Solving the phase problem in fiber diffraction. Application to tobacco mosaic virus at 3.6 Å resolution

The diffracting particles that give rise to a fiber diffraction pattern are randomly oriented about the fiber axis and, in consequence, the diffraction pattern is cylindrically averaged. The phase problem in fiber diffraction is not only to determine the phase in the usual crystallographic sense, but to overcome the loss of information from this averaging. This has been done by a multi-dimensional analog of protein crystallographic isomorphous replacement, combined with the use of information from the fine splitting of layer lines that occurs when a helical structure repeats approximately, but not exactly, in a given number of turns. The phases thus determined have been refined by a solvent-flattening procedure. They have been further refined by assuming the separation of cylindrically averaged Bessel-order terms (from multi-dimensional isomorphous replacement at an early stage and from a model at a later stage) and applying conventional isomorphous replacement (two-dimensional isomorphous replacement) to determine the phases of the terms. Cycles of model building and two-dimensional isomorphous replacement were found in the case of tobacco mosaic virus to improve greatly the quality of the electron density map, and enabled an atomic model of the virus to be built based on a highly interpretable map at 3.6 Å resolution with five Bessel orders (terms overlapping because of cylindrical averaging) separated.