Consider an enzymatic reaction that follows Michaelis-Menten kinetics. Let \( K_M \), \( S \),
and \( V_{max} \) denote the Michaelis constant, substrate concentration, and
maximum reaction rate, respectively. Which of the following statements is/are
TRUE?
Show Hint
- For \( S \ll K_M \), the reaction is apparent first-order in \( S \).
- For \( S \gg K_M \), the reaction rate is nearly independent of \( S \).
- For \( S = K_M \), the rate of reaction equals \( V_{max} \).
- \( K_M \) is independent of the total enzyme concentration.
The Correct Option is A, B, D
Solution and Explanation
Michaelis-Menten kinetics provides a framework for understanding how enzymatic reaction rates depend on substrate concentration.
Step 1: Low Substrate Concentration (\( S \ll K_M \)):
At low substrate concentrations, the reaction rate equation simplifies to \( V = \frac{V_{max} \times S}{K_M} \), indicating a first-order dependence on \( S \) because the rate is linearly proportional to \( S \).
Step 2: High Substrate Concentration (\( S \gg K_M \)):
When substrate concentrations are much higher than \( K_M \), the enzyme sites are nearly all saturated, making the rate approach \( V_{max} \) and becoming essentially independent of any additional increase in \( S \).
Step 3: Independence of \( K_M \) from Enzyme Concentration:
\( K_M \) is a characteristic of the enzyme-substrate affinity and is not dependent on the total concentration of the enzyme. It reflects the substrate concentration at which the reaction rate is half of \( V_{max} \) and remains constant for a given enzyme and substrate under specific conditions.
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