An enzyme sample contains 24 mg protein/mL. Of this sample, 20 microliters in a standard incubation volume of 0.1 mL catalyzed the incorporation of glucose into glcogen at a rate of 1.6 nmol/min. Of this sample, 50 mL were fractionated by ammonium sulfate precipitation. The fraction precipitating between 30 and 50% saturation was redissolved in a total volume of 10 mL and dialyzed. The solution after dialysis had 12 mL and contained 30 mg protein/mL. Of the purified fraction, 20 microliters catalyzed the reaction rate of 5.9 nmol/min under the standard assay conditions. calculate the following:

A. The recovery of enzyme after the ammonium sulfate step.
B. The fold purification after the ammonium sulfate step.

by the way, this question is different from the previous question i asked.

To calculate the recovery of enzyme after the ammonium sulfate step, we need to determine the amount of enzyme recovered after fractionation and dialysis, compared to the initial amount of enzyme in the original sample.

First, let's calculate the initial amount of enzyme in the original sample (before fractionation and dialysis):
Original sample concentration = 24 mg protein/mL
Original sample volume = 50 mL

Total amount of enzyme in original sample = Original sample concentration * Original sample volume
= 24 mg protein/mL * 50 mL
= 1200 mg protein

Next, let's calculate the amount of enzyme recovered after fractionation and dialysis:
Final solution concentration after dialysis = 30 mg protein/mL
Final solution volume after dialysis = 12 mL

Total amount of enzyme in the final solution = Final solution concentration * Final solution volume
= 30 mg protein/mL * 12 mL
= 360 mg protein

Finally, we can calculate the recovery of enzyme after the ammonium sulfate step:
Recovery (%) = (Amount of enzyme recovered / Initial amount of enzyme) * 100
= (360 mg protein / 1200 mg protein) * 100
= 30%

Therefore, the recovery of enzyme after the ammonium sulfate step is 30%.

To calculate the fold purification after the ammonium sulfate step, we need to determine how much the purification process has concentrated the enzyme compared to the original sample.

First, let's calculate the specific activity of the original sample:
Enzyme activity from original sample = 1.6 nmol/min
Initial sample volume used in the assay = 0.1 mL

Specific activity (SA) of the original sample = Enzyme activity from original sample / Initial sample volume used in the assay
= 1.6 nmol/min / 0.1 mL
= 16 nmol/min/mL

Next, let's calculate the specific activity of the purified fraction:
Enzyme activity from purified fraction = 5.9 nmol/min
Volume of purified fraction used in the assay = 20 μL, which is equivalent to 0.02 mL

Specific activity (SA) of the purified fraction = Enzyme activity from purified fraction / Volume of purified fraction used in the assay
= 5.9 nmol/min / 0.02 mL
= 295 nmol/min/mL

Finally, we can calculate the fold purification:
Fold purification = Specific activity of the purified fraction / Specific activity of the original sample
= 295 nmol/min/mL / 16 nmol/min/mL
= 18.44

Therefore, the fold purification after the ammonium sulfate step is 18.44.