Question

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?

Answer 1

Explanation:

The given data is as follows.

        $V_{max} = 6.8 \times 10^{-10} \mu mol/min$

          $K_{m} = 5.2 \times 10^{-6} M$

Now, according to Michaelis-Menten kinetics,

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

where, S = substrate concentration = $10.4 \times 10^{-6}$ M

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

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

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

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

                              = $4.5 \times 10^{-10} \mu mol/min$

This means that $V_{o}$ would approache $V_{max}$.