Syntactic Model of Metabolic Pathways

Positional Isotopomers of Pyruvate

C OO-

OCCH3

C OO-

OCCH3

C OO-

OCCH3

C OO-

OCCH3

C OO-

OCCH3

C OO-

OCCH3

C OO-

OCCH3

C OO-

OCCH3

13

13

13

13

13

13

13

13

13

13

13

13

Citric Acid Cycle, IllustratingFlow of Atoms from Acetyl CoA

a c e t y l - C o Am a l a t e o x a l o a c e t a t e

a s p a r t a t e g l u t a m a t e

- k e t o g l u t a r a t e

c i t r a t e

s u c c i n a t ef u m a r a t e

1

a

b

2

3

b

1

4

4

4

a

a

bc

d

ef

ef

Isotopomers of Citric Acid Cycle Intermediates Produced from [2-13C]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: [2-13C]acetate)

[4-13C]citrate [3,4-13C]citrate [2,4-13C]citrate

[2,3,4-13C]citrate [1,3,4-13C]citrate [2,4,6-13C]citrate

Three Turns

One turn Two Turns

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

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

C5

C1 C2 C4 C3

Computer Simulation of Fractional Enrichment of Computer Simulation of Fractional Enrichment of Carbons of Glutamate in Heart (substrate: [2-Carbons of Glutamate in Heart (substrate: [2-1313C]acetate)C]acetate)

Computer Simulation of Isotopomers of Glutamate Present in Perfused Heart During Administration of [2-13C]acetate

0.00 1.07 2.14 3.20 4.27 5.34

Time (min)

0.00

0.20

0.40

0.60

0.80

1.00

Mol

e F

ract

ion[---] [4-13C]- [3,4-13C] [2,4-13C]

[2,3,4-13C] [1,3,4-13C] [1,2,3,4-13C]-

Computer Simulation of Isotopomers of Glutamate Present in Perfused Heart During Administration of [2-13C]acetate

0 11 21 32 43 54

Time (min)

0.00

0.20

0.40

0.60

0.80

1.00

Mol

e F

ract

ion

[--] [4-13C] [3,4-13C] [2,4-13C]

[2,3,4-13C] [1,3,4-13C] [1,2,3,4-13C]

Syntactic Model of Metabolic PathwaysSyntactic Model of Metabolic Pathways ProblemProblem

Writing differential equations for positional isotopomers of Writing differential equations for positional isotopomers of metabolic intermediates is time-consuming, complicated and metabolic intermediates is time-consuming, complicated and error-proneerror-prone

ResponseResponse Description of metabolic transformations by means of Description of metabolic transformations by means of

“syntactic rules”“syntactic rules” Stochastic simulation of a Poisson process model of chemical Stochastic simulation of a Poisson process model of chemical

kineticskinetics OutcomeOutcome

Monte Carlo simulation of time-dependent concentrations of Monte Carlo simulation of time-dependent concentrations of all positional isotopomers of each metabolic poolall positional isotopomers of each metabolic pool

Predicts multiplets and fractional enrichments observed with Predicts multiplets and fractional enrichments observed with NMR spectroscopyNMR spectroscopy

Simulation of the Citric Acid Cyclewith the Syntactic Model

OAA

AcCoA

citrate

synthase

KG

citrate

malate

OAA

AcCoA

citrate

synthase

KG

citrate

malate

Select a chemical

reaction.

Select reactant

molecules randomly,

from among all

other molecules of

the same species.

Syntactic rules

dictate the transfer

of atoms from

reactants to newly

formed product

molecules.

Syntactic Model: DetailsSyntactic Model: Details Variables of ModelVariables of Model

Concentration of each positional isotopomer Concentration of each positional isotopomer of each metaboliteof each metabolite

Simulation of Elapsed TimeSimulation of Elapsed Time Mean time of occurrence of next chemical Mean time of occurrence of next chemical

reaction is calculated from current rates of reaction is calculated from current rates of reactionsreactions

Uses a stochastic model of enzyme kinetics, Uses a stochastic model of enzyme kinetics, equivalent to integration of the Michaelis-equivalent to integration of the Michaelis-Menten equation for each enzyme.Menten equation for each enzyme.

Flowchart of Syntactic Simulation

Initialize unlabelled metabolic pools

Select flux

Break reactants into constituent

carbons and form products

Select reactant molecules

Add product molecules to appropriate pools

STOP

START

FINISHED ?

Syntactic Rule for Citrate Synthase

ab

citratesynthase

1

2

3

4

oxaloacetate citrate

COO¯

C=O

CH2

COO¯ COO¯

CH2

COO¯CHO

CH2

COO¯C - S-CoA

O

CH2 - 4

3

b

a

2 1

acetyl-CoA

Syntactic Rule for TransaldolaseSyntactic Rule for Transaldolase

sedoheptulose glyceraldehyde erythrose fructose

7-phosphate 3-phosphate 4-phosphate 6-phosphate

Transaldolase: Syntactic Rule Transaldolase: Syntactic Rule and Differential Equation for One Isotopomerand Differential Equation for One Isotopomer

+ [[1,3,4,6,7-13C ] S-7-P] + [[1,3,5,6,7-13C ] S-7-P] + [[1,3,4,5,6,7-13C ] S-7-P]

+ [[1,3,6,7- 1 3C ] S-7-P] + [[1,3,4,6- 1 3C ] S-7-P] + [[1,3,6- 1 3C ] S-7-P]

+ [[1,3,4,7- 13C ] S-7-P] + [[1,3,5,7- 13C ] S-7-P] + [[1,3,4,5,7- 13C ] S-7-P]

+ [[1,3,5,6-13C ] S-7-P] + [[1,3,4,5,6- 13C ] S-7-P] + [[1,3,7- 13C ] S-7-P]

+ [[1,3,4-13C ] S-7-P] + [[1,3,5- 13C ] S-7-P] + [[1,3,4,5- 13C ] S-7-P]

[[1,3,4,5- 1 3C ] F-6-P] = [[1,2- 1 3C ] G-3-P] [[1,3- 1 3C ] S-7-P]ddt

K {

}

Comparison: Syntactic Approach versus Conventional Approach

Syntactic DifferentialSyntactic Differential Rules EquationsRules Equations

Citric Acid Cycle 35 180Citric Acid Cycle 35 180

Pentose Phosphate Pathway 69 504Pentose Phosphate Pathway 69 504

Transaldolase 10 80Transaldolase 10 80

Comparison of Conventional and Syntactic Approaches to Prediction of Positional Isotopomers

of the Citric Acid Cycle

Isotopic Syntactic Differential Labels Rules Equations

1 35 180

2 35 359

3 35 6288

An Application of the Syntactic ModelAn Application of the Syntactic Model Testing and verification of formulas for estimating anaplerosis from isotopomer distributions

Anaplerosis: Chemical reactions that increase the mass of the chemical intermediates of the citric acid cycle Detection of underestimation in current formulas for Detection of underestimation in current formulas for

relative anaplerosisrelative anaplerosis Proposal of alternate formulas involving isotopomer Proposal of alternate formulas involving isotopomer

fractionsfractions Testing of new formulas, using computer simulationTesting of new formulas, using computer simulation Cohen and Bergman, Cohen and Bergman, Amer. J. PhysiolAmer. J. Physiol, 273:E1228-, 273:E1228-

42, 1997 42, 1997