The specific activity of an enzyme is a measure of its catalytic efficiency per unit of protein. It is calculated using the formula:
$ \text{Specific Activity} = \frac{\text{Enzyme Activity}}{\text{Protein Concentration}} $
The enzyme preparation has an activity of 2 Units per 20 $\mu$l. To find the activity per milliliter (ml), we first convert $\mu$l to ml:
Now, calculate the activity in Units per ml:
$ \text{Activity per ml} = \frac{2 \text{ Units}}{0.02 \text{ ml}} = 100 \text{ Units/ml} $
The protein concentration is given directly:
$ \text{Protein Concentration} = 0.4 \text{ mg/ml} $
Using the formula for specific activity:
$ \text{Specific Activity} = \frac{100 \text{ Units/ml}}{0.4 \text{ mg/ml}} $
$ \text{Specific Activity} = \frac{100}{0.4} \ \frac{\text{Units}}{\text{mg}} $
$ \text{Specific Activity} = 250 \ \frac{\text{Units}}{\text{mg}} $
Therefore, the specific activity of the enzyme is 250 Units/mg.