Dependence of DNA persistence length on ionic strength and ion type

Even though the persistence length $L_P$ of double-stranded DNA plays a pivotal role in cell biology and nanotechnologies, its dependence on ionic strength $I$ lacks a consensual description. Using a high-throughput single-molecule technique and statistical physics modeling, we measure $L_P$ in presence of monovalent (Li$^+$, Na$^+$, K$^+$) and divalent (Mg$^{2+}$, Ca$^{2+}$) metallic and alkyl ammonium ions, over a large range 0.5 mM $\leq I\leq 5$ M. We show that linear Debye-H\"uckel-type theories do not describe even part of these data. By contrast, the Netz-Orland and Trizac-Shen formulas, two approximate theories including non-linear electrostatic effects and the finite DNA radius, fit our data with divalent and monovalent ions, respectively, over the whole $I$ range. Furthermore the metallic ion type does not influence $L_P(I)$, in contrast to alkyl ammonium monovalent ions at high $I$.