Which of the following statements about Michaelis-Menten kinetics is correct?
I. A high Michaelis constant (`K_(m)`) indicates a high affinity of an enzyme for its substrate.
II. A low Michaelis constant (`K_(m)`) indicates a high affinity of an enzyme for its substrate.
III. The Michaelis constant (`K_(m)`) of an enzyme increases when the enzyme concentration is increased.
IV. The Michaelis constant (`K_(m)`) of an enzyme is unchanged when the enzyme concentration is increased.

Options

A. I and II are correct
B. II and III are correct
C. ll and IV are correct
D. I and III are correct

Answer

To determine which statements about Michaelis-Menten kinetics are correct, we need to analyze each statement based on our understanding of the Michaelis constant (Km) and its relationship with enzyme activity.

### Step-by-Step Solution:

1. **Understanding Km**: The Michaelis constant (Km) is a measure of the affinity of an enzyme for its substrate. It is defined as the substrate concentration at which the reaction velocity is half of the maximum velocity (Vmax).

2. **Analyzing Statement I**:
- Statement: "A high Michaelis constant (Km) indicates a high affinity of an enzyme for its substrate."
- Analysis: This statement is incorrect. A high Km value indicates a low affinity of the enzyme for its substrate because it requires a higher concentration of substrate to reach half of Vmax.

3. **Analyzing Statement II**:
- Statement: "A low Michaelis constant (Km) indicates a high affinity of an enzyme for its substrate."
- Analysis: This statement is correct. A low Km value means that the enzyme can achieve half of Vmax at a lower substrate concentration, indicating a high affinity for the substrate.

4. **Analyzing Statement III**:
- Statement: "The Michaelis constant (Km) of an enzyme increases when the enzyme concentration is increased."
- Analysis: This statement is incorrect. The Km value is an intrinsic property of the enzyme-substrate interaction and does not change with enzyme concentration.

5. **Analyzing Statement IV**:
- Statement: "The Michaelis constant (Km) of an enzyme is unchanged when the enzyme concentration is increased."
- Analysis: This statement is correct. The Km remains constant regardless of changes in enzyme concentration, as it is a characteristic of the enzyme's affinity for the substrate.

### Conclusion:
From the analysis, we find that:
- Statement II and Statement IV are correct.
- Statements I and III are incorrect.

### Final Answer:
The correct statements about Michaelis-Menten kinetics are:
- II. A low Michaelis constant (Km) indicates a high affinity of an enzyme for its substrate.
- IV. The Michaelis constant (Km) of an enzyme is unchanged when the enzyme concentration is increased.

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