Substituting equation 27 into equation 26 yields the Michaelis-Menten e [S] max [S]+ KM (28) This equation accounts for the kinetic data given in Figure 8-15.At very low substrate concentration, when [S] is much less than KM, V [s]Vmax/KMi that is, the rate is directly proportional to the substrate concentration. At high substrate concentration, when [S] is much greater than KM, V=Vmax; that is, the rate is maximal, independent of substrate concentration. When s<< Km, V=SImar/K When s>> Kmg V=V
When [S] << Km, V = [S] Vmax/Km When [S] >> Km, V = Vmax
The meaning of KM is evident from equation 28. When [S]= KM,then V= Vmax/2. Thus, KM is equal to the substrate concentration at which the reac- tion rate is half its maximal value [S] max [S]+ KM (28)
192Part‖l PROTEINS nax max max 2 c K Substrate concentration [S] Figure 8-15 A plot of the reaction velocity V as a function of the substrate concentra- tion [S] for an enzyme that obeys Michaelis-Menten kinetics(Vmax is the maximal velocity and Km is the Michaelis constant)
Vmax and Km cAn BE DETERMINED BY VARYING THE SUBSTRATE CONCENTRATION The Michaelis constant, KM, and the maximal rate, Vmax, can be readily derived from rates of catalysis measured at different substrate concentra- tions if an enzyme operates according to the simple scheme given in equation 14. It is convenient to transform the Michaclis-Menten equation into one that gives a straight-line plot. This can be done by taking the reciprocal of both sides of equation 28 to give KM 99 max max S The Lineweaver-Burk plot [S] V= V max [S]+ KM (28)
The Lineweaver-Burk plot
A plot of l/Versus 1/[S], called a Lineweaver- Burk plot, yields a straight line with an intercept of 1/Vmax and a slope of KM/Vmax(Figure 8-16) Alternatively, KM and Vmax can be obtained by fitting the data to equa- tion 28 using a computer program Part Il A plot of 1/Versus 1/[S, called a Lineweaver- Burk plot, yields a straight PROTEINS line with an intercept of l/Vmax and a slope of KM/Vmax( Figure 8-16) Alternatively, KM and Vmax can be obtained by fitting the data to equa tion 28 using a computer program Figure 8-16 double-reciprocal plot of enzyme kinetics: 1/v is plotted as a function of 1/[S]. The slope is KM/Vmax Intercept =-1/KM Intercept =1/vna intercept on the vertical axis is 1/Vmax, and the intercept on the horizontal axis is -1/KM