Q.62 First order deactivation rate constants for soluble and immobilized amyloglucosidase
enzyme are 0.03 min-1 and 0.005 min-1, respectively. The ratio of half-life of the immobilized
enzyme to that of the soluble enzyme is (rounded off to the nearest integer) _________
Enzyme Half-Life Ratio: Immobilized vs Soluble Amyloglucosidase (0.03 & 0.005 min⁻¹)
This problem compares the operational stability of soluble and immobilized forms of amyloglucosidase during first-order deactivation, based on their rate constants.
Half-Life Formula
For first-order kinetics:
t₁/₂ = ln(2) / k where ln(2) ≈ 0.693
Half-Life Calculation
Soluble enzyme:
k = 0.03 min⁻¹
t₁/₂ = 0.693 / 0.03 = 23.1 min
Immobilized enzyme:
k = 0.005 min⁻¹
t₁/₂ = 0.693 / 0.005 = 138.6 min
Ratio Determination
Half-life ratio:
t₁/₂(immobilized) / t₁/₂(soluble)
= (0.693/0.005) / (0.693/0.03)
= 0.03 / 0.005
= 6
Thus, immobilization increases enzyme lifespan sixfold.
Comparison Table
| Parameter | Soluble | Immobilized | Notes |
|---|---|---|---|
| k (min⁻¹) | 0.03 | 0.005 | Deactivation constant |
| t₁/₂ (min) | 23.1 | 138.6 | 0.693/k |
| Ratio | 1 | 6 | Half-life imm/sol |
Conclusion
Immobilization substantially stabilizes amyloglucosidase, lowering its deactivation rate and extending its usable lifetime in industrial bioprocesses.
