150. One microgram of a pure enzyme (MW: 92,000) catalyzed a reaction at a rate of 0.50 µmoles/min under
optimum conditions. The specific activity of the enzyme [(µmoles/min)/mg protein] is:
(1) 0.5
(2) 5.0
(3) 500
(4) 5000

Detailed Explanation:

Question:
One microgram of a pure enzyme (MW: 92,000) catalyzed a reaction at a rate of 0.50 µmoles/min under optimum conditions. What is the specific activity of the enzyme?

Options:

1. 0.5

2. 5.0

3. 500

4. 5000

Solution:

To calculate the specific activity of an enzyme, we use the following formula:

Specific Activity=Reaction rate (µmoles/min)Amount of enzyme (mg)\text{Specific Activity} = \frac{\text{Reaction rate (µmoles/min)}}{\text{Amount of enzyme (mg)}}Specific Activity=Amount of enzyme (mg)Reaction rate (µmoles/min)​

Step 1: Calculate the amount of enzyme in milligrams (mg)

We know that the enzyme’s molecular weight (MW) is 92,000, and we have 1 µg of enzyme. To convert this into milligrams (mg):

$$1\mu g=0.001mg$$

Step 2: Calculate the specific activity

Given that the enzyme catalyzed the reaction at a rate of 0.50 µmoles/min and the enzyme amount is 0.001 mg, we can now calculate the specific activity:

Specific Activity=0.50 μmoles/min0.001 mg=500 (μmolesmin⋅mg)\text{Specific Activity} = \frac{0.50 \, \mu \text{moles/min}}{0.001 \, \text{mg}} = 500 \, \left( \frac{\mu \text{moles}}{\text{min} \cdot \text{mg}} \right)Specific Activity=0.001mg0.50μmoles/min​=500(min⋅mgμmoles​)

Thus, the specific activity of the enzyme is 500 µmoles/min/mg.

Correct Answer:

The correct answer is (3) 500.

Conclusion:

To calculate the specific activity of an enzyme, we need to know the enzyme’s reaction rate and its amount in milligrams. In this case, we found that the enzyme’s specific activity was 500 µmoles/min/mg, based on the given data. This calculation is crucial in determining the efficiency and effectiveness of an enzyme in biochemical processes.