An enzyme is governed by Michaelis-Menten Kinetics. The apparent 𝐾𝑀 increases four fold due to the addition of inhibitor but the reaction rate declines by 50%. The substrate concentration in the reaction is:
A. 𝑆 = 𝐾𝑀
B. 𝑆 = 2 𝐾𝑀
C. 𝑆 = 3 𝐾𝑀
D. 𝑆 = 4 𝐾

Title: Understanding Michaelis-Menten Kinetics with Inhibitor Impact on KMK_M and Reaction Rate

Slug: michaelis-menten-kinetics-inhibitor-effect

Meta Description: Explore how inhibitors affect enzyme kinetics. Learn how a fourfold increase in KMK_M with 50% rate reduction reveals the substrate concentration in Michaelis-Menten reactions.

Michaelis-Menten Kinetics and Inhibitor Influence

Enzyme kinetics is a cornerstone of biochemistry, with the Michaelis-Menten model being one of the most widely used frameworks to describe the rate of enzymatic reactions. In this model, the reaction rate depends on the substrate concentration [S][S], the maximum velocity

V     =  Vmax/Km +Km

Problem Statement:

An enzyme follows Michaelis-Menten kinetics. Upon adding an inhibitor:

• The apparent Km increases 4-fold
• The reaction rate drops by 50%

1/2 V=Vmax[S]\ 4KM+[S]

We are to determine the substrate concentration [S][S] relative to the original Km

✅ Correct Answer: B.   S=2Km = 2Km

Step-by-Step Explanation

Michaelis-Menten Equation:

Why the Other Options Are Incorrect

• A.     S=Km            S = Km → Would not result in a 50% reduction with 4x Km
• C. S=3Km               S = 3Km  and
•  D. S=4Km      = 4Km  → Would give lesser effect than 50% drop

Key Takeaways

• A fourfold increase in Km with 50% rate drop points to competitive inhibition.
• Substrate concentration at this point is twice the original Km