# One-Loop Fluctuation Entropy of Charge Inversion in DNA

## TL;DR

This paper models charge inversion in DNA using a lattice-gas approach, incorporating fluctuation corrections to mean-field theory, revealing significant effects on entropy especially when dimers are repelled from DNA.

## Contribution

It introduces a lattice-gas model with fluctuation corrections to better understand charge inversion and entropy in DNA solutions, advancing beyond mean-field approximations.

## Key findings

- Fluctuation corrections significantly affect entropy calculations.
- Charge distributions depend on dimer orientation and concentration.
- Model captures correlation-driven charge inversion phenomena.

## Abstract

Experiments have revealed correlation-driven behavior of DNA in charged solutions, including charge inversion and condensation. This paper presents calculations of a lattice-gas model of charge inversion for the adsorption of charged dimers on DNA. Each adsorption site is assumed to have either a vacancy or a positively-charged dimer attached with the dimer oriented either parallel or perpendicular to the double helix DNA chain. The entropy and charge distributions of these three species are calculated including the lowest order fluctuation corrections to mean-field theory. We find that the inclusion of the fluctuation terms has a significant effect on the entropy, primarily in the regime where the dimers are repelled from the DNA molecule and compete with the chemical potential in solution.