# Clever coiling

22/03/2005

Something about nature loves a helix, the ubiquitous spiral shape taken on by DNA and many other molecules found in the cells of living creatures. Now physicists Randall Kamien and Yehuda Snir, from University of Pennsylvania, may have a mathematical answer to why this shape is so common in nature.

"The classic answer is that helices are helical because the shape is dictated by bonds between molecules. But that only answers how a helix is formed and not why they are that shape," said Kamien, a professor in Penn Department of Astronomy and Physics. "It turns out that a helix, essentially, is a great way to bunch up a very long molecule, such as DNA, in a crowded place, such as a cell."

Kamien and Snir modelled the contents of a cell as a solid tube in a solution of hard spheres (the tubes could represent parts of proteins and the spheres other molecules in the cell). As far as the spheres are concerned, the tube not only takes up the space it occupies in the cell, but also excludes them from being in a region around the tube that is dependent on the size of the spheres. This reduction in space increases the energy of the arrangement - the more "squashed" they are, the higher the energy. But in nature things tend to the have the lowest energy possible. By bending the tube into a helix (actually, the tube is bent so that it is centred on a helix curve), the amount of space denied to the spheres is reduced, as the excluded region begins to overlap on the turns. But there is a balancing act between the energy going in to bending the tube, and the energy released by giving the spheres more space, and this balance is affected by the relative sizes and geometries of the spheres and tube.

The tube (with radius t) actually excludes the spheres (with radius r) from a cylindrical
region of space with radius t+r (Figure A).
However as the tube bends into a helix, the excluded region outside the tube overlaps
on the bend, and reducing the size of the excluded volume (Figure B).
(Image reprinted with permission from Snir and Kamien, SCIENCE 307:1067 (2005).