The GATE Grind

GATE 2025 CH – Question 31

Chemical Reaction Engineering · Enzyme kinetics: Michaelis-Menten and Monod models · 1 mark · Multiple select

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?

  1. For $S \ll K_M$, the reaction is apparent first-order in $S$.
  2. For $S \gg K_M$, the reaction rate is nearly independent of $S$.
  3. For $S = K_M$, the rate of reaction equals $V_{max}$.
  4. $K_M$ is independent of the total enzyme concentration.

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Show answer and explanation

Correct answer: (A) For $S \ll K_M$, the reaction is apparent first-order in $S$.; (B) For $S \gg K_M$, the reaction rate is nearly independent of $S$.; (D) $K_M$ is independent of the total enzyme concentration.

Explanation

The rate is $r = \frac{V_{max}S}{K_M + S}$. For $S \ll K_M$ it becomes $\frac{V_{max}}{K_M}S$, which is first order. For $S \gg K_M$ it becomes $V_{max}$, independent of $S$. At $S = K_M$ the rate is $\frac{V_{max}}{2}$, not $V_{max}$. $K_M = \frac{k_{-1} + k_2}{k_1}$ depends only on rate constants, so it does not depend on the enzyme concentration (while $V_{max} = k_2E_0$ does).