In an earlier page we have seen that it is possible to introduce Michaelis-Menten kinetics into metabolic simulation models by specifying a K_m and a V_max 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:

(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:

Note that D2 modulates the apparent K_m of reaction rate B3, not the V_max of this reaction rate.

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:

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

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.

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.

[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].