Syntactic Model of Metabolic Pathways

Positional Isotopomers of Pyruvate

Citric Acid Cycle, Illustrating Flow of Atoms from Acetyl CoA

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

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

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

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

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

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]-

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]

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

Simulation of the Citric Acid Cycle with the Syntactic Model

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.

Flowchart of Syntactic Simulation

Syntactic Rule for Citrate Synthase

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

Transaldolase: Syntactic Rule and Differential Equation for One Isotopomer

Comparison: Syntactic Approach versus Conventional Approach Syntactic Differential Syntactic Differential Rules Equations Rules Equations Citric Acid Cycle Pentose Phosphate Pathway Transaldolase 10 80

Comparison of Conventional and Syntactic Approaches to Prediction of Positional Isotopomers of the Citric Acid Cycle IsotopicSyntactic Differential LabelsRulesEquations

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:E , 1997