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Use graphical analysis (see Box 6-1 and its associated Living Graph) to determine the Km and Vmax for this enzyme preparation and substrate.

11. 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 Vmax and rearranging gives the Eadie-Hofstee equation:

A plot of V0 vs. V0/[S] for an enzyme-catalyzed reaction is shown below. The blue curve was obtained in the absence of inhibitor. Which of the other curves (A, B, or C) shows the enzyme activity when a competitive inhibitor is added to the reaction mixture? Hint: See Equation 6-30.

12. The Turnover Number of Carbonic Anhydrase

Carbonic anhydrase of erythrocytes (Mr 30,000) has one of the highest turnover numbers we know of. It catalyzes the reversible hydration of CO2:

" H2CO3

This is an important process in the transport of CO2 from the tissues to the lungs. If 10.0 ^g of pure carbonic anhydrase catalyzes the hydration of 0.30 g of CO2 in 1 min at 37 °C at Vmax, what is the turnover number (kcat) of carbonic anhy-drase (in units of min-1)?

13. Deriving a Rate Equation for Competitive Inhibition The rate equation for an enzyme subject to competitive inhibition is

Beginning with a new definition of total enzyme as

and the definitions of a and KI provided in the text, derive the rate equation above. Use the derivation of the MichaelisMenten equation as a guide.

14. Irreversible Inhibition of an Enzyme Many enzymes are inhibited irreversibly by heavy metal ions such as Hg2+, Cu2+, or Ag+, which can react with essential sulfhydryl groups to form mercaptides:

The affinity of Ag+ for sulfhydryl groups is so great that Ag+ can be used to titrate —SH groups quantitatively. To 10.0 mL of a solution containing 1.0 mg/mL of a pure enzyme, an investigator added just enough AgNO3 to completely inactivate the enzyme. A total of 0.342 ^mol of AgNO3 was required.

Calculate the minimum molecular weight of the enzyme. Why does the value obtained in this way give only the minimum molecular weight?

15. Clinical Application of Differential Enzyme Inhibition Human blood serum contains a class of enzymes known as acid phosphatases, which hydrolyze biological phosphate esters under slightly acidic conditions (pH 5.0):

Acid phosphatases are produced by erythrocytes, the liver, kidney, spleen, and prostate gland. The enzyme of the prostate gland is clinically important, because its increased activity in the blood can be an indication of prostate cancer. The phosphatase from the prostate gland is strongly inhibited by tartrate ion, but acid phosphatases from other tissues are not. How can this information be used to develop a specific procedure for measuring the activity of the acid phos-phatase of the prostate gland in human blood serum?

16. Inhibition of Carbonic Anhydrase by Aceta-zolamide Carbonic anhydrase is strongly inhibited by the drug acetazolamide, which is used as a diuretic (i.e., to increase the production of urine) and to lower excessively high pressure in the eye (due to accumulation of intraocular fluid) in glaucoma. Carbonic anhydrase plays an important role in these and other secretory processes, because it participates in regulating the pH and bicarbonate content of several body fluids. The experimental curve of initial reaction velocity (as percentage of Vmax) versus [S] for the carbonic anhydrase reaction is illustrated below (upper curve). When the experiment is repeated in the presence of acetazolamide, the lower curve is obtained. From an inspection of the curves and your knowledge of the kinetic properties of competitive and mixed enzyme inhibitors, determine the nature of the inhibition by acetazolamide. Explain your reasoning.

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