# DBT JRF 2022 — Question 27

Exam: DBT JRF 2022 · Section: A · Topic: Biochemistry › Enzyme Kinetics - Michaelis-Menten · Difficulty: Medium

## Question

An enzyme is governed by Michaelis-Menten Kinetics. The apparent $K_M$ increases four fold due to the addition of inhibitor but the reaction rate declines by 50%. The substrate concentration in the reaction is:

## Options

- **A.** $S = K_M$
- **B.** $S = 2K_M$
- **C.** $S = 3K_M$
- **D.** $S = 4K_M$

## Answer

Option B

## Explanation

Michaelis-Menten kinetics with competitive inhibitor: In competitive inhibition: • Apparent $K_M' = 4K_M$ (given, 4-fold increase) • $V_{max}$ remains unchanged • Reaction rate halved: $v' = \frac{v}{2}$ From Michaelis-Menten equation: $v = \frac{V_{max}[S]}{K_M + [S]}$ and $\frac{v}{2} = \frac{V_{max}[S]}{4K_M + [S]}$ Dividing the first by the second: $2 = \frac{4K_M + [S]}{K_M + [S]}$ $2K_M + 2[S] = 4K_M + [S]$ $[S] = 2K_M$ Answer: $S = 2K_M$ (Option 2).

Source: https://mypyqbuddy.com/questions/an-enzyme-is-governed-by-michaelis-menten-kinetics-the-6a104cd5920734408bc0c6f8