Calculating specific activity in enzyme purification: A purified sample contains 10 μg of protein and an enzyme activity of 1 unit (1 μmol ATP synthesized per second). What is the specific activity of this final sample?

Introduction / Context:
Specific activity is a central metric in enzyme purification, defined as catalytic units per milligram of total protein. It summarizes both purity and functional yield across steps.

Given Data / Assumptions:

• Total protein in the sample: 10 μg.
• Total activity: 1 unit (1 μmol product per second).
• Units are per second; mass must be expressed in mg.

Concept / Approach:
Specific activity = total activity / mass of protein. Convert micrograms to milligrams before division to keep units consistent.

Step-by-Step Solution:
Convert mass: 10 μg = 10 * 10^-6 g = 0.01 mg.Compute: specific activity = 1 unit / 0.01 mg.Result: 100 units/mg.

Verification / Alternative check:
Check dimensions: (units) / (mg) gives units/mg. If the same activity were in 1 mg, value would be 1 unit/mg; because mass is 100× smaller (0.01 mg), specific activity is 100× larger (100 units/mg).

Why Other Options Are Wrong:

• 50 or 0.1 units/mg: Arise from incorrect mass conversion or arithmetic.
• 1,000 or 10,000 units/mg: Overestimate by factors of 10–100.

Common Pitfalls:
Forgetting to convert μg to mg; confusing specific activity with total activity; neglecting to report standardized units.

Final Answer:
100 units/mg.