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

Dependence of DNA persistence length on ionic strength and ion type