Electron Crystallography of Biological Macromolecules

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

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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

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