Coordinated use of isomorphous replacement and layer-line splitting in the phasing of fiber diffraction data

In order to calculate electron density maps from fiber diffraction patterns, the terms which superimpose because of cylindrical averaging of the pattern must be separated and their phases determined. This can be done using a technique analogous to the isomorphous replacement method of protein crystallography, but large numbers of heavy-atom derivatives are required. Because of the cylindrical averaging, the number of derivatives increases with increasing resolution. This paper describes a method for measuring the fine splitting of layer lines which occurs when a helical structure repeats approximately, but not exactly, in a given number of turns, and for using this as a source of phase information. The amount of phase information obtainable from each heavy-atom derivative is theoretically doubled since differences in both layer-line intensity and apparent layer-line position can be used, and this substantially increases the resolution attainable with a limited number of derivatives. The method is used to calculate an electron density map of tobacco mosaic virus at 6.7 Å resolution using only two derivatives instead of the four which would have been required using previously available methods.