Calculation of the electrostatic energy of two charged helices on rods in a generalized braid geometry

TL;DR

This paper presents a generalized method for calculating the electrostatic interaction energy between two charged helices on rods within a braid, considering screened electrostatics and small curvature and tilt angle approximations.

Contribution

It introduces a new calculation approach for electrostatic energy in braided charged rods that does not assume a predefined braid geometry.

Findings

Derived local expressions for electrostatic energy in braid structures.

Extended previous straight braid calculations to more general geometries.

Utilized approximations for small curvature and tilt angle.

Abstract

This is a technical document that outlines a calculation of an electrostatic interaction energy between two rods, with charge helices on them, forming a braid. We deal here with screened electrostatics. A general braid geometry is considered, though to obtain local expressions for the energy the curvature of the rods is considered to be small. Further approximations are made for small tilt angle. This is a generalization of the calculations given in the supplemental material of [R. Cortini et Al, Biophys. J. 101 875 (2011)] for a straight symmetric braid structure, using a different method of calculation where the braid geometry does not need to be supposed a priori.