Ebook: 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.

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The first part of the book introduces the array of tools currently in use in structure determination, originating from mathematical, computational and experimental approaches. It displays the variety and ingenuity of old and new phasing approaches developed to solve increasingly complex structures. Some of the papers focus on recent developments that have given older methods a new lease of life. Equally impressive are the presentations of newer approaches which take advantage of recent experimental, mathematical and computational advances.
The second part of the book focuses on applications to macromolecular structures, displaying the incredible progress that has been achieved in recent years.
The book concludes with a series of presentations on the latest developments, providing a view of the newest phasing methodologies. It offers the promise of many more achievements yet to come.

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The first part of the book introduces the array of tools currently in use in structure determination, originating from mathematical, computational and experimental approaches. It displays the variety and ingenuity of old and new phasing approaches developed to solve increasingly complex structures. Some of the papers focus on recent developments that have given older methods a new lease of life. Equally impressive are the presentations of newer approaches which take advantage of recent experimental, mathematical and computational advances.
The second part of the book focuses on applications to macromolecular structures, displaying the incredible progress that has been achieved in recent years.
The book concludes with a series of presentations on the latest developments, providing a view of the newest phasing methodologies. It offers the promise of many more achievements yet to come.
Content:
Front Matter....Pages i-x
Front Matter....Pages 1-1
The Phase Problem of X-Ray Crystallography: Overview....Pages 3-10
A Simple Introduction to Direct Methods....Pages 11-18
An Elementary Introduction to Direct Methods....Pages 19-26
A Simple Introduction to Patterson Methods....Pages 27-32
An Introduction to Probability Theory....Pages 33-44
Front Matter....Pages 45-45
Intensity Statistics and Normalization....Pages 47-71
Invariants, Seminvariants and Phase Relationships....Pages 73-78
Sayre Equation, Tangent Formula and SAYTAN....Pages 79-85
Probabilistic Phasing Methods Versus Macromolecular Crystallography....Pages 87-97
Introduction To the Use of Non-Crystallographic Symmetry in Phasing....Pages 99-108
An Introduction to Maximum entropy in Action....Pages 109-117
Crystal Structure Refinement Incorporating Chemical Information....Pages 119-130
Location of Heavy Atoms by Automated Patterson Interpretation....Pages 131-141
New Applications of Simulated Annealing in Crystallographic Refinement....Pages 143-157
Figures of Merit for Evaluating Phases....Pages 159-167
Introduction to Density Modification....Pages 169-179
An Integrated Graphical User Interface for Crystallographic Software....Pages 181-186
Isomorphous Replacement: A Survey of Recent Developments....Pages 187-197
A Theoretical Study on the Measurability of Bijvoet Differences in Macromolecular Crystals....Pages 199-209
Multiwavelength Anomalous Diffraction in Macromolecular Crystallography....Pages 211-225
Front Matter....Pages 45-45
The Solvent Contrast Variation Method....Pages 227-237
Obtaining Phases from Electron Microscopy for Solving Protein Structures....Pages 239-250
The Phase Problem: A Problem in Constrained Global Optimization....Pages 381-388
SHELX Applications to Macromolecules....Pages 389-400
Model Based Very Low Resolution Phasing....Pages 401-411
Use of Non-Crystallographic Symmetry for Ab Initio Phasing of Virus Structures....Pages 413-419
Front Matter....Pages 421-431
Solving a Heavy-Atom Substructure by Direct Methods....Pages 433-442
Direct Methods in Relation to Isomorphous Data....Pages 251-251
Integration of Direct Methods with SIR Techniques....Pages 253-273
Direct Methods of Solving Phase Ambiguities in Macromolecular Structures....Pages 275-284
Phase Refinement....Pages 285-295
On the Use of Partial Structure Information in Ab Initio Direct Methods....Pages 297-305
Direct Methods with Electron Microscope Information....Pages 307-310
Density Modification and Direct Methods....Pages 311-316
Molecular Scene Analysis and Its Role in Protein Structure Determination....Pages 317-327
Membrane Proteins Solved by Electron Microscopy and Electron Diffraction....Pages 329-337
The Phase Problem: A Problem in Constrained Global Optimization....Pages 339-359
SHELX Applications to Macromolecules....Pages 361-380
Model Based Very Low Resolution Phasing....Pages 381-388
Use of Non-Crystallographic Symmetry for Ab Initio Phasing of Virus Structures....Pages 389-400
Front Matter....Pages 401-411
Direct Methods, and the use of Synchrotron Radiation for Macromolecular Crystallography....Pages 413-419
The Likelihood Based Choice of Priors in Statistical Approaches to the Phase Problem....Pages 421-431
Front Matter....Pages 433-442
Developments in Maximum Entropy and Likelihood....Pages 443-443
Reinvestigation of the Use of Patterson Maps to Extrapolate Data to Higher Resolution....Pages 445-450
Intensity Oversampling from Crystallographic Sampling via Discrete Hilbert Transforms....Pages 451-454
Applications of Direct Methods with Single Isomorphous Replacement or One-Wavelength Anomalous Scattering Data....Pages 443-443
Direct Methods and Molecular Replacement Techniques: The Translation Problem....Pages 455-462
Holographic Methods in X-Ray Crystallography....Pages 463-468
A Comparison of Two Algorithms for Electron Density Map Improvement by Introduction of Atomicity: Skeletonization, and Map Sorting Followed by Refinement....Pages 469-473
Real-Space Refinement Using RSRef....Pages 475-478
Towards the Enantiomorph Specific Probabilistic Theory of the Structure Invariants....Pages 479-485
Back Matter....Pages 487-497
....Pages 499-502