Chapter 3, Problem 18P

Interpretation Introduction

Interpretation:

The given table should be completed.

Concept introduction:

The formula to calculate specific activity of the protein is as follows:

$\text{Specific activity}=\frac{\text{total activity of the protein}}{\text{total amount of protein}}$   ....... (1)

The formula to calculate the percentage yield is as follows:

$\%\text{yield}=\frac{\text{total enzyme activity}}{\text{starting total activity}}\times 100$   ....... (2)

The formula to calculate the purification level is as follows:

$\text{Purification level}=\frac{\text{specific activity}}{\text{initial specific activity}}$   ....... (3)

Answer to Problem 18P

The given table is completed as follow:

$\begin{array}{cccccc}\begin{array}{l}\text{Purification}\\ \text{procedure}\end{array}& \begin{array}{l}\text{Total protein}\\ \left(\text{mg}\right)\end{array}& \begin{array}{l}\text{Total Activity}\\ \left(\text{units}\right)\end{array}& \begin{array}{l}\text{Specific}\\ \text{acitivity}\\ \left(\text{units/mg}\right)\end{array}& \begin{array}{l}\text{Purification}\\ \text{level}\end{array}& \begin{array}{l}\text{Yield}\\ \left(\text{\%}\right)\end{array}\\ \text{Crude extract}& 20000& 4000000& 200& 1& 100\\ \begin{array}{l}{\left({\text{NH}}_4\right)}_2{\text{SO}}_4\\ \text{precipitation}\end{array}& 5000& 3000000& 600& 3& 75\\ \begin{array}{l}\text{DEAE-cellulose}\\ \text{chromatography}\end{array}& 1500& 1000000& 667& 3.3& 25\\ \begin{array}{l}\text{Gel-filtration}\\ \text{chromatography}\end{array}& 500& 750000& 1500& 7.5& 19\\ \begin{array}{l}\text{Affinity}\\ \text{chromatography}\end{array}& 45& 675000& 15000& 75& 17\end{array}$

Explanation of Solution

The formula to calculate specific activity of the protein is as follows:

$\text{Specific activity}=\frac{\text{total activity of the protein}}{\text{total amount of protein}}$   ....... (1)

Specific activity for crude extract is as follows:

Substitute $4000000\text{ unit}$ for total activity of protein and $20000$ for total amount of protein in equation (1)

$\begin{array}{c}\text{Specific activity}=\frac{4000000\text{ unit}}{\text{20000 mg}}\\ =200\text{ unit/mg}\end{array}$

Specific activity for ${\left({\text{NH}}_4\right)}_2{\text{SO}}_4$ precipitation is as follows:

Substitute $3000000\text{ unit}$ for total activity of protein and $5000$ for total amount of protein in equation (1)

$\begin{array}{c}\text{Specific activity}=\frac{3000000\text{ unit}}{\text{5000 mg}}\\ =600\text{ unit/mg}\end{array}$

Specific activity for DEAE-cellulose chromatography is as follows:

Substitute $1000000\text{ unit}$ for total activity of protein and $1500$ for total amount of protein in equation (1)

$\begin{array}{c}\text{Specific activity}=\frac{1000000\text{ unit}}{\text{1500 mg}}\\ =666.67\text{ unit/mg}\end{array}$

Specific activity for gel-filtration chromatography is as follows:

Substitute $750000\text{ unit}$ for total activity of protein and $500$ for total amount of protein in equation (1)

$\begin{array}{c}\text{Specific activity}=\frac{750000\text{ unit}}{\text{500 mg}}\\ =1500\text{ unit/mg}\end{array}$

Specific activity for affinity chromatography is as follows:

Substitute $675000\text{ unit}$ for total activity of protein and $45$ for total amount of protein in equation (1)

$\begin{array}{c}\text{Specific activity}=\frac{675000\text{ unit}}{\text{45 mg}}\\ =15000\text{ unit/mg}\end{array}$

The formula to calculate purification level is as follows:

$\text{Purification level}=\frac{\text{specific activity}}{\text{initial specific activity}}$   ....... (3)

Purification level for crude extract:

Substitute $200\text{ unit/mg}$ for specific activity for crude extract and $200\text{ unit/mg}$ for initial specific activity in equation (3)

$\begin{array}{c}\text{Purification level}=\frac{200\text{ unit/mg}}{200\text{ unit/mg}}\\ =1\end{array}$

Purification level for ${\left({\text{NH}}_4\right)}_2{\text{SO}}_4$ precipitation:

Substitute $600\text{ unit/mg}$ for specific activity for ${\left({\text{NH}}_4\right)}_2{\text{SO}}_4$ precipitation and $200\text{ unit/mg}$ for initial specific activity in equation (3)

$\begin{array}{c}\text{Purification level}=\frac{600\text{ unit/mg}}{200\text{ unit/mg}}\\ =3\end{array}$

Purification level for DEAE-cellulose chromatography:

Substitute $666.67\text{ unit/mg}$ for specific activity for DEAE-cellulose chromatography and $200\text{ unit/mg}$ for initial specific activity in equation (3)

$\begin{array}{c}\text{Purification level}=\frac{666.67\text{ unit/mg}}{200\text{ unit/mg}}\\ =3.33\end{array}$

Purification level for gel-filtration chromatography:

Substitute $1500\text{ unit/mg}$ for specific activity for gel-filtration chromatography and $200\text{ unit/mg}$ for initial specific activity in equation (3)

$\begin{array}{c}\text{Purification level}=\frac{1500\text{ unit/mg}}{200\text{ unit/mg}}\\ =7.5\end{array}$

Purification level for affinity chromatography:

Substitute $15000\text{ unit/mg}$ for specific activity for affinity chromatography and $200\text{ unit/mg}$ for initial specific activity in equation (3)

$\begin{array}{c}\text{Purification level}=\frac{15000\text{ unit/mg}}{200\text{ unit/mg}}\\ =75\end{array}$

The formula to calculate percentage yield is as follows:

$\%\text{yield}=\left(\frac{\text{total enzyme activity}}{\text{starting total activity}}\right)100$   ....... (2)

Percentage yield for crude extract:

Substitute $4000000\text{ unit/mg}$ for total enzyme activity for crude extract and $4000000\text{ unit/mg}$ for starting total activity in equation (2)

$\begin{array}{c}\%\text{yield}=\left(\frac{4000000\text{ unit/mg}}{4000000\text{ unit/mg}}\right)100\\ =100\end{array}$

Percentage yield for ${\left({\text{NH}}_4\right)}_2{\text{SO}}_4$ precipitation:

Substitute $3000000\text{ unit/mg}$ for total enzyme activity for ${\left({\text{NH}}_4\right)}_2{\text{SO}}_4$ precipitation and $4000000\text{ unit/mg}$ for starting total activity in equation (1)

$\begin{array}{c}\%\text{yield}=\left(\frac{3000000\text{ unit/mg}}{4000000\text{ unit/mg}}\right)100\\ =75\%\end{array}$

Percentage yield for DEAE-cellulose chromatography:

Substitute $1000000\text{ unit/mg}$ for total enzyme activity for DEAE-cellulose chromatography and $4000000\text{ unit/mg}$ for starting total activity in equation (1)

$\begin{array}{c}\%\text{yield}=\left(\frac{1000000\text{ unit/mg}}{4000000\text{ unit/mg}}\right)100\\ =25\%\end{array}$

Percentage yield for gel-filtration chromatography:

Substitute $1000000\text{ unit/mg}$ for total enzyme activity for gel-filtration chromatography and $4000000\text{ unit/mg}$ for starting total activity in equation (1)

$\begin{array}{c}\%\text{yield}=\left(\frac{750000\text{ unit/mg}}{4000000\text{ unit/mg}}\right)100\\ =18.75\%\\ \approx 19\%\end{array}$

Percentage yield for affinity chromatography:

Substitute $675000\text{ unit/mg}$ for total enzyme activity for affinity chromatography and $4000000\text{ unit/mg}$ for starting total activity in equation (1)

$\begin{array}{c}\%\text{yield}=\left(\frac{675000\text{ unit/mg}}{4000000\text{ unit/mg}}\right)100\\ =16.875\%\\ \approx 17\%\end{array}$