Noncompetitive inhibition Lineweaver-Burk equation

To derive the Lineweaver-Burk equations, we proceed by simply taking the reciprocals of each side of the equations expressing v0 as a function of [S]0 in Table 9-1. The corresponding graphs of l/u0 versus l/[S]o have varying slopes, intercepts, or both as [I] is varied. Pure noncompetitive inhibition shows lines... 

For each of the four types of inhibition of a Michaelis-Menten enzyme [competitive, Eq. (5.25) noncompetitive and mixed Eq. (5.29) and uncompetitive, Eq. (5.32)], derive the corresponding Lineweaver-Burk equations [Eqs. (5.26), and (5.30), respectively] and draw the characteristic plots that are the basis for the rapid visnal identification of which type of inhibition apphes when analyzing enzyme kinetic data. 

To derive the Lineweaver-Burk equations, we proceed by taking the reciprocals of each side of Eqs. (5.25), (5.29), and (5.32). The corresponding graphs of 1/vq versus l/[S]o have various characteristic changes in slopes and intercepts as [I] is varied. Competitive inhibition gives lines that all intersect on the ordinate. Pure noncompetitive inhibition (in which K, = K,) gives lines that all intersect on the abscissa. For anti- or uncompetitive inhibition, the telltale feature is that the set of lines are all parallel to each other. For mixed inhibition [K K in Eq. (5.32)], both the slopes and the intercepts on the ordinate and abscissa differ for different values of [I] see Fig. 5-31. 

This equation predicts that both the slope and the l/v0 intercept of a Lineweaver-Burk plot will increase with increasing inhibitor concentration, but the intercept on the 1/[S]0 axis (-1 Km) will not change. A series of plots for several experiments with different concentrations of inhibitor will all pass through the l/[S]o intercept as shown in Fig. 9-4(6), indicating that pure noncompetitive inhibition does not alter Km. 

The expressions for both the slope and the intercept in the equation for a Lineweaver-Burk plot of an uninhibited reaction have been replaced by more complicated expressions in the equation that describes noncompetitive inhibition. This interpretation is borne out by the observed results. With a pure, noncompetitive inhibitor, the binding of substrate does not affect the binding of inhibitor, and vice versa. Because the 7 is a measure of the affinity of the enzyme and substrate, and because the inhibitor does not affect the binding, the 7 does not change with noncompetitive inhibition. 

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