How to Calculate Michaelis Constant Km from Lineweaver-Burk Plot

Q.21 An enzyme-catalyzed conversion of a substrate at 298 K proceeds by a Michaelis-Menten mechanism. The Lineweaver-Burk plot for the analysis of the experimental data has an intercept along the y-axis of 0.357 mmol–1 dm3 s and a slope of 2.10 s. The CORRECT Michaelis constant for the reaction is ________ (rounded off to 2 decimal places). (A) 5.88 mmol dm–3 (B) 5.88 mmol dm–3 s–1 (C) 2.80 mmol dm–3 (D) 2.80 mmol dm–3 s–1

Q.21 An enzyme-catalyzed conversion of a substrate at 298 K proceeds by a Michaelis-Menten mechanism.

The Lineweaver-Burk plot for the analysis of the experimental data has an intercept along the
y-axis of 0.357 mmol–1 dm3 s and a slope of 2.10 s.
The CORRECT Michaelis constant for the reaction is ________ (rounded off to 2 decimal places).
  • (A) 5.88 mmol dm–3
  • (B) 5.88 mmol dm–3 s–1
  • (C) 2.80 mmol dm–3
  • (D) 2.80 mmol dm–3 s–1

The Michaelis constant (Km) for this enzyme reaction is 5.88 mmol dm⁻³, corresponding to option (A).

This value comes from analyzing the Lineweaver-Burk plot data using the standard enzyme kinetics equations. The calculation confirms the correct units and eliminates other options.

Lineweaver-Burk Equation

The Lineweaver-Burk plot transforms the Michaelis-Menten equation into a linear form:

1/v=Km/Vmax.1/[S]+1/[Vmax]

Here, the y-intercept equals 1/Vmax=0.357 mmol-1dm³s, so Vmax=1/0.357≈2.80 mmol dm⁻³ s⁻¹.
The slope equals km/Vmax= 2.10 s.

Km Calculation

Solve for Km: Km=slope × Vmax=2.10×2.80=5.88 mmol dm⁻³

Km represents substrate concentration at half Vmax and carries units of concentration (mmol dm⁻³).

Option Analysis

Option Value Units Correct? Reason
(A) 5.88 mmol dm⁻³ ✅ Yes Matches Km = slope/Vmax with correct concentration units
(B) 5.88 mmol dm⁻³ s⁻¹ ❌ No Wrong units (rate, not concentration)
(C) 2.80 mmol dm⁻³ ❌ No Equals Vmax, not Km
(D) 2.80 mmol dm⁻³ s⁻¹ ❌ No Matches Vmax value and units

Discover how to determine the Michaelis constant (Km) from a Lineweaver-Burk plot in enzyme kinetics

This guide solves the exact CSIR NET question with y-intercept 0.357 mmol⁻¹ dm³ s and slope 2.10 s, yielding Km = 5.88 mmol dm⁻³.

Michaelis-Menten to Lineweaver-Burk Transformation

The hyperbolic Michaelis-Menten curve (v =Vmax[S]/Km+[S] becomes linear when taking reciprocals. Plot 1/v vs 1/[S]: y-intercept = 1/Vmax, slope = Km/Vmax.

Step-by-Step Km Calculation

  1. Vmax =1/0.357 = 2.80 mmol dm⁻³ s⁻¹
  2. Km = 2.10 × 2.80 = 5.88 mmol dm⁻³

This matches option (A). Options with rate units (s⁻¹) fail as Km measures concentration.

Why Lineweaver-Burk Matters for CSIR NET

Essential for analyzing enzyme inhibition and kinetics in competitive exams. Modern tools prefer nonlinear fitting, but this method remains standard.

 

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