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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, V 0 , of penicillinase if the penicillin concentration were 10.4 × 10 − 6 M?

Respuesta :

Answer : The initial reaction velocity [tex]V_o[/tex] would approach [tex]V_{max}[/tex]

Explanation :

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} M[/tex]

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

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

[tex]V_o[/tex] = initial reaction velocity = ?

Now put all the given values into the above formula, we get:

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

Therefore, the initial reaction velocity [tex]V_o[/tex] would approach [tex]V_{max}[/tex]