Specific Activity of Your Tyrosinase Extract

In Assignment 2, you calculated activity in units of tyrosinase activity per volume (U/mL). In principle, this is an activity measure that is comparable between groups. However, in practice, variations in extraction technique from group to group affects how much of the total protein in the mushroom was actually extracted from a given sample. Because of this problem, a more comparable measure is Units of tyrosinase activity per mass of total protein (U/mg of protein), which we will define as specific activity:

$$ \textit{Specific Activity } \mathrm{(U/mg)} = \frac{\textit{Relative Activity } \mathrm{(U/ml)}}{\textit{Total Protein Concentration } \mathrm{(mg/ml)}} $$

When you derive a value from the multiplication or division of two measurements, the relative uncertainty for the derived value is the square root of the sum of the squares of the relative uncertainties of the measurements used to calculate it. For example, for the following molecular weight calculation,

$$ \frac{862 \pm 3\ \mathrm{g}}{1.51 \pm 0.02\ \mathrm{mol}} = 571\ \frac{\mathrm{g}}{\mathrm{mol}} $$

the uncertainty is

$$ \textit{Error} = \textit{Value} \times \sqrt{ \left( \frac{\textit{error}_1}{\textit{mean}_1} \right)^2 + \left( \frac{\textit{error}_2}{\textit{mean}_2} \right)^2 } = 571 \times \sqrt{ \left( \frac{3}{862} \right)^2 + \left( \frac{0.02}{1.51} \right)^2 } = 8. $$

The reported value is 571 ± 8 g/mol.

At the start of lab, prepare to discuss your protein concentration results. Once the class selects one protein concentration method to use, you will calculate specific activity and use this sum-of-squares method to calculate the error on your specific activity measurement. You will enter your results into the shared data spreadsheet before you leave lab.