Penicillinase is an enzyme secreted by certain bacteria to inactivate the antibiotic penicillin. A typical form of the enzyme with a molecular weight of 30,000 has a single active site, a catalytic constant of 2000 s-1 and a Michaelis constant KM = 5.0 X 10-5 M. In response to treatment with 5 mol of penicillin, a 1.00 mL suspension of certain bacterial cells release 0.04 μg of the enzyme.
a. Assuming that the enzyme equilibrates quickly with its substrate, what fraction of the enzyme will be complexed with penicillin in the early stages of the reaction?
b. How long will it take for half of the penicillin present initially to become inactivated?
c. What concentration of penicillin would cause the enzyme to react at half its maximum velocity Vmax?
d. A second suspension of bacterial cells releases 0.06 μg mL-1 of the enzyme. Will this affect the answer to parts (b) or (c)? If so, by how much?
e. An antibiotically inactive analog of penicillin serves as a competitive inhibitor to penicillinase. If the enzyme has the same affinity for inhibitor as for substrate, what concentration of inhibitor is required to decrease the rate of disappearance of penicillin fivefold at low (subsaturating) penicillin concentration?
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