Symmetries of Electrostatic Interaction between DNA Molecules

TL;DR

This paper models electrostatic interactions between DNA molecules, revealing a symmetry group that classifies potential phases, including cholesteric and snowflake structures, depending on phosphate charge modifications.

Contribution

It introduces a novel symmetry group for DNA electrostatic interactions and classifies possible molecular phases based on this symmetry.

Findings

Identification of an eighth-order symmetry group ${\

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Abstract

We study a model for pair interaction $U$ of DNA molecules generated by the discrete dipole moments of base-pairs and the charges of phosphate groups, and find noncommutative group of eighth order ${\cal S}$ of symmetries that leave $U$ invariant. We classify the minima using group ${\cal S}$ and employ numerical methods for finding them. The minima may correspond to several cholesteric phases, as well as phases formed by cross-like conformations of molecules at an angle close to $\rm{90}^{o}$, "snowflake phase". The results depend on the effective charge $Q$ of the phosphate group which can be modified by the polycations or the ions of metals. The snowflake phase could exist for $Q$ above the threshold $Q_C$. Below $Q_C$ there could be several cholesteric phases. Close to $Q_C$ the snowflake phase could change into the cholesteric one at constant distance between adjacent molecules.