(FEB 2022-1)
28. The enzyme alkaline phosphatase was tested for its catalytic activity using the substrate para- nitrophenylphosphate. The K_M obtained was 10 mM and Vmax was 100umol/min. Which one of the following options represents the initial velocity of the reaction at a substrate concentration of 10 mM?
(1) 50 µmol/min                                     (2) 100 µmol/min
(3) 500 µmol/min                                   (4) 20 µmol/min

The correct answer is (1) 50 µmol/min.

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Introduction

The Michaelis-Menten equation serves as the cornerstone for enzyme kinetics, relating reaction velocity to substrate concentration. This article explains how to calculate initial velocity V0V0 from known KmKm, VmaxVmax, and substrate concentration, using alkaline phosphatase’s activity toward para-nitrophenylphosphate as an example. This understanding is essential for students and researchers analyzing enzyme behavior in biochemical reactions and laboratory assays.

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Given Data

• Km=10 mMKm=10 mM

• Vmax=100 μmol/minVmax=100μmol/min

• Substrate concentration, $[S]=10\text{ mM}$

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Michaelis-Menten Equation

The initial velocity V0V0 of an enzyme-catalyzed reaction is given by:

V0=Vmax[S]Km+[S]V0=Km+[S]Vmax[S]

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Calculation

Substitute the given values:

V0=100×1010+10=100020=50 μmol/minV0=10+10100×10=201000=50μmol/min

Therefore, the initial velocity at substrate concentration 10 mM is 50 µmol/min.

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Explanation

• Since substrate concentration equals KmKm, the initial velocity is exactly half of VmaxVmax.

• This is consistent with the definition of KmKm as the substrate concentration at half-maximal velocity.

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Practical Implications

• Understanding how to compute V0V0 helps in designing enzyme assays.

• Enables interpretation of enzyme efficiency and substrate affinity.

• Assists in comparing enzyme activities and inhibitor effects.

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Summary Table

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Conclusion

Applying the Michaelis-Menten equation with the given values shows that at a substrate concentration equal to KmKm, the enzymatic reaction achieves half of its maximum velocity. Hence, for the alkaline phosphatase acting on para-nitrophenylphosphate, the initial velocity under these conditions is 50 µmol/min.