# Preferential interaction coefficient for nucleic acids and other cylindrical poly-ions

## TL;DR

This paper derives precise analytical expressions for the Coulombic contribution to the salt-polyion preferential interaction coefficient in nucleic acids, valid at low salt concentrations and cylindrical geometry, emphasizing highly charged poly-ions.

## Contribution

It provides new analytical formulas for the preferential interaction coefficient and electric potential around highly charged cylindrical poly-ions, extending previous models beyond counter-ion condensation.

## Key findings

- Accurate analytical expressions for the Coulombic contribution at low salt.
- Formulas valid for any electrolyte charge ratio $z_-$:$z_+$.
- Enhanced understanding of electric potential near poly-ions.

## Abstract

The thermodynamics of nucleic acid processes is heavily affected by the electric double-layer of micro-ions around the polyions. We focus here on the Coulombic contribution to the salt-polyelectrolyte preferential interaction (Donnan) coefficient and we report extremely accurate analytical expressions valid in the range of low salt concentration (when polyion radius is smaller than the Debye length). The analysis is performed at Poisson-Boltzmann level, in cylindrical geometry, with emphasis on highly charged poly-ions (beyond ``counter-ion condensation''). The results hold for any electrolyte of the form $z_-$:$z_+$. We also obtain a remarkably accurate expression for the electric potential in the vicinity of the poly-ion.