Direct Methods for Solving Macromolecular Structures

This book of the proceedings of the 1997 NATO Advanced Study Institute (ASI) on Direct Methods for Solving Macromolecular Structures was assembled from the lecturers' contributions and represents a comprehensive and in-depth overview of crystallographic structure determination methods for macromolecules. While having a focus based on the direct methods, the Institute adopted an inclusive and broad perspective. Thus, both direct and experimental phasing techniques are presented in this book, highlighting their complementarities and synergies. As weil, methodologies spanning the full crystallographic image reconstruction process - from low resolution envelope definition to high resolution atomic refinement- are discussed. The first part of the book introduces the array of tools currently used in structure determination, whether originating from a mathematical, computational or experimental framework. This section of the book displays the variety and ingenuity of old and new phasing approaches developed to solve increasingly complex structures. Some of the contributions focus on recent developments and/or implementations that have given older approaches a new life. A case in point is the re-implementation of Buerger's superposition approach, which is now solving protein structures. Another beautiful example is found in the introduction to the traditional multiple isomorphous replacement approach where new techniques, such as site-directed mutagenesis and the use of inert gases in the preparation of heavy atom derivatives, are described. Equally impressive are the presentations of newer approaches, which take advantage of advances on the experimental front (e. g.

Table of Contents:
The phase problem of x-ray crystallography: overview.- A simple introduction to direct methods.- An elementary introduction to direct methods.- A simple introduction to Patterson methods.- An introduction to probability theory.- Intensity statistics and normalization.- Invariants, seminvariants and phase relationships.- Sayre equation, tangent formula and SAYTAN.- Probabilistic phasing methods versus macromolecular crystallography.- to the use of non-crystallographic symmetry in phasing.- An introduction to maximum entropy in action.- Crystal structure refinement incorporating chemical information.- Location of heavy atoms by automated Patterson interpretation.- New applications of simulated annealing in crystallographic refinement.- Figures of merit for evaluating phases.- to density modification.- An integrated graphical user interface for crystallographic software.- Isomorphous replacement: a survey of recent developments.- A theoretical study on the measurability of Bijvoet differences in macromolecular crystals.- Multiwavelength anomalous diffraction in macromolecular crystallography.- The solvent contrast variation method.- Obtaining phases from electron microscopy for solving protein structures.- Solving a heavy-atom substructure by direct methods.- Direct methods in relation to isomorphous data.- Integration of direct methods with SIR techniques.- Direct methods of solving phase ambiguities in macromolecular structures.- Phase refinement.- On the use of partial structure information in ab initio direct methods.- Direct methods with electron microscope information.- Density modification and direct methods.- Molecular scene analysis and its role in protein structure determination.- Membrane proteins solved by electron microscopy and electron diffraction.- The phase problem: a problem in constrained global optimization.- Shake-and-Bake: applications and advances.- SHELX applications to macromolecules.- Ab initio determination of a low resolution molecular envelope by direct methods.- Model based very low resolution phasing.- Use of non-crystallographic symmetry for ab initio phasing of virus structures.- Direct methods, and the use of synchrotron radiation for macromolecular crystallography.- The likelihood based choice of priors in statistical approaches to the phase problem.- Developments in maximum entropy and likelihood.- Extending the resolving power of Shake-and-Bake.- Reinvestigation of the use of Patterson maps to extrapolate data to higher resolution.- Intensity oversampling from crystallographic sampling via discrete Hilbert transforms.- Applications of direct methods with single isomorphous replacement or one wavelength anomalous scattering data.- Direct methods and molecular replacement techniques: the translation problem.- Holographic methods in x-ray crystallography.- A comparison of two algorithms for electron density map improvement by introduction of atomicity: skeletonization, and map sorting followed by refinement.- Real-space refinement using RsRef.- Towards the enantiomorph specific probabilistic theory of the structure invariants.