The effect of pH on charge inversion and condensation of DNA.

Charge inversion and condensation of DNA in solutions of trivalent and quadrivalent counterions are significantly influenced by the pH value of the solution. We systematically investigated the condensation and charge compensation of DNA by spermidine, hexammine cobalt(iii) (cohex, [Co(NH3)6](3+)) and spermine in solutions of a wide range of pH values from 3 to 9.3 by dynamic light scattering, magnetic tweezers, and atomic force microscopy. In trivalent counterion solution, we found that there is a critical concentration (0.75 mM for cohex and 0.5 mM for spermidine), under which the electrophoresis mobility of DNA initially increases, reaches a maximum, and finally decreases when the pH value is decreased. In contrast, above the critical concentration, the electrophoretic mobility of DNA increases monotonously with decreasing pH value of the solution. The corresponding condensing force has the same dependence on the pH value. However, for the case of quadrivalent counterions, the electrophoretic mobility of DNA is monotonously promoted by lowering the pH value of the solution at any concentration of counterions in which charge inversion of DNA may occur. In atomic force microscopy images and force spectroscopy of magnetic tweezers, we found that maximal charge neutralization and condensation force correspond to the most compact DNA condensation. We propose a mechanism of promoting DNA charge neutralization: small and highly mobile hydrogen ions tend to attach to the DNA-counterion complex to further neutralize its remaining charge, which is related to the surface area of the complex. Therefore, this further neutralization is prominent when the complex is toroidal which corresponds to the case of mild ion concentration while it is less prominent for more compact globules or rod complexes at high counterion concentration.