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Annual Review of Biophysics and Biophysical Chemistry

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Crystallography, Information theory


Macromolecular crystallographicy is a unique tool for imaging the structures of proteins and nucleic acids. Images are obtained from the Fourier transform of the diffraction pattern of the crystal by use of X-ray, neutron, and / or electron scattering. When X-ray and neutron scattering are used only diffraction amplitudes are experimentally measured, and phases have to be obtained. Multiple isomorphous replacement (MIR) has been the technique of choice for solving this phase problem in the determination of most macromolecular structures. Unfortunately, the method is extremely time consuming, especially when compared with the solution techniques available for small molecules; moreover, structure solution by MIR, even after many years of work, is hardly guaranteed. These drawbacks have stimulated efforts to enhance MIR as a phasing technique. The methods discussed in this paper (without exhaustive coverage, owing to space limitations) have so far been used to refine and/or to extend MIR phases, and also to open up the possibility of ab initio phase determination.

Following the early fundamental work of Karle & Hauptman (34, 35) and Sayre (60), reciprocal-space direct methods were applied to solve the structure of the majority of small molecules (via widely used packages, e.g. MULTAN and SHELX). These methods are used to derive phases statistically from the atomic character of the density. The extension of these methods to macromolecular crystallography is beyond the scope of this review.

Macromolecules present a more difficult problem. The diffraction data are rarely obtained at high enough resolution for the application of the atomicity constraint. Also, the accuracy of the phase predictions by reciprocal-space direct methods decreases with the size of the molecule. However, there are other a priori physical constraints applicable to macro-molecular density functions, e.g. continuity and solvent flatness. These constraints are more readily expressed in real space than in reciprocal space. Procedures that exploit such physical constraints in real space are commonly known as density modification (DM) methods. These techniques do not merely consist of real space imposition of a priori physical constraints, but also include reciprocal-space steps of comparable importance. These mixed real and reciprocal-space DM algorithms are the main subject of this review.


This work was authored as part of the Contributor's official duties as an Employee of the United States Government and is therefore a work of the United States Government. In accordance with 17 U.S.C. 105, no copyright protection is available for such works under U.S. Law.



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