Question

Which of the following parameters remains unchanged in the two Lineweaver-Burk plots of an enzyme drawn in the absence and presence of a competitive inhibitor respectively?

• A. Michaelis Menten constant (Km)
• B. Slope
• C. X-intercept
• D. Y-intercept

Hint:

Competitive Inhibition:
Vmax = Unchanged (Y-intercept is the same).
Km = Increases (Lines cross exactly on the Y-axis).
Mnemonic: "Competition? High Substrate can still reach the Finish line (Vmax)!"

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
The question explores the kinetics of enzyme inhibition, specifically focusing on competitive inhibition and its representation on a Lineweaver-Burk plot (double-reciprocal plot).
Competitive inhibition occurs when an inhibitor molecule closely resembles the substrate and competes for the same active site on the enzyme.
Key Formula or Approach:
The Lineweaver-Burk equation is a linear transformation of the Michaelis-Menten equation:
\[ \frac{1}{v} = \frac{K_m}{V_{max}} \cdot \frac{1}{[S]} + \frac{1}{V_{max}} \]
This follows the form of a straight line equation \( y = mx + c \), where:
- The Slope (\( m \)) is \( K_m / V_{max} \).
- The Y-intercept (\( c \)) is \( 1 / V_{max} \).
- The X-intercept is \( -1 / K_m \).

Step 2: Detailed Explanation:

• Mechanism of Competitive Inhibition: In competitive inhibition, the inhibitor (I) binds only to the free enzyme (E), preventing the substrate (S) from binding. This effectively reduces the concentration of free enzyme available for the substrate.

• Effect on \( V_{max} \): If the substrate concentration is increased to a sufficiently high level, it will eventually outcompete all inhibitor molecules for the active sites. Therefore, the maximum velocity (\( V_{max} \)) that the enzyme can reach remains identical to the uninhibited state.

• Effect on \( K_m \): Because the substrate must "fight" the inhibitor for the site, more substrate is required to reach half of the maximum velocity. This causes an increase in the apparent Michaelis constant (\( K_m \)). Specifically, \( K_{m,app} = K_m(1 + [I]/K_i) \).

• Graphical Representation: On a Lineweaver-Burk plot, the absence of a change in \( V_{max} \) means that the value of \( 1 / V_{max} \) stays constant. Since \( 1 / V_{max} \) is the point where the line crosses the vertical axis (Y-intercept), this point remains fixed.

• Changes in Other Parameters: The slope increases because the numerator (\( K_m \)) gets larger while the denominator (\( V_{max} \)) stays the same. The X-intercept (\( -1/K_m \)) moves closer to zero as \( K_m \) increases.

Step 3: Final Answer:
In competitive inhibition, the Y-intercept remains unchanged because the maximum velocity (\( V_{max} \)) of the reaction is not altered.