Phasing in crystallography a modern perspective
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| Sprache: | English |
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Oxford Univ. Press
2014
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| Ausgabe: | 1. ed. |
| Schriftenreihe: | IUCr texts on crystallography
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| 245 | 1 | 0 | |a Phasing in crystallography |b a modern perspective |c Carmelo Giacovazzo |
| 250 | |a 1. ed. | ||
| 264 | 1 | |a Oxford |b Oxford Univ. Press |c 2014 | |
| 300 | |a XVI, 414 S. |b Ill., graph. Darst. | ||
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| 830 | 0 | |a IUCr texts on crystallography |v 20 |w (DE-604)BV002805877 |9 20 | |
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Datensatz im Suchindex
| _version_ | 1804150547733807104 |
|---|---|
| adam_text | Contents
Symbols
and notation
xvii
1
Fundamentals of crystallography
ι
1.1
Introduction
1
1.2
Crystals and crystallographic symmetry in direct space
1
1.3
The reciprocal space
5
1.4
The structure factor
11
1.5
Symmetry in reciprocal space
12
1.5.1
Friedel law
12
1.5.2
Effects of symmetry operators in reciprocal space
12
1.5.3
Determination of reflections with restricted phase values
13
1.5.4
Systematic absences
15
1.6
The basic postulate of structural crystallography
17
1.7
The legacy of crystallography
24
2
Wilson statistics
27
2.1
Introduction
27
2.2
Statistics of the structure factor: general considerations
28
2.3
Structure factor statistics in PI and P
29
2.4
The P{z) distributions
35
2.5
Cumulative distributions
35
2.6
Space group identification
36
2.7
The centric or acentric nature of crystals: Wilson statistical analysis
42
2.8
Absolute scaling of intensities: the Wilson plot
43
2.9
Shape of the Wilson plot
47
2.10
Unit cell content
49
Appendix 2.A Statistical calculations in PI and
ΡΪ
50
2.
A.I Structure factor statistics in PI
50
2.A.2 Structure factor statistics in
ΡΪ
52
Appendix 2.B Statistical calculations in any space group
53
2.B.
1
The algebraic form of the structure factor
53
2.B.2 Structure factor statistics for centric and acentric space groups
55
Appendix 2.C The Debye formula
58
3
The origin problem, invariants, and seminvariants
60
3.1
Introduction
60
3.2
Origin, phases, and symmetry operators
61
xii Contents
3.3
The concept of structure invariant
63
3.4
Allowed or permissible origins in primitive space groups
65
3.5
The concept of structure
seminvariant 69
3.6
Allowed or permissible origins in centred cells
76
3.7
Origin definition by phase assignment
81
4
The method of joint probability distribution
functions, neighbourhoods, and representations
83
4.1
Introduction
83
4.2
Neighbourhoods and representations
87
4.3
Representations of structure seminvariants
89
4.4
Representation theory for structure invariants extended to
isomorphous data
91
Appendix 4.A The method of structure factor joint probability
distribution functions
93
4.
A. I Introduction
93
4.
A.
2
Multivariate distributions in centrosymmetric structures:
the case of independent random variables
94
4.A.3 Multivariate distributions in non-centrosymmetric
structures: the case of independent random variables
97
4.A.4 Simplified joint probability density functions in the
absence of prior information
99
4.A.5 The joint probability density function when some prior
information is available
102
4.A.6 The calculation of P(E) in the absence of prior
information
103
5
The probabilistic estimation of triplet
and quartet invariants
104
5.1
Introduction
104
5.2
Estimation of the triplet structure invariant via its first
representation: the PI and the
PÏ
case
104
5.3
About triplet invariant reliability
108
5.4
The estimation of triplet phases via their second representation
110
5.5
Introduction to quartets
112
5.6
The estimation of quartet invariants in PI and
PÏ
via their
first representation: Hauptman approach
112
5.7
The estimation of quartet invariants in PI and PI via their
first representation: Giacovazzo approach
115
5.8
About quartet reliability
116
Appendix 5.A The probabilistic estimation of the triplet
invariants in PI
117
Appendix 5.B Symmetry inconsistent triplets
120
Appendix 5.C The
/ m
formula
121
Appendix 5.D The use of symmetry in quartet estimation
123
Contents xiii
ó
Traditional
direct
phasing procedures
125
6.1
Introduction
125
6.2
The tangent formula
128
6.3
Procedure for phase determination via traditional direct
methods
130
6.3.1
Set-up of phase relationships
131
6.3.2
Assignment of starting phases
134
6.3.3
Phase determination
136
6.3.4
Finding the correct solution
137
6.3.5
Е
-map
interpretation
138
6.3.6
Phase extension and refinement: reciprocal space techniques
140
6.3.7
The limits of the tangent formula
141
6,4
Third generation direct methods programs
144
6.4.1
The shake and bake approach
144
6.4.2
The half-bake approach
147
6.4.3
The SIR2000-N approach
148
Appendix 6.A Finding quartets
149
Joint probability distribution functions when
a model is available: Fourier syntheses
151
7.1
Introduction
151
7.2
Estimation of the two-phase structure invariant (0h
-
φρίί)
152
7.3
Electron density maps
155
7.3.1
The ideal Fourier synthesis and its properties
156
7.3.2
The observed Fourier synthesis
162
7.3.3
The difference Fourier synthesis
164
7.3.4
Hybrid Fourier syntheses
166
7.4
Variance and covariance for electron density maps
168
7.5
Triplet phase estimate when a model is available
170
Appendix 7.A Estimation of
<тд
173
Appendix 7.B Variance and covariance expressions for electron
density maps
174
Appendix 7.C Some marginal and conditional
probabilities of
Ρ^,Κρ,φ,φρ)
176
8
Phase improvement and extension
177
8.1
Introduction
177
8.2
Phase extension and refinement via direct space procedures:
EDM techniques
177
8.3
Automatic model building
184
8.4
Applications
188
Appendix 8.A Solvent content, envelope definition, and solvent modelling
190
8.A.1 Solvent content according to Matthews
190
8.A.2 Envelope definition
191
8.A.3 Models for the bulk solvent
192
Appendix 8.B Histogram matching
193
Appendix 8.C A brief outline of the ARPIwARP procedure
196
xiv Contents
9 Charge
flipping and VLD
[vive /a différence)
198
9.1
Introduction
198
9.2
The charge flipping algorithm
199
9.3
The VLŰ
phasing method
201
9.3.1
The algorithm
201
9.3.2
VLD
and hybrid Fourier syntheses
205
9.3.3
VLD
applications to
ab initio
phasing
205
Appendix 9.A About
VLD
joint probability distributions
206
9.A.
1
The
VLD
algorithm based on difference Fourier synthesis
206
9.A.
2
The
VLD
algorithm based on hybrid Fourier syntheses
211
Appendix 9.B The RELAX algorithm
212
10
Patterson methods and direct space properties
214
10.1
Introduction
214
10.2
The Patterson function
215
10.2.1
Mathematical background
215
10.2.2
About interatomic vectors
216
10.2.3
About Patterson symmetry
217
10.3
Deconvolution of Patterson functions
218
10.3.1
The traditional heavy-atom method
219
10.3.2
Heavy-atom search by translation functions
220
10.3.3
The method of implication transformations
221
10.3.4
Patterson superposition methods
223
10.3.5
The
С
-map
and superposition methods
225
10.4
Applications of Patterson techniques
227
Appendix 10.A Electron density and phase relationships
230
Appendix 10.B Patterson features and phase relationships
232
11
Phasing via electron and neutron diffraction data
234
1
1.1
Introduction
234
1
1
.2
Electron scattering
235
11.3
Electron diffraction amplitudes
236
1
1
.4
Non-kinematical character of electron diffraction amplitudes
237
11.5
A traditional experimental procedure for electron
diffraction studies
239
1
1
.6
Electron microscopy, image processing, and phasing methods
241
11.7
New experimental approaches: precession and rotation cameras
244
11.8
Neutron scattering
245
11.9
Violation of the
positivity
postulate
247
Appendix 11.A About the elastic scattering of electrons: the
kinematical approximation
249
12
Phasing methods for powder data
252
12.1
Introduction
252
12.2
About the diffraction pattern: peak overlapping
253
Contents xv
12.3
Modelling
the diffraction pattern
258
12.4
Recovering Fhki 2 from powder patterns
260
12.5
The amount of information in a powder diagram
263
12.6
Indexing of diffraction patterns
264
12.7
Space group identification
266
12.8
Ab initio
phasing methods
267
12.9
Non-ab initio phasing methods
270
|НН
ndix 12.A Minimizine texture effects
272
13
Molecular replacement
275
13.1
Introduction
275
13.2
About the search model
277
13.3
About the six-dimensional search
279
13.4
The algebraic bases of vector search techniques
280
13.5
Rotation functions
282
13.6
Practical aspects of the rotation function
284
13.7
The translation functions
286
13.8
About stochastic approaches to MR
289
13.9
Combining MR with trivial prior information: the
ARCMBOLDO approach
289
13.10
Applications
291
Appendix 13.A Calculation of the rotation function in
orthogonalized crystal axes
294
I3.A.1 The orthogonalization matrix
294
13.
A.
2
Rotation in Cartesian space
295
13.A.3 Conversion to fractional coordinates
297
13.A.4 Symmetry and the rotation function
299
Appendix 13.B Non-crystallographic symmetry
304
13.B.1 NCS symmetry operators
304
13.B.2 Finding NCS operators
305
13.B.3 The translational NCS
308
Appendix 13.C Algebraic forms for the rotation and translation functions
311
14
Isomorphous replacement techniques
314
14.1
Introduction
314
14.2
Protein soaking and co-crystallization
315
14.3
The algebraic bases of SIR techniques
317
14.4
The algebraic bases of MIR techniques
320
14.5
Scaling of experimental data
322
14.6
The probabilistic approach for the SIR case
323
14.7
The probabilistic approach for the MIR case
327
14.8
Applications
329
Appendix 14.A The SIR case for centric reflections
330
Appendix 14.B The SIR case: the one-step procedure
331
Appendix 14.C About methods for estimating the scattering
power of the heavy-atom substructure
333
xvi Contents
15
Anomalous
dispersion techniques
335
15.1
Introduction
335
15.2
Violation
of the Friedel law as basis of the phasing method
337
15.3
Selection of dispersive atoms and wavelengths
340
15.4
Phasing via SAD techniques: the algebraic approach
344
15.5
The
SIRAS
algebraic bases
347
15.6
The MAD algebraic bases
352
15.7
The probabilistic approach for the SAD-MAD case
354
15.8
The probabilistic approach for the SIRAS-MIRAS case
360
15.9
Anomalous dispersion and powder crystallography
363
15.10
Applications
364
Appendix 15.A A probabilistic formula for the SAD case
365
Appendix 15.B Structure refinement for MAD data
366
Appendix 15.C About protein phase estimation in the
SIRAS
case
368
Appendices
370
Appendix M.A Some basic results in probability theory
370
M.A.I Probability distribution functions
370
M.A.
2
Moments of a distribution
371
M.A.3 The characteristic function
371
M.A.4
Cumulants
of a distribution
373
M.A.
5
The normal or Gaussian distribution
374
M.A.6 The central limit theorem
375
M.A.7 Multivariate distributions
375
M.A.8 Evaluation of the moments in structure factor distributions
377
M.A.9 Joint probability distributions of the signs of the
structure factors
379
M.A.
10
Some measures of location and dispersion in the
statistics of directional data
380
Appendix M.B Moments of the P(Z) distributions
382
Appendix M.C The gamma function
382
Appendix M.D The Hermite and Laguerre polynomials
383
Appendix M.E Some results in the theory of Bessel functions
385
M.E,
1
Bessel functions
385
M.E.2 Generalized hypergeometric functions
389
Appendix M.F Some definite integrals and formulas of frequent application
390
References
394
Index
412
Modern crystallographic methods originate from the synergy of two main research streams,
the small-molecule and the macromolecular streams. The first stream was able to definitively solve
the phase problem for molecules up to
200
atoms in the asymmetric unit. The achievements obtained
by rhc macromolecular stream arc also impressive. A huge number of protein structures have been
deposited in the Protein Data Hank. The solution of them is no longer reserved to an elite group
of scientists, but may be attained in a large number of laboratories around the world, even by
young scientists.
The synergy of the two research streams has allowed the tailoring of new probabilistic approaches
to deal with larger structures, errors in the experimental data, and modest data resolution. Traditional
phasing techniques like
ab
tnitio, molecular replacement, isomorphous replacement,
лт
anomalous
dispersion techniques have been revisited. The new approaches have been implemented in robust
phasing programs, which have been organized in automatic pipelines usable even by non-experts.
Protein structures, which
50
years ago could take months or even years to solve, can now be solved
in a matter of hours, partly also due to technological
adv
anees
in computer science.
This book describes all modern crystallographic phasing methods, and introduces a new rational
classification of them. A didactic approach is used, with the techniques described simply and logically
in the main text, and further mathematical details confined to the Appendices for motivated readers.
Numerous figures and applicative details illustrate the text.
Carmelo
Giacovazzo is Professor of Crystallography at
Rari
University, Italy, and Associate of
Istituto
di Cristallografia, CNR, Bari.
This textbook of basic to advanced material is by one of the foremost experts on phasing methods
in crystallography. Joint winner of the IUCr201
1
Ewald Medal
and Prize,
( ármelo
Giacovazzo presents
a coherent synthesis of mathematical methods for crystal structures of all molecule sizes as well as
current practice in the discipline, The author describes what works today, within a helpful historical
context, making it a book for our time. John R. Helliwell, University of Manchester
Active researchers will rind the book extremely useful in order to understand the historical develop¬
ments, advantages,
лпа
limitations of the conceptually different methods for crystallographic phasing.
Newcomers and students
w
ill find it a clarifying introduction and overview of the tools and trends
available in modern crystallographic research. There is no doubt that the volume will soon be another
landmark text in the world of crystallography/
Gilberto
Artioli, University of
Padova
Cover image: The central part of the figure shows
л
molecular organic fragment .is part ofa crystal structure,
overlapping ith
л
second figure representing
ι
m
w
hite
■
an X-ray beam producing ,i single crystal
diffraction
pattern.
Emage created by
(curado
(
oiocci.
ISBN
978-0-19-968699-5
UNIVERSITY PRESS
www.oup.com
780199
686995
|
| any_adam_object | 1 |
| author | Giacovazzo, Carmelo |
| author_GND | (DE-588)1037092066 |
| author_facet | Giacovazzo, Carmelo |
| author_role | aut |
| author_sort | Giacovazzo, Carmelo |
| author_variant | c g cg |
| building | Verbundindex |
| bvnumber | BV041147091 |
| classification_rvk | UQ 1000 UQ 3000 VE 9350 |
| ctrlnum | (OCoLC)869848889 (DE-599)BVBBV041147091 |
| discipline | Chemie / Pharmazie Physik |
| edition | 1. ed. |
| format | Book |
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| id | DE-604.BV041147091 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:40:40Z |
| institution | BVB |
| isbn | 9780199686995 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-026122621 |
| oclc_num | 869848889 |
| open_access_boolean | |
| owner | DE-11 DE-19 DE-BY-UBM DE-703 DE-29T DE-20 DE-188 |
| owner_facet | DE-11 DE-19 DE-BY-UBM DE-703 DE-29T DE-20 DE-188 |
| physical | XVI, 414 S. Ill., graph. Darst. |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | Oxford Univ. Press |
| record_format | marc |
| series | IUCr texts on crystallography |
| series2 | IUCr texts on crystallography |
| spelling | Giacovazzo, Carmelo Verfasser (DE-588)1037092066 aut Phasing in crystallography a modern perspective Carmelo Giacovazzo 1. ed. Oxford Oxford Univ. Press 2014 XVI, 414 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier IUCr texts on crystallography 20 Kristallstrukturanalyse (DE-588)4137204-9 gnd rswk-swf Kristallographie (DE-588)4033217-2 gnd rswk-swf Phasenproblem (DE-588)4503793-0 gnd rswk-swf Kristallographie (DE-588)4033217-2 s Kristallstrukturanalyse (DE-588)4137204-9 s Phasenproblem (DE-588)4503793-0 s DE-604 IUCr texts on crystallography 20 (DE-604)BV002805877 20 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026122621&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026122621&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Giacovazzo, Carmelo Phasing in crystallography a modern perspective IUCr texts on crystallography Kristallstrukturanalyse (DE-588)4137204-9 gnd Kristallographie (DE-588)4033217-2 gnd Phasenproblem (DE-588)4503793-0 gnd |
| subject_GND | (DE-588)4137204-9 (DE-588)4033217-2 (DE-588)4503793-0 |
| title | Phasing in crystallography a modern perspective |
| title_auth | Phasing in crystallography a modern perspective |
| title_exact_search | Phasing in crystallography a modern perspective |
| title_full | Phasing in crystallography a modern perspective Carmelo Giacovazzo |
| title_fullStr | Phasing in crystallography a modern perspective Carmelo Giacovazzo |
| title_full_unstemmed | Phasing in crystallography a modern perspective Carmelo Giacovazzo |
| title_short | Phasing in crystallography |
| title_sort | phasing in crystallography a modern perspective |
| title_sub | a modern perspective |
| topic | Kristallstrukturanalyse (DE-588)4137204-9 gnd Kristallographie (DE-588)4033217-2 gnd Phasenproblem (DE-588)4503793-0 gnd |
| topic_facet | Kristallstrukturanalyse Kristallographie Phasenproblem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026122621&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026122621&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV002805877 |
| work_keys_str_mv | AT giacovazzocarmelo phasingincrystallographyamodernperspective |