Question

Molecular mass by sodium dodecylsulfate–gel electrophoresis. Ferritin is a hollow iron-storage protein 74 consisting of 24 subunits that are a variable mixture of heavy (H) and light (L) chains,arranged in octahedral symmetry. The hollow center, with a diameter of 8 nm, can hold up to 4 500 iron atoms in the approximate form of the mineral ferrihydrite $\mathbf{(}\mathbf{5}{\mathbf{Fe}}_{\mathbf{1}}\mathbf{}{\mathbf{O}}_{\mathbf{3}}\mathbf{\times }\mathbf{9}{\mathbf{H}}_{\mathbf{2}}\mathbf{}\mathbf{O}\mathbf{)}$Iron(II) enters the protein through eight pores located on the threefold symmetry axes of the octahedron. Oxidation to Fe(III) occurs at catalytic sites on the H chains. Other sites on the inside of the L chains appear to nucleate the crystallization of ferrihydrite. Migration times for protein standards and the ferritin subunits are given in the table. Prepare a graph of log(molecular mass) versus 1/(relative migration time), where relative migration time 5 (migration time)/(migration time of marker dye). Compute the molecular mass of the ferritin light and heavy chains. The masses of the chains, computed from amino acid sequences, are 19 766 and 21 099 Da.

Short answer

Relative migration time is calculated as

$$\begin{gathered} -\mathrm{light}\mathrm{chain}{\mathrm{t}}_{\mathrm{rel}}=17.07/13.17=1.296 \\ -\mathrm{heavy}\mathrm{chain}{\mathrm{t}}_{\mathrm{rel}}=17.97/13.17=1.364 \end{gathered}$$

Molar mass is calculated as

$\mathrm{molar}\mathrm{mass}={10}^{\log \left(\mathrm{MM}\right)}={10}^{4.372}=23500\mathrm{Da}$

Step-by-step solution

Step 1:Graph of molecular mass Vs 1/relative migration time.

Graph is shown below

$\mathrm{If}\mathrm{you}\mathrm{made}\mathrm{a}\mathrm{graph}\mathrm{in}\mathrm{Excel}\mathrm{you}\mathrm{would}\mathrm{get}\mathrm{the}\mathrm{equation}\mathrm{y}=-3.4349\mathrm{x}+6.889$

$\mathrm{where}\mathrm{y}\mathrm{is}\log (\mathrm{MM})\mathrm{and}\mathrm{x}\mathrm{is}1/{\mathrm{t}}_{\mathrm{rel}}\mathrm{so}\mathrm{it}\mathrm{can}\mathrm{be}\mathrm{written}\mathrm{as}\log (\mathrm{MM})=-3.4349/{\mathrm{t}}_{\mathrm{rel}}+6.889$

Step 2:Calculate the relative migration time for ferritin light and heavy chains

Calculating the relative migration time for ferritin light and heavy chain

$\mathrm{relative}\mathrm{migration}\mathrm{time}=(\mathrm{migration}\mathrm{time})/(\mathrm{migration}\mathrm{time}\mathrm{of}\mathrm{Orange}\mathrm{G}\mathrm{marker}\mathrm{dye})$

$$\begin{gathered} -\mathrm{light}\mathrm{chain}{\mathrm{t}}_{\mathrm{rel}}=17.07/13.17=1.296 \\ -\mathrm{heavy}\mathrm{chain}{\mathrm{t}}_{\mathrm{rel}}=17.97/13.17=1.364 \end{gathered}$$

Calculate the molar masses

$\mathrm{use}\log (\mathrm{MM})=-3.4349/{\mathrm{t}}_{\mathrm{rel}}+6.889$and Calculate the molar masses.

Light chain log $\left(\mathrm{MM}\right)=-3.4349/1.296+6.889=4.239$

$$\begin{gathered} \mathrm{molar}\mathrm{mass}={10}^{\log \left(\mathrm{MM}\right)}={10}^{4.239}=17300\mathrm{Da} \\ -\mathrm{heavy}\mathrm{chain}\log (\mathrm{MM})=-3.4349/1.364+6.889=4.372 \\ \mathrm{molar}\mathrm{mass}={10}^{\log \left(\mathrm{MM}\right)}={10}^{4.372}=23500\mathrm{Da} \end{gathered}$$