The correct answer is (1).

Introduction

Enzyme inhibition is a cornerstone of biochemistry and pharmacology, and visualizing its effects on kinetic parameters is essential. The Lineweaver-Burk double reciprocal plot provides a clear way to distinguish between competitive, non-competitive, and uncompetitive inhibition based on their effects on VmaxVmax and KmKm. In reversible non-competitive inhibition, the x-intercept—used for determining KmKm—remains unchanged, even though the slope and y-intercept change. This article explains how to use the correct plot to determine KmKm in the presence of reversible non-competitive inhibitors.

Basis of Non-Competitive Inhibition

• Non-competitive inhibitors bind to sites other than the active site, affecting enzyme activity regardless of substrate concentration.

• This mechanism lowers VmaxVmax but does not alter KmKm (enzyme’s affinity for substrate remains the same).

• The effect can be visualized using the Lineweaver-Burk plot ($1/V$ vs. $1/[S]$), which linearizes Michaelis-Menten kinetics.

Lineweaver-Burk Plot Features in Non-Competitive Inhibition

• y-intercept (1/Vmax1/Vmax) increases: Indicates decrease in VmaxVmax.

• x-intercept (−1/Km−1/Km) remains the same: Indicates KmKm is unchanged.

• Both inhibitor and no-inhibitor lines intersect the x-axis at the same point.

• The slopes differ due to the decrease in VmaxVmax.

Correct Plot Identification

• In the provided images:

  • Plot (1) shows two lines (with and without inhibitor) intersecting at the same x-intercept (−1/Km−1/Km), but with different slopes and y-intercepts.

  • This matches the textbook case for reversible non-competitive inhibition.

Why Other Plots Are Incorrect

• Plot (2): Lines have different x-intercepts—indicative of competitive inhibition, not non-competitive.

• Plot (3) and (4): Do not reflect the unchanged x-intercept which is unique to non-competitive inhibition.

Summary Table: Lineweaver-Burk Changes

Conclusion

In reversible non-competitive enzyme inhibition, the Lineweaver-Burk plot for Km determination is identified by the unchanged x-intercept regardless of the presence of inhibitor. This is represented by plot (1), where both lines intersect the x-axis at the same position.