Q.35 The enzyme α-amylase used in starch hydrolysis has an affinity constant (Km) variable
of 0.005 M. To achieve one-fourth of the maximum rate of hydrolysis, the required starch
concentration in mM (rounded off to two decimal places) is _________.
α-Amylase, a key enzyme in starch hydrolysis, follows Michaelis-Menten kinetics where Km represents the substrate concentration at half Vmax. For one-fourth Vmax (0.25 Vmax), the starch concentration [S] equals Km, given as 0.005 M or 5 mM. Rounded to two decimal places, the answer is 5.00 mM.
Michaelis-Menten Basics
The Michaelis-Menten equation is:
v = Vmax[S] / (Km + [S])
Here:
- v = reaction velocity
- [S] = substrate concentration
- Vmax = maximum reaction rate
- Km = substrate concentration at v = ½ Vmax
Lower Km indicates greater enzyme affinity. α-Amylase typically shows a high affinity for starch under steady-state, uninhibited reaction conditions assumed in this model.
Solving for ¼ Vmax
Setting v = ¼ Vmax gives:
¼ Vmax = Vmax[S] / (Km + [S])
Cancel Vmax and solve:
[S] = Km
With Km = 0.005 M:
[S] = 0.005 M = 5 mM
Final Answer: 5.00 mM
Common Options Explained
- 5.00 mM: Correct – [S] = Km gives exactly 0.25 Vmax.
- 1.25 mM: Incorrect – gives v ≈ 0.20 Vmax.
- 2.50 mM: Incorrect – yields v ≈ 0.33 Vmax.
- 10.00 mM: Incorrect – gives v ≈ 0.67 Vmax.
GATE BT Context
This matches GATE Biotechnology 2021 Q35 assessing Michaelis-Menten kinetics. Although α-amylase Km varies widely across biological sources, the value of 0.005 M is specified in the question.
