Helical Imperative: Paradigm of Growth, Form and Function


Helices appear at every anatomical level across the nine (or so) orders of magnitude that span the range of size between molecules and the biggest organisms. They provide solutions to any number of the challenges of growth and form, structure and function including significantly movement, that evolution has thrown up. This essay explores the helix both as an abstract mathematical idea, with its stark elegance, simplicity and economy, and the ‘real’ helical structures that contribute to the richness and complexity of the living world – and the relationship between them. Helical structures are so pervasive that the helix can perhaps be regarded as providing a unifying and even necessary structural principle for life. The helical idea goes a long way to explain why life at its most fundamental level of genes and proteins depends on two classes of small enantiomeric molecules, amino acids and nucleotides, significantly the molecules in each of the two classes all possessing the same hand. Life's apparent requirement for helical symmetry at the deep molecular level forces the uniformity.

Key Concepts:

  • Bilateral or ‘mirror’ symmetry is the most obvious symmetry at the level of whole animals, but helical symmetry is far commoner overall and at every anatomical level.

  • Helical symmetry lies at the heart of the structural molecular biology – the result of simple repetitive algorithms of growth based on thermodynamic ‘equivalence’.

  • The huge range (tens of thousands) of extant and extinct molluscan (and other) shell‐types shows the scope of achievable variations on a simple parameterised structural theme, the conical helix or concho‐spiral.

  • Thought of in engineering terms, living things are best thought of as tension structures, held together and stabilised by fibres. Most fibres are typically helices. It is a good question whether life is conceivable in any other way.

  • Because of its simple but striking geometry, a helix is a particularly clear example of an enantiomorphic object. The two mutual mirror image forms are not superposable. Whether in the real world both forms actually occur, or not, turns out to be a rather deep question.

Keywords: helix; spiral; handedness; enantiomer; form; function

Figure 1.

Circular helix: a curve drawn on the surface of a circular cylinder which cuts lines parallel to its axis (generators) at a constant angle. It can be thought of as the line of intersection of a helicoid with a cylinder. The interval between successive crossings of the same generator is the ‘pitch’ of the helix. Courtesy Matthew Galloway.

Figure 2.

Schematic drawing of the concho‐spiral, the shape of virtually all gastropod shells, both extant and extinct. It is the line of intersection of a cylinder erected on a logarithmic (exponential) spiral, and a cone. The helical path cuts the cone's generators at successive points in a geometrical as opposed to an arithmetical progression. For both the concho‐spiral and the circular helix, the ratio of the ‘curvature’ and ‘torsion’ of the curve at any point are in a constant ratio, which provides a general mathematical definition of the ‘helix’. Courtesy Matthew Galloway.

Figure 3.

Spiral, that is, helical staircase; Temple de la Sagrada Familia, Barcelona. It brings out the elegance and economy of the helicoid very strikingly. Courtesy Diane Galloway.

Figure 4.

Left‐ (rare) and right‐(common) handed mirror image forms of Partula suturalis, the Moorean tree snail. Courtesy Robert Robertson, The Smithsonian Institute.

Figure 5.

Two kinds of helical structure. (a) Tobacco mosaic virus (TMV): A hollow tube constructed of globular protein molecules arranged on a continuous helical path – the genetic or ontogenic spiral. In TMV it is right‐handed. The viral RNA follows this helical path. About proteins constitute the pitch. (b) Cotton fibre cell: a complex multilayered cylindrical structure made by winding polysaccharide fibres. The fibres follow both right‐ and left‐handed paths. They often abruptly change hand. Reproduced from Galloway , with permission from Springer Basel AG.

Figure 6.

Three dimensional structure of RNA polymerase II, an enzyme involved in transcribing DNA. It illustrates dramatically the prevalent helical secondary structure so often a feature of globular proteins. Courtesy Roger Kornberg.

Figure 7.

Double‐helical tree growing on Elephant Trunk Hill, Guilin, China, in 2009. Courtesy Diane Galloway.



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Galloway, John(Jun 2010) Helical Imperative: Paradigm of Growth, Form and Function. In: eLS. John Wiley & Sons Ltd, Chichester. http://www.els.net [doi: 10.1002/9780470015902.a0003673.pub2]