Q.38
In the following enzyme-catalyzed reaction which follows Michaelis–Menten kinetics:
E + S
⇌
k1 k−1
ES →k2 E + P
Km is equal to
Options:
(A) k−1 / (k1k2)
(B) (k1k2) / k−1
(C) k1 / (k2 + k−1)
(D) (k2 + k−1) / k1
Michaelis Constant (Km) in Michaelis–Menten Kinetics
Michaelis–Menten kinetics describes the rate of enzyme-catalyzed
reactions. One of the most important parameters in this model is the
Michaelis constant (Km), which reflects the
affinity between an enzyme and its substrate.
Given Enzyme Reaction
E + S
&xrightleftharpoons;k1k−1
ES
&xrightarrow;k2
E + P
Key Concept: Michaelis Constant
The Michaelis constant is defined as the ratio of the rate constants
for breakdown of the enzyme–substrate complex to the rate constant
for its formation.
Km = (Rate of ES breakdown) / (Rate of ES formation)
Derivation of Km
The ES complex can break down in two ways:
- Back to E + S with rate constant k−1
- Forward to product with rate constant k2
Therefore:
Km = (k−1 + k2) / k1
Correct Answer
Option (D): (k2 + k−1) / k1
Summary Table
| Rate Constant | Meaning |
|---|---|
| k1 | Formation of ES complex |
| k−1 | Dissociation of ES to E + S |
| k2 | Formation of product |
| Km | (k−1 + k2) / k1 |
Conclusion
For an enzyme-catalyzed reaction following Michaelis–Menten kinetics,
the Michaelis constant depends on both ES dissociation and product
formation rates.
Hence, the correct expression is:
(k2 + k−1) / k1
Therefore, the correct answer is Option (D).
