Mean free path and peak dispersion in the geometration motion in gel electrophoresis

The concept of the mean free path, i.e., the mean distance between subsequent collisions of DNA molecules with gel fibers, is introduced to the model description of the geometration effect. A new formula is derived for the correction to the velocity v of long molecules in gel due to the geometration process: v = v(r)/(1+3s/4b), where v(r) is the velocity without geometration, s is the molecule length and b is the mean free path of molecules. The peak dispersion sigma(x) is evaluated with the same model approach. We get the contribution to the bandwidth from the geometration effect. For b = s the bandwidth is about 2(sx)(1/2), where x is the length of the path of the molecules in gel. The results are compared with experimental data on the linearized plasmid pKecNOS in 4% agarose gel.