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Penicillinase, also known as β‑lactamase, is a bacterial enzyme that hydrolyzes and inactivates the antibiotic penicillin. Penicillinase follows simple Michaelis–Menten kinetics and reaches half its maximal rate of 6.8×10−10 µmol⋅min−1 when the penicillin concentration is 5.2×10−6 M. What would happen to the initial reaction velocity, ????0, of penicillinase if the penicillin concentration were 10.4×10−6 M?

Respuesta :

Explanation:

The given data is as follows.

        [tex]V_{max} = 6.8 \times 10^{-10} \mu mol/min[/tex]

          [tex]K_{m} = 5.2 \times 10^{-6} M[/tex]

Now, according to Michaelis-Menten kinetics,

              [tex]V_{o} = V_{max} \times [\frac{S}{(S + Km)}][/tex]

where, S = substrate concentration = [tex]10.4 \times 10^{-6}[/tex] M

Now, putting the given values into the above formula as follows.

        [tex]V_{o} = V_{max} \times [\frac{S}{(S + Km)}][/tex]

        [tex]V_{o} = 6.8 \times 10^{-10} \mu mol/min \times [\frac{10.4 \times 10^{-6} M}{(10.4 \times 10^{-6}M + 5.2 \times 10^{-6} M)}][/tex]

            [tex]V_{o} = 6.8 \times 10^{-10} \mu mol/min \times 0.667[/tex]

                              = [tex]4.5 \times 10^{-10} \mu mol/min[/tex]

This means that [tex]V_{o}[/tex] would approache [tex]V_{max}[/tex].

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