(JUNE 2004)
26. During an enzyme assay if the initial velocity Vo = ¹/₂ Vmax, then substrate concentration
will be equal to
(1) α Km                                                 (2) Km
(3) ¹/₂ Km                                               (4) 0.2 Km

The correct answer is (2) Km.

Introduction

In enzyme kinetics, a critical parameter is the Michaelis constant, KmKm, which provides insights into enzyme-substrate affinity and catalytic efficiency. One commonly encountered situation is determining the substrate concentration when the enzyme’s initial velocity is half of its maximal velocity, V0=12VmaxV0=21Vmax. This article explains why this substrate concentration equals KmKm according to the Michaelis-Menten model, clarifying key concepts for biochemistry students and professionals.

Michaelis-Menten Equation Recap

The Michaelis-Menten equation describes the relationship between the initial velocity v0v0 of an enzyme-catalyzed reaction and substrate concentration $[S]$:

v0=Vmax[S]Km+[S]v0=Km+[S]Vmax[S]

Where,

• VmaxVmax = Maximum reaction velocity, when the enzyme is saturated with substrate.

• KmKm = Michaelis constant, the substrate concentration at which velocity is half of VmaxVmax.

Substrate Concentration at v0=12Vmaxv0=21Vmax

Setting v0=12Vmaxv0=21Vmax, substitute into the Michaelis-Menten equation:

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

Divide both sides by VmaxVmax:

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

Cross multiply:

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

Simplify:

Km=[S]Km=[S]

This confirms that the substrate concentration at which the initial velocity reaches half of its maximal value is precisely KmKm, the Michaelis constant.

Interpretation of KmKm

• KmKm is a measure of enzyme affinity for substrate:

  • Low KmKm indicates high affinity (enzyme saturates at low substrate concentration).

  • High KmKm indicates low affinity (requires higher substrate concentration).

• The equation holds under assumptions of Michaelis-Menten kinetics, such as steady-state conditions and enzyme saturation dynamics.

Practical Implications

• In enzyme assays, knowing KmKm helps in selecting appropriate substrate concentrations for activity measurement.

• KmKm informs drug design and enzyme inhibition strategies.

• It provides comparative metrics among enzymes for biotech and pharmaceutical development.

Summary Table

Conclusion

In Michaelis-Menten enzyme kinetics, when the initial reaction velocity is half of the maximal velocity, the substrate concentration equals the Michaelis constant KmKm. This concept is fundamental for understanding enzymatic function, assay design, and substrate affinity characterization, making it essential knowledge in biochemistry and related fields.