(JUNE 2010)
27. Km for enzyme is equal to where
(1) V₀=Vmax                                           (2) 2V₀= Vmax
(3) 4V₀=Vmax                                         (4) V₀ = 2 Vmax

The correct answer is (2)

Introduction

In enzymatic reactions, the initial reaction velocity (V0V0) depends on substrate concentration, enzyme affinity, and catalytic efficiency. The Michaelis constant (KmKm) is a critical parameter defined as the substrate concentration at which the enzyme-catalyzed reaction reaches half of its maximum velocity (Vmax⁡Vmax). This concept is fundamental in biochemistry and enzymology, helping in characterizing enzyme behavior and substrate affinity. This article explains why the substrate concentration corresponding to V0=12Vmax⁡V0=21Vmax equals KmKm with detailed biochemical foundations.

Michaelis-Menten Equation

The Michaelis-Menten equation expresses the initial velocity V0V0 as a function of substrate concentration $[S]$:

V0=Vmax⁡[S]Km+[S]V0=Km+[S]Vmax[S]

Where:

• V0V0 = Initial velocity

• Vmax⁡Vmax = Maximum velocity when enzyme is saturated

• KmKm = Michaelis constant, substrate concentration at half maximal velocity

Derivation of Substrate Concentration at Half Vmax⁡Vmax

Set V0=12Vmax⁡V0=21Vmax:

12Vmax⁡=Vmax⁡[S]Km+[S]21Vmax=Km+[S]Vmax[S]

Divide both sides by Vmax⁡Vmax:

12=[S]Km+[S]21=Km+[S][S]

Cross multiplying:

Km+[S]=2[S]Km+[S]=2[S]

Rearranged for $[S]$:

Km=[S]Km=[S]

This confirms that the substrate concentration at half-maximal velocity equals KmKm.

Significance of Km

• KmKm reflects the enzyme’s affinity for the substrate; lower KmKm means higher affinity.

• It allows prediction of enzyme activity under varying substrate levels.

• Helps in understanding enzyme behavior in metabolic pathways and drug interactions.

Practical Use of Km in Enzyme Assays

• Knowing KmKm helps set substrate concentration for optimal enzyme assay conditions.

• Ensures accurate and reproducible measurement of enzyme activity.

• Enables comparison between enzyme variants or inhibitors.

Summary Table

Conclusion

The Michaelis constant (KmKm) corresponds to the substrate concentration at which an enzyme-catalyzed reaction proceeds at half its maximum velocity. This critical relationship underpins enzyme kinetics studies and informs biochemical assays, drug development, and metabolic regulation.

This thorough elucidation equips students and researchers with a fundamental understanding of enzyme-substrate dynamics critical for success in biochemistry and molecular biology exams and research.