Introduction

Enzyme kinetics helps us understand how enzymes behave in the presence and absence of inhibitors.
A commonly used graphical method is the Lineweaver–Burk plot, which is a double
reciprocal plot of reaction velocity and substrate concentration.

In this question, enzyme kinetics is studied in the presence (+I) and absence (–I) of a reversible inhibitor,
and the dissociation constant (Ki) is to be determined.

Understanding the Given Graph

• Y-axis represents 1/V₀
• X-axis represents 1/[S]
• Two straight lines are observed: one with inhibitor (+I) and one without inhibitor (–I)

Both lines intersect at the same Y-intercept, indicating that V_max remains unchanged.
However, the slope increases in the presence of inhibitor.

This behavior is characteristic of competitive inhibition.

Theory: Competitive Inhibition

For competitive inhibition, the slope of the Lineweaver–Burk plot changes according to the equation:

Slope_+I = Slope_–I (1 + [I]/K_i)

Where:

• [I] = concentration of inhibitor
• K_i = dissociation constant of enzyme–inhibitor complex

Data Given

• Inhibitor concentration, [I] = 3.0 × 10⁻³ M
• Slope with inhibitor is approximately double the slope without inhibitor

Calculation of Ki

Since the slope doubles:

1 + [I]/K_i = 2

Solving:

[I]/K_i = 1

K_i = [I] = 3.0 × 10⁻³ M

Correct Answer

Option (C): 3 × 10⁻³ M

Explanation of All Options

Option (A): 1 × 10⁻³ M

This value would produce a much larger slope increase than observed in the graph.

Option (B): 2 × 10⁻³ M

This would give a slope ratio of 2.5, which does not match the graph.

Option (C): 3 × 10⁻³ M

This perfectly matches the observed two-fold increase in slope.

Option (D): 4 × 10⁻³ M

This value would cause a smaller slope increase than shown in the graph.

Final Conclusion

The inhibitor shows competitive inhibition, and the dissociation constant
(K_i) calculated from the Lineweaver–Burk plot is:

3 × 10⁻³ M