Optical and Computer Simulations of Wave Diffraction by Helical Structures : from DNA yo Carbon Nanotubes

Abstract

The celebrated X-ray fiber diagram obtained by Rosalind Franklin for the paracrystalline phase of B-DNA is examined at a non technical level. The most prominent features of the intensity distribution in the diagram are reviewed in relation to the corresponding structural properties of the molecule. Optical diffraction experiments (optical trans¬ forms) are performed to reproduce each of several features separately, namely the layer-lines, the maltese cross, the diamond repeats and the missing 4th layer-line. These experiments make use of a single slide (available from the authors on demand) containing a photographic film reduction of four simplified planar models of the DNA backbone which serve as diffraction gratings for the coherent red light of a He-Ne laser or a solid-state laser pointer. No special optics is required. The simulations bring out all of the crucial geometrical parameters of the Watson-Crick double helix. The paper then gives a simple derivation of the formula established by Cochran Crick and Vand (CCV) for the Fourier transform of a helical molecule such as DNA. An application of the CCV theory is made to the computer simulation of wave diffraction by the recently discovered chiral carbon nanotubes which can be described as a collection of regular carbon helices. Computer sim¬ ulated micrographs are compared to observed electron diffractograms of single nanotubes.