Il. The Eadie- Hofstee Equation One transformation of the Michaelis-Menten equation is the Lineweaver Burk, or double-reciprocal, equation. Multiplying both sides of the Lineweaver-Burk equation by Vm and re- arranging gives the Eadie-Hofstee equation: Vo=(k)o+ v A plot of Vo vs Vo/S for an enzyme-catalyzed reaction is shown below V K V V The blue curve was obtained in the absence of in hibitor. Which of the other curves(A, B, or C)shows the enzyme activity when a competitive inhibitor is added to the reaction mixture?
SIGNIFICANCE OF KM AND Vmax VALUES The KM values of enzymes range widely (Table 8-2). For most enzymes, KM lies between 10-1 and 10-7M. The KM value for an enzyme depends on the particular substrate and also on environmental conditions such as pH, temperature, and ionic strength
Table 8-2 K M values of some enzymes Enzyme Substrate KLum) Chymotrypsin Acetyl-L-tryptophanamide 5000 Lysozyme Hexa-N-acetylglucosamine 6 B-Galactosidase Lactose 4000 Threonine deaminase Threonine 5000 Carbonic anhydrase CO 8000 Penicillinase Benzylpenicillin 50 ruvate carboxylase Pyruvate 400 HCO3 1000 ATP Arginine-tRNA synthetase Arginine tRNA 0.4 ATP 300
The Michaelis constant km has two meanings.First,KM is the concentration of substrate at which half the active sites are filled. Once the Km is known, the fraction of sites filled Es at any substrate concentration can be calculated from / V [S] ES (30 max [S]+ Km
Second, Km is related to the rate constants of the individual steps in the catalytic scheme given in equation 14. In equation 20, KM is defined as (k2+ k3)/kl. Consider a limiting case in which k2 is much greater than ks. This means that dissociation of the ES complex to E and S is much more rapid than formation of E and product. Under these conditions (k2>k3) E+S ES E+P (14) 2 Equation 19 can be simplified by defining a new constant, KM, called the Michaelis constant k+ k KI M (20)