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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. glucose. pyruvate. phosphoenolpyruvate. acetyl -CoA. oxaloacetate. - PowerPoint PPT Presentation
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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