Shielding effects of small ions in gel electrophoresis of DNA

Results of free electrophoresis and free sedimentation of charged rods are introduced to allow for electrical double-layer effects in the gel electrophoresis of DNA, modeled as a random flight sequence of rodlike Kuhn chain elements. The kinetics of DNA is shown to depend strongly on the orientation of the chain elements with respect to the external field and with respect to the direction of their velocity. The new theory gives approximate agreement between the DNA charge derived from electrophoresis of free and tethered DNA (close to 1.0e per DNA phosphate in both cases), compared with the earlier discrepancy of a factor 10 or 20 for the theory without shielding by salt. As part of a realistic force field for macromolecular dynamics simulation, the small ion effects are included in an expression for the gel forces restraining the DNA in gel electrophoresis from moving as in free electrophoresis.