A. Szoke et al., HOLOGRAPHIC METHODS IN X-RAY CRYSTALLOGRAPHY .5. MULTIPLE ISOMORPHOUSREPLACEMENT, MULTIPLE ANOMALOUS-DISPERSION AND NON-CRYSTALLOGRAPHIC SYMMETRY, Acta crystallographica. Section A, Foundations of crystallography, 53, 1997, pp. 291-313
The holographic method for the recovery of the electron density of mac
romolecules is based on the expansion of the electron density into Gau
ssian basis functions. The technique makes consistent use of real- and
reciprocal-space information to produce electron-density maps. It enf
orces positivity of the recovered electron density and makes effective
use of previously known information about the electron density, such
as knowledge of a solvent region or knowledge of a partial structure.
In this paper, we summarize the theory underlying the holographic meth
od, and describe how we extend the range of information that can be us
ed by the method to include information from multiple-isomorphous-repl
acement (MLR) data, multiple-anomalous-dispersion (MAD) data and knowl
edge of non-crystallographic symmetry. The convergence properties and
the limiting accuracy of the method are discussed. Its power for synth
etic problems is demonstrated and the method is applied to experimenta
lly measured MIR data from kinesin, a motor protein domain that has re
cently been solved. Appendix A gives a detailed description of the alg
orithms and the equations used in EDEN, the computer program that impl
ements the holographic method.