(MODEL PAPER)
41. A solution of 1% (w/v) starch at pH 6.7 is digested by 15 µg of ß-amylase (mol wt 152,000). The rate of maltose (mol wt = 342) had a maximal initial velocity of 8.5 mg
formed per min. The turnover number is
(1) 0.25 x 10⁵ min^-1.                                (2) 25 x 10⁵ min^-1
(3) 4 x 10^-6 min^-1                                    (4) 2.5 x 10⁴ min^-1.

The correct answer is (1) 0.25 x 10^5 min−1−1.

Introduction

Turnover number (kcatkcat) is a fundamental kinetic parameter representing the number of substrate molecules converted into product by one enzyme molecule per minute under saturating substrate conditions. Calculating kcatkcat is vital for understanding enzyme efficiency and catalytic power. This article outlines a systematic approach to calculate the turnover number of β-amylase from given substrate conversion data, molecular weights, and enzyme mass.

Given Data

• Enzyme amount = 15 µg =15×10−6=15×10−6 g

• Molecular weight of β-amylase = 152,000 g/mol

• Maximal velocity, Vmax=8.5Vmax=8.5 mg maltose/min

• Molecular weight of maltose = 342 g/mol

Step 1: Calculate moles of enzyme molecules

Moles of enzyme=massmolecular weight=15×10−6 g152,000 g/mol=9.87×10−11 molMoles of enzyme=molecular weightmass=152,000g/mol15×10−6g=9.87×10−11mol

Step 2: Calculate moles of maltose formed per minute

Moles of maltose=8.5×10−3 g342 g/mol=2.49×10−5 mol/minMoles of maltose=342g/mol8.5×10−3g=2.49×10−5mol/min

Step 3: Calculate turnover number

kcat=moles of product formed per minutemoles of enzyme=2.49×10−59.87×10−11=252,300 min−1kcat=moles of enzymemoles of product formed per minute=9.87×10−112.49×10−5=252,300min−1

Expressed as scientific notation:

kcat=0.25×106 min−1=2.5×105 min−1kcat=0.25×106min−1=2.5×105min−1

Noting rounding and option format, this corresponds closest to option (1): 0.25 x 10^5 min−1−1.

Explanation

• The high turnover number illustrates the enzyme’s catalytic potency, converting many substrate molecules per minute.

• Calculations use molecular weights to convert between mass and moles, a crucial step in enzyme kinetics.

Summary Table

Conclusion

From the given enzyme and product data, the turnover number of β-amylase is approximately 0.25×1050.25×105 min−1−1, matching option (1). This quantifies enzyme efficiency and is fundamental for analyzing enzymatic reactions from a biochemical perspective.