have been determined by a nonlinear least squares analysis of glutamate labeling kinetics from [1-13C]glucose, [4-13C]beta-hydroxybutyrate, or [2-13C]acetate using 13C NMR spectroscopy. With glucose as substrate, the malate-aspartate shuttle flux was too slow to account for the reducing equivalents generated by glycolysis and to predict the observed oxygen consumption rate. For acetate and beta-hydroxybutyrate, the malate-aspartate shuttle had to be reversed for the network to agree with the observed oxygen consumption and glutamate labeling. Thus, an additional redox shuttle was required to reoxidize the NADH produced by cytoplasmic malate dehydrogenase. Using this model there was good agreement between the experimentally determined oxygen consumption and glutamate labeling and the calculated values of these parameters from the model for all substrates. The contribution of exogenous substrate to the overall tricarboxylic acid (TCA) cycle flux, 89.6 +/- 6.5% (mean +/- S.D.) as measured in the tissue extracts compared well with 91.4 +/- 4.2% calculated by the model. The ratio of TCA cycle flux to oxygen consumption for acetate, was 2.2 +/- 0.1, indicating that NADH production is principally accounted for by TCA cycle flux. For glucose or beta-hydroxybutyrate, this ratio was 2.9 +/- 0.2, consistent with the existence of other NADH producing reactions (e.g. glycolysis, beta-hydroxybutyrate oxidation).

Estimation of TCA cycle flux, aminotransferase flux, and anaplerosis in heart: validation with syntactic model

Weiss et al. (Circ. Res. 70: 392-408, 1992) proposed a model of the citric acid cycle (CAC) in myocytes and a system of 17 differential equations that can be used to describe the changes over time in enrichment of carbons C-2 and C-4 of glutamate under conditions of metabolic steady state. They also proposed an empirical measure (KT) of flux through the CAC, which has been shown to be correlated to O2 consumption in rat hearts perfused with acetate or a mixture of glucose and acetate. We report a new method for estimation of the absolute rate of the flux through the CAC in heart (vTCA), without the numerical solution of differential equations. Unlike KT, our estimate is equal to the rate of flux catalyzed by the alpha-ketoglutarate dehydrogenase complex (vTCA), not merely correlated with it. We also estimate the rate of flux catalyzed by aspartate aminotransferase (vTA) and by NADP(+)-dependent malic enzyme (an anaplerotic reaction). The formula for vTCA during administration of [2-13C]acetate is as follows: vTCA = M[(C-2ssLC-4)/[C-4ss(LC-4-LC-2)]], where C-2ss and C-4ss represent steady-state fractional enrichment, LC-2 and LC-4 represent dominant rate constants of C-2 and C-4 of glutamate, respectively, and M is the sum of concentrations of aspartate, glutamate, and intermediates of the CAC. The assumptions underlying our formula are as follows: 1) metabolic steady state is maintained, 2) exchange of molecules between cytosolic and mitochondrial compartments is rapid, 3) 13C enters pools of the CAC only from acetyl CoA via citrate synthase, 4) [citrate]/[glutamate] < 1 + (vTCA/vTA), and 5) (m-[glutamate])/M < C-2ss/C-4ss.