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

    Considering Feedback Inhibition

    In an earlier page we have seen that it is possible to introduce Michaelis-Menten kinetics into metabolic simulation models by specifying a Km and a Vmax for each reaction rate. Once this is accomplished it is straight-forward to introduce feedback inhibition control within the pathway by allowing the pool size of the end-product to competitively or non-competitively inhibit one of the reactions involved in its own synthesis.

    Consider, for example, the metabolic scheme in Fig. 30 (below) in which no feedback control is initially envisaged [i.e. option "None" of the Inhibition option menu is selected]. Rate B3 does not respond to the end-product pool size, but rather only to the substrate pool size (A2), thus:

    Rate B3 = (Vm2*A2)/(Km2+A2)

    Fig. 30. Radiolabeling kinetics assuming rates of metabolism have Michaelis-Menten kinetics with no feedback inhibition by end-product D on rate B3

    (Km values are given in units of nmol.gfw-1 and Vm values are given in units of nmol.min-1.gfw-1).

    When the "Competitive" Inhibition option is selected (see Fig. 31) rate B3 becomes a function not only of the substrate pool size (A2) but also the pool size of the end-product (D2) determined by the Ki for the feedback inhibitor [i.e. the concentration of pool D (nmol.gfw-1) giving 50% inhibition], as follows:

    Rate B3 = (Vm2*A2)/((Km2+(Km2*D2/Ki))+A2)

    Note that D2 modulates the apparent Km of reaction rate B3, not the Vmax of this reaction rate.

    Fig. 31. Radiolabeling kinetics assuming rates of metabolism have Michaelis-Menten kinetics with competitive feedback inhibition by end-product D on rate B3 assuming Ki = 40 nmol.gfw-1

    When the "Non-competitive" Inhibition option is selected (see Fig. 32) rate B3 again becomes a function of the substrate pool size (A2), the pool size of the end-product (D2), and the Ki of reaction B3 for the end-product [the concentration of pool D (nmol.gfw-1) giving 50% inhibition], as follows:

    Rate B3 = ((Vm2/(1+(D2/Ki)))*A2)/(Km2+A2)

    But note here that D2 modulates the apparent Vmax of rate B3 rather than the Km of this reaction rate.

    Fig. 32. Radiolabeling kinetics assuming rates of metabolism have Michaelis-Menten kinetics with non-competitive feedback inhibition by end-product D on rate B3 assuming Ki = 40 nmol.gfw-1

    In the simulations shown in Figs. 31 and 32 (above), a Ki of 40 nmol.gfw-1 is assumed. Shown in Figs. 33 and 34 (below) are simulations in which the Ki is reduced to 10 nmol.gfw-1. Note that in these scenarios, both the non-competitive (Fig. 33) and the competitive (Fig. 34) modes of inhibition lead to substantial reduction in the flux of radiolabel to end-product D, and expansion of the pool of A, as expected.

    Fig. 33. Radiolabeling kinetics assuming rates of metabolism have Michaelis-Menten kinetics with non-competitive feedback inhibition by end-product D on rate B3 assuming Ki = 10 nmol.gfw-1

    Fig. 34. Radiolabeling kinetics assuming rates of metabolism have Michaelis-Menten kinetics with competitive feedback inhibition by end-product D on rate B3 assuming Ki = 10 nmol.gfw-1

    Note that there is greater inhibition of the radiolabel incorporation into pools B, C, and D in the non-competitive inhibition model (Fig. 33) than the competitive inhibition model (Fig. 34). This is a consequence of the expansion of the pool of A. In the competitive inhibition model the elevated pool of A competes with the end-product (D) and so alleviates some of the feedback inhibition. In the non-competitive model, feedback inhibition is unaffected by substrate concentration.

    Because rates C3 and D3 are not feedback sensitive, some continued synthesis of end-product D can occur from the unlabeled pools of C (C2) and (D2) during the simulation time-course. Consequently, despite substantial inhibition of radiolabel incorporation into pool D in the non-competitive model when Ki = 10 nmol.gfw-1 [see left hand graph panel of Fig. 33] the pool size of D continues to rise [see center graph panel of Fig. 33]. This expansion of the pool of D occurs at the expense of pools B and C.

    [Visual Basic program code used for simulations shown in Figs. 30 - 34]

    [Java Applet versions of the above program are available with either competitive feedback inhibition or non-competitive feedback inhibition. These applets should function with any Java-enabled browser, including Microsoft Internet Explorer 3.0 or above, or Netscape Navigator 3.0 or above].

    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