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  • 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
  • Computer Simulation of Metabolism

    Effects of Varying Rates and Pool Sizes - A Sample Program

    The following figures illustrate the effects of varying rates of synthesis and utilization and pool sizes on the labeling kinetics of intermediates of the hypothetical pathway shown in Fig. 1 of the Introduction. The program used to generate the simulations which follow was written in Microsoft Visual Basic 5.0 (see program code and illustrations of program object properties in Figs. 14, 15 and 16). Individual rates and pool sizes are varied for each program run, and output from the program is shown as plots of isotope abundance versus time (lower left graph panel), and pool size versus time (lower right graph panel). Figures represent screen captured images of program inputs (initial isotope abundances, pool sizes, and rates) in the upper section, and outputs in the graph panels of the lower section. Color codes used for Figures 5 to 13 are: (lower left graph panels, isotope abundance) A1 = black, B1 = green, C1 = blue, D1 = red; (lower right graph panels, pool sizes) B2 = green, C2 = blue, D2 = red.

    Varying Rates

    Fig. 5. Assumptions : starting isotope abundances, A1 = 90%, B1 = 0%, C1 = 0%, D1 = 0%; starting pool sizes (nmol.gfw-1), B2 = 600, C2 = 500, D2 = 400; rates (nmol.h-1.gfw-1), B3 = B4 = 5000, C3 = C4 = 2000, D3 = D4 = 1000. Note that because influx to each pool is equal to efflux from that pool, the system remains in steady-state (i.e. the pool size of each of the intermediates remains constant with time).

    Fig. 6. Assumptions : starting isotope abundances, A1 = 90%, B1 = 0%, C1 = 0%, D1 = 0%; starting pool sizes (nmol.gfw-1), B2 = 600, C2 = 500, D2 = 400; rates (nmol.h-1.gfw-1), B3 = B4 = 5000, C3 = C4 = 3000, D3 = D4 = 2000. Note that the increased rates of synthesis and utilization of pools C and D lead to more rapid labeling of C and D in comparison to Fig. 5.

    Fig. 7. Assumptions : starting isotope abundances, A1 = 90%, B1 = 0%, C1 = 0%, D1 = 0%; starting pool sizes(nmol.gfw-1), B2 = 600, C2 = 500, D2 = 400; rates (nmol.h-1.gfw-1), B3 = B4 = 5000, C3 = C4 = 4000, D3 = D4 = 3000. Note that the increased rates of synthesis and utilization of pools C and D lead to more rapid labeling of C and D in comparison to Fig. 6.

    Fig. 8. Assumptions : starting isotope abundances, A1 = 90%, B1 = 0%, C1 = 0%, D1 = 0%; starting pool sizes (nmol.gfw-1), B2 = 600, C2 = 500, D2 = 400; rates (nmol.h-1.gfw-1), B3 = B4 = 5000, C3 = C4 = 1000, D3 = D4 = 500. Note that the decreased rates of synthesis and utilization of pools C and D lead to marked reductions in the rate of labeling of C and D in comparison to Fig.7. However, because influx to each pool is equal to efflux from that pool, the system remains in steady-state (i.e. the pool size of each of the intermediates remains constant with time).

    Fig. 9. Assumptions : starting isotope abundances, A1 = 90%, B1 = 0%, C1 = 0%, D1 = 0%; starting pool sizes (nmol.gfw-1), B2 = 600, C2 = 500, D2 = 400; rates (nmol.h-1.gfw-1), B3 = B4 = 5000, C3 = C4 = 1000, D3 = 500, D4 = 200. In this specific example, a non-steady-state is envisaged, such that the rate of utilization of pool D is less than the rate of synthesis of pool D. Consequently the pool expands at the rate D3 - D4 = 300 nmol.h-1.gfw-1.

    Fig. 10. Assumptions : starting isotope abundances, A1 = 90%, B1 = 0%, C1 = 0%, D1 = 0%; starting pool sizes (nmol.gfw-1), B2 = 600, C2 = 500, D2 = 400; rates (nmol.h-1.gfw-1), B3 = B4 = 5000, C3 = C4 = 1000, D3 = 500, D4 = 600. In this specific example, the rate of utilization of pool D exceeds its rate of synthesis so that the pool size of metabolite D decreases at the rate D3 - D4 = -100 nmol.h-1.gfw-1.

    Varying Pool Sizes

    In all of the above examples, starting pool sizes of intermediates were fixed at B2 = 600, C2 = 500 and D2 = 400 nmol.gfw-1 and simulations were run at different rates of synthesis and utilization. The following figures illustrate effects of varying pool sizes on isotope labeling kinetics assuming fixed rates of synthesis and utilization (B3 = B4 = 5000, C3 = C4 = 2000, and D3 = D4 = 1000 nmol.h-1.gfw-1).

    Fig. 11. Assumptions : B2 = 900, C2 = 800, D2 = 700 nmol.gfw-1.

    Fig. 12. Assumptions : B2 = 100, C2 = 800, D2 = 900 nmol.gfw-1.

    Fig. 13. Assumptions : B2 = 500, C2 = 100, D2 = 50 nmol.gfw-1.

    The Visual Basic 5.0 program code used to perform the simulations shown in Figs. 5 to 13, above, is attached. Fig. 14, Fig. 15 and Fig. 16 show several of the objects on the Form (Form1) to which the program code refers.

    Thus, Fig. 14 illustrates certain of the properties of the command button, Command1 (the "Start" button), which, when "clicked", executes the first major subroutine of the program code. The object Command2 (the "End" button), when clicked, serves to end the program by unloading the form (Form1) upon which all of the objects are placed.

    Fig. 15 illustrates certain of the properties of the text box, Text13; as indicated in the program code, the Text property of object Text13 is transferred to the variable D4 when Command1 (the Start button) is "clicked". Similarly the contents of the text boxes Text1 to Text12 are assigned to specific variables at the beginning of each run, as specified in the program code.

    Fig. 16 illustrates certain of the properties of the picture box, Picture1, where the isotope abundance values are plotted in the lower left graph panel. The object Picture2 is used for plotting pool sizes in the lower right graph panel. Note that the Picture1 and Picture2 picture boxes are both pre-loaded with a .bmp picture file of the graph box (including tick marks) upon which the simulated values are superimposed during each program run. The picture boxes are "refreshed" at the beginning of each run, as indicated in the program code.

    Download the Visual Basic program illustrated above. To run this program you must have Visual Basic 5.0 (or greater) installed on your computer.

    Download an enhanced version of this Visual Basic program capable of simulating "chase" stable isotope tracer kinetics, with rates expressed in minutes rather than hours, and with adjustable graph axes. To run this program you must have Visual Basic 5.0 (or greater) installed on your computer.

    Interactive client-side versions of the latter program are available in various formats that do not require Visual Basic:

  • VBScript, single-page. This interactive web page uses VBScript, and requires Microsoft Internet Explorer 3.0 or above to function. Note that this program will not work with Netscape Navigator which does not support VBScript. This VBScript model produces simulated values in tabular rather than in graphical format, and expresses rates in units of minutes, rather than hours.
  • VBScript, with 4 resizable frames. This interactive web page uses VBScript, and requires Microsoft Internet Explorer 3.0 or above to function. Note that this program will not work with Netscape Navigator which does not support VBScript. This model provides a comparison of tabulated model output with an image of graphical output from a Visual Basic model using identical default starting values and assumptions. Rates are expressed in minutes rather than hours.
  • JavaScript, single-page. This JavaScript program should function with both Netscape Navigator and Microsoft Internet Explorer 3.0 or above. This JavaScript model produces simulated values in tabular rather than in graphical format, and expresses rates in units of minutes rather than hours.
  • JavaScript, with 4 resizable frames. This JavaScript program should function with both Netscape Navigator and Microsoft Internet Explorer 3.0 or above. This JavaScript model provides a comparison of tabulated model output with an image of graphical output from a Visual Basic model using identical default starting values and assumptions. Rates are expressed in minutes rather than hours.
  • Java applet, single-page. This applet should function with any Java-enabled browser, including Microsoft Internet Explorer 3.0 or above, or Netscape Navigator 3.0 or above. Output from the model is in graphical format, and time units are expressed in minutes rather than hours. "Definitions" of variables are provided in a resizable window.

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  • 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