Proteins A and B having a molecular weight of 16500 and 35400 move 1.3 cm and 4.6 cm, respectively, when
electrophoresed through a gel. What is the molecular weight of protein C, which moves 2.8 cm in the same gel?
a. 3 kD

b. 13kD

c. 23 kD

d. 33 kD

To determine the molecular weight (MW) of protein C based on its migration distance, we use the log-linear relationship between relative migration (Rf) and molecular weight in SDS-PAGE:

$$\log (MW)=a+b\cdot \text{Migration Distance}$$

Given Data

• Protein A: MW = 16,500 Da → Migration = 1.3 cm
• Protein B: MW = 35,400 Da → Migration = 4.6 cm
• Protein C: Migration = 2.8 cm → Find MW?

Step 1: Take Log of Molecular Weights

log⁡(16500)=4.217

$$\log (35400)=4.549$$

Step 2: Set Up the Linear Equation

Using the linear equation form:

                 log⁡(MW)=      a+b⋅  Migration                  

We set up two equations:

1. For Protein A: 4.217=a+b (1.3)

          For Protein B: 4.549=a+b(4.6)

Step 3: Solve for “a” and “b”

Subtracting the two equations:

(4.549−4.217)=b(4.6−1.3)

0.332=b(3.3)

b=0.101

Substituting into the first equation:

   4.217      =      a+(0.101)(1.3)

   4.217      =  a+0.1313

    a=4.086

Step 4: Solve for Protein C (Migration = 2.8 cm)

log(MW)=4.086+(0.101×2.8)

log(MW)=4.086+0.2828

log(MW)=4.368

Step 5: Convert Back to MW

MW=104.368≈23,300 Da

$$So$$$$23kD$$

Correct answer: (c) 23 kD.