Improving Crystallographic Macromolecular Images

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.

Contents

Perspectives and Overview………………………………………….............	352
Algorithms………………………………………………...............................	353
Density Modification………………………....................................................	354
Positivity…………………………….................................................	354
Atomicity……………………………................................................	355
Boundedness…………………………..............................................	356
Solvent Flatness……………..............................................................	356
Map Continuity and Use of a Partial Model.....................................	360
Noncrystallographic Symmetry…………...........................................	360
Multiple Crystal Forms………............................................................	361
Merging of Calculated and Observed Amplitudes and Phases…............	362
Replacing the Phases….......................................................................	362
Merging the Amplitudes and Replacing the Phases……………...	362
Merging the Phases……….................................................................	363
Merging Both the Amplitudes and the Phases……........................	363
Some New Developments…….......................................................................	364
Combined Omit Map Technique……................................................	364
Minimization Techniques Using Modification Constraints..........	364
Results and Conclusions………………......................................................	366