Q: Consider two DNA molecules: one 400 base pairs long, the other 800 base pairs long. Assuming that each is a rigid rod of dimeter 2.5 nm, with a length of 0.34 nm per base pair, calculate the ratio of the electrophoretic mobilities of these two molecules using the following approximation:

f ~ 3phL/ln(L/b)

where L is the length and b is the dimeter.

Solution

Knowing that the electrophoretic mobility is proportional to the charge and inversely proportional to the viscosity coefficient,

U ~ KL/f = (K/3ph)ln(L/b)

where K is the linear charge density of the rod. Then, the electrophoretic mobility of the 400 bp DNA molecule U400 can be written as

U400 ~ KL400/f400 = (K/3ph)ln(L400/b)

Similarly, the electrophoretic mobility of the 800 bp DNA molecule U800 can be written as

U800 ~ KL800/f800 = (K/3ph)ln(L800/b)

The length of these two DNA molecules is proportional to the number of base pairing. Therefore, the ratio of these two mobilities is,

R = U400/U800 = ln(L400/b)/ln(L800/b) = ln(400*0.34/2.5)/ln(800*0.34/2.5) = 3.996/4.690 = 0.82