Direct determination of X-ray phases for tobacco mosaic virus protein using non-crystallographic symmetry

The basic structural unit of tobacco mosaic virus (TMV) protein crystals is a ring of seventeen identical subunits. This non-crystallographic 17-fold symmetry has been used to determine signs of the X-ray refiexions in the centrosymmetric hk0 projection, in two different but related ways. The results are compared with those obtained by Gilbert [Ph.D. Thesis (1970), Univ. of Cambridge] using the method of single isomorphous replacement (SIR), and are shown to agree well for reflexions with (h + k) even. Owing to the special positions of the bound heavy atoms, reliable signs have not hitherto been available for reflexions with (h + k) odd. Evidence is presented to show that those obtained from the non-crystallographic symmetry are essentially correct.