Dependence of DNA persistence length on ionic strength of solutions with monovalent and divalent salts: a joint theory-experiment study

Using high-throughput Tethered Particle Motion single molecule experiments, the double-stranded DNA persistence length, $L_p$, is measured in solutions with Na$^+$ and Mg$^{2+}$ ions of various ionic strengths, $I$. Several theoretical equations for $L_p(I)$ are fitted to the experimental data, but no decisive theory is found which fits all the $L_p$ values for the two ion valencies. Properly extracted from the particle trajectory using simulations, $L_p$ varies from 30~nm to 55~nm, and is compared to previous experimental results. For the Na$^+$ only case, $L_p$ is an increasing concave function of $I^{-1}$, well fitted by Manning's electrostatic stretching approach, but not by classical Odjik-Skolnick-Fixman theories with or without counter-ion condensation. With added Mg$^{2+}$ ions, $L_p$ shows a marked decrease at low $I$, interpreted as an ion-ion correlation effect, with an almost linear law in $I^{-1}$, fitted by a proposed variational approach.