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

TL;DR

This study combines high-throughput experiments and theoretical modeling to investigate how DNA's persistence length varies with ionic strength and ion valency, revealing complex behaviors not fully captured by existing theories.

Contribution

It provides new experimental data and proposes a variational theoretical approach to better understand DNA stiffness dependence on ionic conditions, especially with divalent ions.

Findings

DNA persistence length varies from 30 nm to 55 nm.

Na+ ions increase $L_p$ with ionic strength, fitting Manning's model.

Mg2+ ions cause a marked decrease in $L_p$ at low ionic strength.

Abstract

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.