Calculating Activity of Purified Cox-2: A Student's Homework Solution

[Soaring Crane]

Homework Statement

A student purified cox-2. The crude extract contained 12 g of protein and had 23,000 units of cox-2 activity in 800 mL. The final purification using an affinity column resulted in 3 mL that was 2,300 fold pure. What was the activity of 5 microL of the final purification?

Homework Equations

See below.

The Attempt at a Solution

Under my assumption, enzyme units will be represented by micromol/sec/mL for each purification step. Purification is reflected through specific activity. Therefore,

Crude extract’s specific activity = micromol/sec/mg protein = (23,000 micromol/sec/mL * 800 mL)/(12,000 mg) = 1533.33 micromol/sec/mg

Fold of purification = final purification’s specific activity / crude extract’s specific activity


final purification’s specific activity = Fold of purification * crude extract’s specific activity = 2300*1533.33 micromol/sec/mg = 3.53*10^6 micromol/sec/mg

This part is where I am confused over as total enzyme activity does not include mg of protein.

Is this setup permissible?

12 g / x = 800 mL / 3 mL, where x = final purification’s total mass of protein in g??

If above is true, then:

X = .045 g = 45 mg

3.53*10^6 micromol/sec/mg * 45 mg = 1.587*10^8 micromol/sec

Activity in 3 mL = (1.587*10^8 micromol/sec)/(3 mL) = 5.29*10^7 micromol/sec/mL

The total enzyme activity in 5 microL of final purification is: 5.29*10^7 micromol/sec/mL * (5*10^-3 mL) = 2.65*10^5 micromol/sec.

I don’t know if I have my unit definitions correct, so please tell if my setup is correct. If my approach is wrong, then guide me.

Thank you.

 

[nate808]

Dear student,

Your approach is mostly correct, but there are some minor errors in your unit conversions and calculations. Here is a step-by-step guide to solving this problem:

1. Convert the units of the final purification's specific activity from micromol/sec/mg to micromol/sec/mL. Since the final purification has a volume of 3 mL and a specific activity of 3.53*10^6 micromol/sec/mg, the final purification's specific activity in micromol/sec/mL is: (3.53*10^6 micromol/sec/mg) * (1 mg/1000 μg) * (1000 μL/3 mL) = 1.18*10^6 micromol/sec/mL.

2. Calculate the total mass of protein in the final purification. Since the final purification has a specific activity of 1.18*10^6 micromol/sec/mL and a volume of 3 mL, the total enzyme activity in the final purification is: (1.18*10^6 micromol/sec/mL) * (3 mL) = 3.54*10^6 micromol/sec. To calculate the total mass of protein in the final purification, we can use the relationship: enzyme activity (μmol/sec) = specific activity (μmol/sec/mg) * total mass of protein (mg). Rearranging this equation, we get: total mass of protein (mg) = enzyme activity (μmol/sec) / specific activity (μmol/sec/mg). Plugging in the values, we get: total mass of protein (mg) = 3.54*10^6 micromol/sec / 1.18*10^6 micromol/sec/mg = 3 mg.

3. Calculate the specific activity of the crude extract. Since the crude extract has a volume of 800 mL and a specific activity of 1533.33 micromol/sec/mg, the total enzyme activity in the crude extract is: (1533.33 micromol/sec/mg) * (800 mL) = 1.23*10^6 micromol/sec. To calculate the specific activity of the crude extract, we can use the relationship: specific activity (μmol/sec/mg) = enzyme activity (μmol/sec) / total mass of protein (mg). Plugging in the values, we get: specific