# Topology of DNA: a honeycomb stable structure under salt effect

## TL;DR

This study uses Atomic Force Microscopy to analyze how salt concentration influences the topological structure of DNA molecules, revealing a stable honeycomb pattern at specific salt levels through topological and fractal measurements.

## Contribution

It introduces a topological and fractal analysis of DNA structures under salt effects, highlighting the formation of a stable honeycomb pattern.

## Key findings

- DNA forms a honeycomb structure at certain salt concentrations
- Topological invariants characterize structural transitions
- Fractal dimension quantifies the complexity of DNA arrangements

## Abstract

Atomic Force Microscopy analysis is employed to study the geometrical and topological properties of $3000$kbp DNA molecules fixed in mica substrates with $MgCl_{2}$. We found that the aggregates on the substrate surface for certain salt concentrations form a honeycomb stable structure with the addition of salt. The honeycomb, and the transition to other structures, were characterized by the \emph{Betti numbers}, which is a topological invariant property and by \emph{Hausdorff-Besicovitch fractal dimension}.