Abstract

Biological structures, unlike those designed and constructed by human structural engineers, are built by a process of self-assembly. The internal machinery of biological cells produces molecular building-blocks in accordance with information encoded in the DNA , and these then find their appointed place in the assembly under construction. The simplest possible self-assembled structure is a uniform helix, or spiral: repeated addition of identical building-blocks in a regular pattern make a uniform helix, which is the simplest space-curve. In this talk I shall discuss three particular spiral structures built from molecular components. 1. The α-helix, an important motif in protein structures; and in particular the way in which two α-helices can be programmed to assemble into a “coiled coil” arrangement. 2. The DNA double-helix. How it can switch between the classical “A” and “B” geometries; and how this kind of change enables us to understand sequence-dependent curvature and flexibility of the molecule – which is important in the recognition of DNA sequences by contacting proteins. 3. Bacterial flagellar filaments – the corkscrew-like organelles which, when rotated by their motors, enable bacteria such as E.coli to swim in their watery environment and navigate towards nutrients. Here the building-block, much larger than those of examples 1 and 2, is a protein molecule which contains a “switch” feature; and this enables the filament to change from a left-handed to a right-handed corkscrew when it is driven in reverse. These examples illustrate the power of evolution to develop highly sophisticated variants of the simplest kind of self-assembled biological structures. Geometry provides an indispensable tool in elucidating the subtle structural phenomena seen in these helices.