Helical Tubes in Crowded Environments

TL;DR

This study models how semi-flexible tubes fold into compact helical shapes in crowded environments, identifying optimal geometries that minimize excluded volume and exploring effects of bending energy and multiple tubes.

Contribution

It introduces a model using excluded volume effects to analyze the optimal helical configurations of semi-flexible tubes in crowded settings.

Findings

Helices with pitch to radius ratio of 2.512 are most compact.

Optimal helices also minimize the global curvature.

Adding bending energy and multiple tubes expands the possible configurations.

Abstract

When placed in a crowded environment, a semi-flexible tube is forced to fold so as to make a more compact shape. One compact shape that often arises in nature is the tight helix, especially when the tube thickness is of comparable size to the tube length. In this paper we use an excluded volume effect to model the effects of crowding. This gives us a measure of compactness for configurations of the tube, which we use to look at structures of the semi-flexible tube that minimize the excluded volume. We focus most of our attention on the helix and which helical geometries are most compact. We found that helices of specific pitch to radius ratio 2.512 to be optimally compact. This is the same geometry that minimizes the global curvature of the curve defining the tube. We further investigate the effects of adding a bending energy or multiple tubes to begin to explore the more complete space of possible geometries a tube could form.