Introduction

The type II dehydroquinase k_cat/K_m ratio is a key measure of catalytic
efficiency in enzyme kinetics. It combines the turnover number (k_cat)
and substrate affinity (K_m) within the Michaelis–Menten framework.
This calculation is commonly tested in biotechnology, biochemistry, and molecular biology examinations.

Given Data

• Molecular mass of enzyme = 18 kDa = 18,000 g·mol^-1
• Enzyme amount = 1.8 μg = 1.8 × 10^-6 g
• V_max = 0.0134 μmol·min^-1
• K_m = 25 μM = 25 × 10^-6 M

Step-by-Step Calculation

Step 1: Convert Enzyme Mass to Moles

Moles of enzyme = (1.8 × 10^-6 g) / (18,000 g·mol^-1)

= 1 × 10^-10 mol

Step 2: Convert V_max to mol·s^-1

V_max = 0.0134 μmol·min^-1
= 0.0134 × 10^-6 mol·min^-1

= (0.0134 × 10^-6) / 60

= 2.233 × 10^-10 mol·s^-1

Step 3: Calculate k_cat

k_cat = V_max / [E]_total = (2.233 × 10^-10 mol·s^-1) / (1 × 10^-10 mol) = 2.233 s^-1

Step 4: Calculate k_cat/K_m

k_cat/K_m = 2.233 s^-1 / (2.5 × 10^-5 M)

= 8.93 × 10⁴ M^-1·s^-1

Final Answer

k_cat/K_m = 8.93 × 10⁴ M^-1·s^-1

Key Concepts

• k_cat (Turnover Number):
  Maximum number of substrate molecules converted per enzyme per second.
• K_m (Michaelis Constant):
  Substrate concentration at which reaction rate is half of V_max.
• k_cat/K_m:
  Measure of catalytic efficiency; diffusion-limited enzymes approach
  10⁸–10⁹ M^-1·s^-1.

Conclusion

This type II dehydroquinase enzyme kinetics example highlights the importance
of correct unit conversion when calculating catalytic efficiency.
The final k_cat/K_m value of
8.93 × 10⁴ M^-1·s^-1
is well within the expected range for metabolic enzymes and is highly relevant
for biotechnology and molecular biology examinations.