The following figure illustrates the sequential labeling of the carbons of intermediates of the citric acid cycle supplied with 100% enriched 3-¹³C-pyruvate (abbreviated P3). This figure is adapted from: Stephanopoulos, G.N., Aristidou, A.A. and Nielsen, J. (1998) "Metabolic Engineering: Principles and Methodologies", Academic Press, San Diego, CA. Abbreviations used are: P = pyruvate, Ac = acetyl-CoA, C = citrate, K = ketoglutarate (2-oxoglutarate), S = succinate, M = malate, O = oxaloacetate. For simplicity, isocitrate and fumarate are omitted from the cycle. Green arrows represent reaction steps generating ¹²CO₂. Blue arrows represent reaction steps generating ¹³CO₂. Numbers adjacent to intermediate symbols refer to the individual isotopomer of each intermediate. Thus, O represents unlabeled oxaloacetate, and O123 represents oxaloacetate labeled in the 1, 2 and 3 positions. Note that in the conversion of 3-¹³C-pyruvate to acetyl-CoA (catalyzed by pyruvate dehydrogenase) ¹²CO₂ is lost, yielding acetyl-CoA labeled in the carbon 2 position (AcCoA2 = Ac2).

It is assumed that the reverse reactions from oxaloacetate to fumarate are very rapid in comparison to the reaction of citrate synthase, resulting in full symmetrical equilibration of label between carbons 1 and 4, and between carbons 2 and 3 in oxaloacetate, malate and fumarate. Thus, O3 is assumed to be in rapid equilibrium with O2 (Stephanopoulos et al., 1998). For these reasons, oxalacetate, malate and fumarate can be considered as a single intermediate.

The following images show time-courses of labeling of the various intermediates of the cycle, assuming the pool sizes and fluxes specified in the text boxes. Note that in these simulations, no removal of oxaloacetate or ketoglutarate in aspartate or glutamate synthesis, respectively, is envisaged.

Removal of oxaloacetate or ketoglutarate from the cycle in amino acid biosynthesis (i.e. aspartate (Asp) or glutamate (Glu) synthesis, respectively) can be compensated by the anaplerotic reaction catalyzed by pyruvate carboxylase that combines pyruvate with CO₂ to produce oxaloacetate to sustain the cycle (Stephanopoulos et al., 1998).

If a ¹³CO₂ is fixed in this reaction, the product would be oxaloacetate labeled in the carbon 3 and carbon 4 positions (O34). If a ¹²CO₂ is fixed in this reaction, the product would be oxaloacetate labeled only in the carbon 3 position (O3). As noted earlier, it is assumed that the reverse reactions from oxaloacetate to fumarate are very rapid in comparison to the reaction of citrate synthase, resulting in full symmetrical equilibration of label between carbons 1 and 4, and between carbons 2 and 3 in oxaloacetate, malate and fumarate. Thus, O34 is assumed to be in rapid equilibrium with O12, and O3 is assumed to be in rapid equilibrium with O2 (Stephanopoulos et al., 1998).

When Ac2 combines with O34 this yields citrate labeled in carbons 1, 2 and 4 (C124), which in turn generates ketoglutarate labeled in carbons 1, 2 and 4 (K124), generating succinate labeled in carbons 1 and 3 (S13) plus ¹³CO₂. S13 then generates equal amounts of fumarate labeled in carbons 1 and 3 or carbons 2 and 4 (not shown) that produce, respectively, M13 and M24 in equal proportions, and hence O13 and O24 in equal proportions.

When Ac2 combines with O12 this yields citrate labeled in carbons 3, 4 and 6 (C346), which in turn generates ketoglutarate labeled in carbons 3 and 4 (K34) plus ¹³CO₂. K34 generates succinate labeled in carbons 2 and 3 (S23) plus ¹²CO₂. S23 then generates fumarate labeled in carbons 2 and 3 (not shown) that produces M23, and hence O23.

Similarly, when Ac2 combines with O3 this yields citrate labeled in carbons 2 and 4 (C24), which in turn generates ketoglutarate labeled in carbons 2 and 4 (K24), generating succinate labeled in carbons 1 and 3 (S13) plus ¹²CO₂. As before, S13 then generates equal amounts of fumarate labeled in carbons 1 and 3 or carbons 2 and 4 (not shown) that produce, respectively, M13 and M24 in equal proportions, and hence O13 and O24 in equal proportions.

When Ac2 combines with O2 this yields citrate labeled in carbons 3 and 4 (C34), which in turn generates ketoglutarate labeled in carbons 3 and 4 (K34) plus ¹²CO₂, generating succinate labeled in carbons 2 and 3 (S23) plus ¹²CO₂. S23 then generates fumarate labeled in carbons 2 and 3 (not shown) that produces M23, and hence O23.

Subsequent turns of the cycle using O13, O24, and O23 as substrates generate the additional isotopomers depicted above.

The time-courses of changes in relative abundance and absolute amounts of isotopomers of citrate, ketoglutarate, succinate, malate and oxaloacetate are simulated in the following 5 figures. Here the fluxes to aspartate and glutamate are each assumed to be 100 nmol.h^-1.gfw^-1 and this is exactly balanced by a flux via pyruvate carboxylase of 200 nmol.h^-1.gfw^-1, and the ¹³CO₂ abundance of the system is assumed to be at a fixed abundance of 0% [i.e. the ¹²CO₂ and ¹³CO₂ generated by the modeled enzyme system is replaced with a CO₂ source of defined ¹³C abundance, here arbitrarily set to 0%].

The above simulations should be compared with model output when the ¹³CO₂ abundance of the system is assumed to be at a fixed abundance of 100%

The assumed precursor-product relationships assumed in the model depicted above, are shown below:

P3 --> Ac2 + 12CO2
P --> Ac + 12CO2


P3 + 13CO2 --> O34 + O12 <--> M34 + M12
P3 + 12CO2 --> O3 + O2 <--> M3 + M2
P + 13CO2 --> O4 + O1 <--> M4 + M1
P + 12CO2 --> O <--> M


O + Ac --> C --> K + 12CO2 --> S + 12CO2 --> M <--> O
O + Ac2 --> C4 --> K4 + 12CO2 --> S3 + 12CO2 --> M3 + M2 <--> O3 + O2
O2 + Ac --> C3 --> K3 + 12CO2 ---> S2 + 12CO2 --> M3 + M2 <--> O3 + O2
O2 + Ac2 --> C34 --> K34 + 12CO2 --> S23 + 12CO2 --> M23 <--> O23
O3 + Ac ---> C2 --> K2 + 12CO2 --> S1 + 12CO2 --> M1 + M4 <--> O1 + O4
O3 + Ac2 --> C24 --> K24 + 12CO2 --> S13 + 12CO2 --> M13 + M24 <--> O13 + O24
O1 + Ac --> C6 --> K + 13CO2 --> S + 12CO2 --> M <--> O
O1 + Ac2 --> C46 --> K4 + 13CO2 --> S3 + 12CO2 --> M3 + M2 <--> O3 + O2
O4 + Ac --> C1 --> K1 + 12CO2 --> S + 13CO2 --> M <--> O
O4 + Ac2 --> C14 --> K14 + 12CO2 --> S3 + 13CO2 --> M3 + M2 <--> O3 + O2
O23 + Ac --> C23 --> K23 + 12CO2 --> S12 + 12CO2 --> M12 + M34 <--> O12 + O34
O23 + Ac2 --> C234 --> K234 + 12CO2 --> S123 + 12CO2 --> M123 + M234 <--> O123 + O234
O13 + Ac --> C26 --> K2 + 13CO2 --> S1 + 12CO2 --> M1 + M4 <--> O1 + O4
O13 + Ac2 --> C246 --> K24 + 13CO2 --> S13 + 12CO2 --> M13 + M24 <--> O13 + O24
O24 + Ac --> C13 --> K13 + 12CO2 --> S2 + 13CO2 --> M3 + M2 <--> O3 + O2
O24 + Ac2 --> C134 --> K134 + 12CO2 --> S23 + 13CO2 --> M23 <--> O23
O12 + Ac --> C36 --> K3 + 13CO2 --> S2 + 12CO2 --> M2 + M3 <--> O2 + O3
O12 + Ac2 --> C346 --> K34 + 13CO2 --> S23 + 12CO2 --> M23 <--> O23
O34 + Ac --> C12 --> K12 + 12CO2 --> S1 + 13CO2 --> M1 + M4 <--> O1 + O4
O34 + Ac2 --> C124 --> K124 + 12CO2 --> S13 + 13CO2 --> M13 + M24 <--> O13 + O24
O123 + Ac --> C236 --> K23 + 13CO2 --> S12 + 12CO2 --> M12 + M34 <--> O12 + O34
O123 + Ac2 --> C2346 --> K234 + 13CO2 --> S123 + 12CO2 --> M123 + M234 <--> O123 + O234
O234 + Ac --> C123 --> K123 + 12CO2 --> S12 + 13CO2 --> M12 + M34 <--> O12 + O34
O234 + Ac2 --> C1234 --> K1234 + 12CO2 --> S123 + 13CO2 --> M123 + M234 <--> O123 + O234

The simple mathematical operations that generate these simulations are illustrated below, using citrate as the example. Each possible isotopomer of citrate produced during either the "pulse" or the "chase" (including the unlabeled species C) is enumerated. The pool size of each citrate isotopomer can initially expand due to synthesis during each iteration (z), depending upon the probability of utilizing unlabeled acetyl-CoA (PuAc) or acetyl-CoA labeled in the carbon 2 position (PuA2) [where PuAc + PuAc2 = 1], the probability of utilizing the various isotopomers of oxaloacetate (e.g. PuO (unlabeled), PuO2, PuO3 .... PuO234; where PuO + PuO2 + PuO3 + .... + PuO234 = 1), and the citrate synthase reaction rate (CS).

C = C + (PuO * z * CS * PuAc)
C4 = C4 + (PuO * z * CS * PuAc2)
C3 = C3 + (PuO2 * z * CS * PuAc)
C34 = C34 + (PuO2 * z * CS * PuAc2)
C2 = C2 + (PuO3 * z * CS * PuAc)
C24 = C24 + (PuO3 * z * CS * PuAc2)
C6 = C6 + (PuO1 * z * CS * PuAc)
C46 = C46 + (PuO1 * z * CS * PuAc2)
C1 = C1 + (PuO4 * z * CS * PuAc)
C14 = C14 + (PuO4 * z * CS * PuAc2)
C23 = C23 + (PuO23 * z * CS * PuAc)
C234 = C234 + (PuO23 * z * CS * PuAc2)
C26 = C26 + (PuO13 * z * CS * PuAc)
C246 = C246 + (PuO13 * z * CS * PuAc2)
C13 = C13 + (PuO24 * z * CS * PuAc)
C134 = C134 + (PuO24 * z * CS * PuAc2)
C36 = C36 + (PuO12 * z * CS * PuAc)
C346 = C346 + (PuO12 * z * CS * PuAc2)
C12 = C12 + (PuO34 * z * CS * PuAc)
C124 = C124 + (PuO34 * z * CS * PuAc2)
C236 = C236 + (PuO123 * z * CS * PuAc)
C2346 = C2346 + (PuO123 * z * CS * PuAc2)
C123 = C123 + (PuO234 * z * CS * PuAc)
C1234 = C1234 + (PuO234 * z * CS * PuAc2)

TotC = C + C1 + C2 + C3 + C4 + C6 + C12 + C13 + C14 + C123 + C124 + C1234 + C134 + C23 + C24 + C26 + C234 + C236 + C246 + C2346 + C34 + C36 + C346 + C46

PuC = C / TotC
PuC1 = C1 / TotC
PuC2 = C2 / TotC
PuC3 = C3 / TotC
PuC4 = C4 / TotC
PuC6 = C6 / TotC
PuC12 = C12 / TotC
PuC13 = C13 / TotC
PuC14 = C14 / TotC
PuC123 = C123 / TotC
PuC124 = C124 / TotC
PuC1234 = C1234 / TotC
PuC134 = C134 / TotC
PuC23 = C23 / TotC
PuC24 = C24 / TotC
PuC26 = C26 / TotC
PuC234 = C234 / TotC
PuC236 = C236 / TotC
PuC246 = C246 / TotC
PuC2346 = C2346 / TotC
PuC34 = C34 / TotC
PuC36 = C36 / TotC
PuC346 = C346 / TotC
PuC46 = C46 / TotC

C = C - (PuC * z * CS)
C1 = C1 - (PuC1 * z * CS)
C2 = C2 - (PuC2 * z * CS)
C3 = C3 - (PuC3 * z * CS)
C4 = C4 - (PuC4 * z * CS)
C6 = C6 - (PuC6 * z * CS)
C12 = C12 - (PuC12 * z * CS)
C13 = C13 - (PuC13 * z * CS)
C14 = C14 - (PuC14 * z * CS)
C123 = C123 - (PuC123 * z * CS)
C124 = C124 - (PuC124 * z * CS)
C1234 = C1234 - (PuC1234 * z * CS)
C134 = C134 - (PuC134 * z * CS)
C23 = C23 - (PuC23 * z * CS)
C24 = C24 - (PuC24 * z * CS)
C26 = C26 - (PuC26 * z * CS)
C234 = C234 - (PuC234 * z * CS)
C236 = C236 - (PuC236 * z * CS)
C246 = C246 - (PuC246 * z * CS)
C2346 = C2346 - (PuC2346 * z * CS)
C34 = C34 - (PuC34 * z * CS)
C36 = C36 - (PuC36 * z * CS)
C346 = C346 - (PuC346 * z * CS)
C46 = C46 - (PuC46 * z * CS)

TotC = C + C1 + C2 + C3 + C4 + C6 + C12 + C13 + C14 + C123 + C124 + C1234 + C134 + C23 + C24 + C26 + C234 + C236 + C246 + C2346 + C34 + C36 + C346 + C46

The Visual Basic 5.0 program "tcap3" for simulating this pathway is available upon request from David Rhodes (drhodes@purdue.edu).