Electron Crystallography of Biological Macromolecules

by Glaeser, Robert; Kenneth Downing; DeRosier, David; Chiu, Wah; Frank, Joachim

• ISBN13: 9780195088717
• ISBN10: 0195088719
• Edition: 1st
• Format: Hardcover
• Copyright: 2007-06-08
• Publisher: Oxford University Press

Summary

This book provides a complete introduction to both the practical details and the theoretical foundations required in order to use electron microscopy as a research tool in structural biology. Planned and written by a group of 5 well-known experts who have pioneered different aspects of the field of electron cryo-microscopy (cryo-EM) of biological macromolecules, this book offers a depth of knowledge and expertise that could only be replicated from the primary literature with great difficulty. Figures and illustrations are used liberally to simplify the understanding of concepts and to provide ready access to examples of biological applications. In addition, numerous boxes provide auxiliary information for those who wish to go more deeply into areas of background with which they may not already be familiar. The organization of topics lends itself well to using this book either to gain a comprehensive mastery of all aspects of the field of cryo-EM or as an authoritative reference source for individual topics within the field.

Author Biography

Robert M. Glaeser is Professor Emeritus of Biochemistry and Molecular Biology at the University of California, Berkeley Kenneth Downing is Senior Staff Scientist in the Life Sciences Division of Lawrence Berkeley Laboratory David DeRosier is Professor Emeritus of Biology at Brandeis University Wah Chiu is Alvin Romansky Professor of Biochemistry at Baylor College of Medicine Joachim Frank is HHMI Investigator and Lab Chief of Computational Biology and Molecular Imaging at the Wadsworth Center, New York State Department of Health

Table of Contents

Introduction	p. 3
Electron crystallography provides access to a unique class of problems in structural molecular biology	p. 3
High-resolution crystallography requires averaging of structures that are present in multiple copies	p. 5
Electron crystallography can produce three-dimensional density maps that are interpretable in terms of an atomic model of the structure	p. 7
Electron crystallography has developed from rich intellectual origins in optics, electron microscopy, and x-ray crystallography	p. 11
Objectives of this book	p. 15
Structure Determination as it has Been Developed Through X-Ray Crystallography	p. 17
Introduction	p. 17
Structure analysis by x-ray crystallography requires well-ordered, three-dimensional crystals	p. 18
The practical steps of data collection and data analysis have become very efficient	p. 19
The Fourier transform plays a central role in understanding the analysis of diffraction data	p. 19
The Fourier transform of a crystal represents discrete, regular samples of the continuous Fourier transform of the molecule	p. 26
The disorder that exists in real crystals can result in easily observed changes in the Fourier transform	p. 32
The Ewald sphere: a powerful mental picture that shows what part of the Fourier transform can be measured for every orientation of the specimen	p. 34
Bragg's law relates the measured scattering angle to the size of the repeat-distance for each sinusoidal term in the Fourier transform of the object	p. 36
Information about the relative phase of each sinusoidal term is lost in diffraction patterns	p. 38
The crystallographic phase problem is usually solved by using additional data obtained from heavy-atom derivatives of the original molecular crystals	p. 39
The three-dimensional electron density of the molecule can be calculated from the experimentally measured amplitudes and phases of the Fourier transform	p. 43
The 3-D density map must be interpreted in terms of other available information, to provide a model of the structure	p. 44
A more accurate estimate of the structure can be obtained by further refinement of the model	p. 46
Published structures are made available through a public-domain database	p. 48
Fourier Optics and the Role of Diffraction in Image Formation	p. 49
Introduction	p. 49
Abbe's diffraction theory of images: image formation is the two-dimensional equivalent of the crystallographer's "inverse Fourier transform"	p. 50
Zernike and the invention of phase contrast microscopy	p. 52
The rigorous diffraction theory of image formation describes images in terms of the inverse Fourier transform	p. 54
The lens as a linear system: transfer functions play an important role in Fourier optics	p. 59
The most common applications of Fourier optics in electron crystallography require that the specimen behaves like a weak phase object	p. 63
The image intensity for a weak phase object remains linear in the projected Coulomb potential	p. 64
The concept of a "phase contrast transfer function" is of central importance in the interpretation of high-resolution images	p. 67
Partial coherence imposes an envelope on the phase contrast transfer function	p. 69
Amplitude contrast can also contribute in an important way to images of thin, biological specimens	p. 72
Single side band images: blocking half of the diffraction pattern produces images whose transfer function has unit gain at all spatial frequencies	p. 74
Tilted illumination produces images for which the transfer function includes both phase errors and amplitude modulations	p. 75
Summary: Fourier optics is an important part of the conceptual foundation of electron crystallography	p. 76
Theoretical Foundations Specific to Electron Crystallography	p. 77
Introduction	p. 77
The single-scattering (kinematic scattering) approximation and the weak phase object approximation are mathematically similar but not identical	p. 78
Proof of the projection theorem	p. 81
Two important simplifications of crystallographic structure analysis occur when the specimen is approximated as a weak phase object	p. 82
Three-dimensional Fourier space is sampled by collecting data at many different tilt angles	p. 83
The resolution of a 3-D reconstruction is determined by the spatial frequency limit of the measurements and by the completeness of 3-D data collection	p. 85
Radiation damage represents a much more important experimental constraint in electron crystallography than in x-ray crystallography	p. 93
Images become very noisy at high resolution due to the finite, "low" exposures which are permitted within acceptable limits of radiation damage	p. 101
Spatial averaging must be used in order to overcome the limited statistical definition that is possible when images are recorded with "safe" levels of electron exposure	p. 102
The amount of averaging required is determined by the number of scattered electrons and by the image quality	p. 104
Instrumentation and Experimental Techniques	p. 106
Introduction	p. 106
The basic design of an electron microscope is much like that of a light microscope	p. 107
Technical features that are specific to electron optics	p. 108
Specimen stages	p. 123
Detectors that are suitable for observing and recording images and diffraction patterns	p. 126
Low-dose techniques make it possible to record high-resolution images and diffraction patterns even from easily damaged specimens	p. 131
Spot-scan imaging can minimize beam-induced movement	p. 134
Samples prepared as self-supported specimens within (or over) holes require additional precautions in order to minimize specimen charging	p. 137
Specimen Preparation	p. 139
Introduction	p. 139
Negative staining provides high contrast as well as excellent stability in the electron beam	p. 140
Metal shadowing produces stable samples which reveal surface topography	p. 142
Glucose and other "sustains" can preserve macromolecular structures to high resolution	p. 145
Contrast matching can be manipulated by using embedding media with different densities	p. 147
Embedding in vitreous ice is the preferred alternative for the preparation of unstained, hydrated specimens	p. 150
Charging and mechanical stability vary with details of the specimen preparation method	p. 159
Preparing extremely flat specimens continues to be one of the most important challenges when working with 2-D crystals	p. 161
Symmetry and Order in Two Dimensions	p. 67
Introduction	p. 167
Classes of symmetry in projection	p. 168
Three-dimensional symmetry classes for monolayer crystals	p. 175
The Fourier transform of a 2-D crystal is sampled at discrete points in two dimensions, but it is continuous in the third dimension	p. 182
Disorder and crystalline defects are an important fact of life	p. 187
Two-Dimensional Crystallization Techniques	p. 194
Introduction	p. 194
Integral membrane proteins represent a natural target for 2-D crystallization	p. 195
Many soluble proteins also form very thin crystals	p. 201
Crystallization at interfaces has potential for wide generality	p. 203
Data Processing: Diffraction Patterns of 2-D Crystals	p. 211
Introduction	p. 211
Diffraction intensities are used in a variety of ways in electron crystallography	p. 212
Data that have been recorded on photographic film must be converted to digital form with a scanning microdensitometer	p. 213
Density versus exposure characteristics can be used to convert the film density to the corresponding value of electron intensity	p. 215
Data can also be collected by direct electronic readout rather than on photographic film	p. 217
The digitized diffraction patterns are then indexed and reduced to the final diffraction intensities	p. 219
Intensities from individual diffraction patterns are merged to form a 3-D data set	p. 225
Factors that affect data quality	p. 230
Data Processing: Images of 2-D Crystals	p. 234
Introduction	p. 234
Optical diffraction is an effective tool for the preliminary evaluation of image quality	p. 235
Conversion of the image to a digital form is necessary for computer processing	p. 237
The fast Fourier transform is an efficient algorithm for numerical computation	p. 244
Images of crystals: indexing the Fourier transform is similar to indexing the electron diffraction pattern	p. 246
Extraction of amplitudes and phases from the indexed Fourier transform	p. 247
Establishing a common phase origin allows data from separate crystals to be merged into a 3-D data set	p. 253
Evaluation of data quality is based on the signal-to-noise ratio	p. 257
Quasi-optical filtering reduces the noise in the image	p. 259
Correction for distortions in the image increases the signal quality	p. 263
Corrections are also required for other systematic image defects	p. 270
High-Resolution Density Maps and their Structural Interpretation	p. 277
Introduction	p. 277
Three-dimensional density maps are computed from discrete samples of the complex structure factors	p. 278
Options for the display of 3-D density maps	p. 279
The missing cone of data results in poorer resolution in the direction perpendicular to the plane o{ the 2-D crystal	p. 282
Interpretation of the high-resolution map involves building the known chemical structure into the 3-D density	p. 288
Accurate atomic-resolution models can also be obtained by docking atomic models of individual components into the 3-D density map of a macromolecular complex	p. 291
Refinement of an atomic-resolution model may proceed in a different way for electron crystallography than is traditionally done in x-ray crystallography	p. 293
Difference Fourier maps	p. 300
Electron Crystallography of Helical Structures	p. 304
Introduction	p. 304
Ideal helices and their diffraction patterns	p. 307
Real helices and their diffraction patterns	p. 318
The hardest step: indexing the diffraction pattern	p. 325
Gathering amplitudes and phases is the next step in the reconstruction process	p. 330
Calculating and interpreting three-dimensional maps	p. 336
Helical particles with a seam can be analyzed by extending the method for helical particles	p. 339
Helical structures can be analyzed using single-particle methods	p. 340
The future looks bright	p. 342
Icosahedral Particles	p. 343
Introduction	p. 343
Description of an icosahedron	p. 344
Local symmetries can be present within an asymmetric unit	p. 347
Theory of icosahedral reconstruction	p. 347
Experimental considerations	p. 349
Data evaluation	p. 351
Image restoration	p. 352
Initial model building and structure refinement	p. 354
Resolution evaluation	p. 360
Poststructure analysis	p. 362
Atomic model determination	p. 363
Single Particles	p. 365
Introduction	p. 365
A certain minimum dose is required to align images of single molecules	p. 368
Due to the lack of symmetries, 3-D imaging requires coverage of the entire angular space	p. 369
Conformational variability increases the total number of images needed to achieve higher resolution	p. 370
Alignment of particles is required for averaging and image reconstruction, and its principal tool is the cross-correlation function	p. 371
Classification may be used to divide the projection set according to viewing directions, conformations, and ligand-binding states	p. 374
Variational patterns among images of macromolecules can be found by using multivariate data analysis or self-organized maps	p. 375
Two useful methods of classification in single particle analysis are hierarchical ascendant classification and K-means clustering	p. 385
Real-space reconstruction techniques can deal with the general 3-D projection geometries encountered in single-particle reconstruction	p. 388
Random-conical and common-lines methods can provide angular relationships among the molecule projections, as a way to jump-start a reconstruction project	p. 395
Angular refinement methods are used to proceed from the initial reconstruction to the final reconstruction	p. 399
Single-particle reconstruction in practice	p. 401
What are the prospects of achieving atomic resolution?	p. 413
Special Considerations Encountered with Thick Specimens	p. 415
Introduction	p. 415
Dynamical diffraction can be described by a number of different, but equivalent mathematical formalisms	p. 416
Conditions when kinematic diffraction theory fails	p. 419
Strong dynamical diffraction effects need not interfere with subsequent refinement of an atomic-resolution model of the structure	p. 424
Fresnel diffraction alone can become significant in thick specimens	p. 426
Curvature of the Ewald sphere destroys the appearance of Friedel symmetry at high resolution and at high tilt angles	p. 428
Inelastic scattering becomes an important consideration in thick specimens	p. 430
A final caution: failure of Friedel symmetry for thick specimens can be due to curvature of the Ewald sphere, dynamical diffraction, or inelastic scattering	p. 437
References	p. 441
Index	p. 469
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