Section 19.5.7.4. Initial models: large unit cells

For large macromolecular aggregates, such as viruses and cytoskeletal filaments, initial models cannot usually be devised using the primary structure of the molecule alone. The largely α-helical filamentous bacteriophages form a rare class of exceptions (Makowski et al., 1980). Molecular-replacement methods, in which initial models are constructed from single-crystal structure determinations of the separated components of the aggregate or from known related structures, can be useful, but because of the limited number of data in a fibre pattern such models can sometimes be difficult to refine.

Multi-dimensional isomorphous replacement (MDIR), an extension of the isomorphous-replacement method of protein crystallography, has been useful in studying helical viruses (Stubbs & Diamond, 1975; Namba & Stubbs, 1985). The dimensions are the real and imaginary parts of the various overlapping structure factors at a given point in the diffraction pattern. Information about both the phases of the structure factors and the relative magnitudes of the overlapping structure factors is obtained from heavy-atom derivatives of the virus; at least twice as many heavy-atom derivatives as the number of significant G terms in equation (19.5.3.7) are required. If the structure of a related aggregate is known, MDIR can be combined with molecular replacement (Namba & Stubbs, 1987a; Wang & Stubbs, 1994); in this case, fewer derivatives are required.

Layer-line splitting (Franklin & Klug, 1955) arises when the helical symmetry of the scattering particles is close to, but not exactly, integral. For example, tobacco mosaic virus (TMV) has 49.02 subunits in three turns of the viral helix. In this case, the G terms in each layer line do not fall at exactly the same Z values in the diffraction pattern. The resulting shifts in the positions of the layer lines can be measured for the native aggregate and, in favourable cases, for heavy-atom derivatives, and used to provide additional phase information (Stubbs & Makowski, 1982). Information from electron microscopy (Beese et al., 1987) and neutron scattering (Nambudripad et al., 1991) has also been used.