(DEC 2007)
29. In a biochemical reaction catalyzed by enzyme following the Michales-Menten equation, what will be the substrate concentration, when the observed velocity of reaction is 90% of the maximum velocity?
(1) 18 Km                                                (2) 9Km
(3) 5 Km                                               (4) 1Km

The correct answer is (2) 9Km.

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Introduction

Enzyme kinetics underpins our understanding of biochemical reactions, particularly those following Michaelis-Menten behavior. The Michaelis-Menten equation relates reaction velocity to substrate concentration, allowing predictions of enzymatic behavior. One important calculation is determining the substrate concentration required to reach a specified fraction of the maximum velocity, such as 90%. This article explains how to calculate this substrate concentration and interprets it with respect to KmKm.

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Michaelis-Menten Equation

The reaction velocity (V0V0) relates to substrate concentration $[S]$ as:

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

Where:

• V0V0: Initial reaction velocity

• VmaxVmax: Maximum reaction velocity

• KmKm: Michaelis constant (substrate concentration at half VmaxVmax)

• $[S]$: Substrate concentration

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Goal: Find $[S]$ when V0=0.9×VmaxV0=0.9×Vmax

Set:

0.9Vmax=Vmax[S]Km+[S]0.9Vmax=Km+[S]Vmax[S]

Divide both sides by VmaxVmax:

0.9=[S]Km+[S]0.9=Km+[S][S]

Cross multiply:

0.9(Km+[S])=[S]0.9(Km+[S])=[S]0.9Km+0.9[S]=[S]0.9Km+0.9[S]=[S]

Subtract $0.9[S]$ from both sides:

0.9Km=[S]−0.9[S]=0.1[S]0.9Km=[S]−0.9[S]=0.1[S]

Solve for $[S]$:

[S]=0.9Km0.1=9Km[S]=0.10.9Km=9Km

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Interpretation

• To reach 90% of VmaxVmax, the substrate concentration needs to be 9 times the KmKm value.

• This shows substrate concentration must be significantly higher than KmKm to approach saturation.

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Practical Importance

• Helps in biochemical assay design ensuring substrate levels are sufficient for near-maximal enzyme activity.

• Assists in understanding enzyme capacity in metabolic regulation.

• Aids drug design by considering substrate/enzyme binding dynamics.

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Summary Table

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Conclusion

For enzyme-catalyzed reactions following Michaelis-Menten kinetics, the substrate concentration required to reach 90% of the maximum velocity is 9 times the Michaelis constant (9Km9Km). This relationship helps define enzyme efficiency and informs protocols for studying enzyme activities in various scientific fields.

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This comprehensive explanation strengthens knowledge of enzyme kinetics principles, equipping students and researchers to analyze and apply Michaelis-Menten theory effectively in practical and academic contexts.