Purdue University Logo
Department of Horticulture and Landscape Architecture
 
Horticulture Home Page
Agriculture Home Page
Purdue Home Page
CFPESP Home Page
Computer Simulation of Metabolism Home Page
  • Introduction
  • Effects of Varying Rates and Pool Sizes - A Sample Program
  • Consideration of Multiple Compartments
  • Consideration of Cycles - The GS/GOGAT Cycle
  • Compounds Receiving Several 13C Atoms from 13CO2
  • Isotopomers of the Citric Acid Cycle Supplied with 3-13C-Pyruvate
  • Modeling Radioactive Precursor Uptake Kinetics
  • Simulation of The Pathway of DMSP Biosynthesis in Enteromorpha intestinalis
  • Simulation of The Pathway of Synthesis of DMSP in Spartina alterniflora
  • Making Rates Linearly or Hyperbolically Responsive to Pool Size Changes
  • Metabolic Engineering of Glycine Betaine Synthesis - Metabolism of 14C-Choline in Transgenic Tobacco Expressing Choline Monooxygenase in the Chloroplast
  • Considering Feedback Inhibition
  • Modeling Allosteric Behavior - Cooperative Substrate Binding
  • Links to Other Metabolic Modeling Resources on the www
  • References
  • Sponsors
  • Computer Simulation of Metabolism

    Isotopomers of the Citric Acid Cycle Supplied with 3-13C-Pyruvate

    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.

    Simulated changes in citrate (C) isotopomers:

    Simulated changes in ketoglutarate (K) isotopomers:

    Simulated changes in succinate (S) isotopomers:

    Simulated changes in oxaloacetate (O) isotopomers:

    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%].

    Simulated changes in citrate (C) isotopomers:

    Simulated changes in ketoglutarate (K) isotopomers:

    Simulated changes in succinate (S) isotopomers:

    Simulated changes in oxaloacetate (O) isotopomers:

    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%

    Simulated changes in citrate (C) isotopomers:

    Simulated changes in ketoglutarate (K) isotopomers:

    Simulated changes in succinate (S) isotopomers:

    Simulated changes in oxaloacetate (O) isotopomers:

    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)
    The total citrate pool (TotC) becomes:
      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 probabilities of utilizing the various citrate isotopomers are simply calculated as follows:
      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
    These probabilities are then applied to the various isotopomers in the utilization of citrate:
      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)
    The total citrate pool (TotC) becomes:
      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 utilization of citrate at the same rate as it is synthesized (CS), causes the total pool of citrate to decline by exactly the amount that it expanded due to synthesis during each iteration, and therefore a steady-state is maintained with respect to total citrate pool size.

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

    Google
    www www.hort.purdue.edu
    David Rhodes
    Department of Horticulture & Landscape Architecture
    Horticulture Building
    625 Agriculture Mall Drive
    Purdue University
    West Lafayette, IN 47907-2010
    Last Update: 8/20/03