Representing Structural Information of Helical Charge Distributions in Cylindrical Coordinates

TL;DR

This paper introduces a method to represent the structural information of helical charge distributions using cylindrical coordinates, facilitating analysis of electric fields in systems like DNA.

Contribution

It provides a straightforward approach to relate cylindrical and helical coordinate representations of electric fields and structure factors in helical charge systems.

Findings

Cylindrical and helical coordinate structure factors are compared.

A simple transformation relates Green functions in both coordinate systems.

Electric field calculations on the helix axis are consistent across methods.

Abstract

Structural information in the local electric field produced by helical charge distributions, such as dissolved DNA, is revealed in a straightforward manner employing cylindrical coordinates. Comparison of structure factors derived in terms of cylindrical and helical coordinates is made. A simple coordinate transformation serves to relate the Green function in cylindrical and helical coordinates. We also compare the electric field on the central axis of a single helix as calculated in both systems.