GATE 2023 BT – Question 54
An enzyme catalyzes $A\to B$ with $k_{cat}=500\ \mathrm{s^{-1}}$. If $V_0=10\ \mathrm{\mu M/s}$, total enzyme concentration is 30 nM and $[A]=40\ \mathrm{\mu M}$, the value of $K_m$ (μM) is ____________.
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Correct answer: 20
Explanation
**Michaelis-Menten equation:** $V_0=\dfrac{V_{max}[A]}{K_m+[A]}$.
**Step 1: $V_{max}$.**
$$V_{max}=k_{cat}[E]_T=500\ \text{s}^{-1}\times0.030\ \mu\text{M}=15\ \mu\text{M/s}$$
(30 nM is 0.030 μM).
**Step 2: solve for $K_m$.**
$$10=\frac{15\times40}{K_m+40}\;\Rightarrow\;K_m+40=60\;\Rightarrow\;K_m=\mathbf{20\ \mu M}.$$