Unified description of electrophoresis and diffusion for DNA and other polyions

The electrophoretic mobilities and diffusion coefficients of single- and double-stranded DNA molecules up to 50,000 bases or base pairs in size have been analyzed, using mobilities and diffusion coefficients either measured by capillary electrophoresis or taken from the literature. The Einstein equation suggests that the electrophoretic mobilities (mu) and diffusion coefficients (D) should be related by the expression mu/D = Q/k(B)T, where Q is the charge of the polyion (Q = ze(o), where z is the number of charged residues and e(o) is the fundamental electronic charge), k(B) is Boltzmann's constant, and T is the absolute temperature. If this equation were true, the ratio mu/zD should be a constant equal to e(o)/k(B)T (39.6 V(-1)) at 20 degrees C. However, the ratio mu/zD decreases with an increase in molecular weight for both single- and double-stranded DNAs. The mobilities and diffusion coefficients are better described by the modified Einstein equation mu/N(m)D = e(o)/k(B)T, where N is the number of repeat units (bases or base pairs) in the DNA and m is a constant equal to the power law dependence of the diffusion coefficients on molecular weight. The average value of the ratio mu/N(m)D is 40 +/- 4 V(-1) for 36 single- and double-stranded DNA molecules of different sizes, close to the theoretically expected value. The generality of the modified Einstein equation is demonstrated by analyzing literature values for sodium polystyrenesulfonate (PSS). The average value of the ratio mu/N(m)D is 35 +/- 6 V(-1) for 14 PSS samples containing up to 855 monomers.