The relative electrophoretic mobilities of a 30-kd protein and a 92-kd protein used as standards on an SDS
polyacrylamide gel are 0.80 and 0.41, respectively. What is the apparent mass of a protein having a mobility of
0.62 on this gel?

a. 5KD

b. 15 kD

c. 50 kD

d. 150 kD

To determine the apparent molecular weight of a protein from its relative electrophoretic mobility (Rf) in SDS-PAGE, we use the log-linear relationship between Rf and molecular weight (MW):

$$\log (MW)=a+b\cdot Rf$$

where:

• Rf = Distance traveled by the protein / Distance traveled by the dye front.
• MW = Molecular weight (in kDa).

We have the standard proteins:

• 30 kDa → Rf = 0.80
• 92 kDa → Rf = 0.41
• Unknown protein → Rf = 0.62

Step 1: Establish the log-linear equation

We take the log (base 10) of the molecular weights:

$$\log (30)=1.477,\log (92)=1.964$$

Using the linear equation form:

$$\log (MW)=a+b\cdot Rf$$

We set up two equations using the given data:

1. $1.477=a+b(0.80)$
2. $1.964=a+b(0.41)$

Step 2: Solve for “a” and “b”

Subtracting the two equations:

$$(1.964-1.477)=b(0.41-0.80)$$ $$0.487=-0.39b$$ $$b=-1.248$$

Substituting b = -1.248 into one equation:

$$1.477=a+(-1.248)(0.80)$$ $$1.477=a-0.998$$ $$a=2.475$$

Step 3: Find MW for Rf = 0.62

$$\log (MW)=2.475+(-1.248)(0.62)$$ $$\log (MW)=2.475-0.774$$ $$\log (MW)=1.701$$

Step 4: Convert back to MW

MW=101.701≈50.4 kDaMW = 10^{1.701} \approx 50.4 \text{ kDa}MW=101.701≈50.4 kDa

Thus, the apparent molecular weight is closest to 50 kDa.

✅ Correct answer: (c) 50 kD.