Computer Simulation of Metabolism
Modeling Radioactive Precursor Uptake Kinetics
The models considered in earlier pages are applicable primarily to stable isotope tracer kinetics in which a precursor is supplied at a high isotope abundance. The supply of this precursor is assumed to be unlimited. Thus, the models discussed so far have not been concerned with changes in the availability of the isotopically labeled precursor. In radiotracer labeling experiments, however, often a trace quantity of a precursor is supplied exogenously at a high specific activity; this supply is finite, and the changes in the availability of the radiolabeled precursor during the labeling experiment can have a profound effect on the isotopic labeling kinetics of metabolites derived therefrom.
Fig. 20, below, depicts a scenario in which a radiolabeled precursor E is supplied exogenously to batches of 1 gfw (gram fresh weight) of plant tissue, at a specific activity E1 (nCi.nmol^{1}) and at a total amount (exogenous pool size) of E2 (nmol.gfw^{1}).
Fig. 20. Model assumptions used to generate simulations shown in Figs. 21  24.
The precursor E is taken up by the plant tissue, where it is metabolized through the pathway A > B > C > D, where D is an endproduct (i.e. is not turnedover). The pool sizes of the intermediates are
A2, B2, C2 and D2 (nmol.gfw^{1}), and their specific radioactivities are A1, B1, C1 and D1 (nCi.nmol^{1}), respectively. The pathway A > B > C > D is envisaged to be continuously drawing from a pool of an unlabeled precursor at specific activity F1 = 0 nCi.nmol^{1} throughout the labeling experiment. The endogenous flux from this unlabeled precursor through the pathway (occurring at rate A3 = B3 = C3 = D3 nmol.min^{1}gfw^{1}) serves to carry the label derived from uptake of E from the medium into the various intermediates and endproduct.
The uptake kinetics of the exogenously supplied precursor E will not be linear. As the exogenous pool of E is depleted by uptake, this will in turn slow down the uptake rate (A4). The simplest way of dealing with such nonlinear uptake
kinetics is to envisage that the uptake rate (A4) is proportional to the exogenous pool size of the precursor, E (E2), thus:
A4 = E2 * k, where k is a constant
Figs. 21  24 show simulations of this scenario, using different values of k:
k = 0.05; Fig. 21
k = 0.1; Fig. 22
k = 0.5; Fig. 23
k = 0.02; Fig. 24
[see also Visual Basic program code used for simulations shown in Figs. 21 24]
As the value of k is decreased from 0.5 to 0.1 to 0.05 to 0.02, keeping all other variables constant, this effectively slows the uptake of the
exogenously supplied radiolabeled precursor, E. Note that in all of these simulations the pool size of A (lower right graph panels, blue) expands from a starting value of 6.0 nmol.gfw^{1} to 10.0
nmol.gfw^{1} as a result of uptake of the 4.0 nmol of E from the medium. The rate of expansion of the pool of A is conditioned by the uptake rate, A4, which in turn is determined by k.
Download an enhanced version of the Visual Basic program illustrated above, including a color key. To run this program you must have Visual Basic 5.0 (or greater) installed on your computer.
Download a modified version of this Visual Basic program accommodating alternative metabolic fates of intermediates (i.e. A, B
and C can be envisaged to be utilized in reactions other than synthesis of B, C and D, respectively). To run this program you must have Visual Basic 5.0 (or greater) installed on your computer.
Interactive clientside versions of the latter program are available in various formats that do not require Visual Basic:
VBScript, singlepage. 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.
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.
JavaScript, singlepage. 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.
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.
Java applet, singlepage. This applet should function with any Javaenabled browser, including Microsoft Internet Explorer 3.0 or above, or Netscape Navigator 3.0 or above. Output from the model is in graphical
format. "Definitions" of variables are provided in a resizable window.
An extension of the above models is to consider the flow of radiolabel through a compartmentalized metabolic pathway. In this JavaScript model, a radiolabeled precursor (P) is supplied exogenously
and enters a pathway A > B > C > D > E, which is envisaged to be continuously drawing from a pool of an unlabeled precursor at specific activity F1 = 0 nCi.nmol^{1} throughout the
labeling experiment. The pools of A, B, C, D, and E, exist as metabolic (met) and storage (stor) pools in equilibrium with one another. This program for simulating radiolabeling kinetics with compartmentation of pools
is also provided as a Java applet. This applet should function with any Javaenabled browser, including Microsoft Internet Explorer 3.0 or above, or Netscape Navigator 3.0 or above. Output from the model is in graphical format.
Download the Visual Basic program for simulating radiolabeling kinetics in a compartmentalized pathway. To run this program you must have Visual Basic 5.0 (or greater) installed on your computer.
