Electrophoresis

Electrophoresis is motion of charged dispersed species relative to a surrounding medium under an applied electric field. The drift depends on electrical driving and friction, including the surrounding ionic atmosphere. Gel electrophoresis adds a porous matrix that makes migration sensitive to molecular size and conformation.

A narrow population band undergoing uniform electrophoresis and ordinary diffusion has mean position $x_0+\mu Et$ and variance ${\sigma }_0^2+2Dt$. This follows from the advection-diffusion equation by changing to the coordinate $x-\mu Et$. For two species with mobility difference $\Delta \mu$, their centre separation is $|\Delta \mu |Et$, whereas diffusion widths grow only as $\sqrt{t}$. Starting from point-like bands with common diffusion coefficient $D$, a required separation of $q$ standard deviations needsA prescribed distance between centres alone is a resolution convention; finite loading widths and other dispersion mechanisms must be included when interpreting actual electrophoresis data.

The electrophoretic mobility $\mu$ is the proportionality coefficient between drift velocity and a weak applied electric field. Its sign specifies motion relative to the field. When only travel distances are used, the mobility magnitude is often intended. For long linear DNA in a weak-field reptation regime, $|\mu |$ can scale inversely with chain length, whereas free-solution mobility is approximately length-independent. Neither law supplies a universal gel electrophoresis size calibration for arbitrary gel concentration, field strength or molecular topology.