Penicillin is hydrolyzed and thereby rendered inactive by penicillinase, an enzy

Question

Penicillin is hydrolyzed and thereby rendered inactive by penicillinase, 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. A plot of 1/V_0 versus 1/[S] indicated the V_max=6.8 times^- 10 mol minute^-1. Assuming one active site per enzyme molecule, the turnover number for penicillinase is 337 s^-1 337 min^-1 600 hour^-1 33 hour^-1 600 s^-1

Explanation / Answer

Mass of enzyme = 29.6 kDa

Mass of a single enzyme molecule = 29.6 kDa = 4.91*10-20 g

Mass present in 10 mL sample = 10-9 g

So, number of molecules of enzyme present = 10-9/(4.91*10-20) = 2.03*1010 molecules

So,Total moles present = E0 = (2.03*1010) / (6.023*1023) = 3.37*10-14 moles

We know,

Vmax = k2*E0

Putting values:

6.8*10-10 = k2 * 3.37*10-14.

Thus, k2 = 2.01*104 min-1 = 337 s-1

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