Uniqueness and the ab initio phase problem in macromolecular crystallography

TitleUniqueness and the ab initio phase problem in macromolecular crystallography
Publication TypeJournal Article
Year of Publication1993
AuthorsBaker, D., Krukowski A. E., & Agard D. A.
JournalActa crystallographica. Section D
Volume49
IssuePt 1
Pagination186-92
Date Published1993 Jan 1
ISSN0907-4449
KeywordsPrimary Publication
Abstract

The crystallographic phase problem is indeterminate in the absence of additional chemical information. A successful ab initio approach to the macromolecular phase problem must employ sufficient chemical constraints to limit the solutions to a manageably small number. Here we show that commonly employed chemical constraints - positivity, atomicity and a solvent boundary - leave the phase problem greatly underdetermined for Fourier data sets of moderate (2.5-3.0 A) resolution. Entropy maximization is also beset by multiple false solutions: electron-density maps are readily generated which satisfy the same Fourier amplitude constraints but have higher entropies than the true solution. We conclude that a successful ab initio approach must make use of high-resolution Fourier data and/or stronger chemical constraints. One such constraint is the connectivity of the macromolecule. We describe a rapid algorithm for measuring the connectivity of a map, and show its utility in reducing the multiplicity of solutions to the phase problem.

Alternate JournalActa Crystallogr. D Biol. Crystallogr.
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