Electrostatic interactions between discrete helices of charge

TL;DR

This paper provides an analytical and numerical study of electrostatic interactions between parallel discrete helices of charge, with implications for biological structures like F-actin and A-DNA.

Contribution

It introduces a symmetry-based analytical framework and Fourier expansion approach for modeling electrostatic interactions between charged helices, applicable to biological molecules.

Findings

Accurate modeling of axial and azimuthal interaction terms.

Energy expressions are insensitive to the specific form of the interaction.

Application to biological structures such as F-actin and A-DNA.

Abstract

We analytically examine the pair interaction for parallel, discrete helices of charge. Symmetry arguments allow for the energy to be decomposed into a sum of terms, each of which has an intuitive geometric interpretation. Truncated Fourier expansions for these terms allow for accurate modeling of both the axial and azimuthal terms in the interaction energy and these expressions are shown to be insensitive to the form of the interaction. The energy is evaluated numerically through application of an Ewald-like summation technique for the particular case of unscreened Coulomb interactions between the charges of the two helices. The mode structures and electrostatic energies of flexible helices are also studied. Consequences of the resulting energy expressions are considered for both F-actin and A-DNA aggregates.