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Homework answers / question archive / Destroying the Trojan horse
Destroying the Trojan horse. Penicillin is hydrolyzed and thereby rendered inactive by penicillinase (also known as ?-lactamase), an enzyme present in some resistant bacteria. The mass of this enzyme in Staphylococcus aureus is 29.6 kd. The amount of penicillin hydrolyzed in 1 minute in a 10-ml solution containing 10-9 g of purified penicillinase was measured as a function of the concentration of penicillin. Assume that the concentration of penicillin does not change appreciably during the assay. (How do you use the Michaelis-Menten equation without Vmax or Km?)
[Penicillin] Amount hydrolyzed mM (nmol) 1 0.11 3 0.25 5 0.34 10 0.45 30 0.58 50 0.61
A. Plot V0 versus [S] and 1/V0 versus 1/[S] for these data. Does penicillinase appear to obey Michaelis-Menten kinetics? If so, what is the value of KM?
B. What is the value of Vmax?
C. What is the turnover number of penicillinase under these experimental conditions? Assume one active site per enzyme molecule.
Answer:
A hyperbolic curve is obtained for the given enzyme for Michaelis Menten kinetics. So, the enzyme follows Michaelis Menten kinetics.
Vmax = 0.6 nM per s
Vmax/2 = 0.3 nM per s
Km = 0.4 uM
Lineweaver Burk Plot -
| 1/S (uM^-1) | 1/Vo (s/nM) |
| 1 | 9.1 |
| 0.34 | 4 |
| 0.2 | 2.9 |
| 0.1 | 2.2 |
| 0.034 | 1.7 |
| 0.02 | 1.6 |
D. Turnover number = Kcat = Vmax/Et = 0.6 ng per s/10^-9 g = 0.6 ng per s/1 ng = 0.6 per second
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