Question

Match List-I with List-II:

Choose the correct answer from the options given below:

• (A) - (IV), (B) - (III), (C) - (II), (D) - (I)
• (A) - (III), (B) - (II), (C) - (I), (D) - (IV)
• (A) - (II), (B) - (I), (C) - (IV), (D) - (III)
• (A) - (III), (B) - (IV), (C) - (I), (D) - (II)

Hint:

Remember the physical meaning of \( K_m \): it is the substrate concentration at which the reaction velocity is exactly half of the maximum velocity (\( V_{\text{max}} / 2 \)). This immediately links (C) to (IV).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
The Michaelis-Menten kinetic model describes how the initial rate of an enzyme-catalyzed reaction (\( v \)) depends on the concentration of the substrate (\( [S] \)):
\[ v = \frac{V_{\text{max}}[S]}{K_m + [S]} \] where \( V_{\text{max}} \) is the maximum velocity when the enzyme is saturated, and \( K_m \) is the Michaelis constant, reflecting the affinity of the enzyme for the substrate.

Step 2: Detailed Explanation:
Let us analyze the biochemical characteristics for each scenario listed:
1. Case A: \( [S] \ll K_m \)
- When substrate concentration is extremely low relative to \( K_m \), the sum in the denominator can be simplified: \( K_m + [S] \approx K_m \).
- The Michaelis-Menten equation simplifies to:
\[ v \approx \frac{V_{\text{max}}}{K_m} [S] \] - Since \( V_{\text{max}} / K_m \) is constant, the initial rate of the reaction is directly proportional to the substrate concentration. This is the definition of first-order kinetics.
Thus, (A) matches with (II).
2. Case B: \( [S] \gg K_m \)
- When the enzyme is saturated with excess substrate, \( K_m + [S] \approx [S] \).
- The equation simplifies to:
\[ v \approx \frac{V_{\text{max}}[S]}{[S]} = V_{\text{max}} \] - The rate of the reaction is constant and independent of the substrate concentration. This corresponds to zero-order kinetics.
Thus, (B) matches with (I).
3. Case C: \( [S] = K_m \)
- Substituting \( [S] = K_m \) directly into the equation:
\[ v = \frac{V_{\text{max}}[S]}{[S] + [S]} = \frac{V_{\text{max}}[S]}{2[S]} = \frac{1}{2} V_{\text{max}} \] - Under these conditions, the rate of the reaction is exactly equal to half of the maximum velocity.
Thus, (C) matches with (IV).
4. Case D: \( [S] < [E_T] \)
- Standard Michaelis-Menten kinetics relies on the assumption that the total substrate concentration is far greater than the total enzyme concentration (\( [S] \gg [E_T] \)), meaning free substrate concentration approximately equals total substrate concentration.
- When the enzyme concentration is high relative to the substrate concentration (\( [S] < [E_T] \)), this free ligand assumption is violated.
- Under these conditions, standard parameters like \( K_m \) and \( V_{\text{max}} \) do not define the reaction kinetics accurately.
Thus, (D) matches with (III).

Step 3: Final Answer:
The correct matching sequence is (A)-(II), (B)-(I), (C)-(IV), and (D)-(III), which corresponds to option (C).