1. Syntactic Model of Metabolic Pathways

2. Positional Isotopomers of Pyruvate

3. Citric Acid Cycle, Illustrating Flow of Atoms from Acetyl CoA

4. Isotopomers of Citric Acid Cycle Intermediates Produced from [2- 13 C]acetate pyruvate acetyl -CoA citrate fumarate malate oxaloacetate alpha-ketoglutarate phosphoenolpyruvate succinate glucose

5. Isotopomers of Citrate Produced By Successive Turns of the Citric Acid Cycle (substrate: [2- 13 C]acetate) [4- 13 C]citrate [3,4- 13 C]citrate [2,4- 13 C]citrate [2,3,4- 13 C]citrate [1,3,4- 13 C]citrate [2,4,6- 13 C]citrate Three Turns One turn Two Turns

6. Multiplets of Carbon C2 of Citrate Produced by 13 C-Labeling

7. 13 C-NMR Spectrum of [U- 13 C]glutamate C5 C1C2C4C3

8. Computer Simulation of Fractional Enrichment of Carbons of Glutamate in Heart (substrate: [2- 13 C]acetate)

9. Computer Simulation of Isotopomers of Glutamate Present in Perfused Heart During Administration of [2- 13 C]acetate [1,3,4- 13 C][1,2,3,4- 13 C]-

10. Computer Simulation of Isotopomers of Glutamate Present in Perfused Heart During Administration of [2- 13 C]acetate [1,3,4- 13 C][1,2,3,4- 13 C]

11. Syntactic Model of Metabolic Pathways ã Problem o Writing differential equations for positional isotopomers of metabolic intermediates is time-consuming, complicated and error-prone ã Response o Description of metabolic transformations by means of “syntactic rules” o Stochastic simulation of a Poisson process model of chemical kinetics ã Outcome o Monte Carlo simulation of time-dependent concentrations of all positional isotopomers of each metabolic pool o Predicts multiplets and fractional enrichments observed with NMR spectroscopy

12. Simulation of the Citric Acid Cycle with the Syntactic Model

13. Syntactic Model: Details ã Variables of Model o Concentration of each positional isotopomer of each metabolite ã Simulation of Elapsed Time o Mean time of occurrence of next chemical reaction is calculated from current rates of reactions o Uses a stochastic model of enzyme kinetics, equivalent to integration of the Michaelis- Menten equation for each enzyme.

14. Flowchart of Syntactic Simulation

15. Syntactic Rule for Citrate Synthase

16. Syntactic Rule for Transaldolase sedoheptuloseglyceraldehydeerythrosefructose 7-phosphate3-phosphate4-phosphate6-phosphate

17. Transaldolase: Syntactic Rule and Differential Equation for One Isotopomer

18. Comparison: Syntactic Approach versus Conventional Approach Syntactic Differential Syntactic Differential Rules Equations Rules Equations Citric Acid Cycle 35 180 Pentose Phosphate Pathway 69 504 Transaldolase 10 80

19. Comparison of Conventional and Syntactic Approaches to Prediction of Positional Isotopomers of the Citric Acid Cycle IsotopicSyntactic Differential LabelsRulesEquations 1 35180 2 35359 3 356288

20. An Application of the Syntactic Model ã ã Testing and verification of formulas for estimating anaplerosis from isotopomer distributions ã ã Anaplerosis: Chemical reactions that increase the mass of the chemical intermediates of the citric acid cycle o Detection of underestimation in current formulas for relative anaplerosis o Proposal of alternate formulas involving isotopomer fractions o Testing of new formulas, using computer simulation o Cohen and Bergman, Amer. J. Physiol, 273:E1228- 42, 1997