The correct answer is (4) Kₛ: 400 μM, Kₘ: 408 μM.

Introduction

Michaelis-Menten kinetics provides a foundation for understanding enzyme-catalyzed reactions. Two important constants—substrate dissociation constant (KsKs) and Michaelis constant (KmKm)—help quantify substrate affinity and kinetic efficiency. This article walks through the calculation of KmKm and KsKs for a given reaction using provided rate constants, culminating in an expertly reasoned answer, ideal for competitive exams and biochemistry training.

Stepwise Calculation

Given data:

• k1=1×108 M−1 s−1k1=1×108M−1s−1 (association rate constant)

• k−1=4×104 s−1k−1=4×104s−1 (dissociation rate constant)

• k2=8×102 s−1k2=8×102s−1 (catalytic rate constant/product formation)

1. Substrate Dissociation Constant (KsKs)

Ks=k−1k1Ks=k1k−1

Substitute values:

Ks=4×1041×108=4×10−4 M=400 μMKs=1×1084×104=4×10−4 M=400μM

2. Michaelis Constant (KmKm)

Km=k−1+k2k1Km=k1k−1+k2

Substitute values:

Km=4×104+8×1021×108=4.08×1041×108=4.08×10−4 M=408 μMKm=1×1084×104+8×102=1×1084.08×104=4.08×10−4 M=408μM

Interpretation

• Ks (400 μM) reflects the enzyme’s basic affinity for the substrate, independent of turnover.

• Km (408 μM) incorporates both substrate binding and catalytic conversion, always slightly higher than Ks if product formation (k2k2) is significant.

• The tiny difference between Km and Ks reflects rapid substrate binding and reasonably efficient product formation.

Significance in Biochemistry

• Calculating both constants helps in understanding not only how an enzyme binds a substrate but also how efficiently it turns a bound substrate into product.

• Km is widely used to compare enzyme efficiency and substrate preference, while Ks focuses solely on binding.

• In experimental design, knowing specific values allows optimization of substrate concentrations to study enzyme kinetics, inhibition, and efficiency.

Summary Table

Conclusion

For the enzyme-catalyzed reaction in question, the calculated values from rate constants are Ks: 400 μM and Km: 408 μM, matching option (4). This demonstrates both substrate binding and catalytic turnover, providing rich insight into enzyme kinetics essential for advanced biochemistry learning and research.