Counterion Condensation vs. Zeta Potential: Can Either Theory Describe the Electrophoresis of DNA and other Polyions?

Abstract

Many textbooks state that the electrophoretic mobility of a polyion is directly proportional to the number of charged residues and inversely proportional to its frictional coefficient. If a series of polyions differ only in the number of charged residues, the frictional coefficients will be approximately constant. Hence, the free solution mobilities are expected to be proportional to the effective charge. However, the mobilities of the charge variants of a given polyion are proportional to the logarithm of the linear charge density, not the first power of the charge. The semilogarithmic relationship between the mobility and the fractional charge of the polyion is observed for single- and double-stranded DNA oligomers, small organic molecules, protein “ladders” and protein sequence mutants.Manning has used counterion condensation theory to derive an equation describing DNA electrophoretic mobility. This equation predicts that the mobilities should depend on the logarithm of the linear charge density, as observed. Surprisingly, the same equation can be used to predict the fractional mobilities of the charge variants of other types of polyions, if the square root of the surface charge density is used as the variable instead of the linear charge density. Mobilities calculated from theories of the zeta potential are less accurate than those calculated from the Manning equation. Hence, the Manning electrophoresis equation appears to have a wider validity than commonly recognized.