Protein Geometry, Classification, Topology and Symmetry: A Computational Analysis of Structure,9780750309851

Protein Geometry, Classification, Topology and Symmetry: A Computational Analysis of Structure

by ;
Edition: 1st
ISBN13: 9780750309851
ISBN10: 0750309857
Format: Hardcover
Pub. Date: 2004-10-01
Publisher(s): CRC Press
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Summary

- Willie Taylor - a recognised leader in mathematical biology/theoretical molecular biology- Protein folding determines function of protein - key research area in molecular biology and biochemistry. Computational power now means problems governing folding can be handled quantitatively.- Reviews principles of protein folding and computational techniques employed- A key area of biophysics - interfaces with many other disciplines.

Table of Contents

Preface xi
1 Introduction 1(16)
1.1 Prologue
1(4)
1.1.1 Scope and aims
1(1)
1.1.2 Why proteins?
2(2)
1.1.3 Outline of the work
4(1)
1.2 Basic principles of protein structure
5(264)
1.2.1 The shapes and sizes of proteins
6(1)
1.2.2 The hydrophobic core
7(1)
1.2.3 Secondary structure
8(1)
1.2.4 Packed layers
9(2)
1.2.5 Barrel structures and β-helices
11(2)
1.2.6 Protein topology
13(2)
1.2.7 Domain structure
15(2)
PART 1 GEOMETRY 17(114)
2 Ellipsoids and embedding
19(30)
2.1 Geometric representations of structure
19(15)
2.1.1 Atomic coordinates
19(3)
2.1.2 Torsion angles
22(4)
2.1.3 Distances
26(1)
2.1.4 Inertial axes
27(5)
2.1.5 The shapes of proteins
32(2)
2.2 Distance geometry
34(15)
2.2.1 Out of hyperspace
35(5)
2.2.2 Interpretation of the eigenvalues
40(1)
2.2.3 Hierarchical inertial embedding
41(4)
2.2.4 Gradual projection
45(2)
2.2.5 Practical method specification
47(2)
3 Sticks to strings
49(44)
3.1 Secondary structure geometries
49(14)
3.1.1 Secondary structure line segments
50(5)
3.1.2 Secondary structure definition
55(2)
3.1.3 Comparison to standard definitions
57(4)
3.1.4 Applications and further developments
61(2)
3.2 Simplified architectures
63(1)
3.2.1 Stick packing
63(2)
3.2.2 Calibrating segment packing
65(3)
3.2.3 Layer architectures
68(2)
3.2.4 Layer-based stick models
70(3)
3.2.5 Polyhedra-based stick models
73(9)
3.2.6 Packing nomenclatures
82(3)
3.2.7 From 3D to 2D
85(2)
3.2.8 From 2D to ID
87(1)
3.2.9 Uniqueness of string descriptors
87(2)
3.2.10 Predicting helix contacts
89(4)
4 Sheets and barrels
93(40)
4.1 β-sheet geometry
93(25)
4.1.1 Sheet chirality
93(1)
4.1.2 Geometric models for a twisted sheet
94(5)
4.1.3 The surface of a twisted sheet
99(12)
4.1.4 Sheet bend and curl
111(2)
4.1.5 β-sandwiches
113(5)
4.2 β-barrels
118(15)
4.2.1 Hyperbolic surfaces
118(2)
4.2.2 Shear and stagger
120(1)
4.2.3 Cylindrical β-barrels
121(4)
4.2.4 Hyperbolic ,β-barrels
125(4)
4.2.5 Optimized barrels
129(2)
PART 2 CLASSIFICATION 131(78)
5 Networks and domains
133(26)
5.1 Hydrogen bond networks
133(10)
5.1.1 α-carbon-based β-sheet definition
134(2)
5.1.2 β-sheet dimensions
136(1)
5.1.3 TBC angle distribution
136(2)
5.1.4 βbarrel identification
138(2)
5.1.5 β-sheet classification
140(3)
5.2 Protein domain definitions
143(16)
5.2.1 Physical methods
143(1)
5.2.2 An Ising model
144(2)
5.2.3 Model evolution and domain extraction
146(1)
5.2.4 Conforming to expectation
147(2)
5.2.5 Setting the granularity level
149(2)
5.2.6 Performance and examples
151(4)
5.2.7 Simultaneous definition on multiple structures
155(1)
5.2.8 Probabilistic definitions
156(1)
5.2.9 Reparsing domains
157(2)
6 Protein structure comparison
159(21)
6.1 Overview of comparison methods
159(13)
6.1.1 Structure representations and degrees of difficulty
160(1)
6.1.2 The DALI method
161(1)
6.1.3 Geometric hashing approach
162(2)
6.1.4 Using structural superposition
164(1)
6.1.5 The SSAP program
165(2)
6.1.6 Iterated double dynamic programming
167(2)
6.1.7 Secondary structure graph matching
169(1)
6.1.8 Stick-figure comparisons
170(2)
6.2 Assessment of significance
172(8)
6.2.1 Score distributions from known structures
173(1)
6.2.2 Random structural models
174(1)
6.2.3 Randomized alignment models
175(1)
6.2.4 Scoring and biological significance
176(1)
6.2.5 Examples
177(3)
7 Classification and fold spaces
180(31)
7.1 Protein structure classification
180(5)
7.1.1 Practical approaches to classification
180(2)
7.1.2 Organization of the classifications
182(1)
7.1.3 Analysis of the classifications
183(2)
7.2 Protein fold spaces
185(2)
7.2.1 Distance geometry projection
185(2)
7.2.2 Simplified fold space
187(1)
7.3 A 'periodic table' for protein structures
187(11)
7.3.1 Classification using ideal stick forms
187(1)
7.3.2 Structure layers become valance shells
188(3)
7.3.3 Matching against all stick forms
191(4)
7.3.4 Reintroducing topology
195(2)
7.3.5 Expanding the classification tables
197(1)
7.4 'Evolutionary' steps in fold space
198(13)
7.4.1 Matching ideal forms
200(1)
7.4.2 Largest common fold
200(3)
7.4.3 Trees of structures
203(4)
7.4.4 Links and islands in fold space
207(2)
PART 3 TOPOLOGY 209(60)
8 Folds, tangles and knots
211(38)
8.1 Topology and knots
211(16)
8.1.1 Introduction
211(1)
8.1.2 Chemical topology
212(1)
8.1.3 Polymer topology
212(2)
8.1.4 True topology of proteins
214(2)
8.1.5 Pseudo-topology of proteins
216(7)
8.1.6 Topology of weak links in proteins
223(2)
8.1.7 Generalized protein knots
225(2)
8.1.8 Knots in random chains
227(1)
8.2 Random walks in fold space
227(11)
8.2.1 Random walks
229(1)
8.2.2 Secondary structure based fake proteins
230(2)
8.2.3 Off-lattice fold combinatorics
232(4)
8.2.4 Classifying topology in fake proteins
236(1)
8.2.5 Local versus global folding
237(1)
8.3 Protein fold complexity
238(11)
8.3.1 Topological indices
238(5)
8.3.2 Local and non-local packing
243(5)
8.3.3 Smoothing folds away
248(1)
9 Structure prediction and modelling
249(20)
9.1 Random folds from distance geometry
249(9)
9.1.1 Outline of the projection strategy
249(1)
9.1.2 Model specification
250(2)
9.1.3 Hydrogen bonds
252(3)
9.1.4 Chirality
255(1)
9.1.5 Scoring
255(1)
9.1.6 Simple models
255(3)
9.2 Modelling with distance geometry
258(3)
9.2.1 Generic preferences
258(1)
9.2.2 Specific interactions
259(1)
9.2.3 Sources of real data
260(1)
9.3 Protein tertiary structure prediction
261(10)
9.3.1 Ab initio prediction
262(1)
9.3.2 Empirical methods
263(2)
9.3.3 Model evaluation
265(2)
9.3.4 Genetic algorithm approach
267(2)
PART 4 SYMMETRY 269(39)
10 Structural symmetry
271(22)
10.1 Symmetry
271(9)
10.1.1 Symmetry from domain duplication
272(5)
10.1.2 Symmetries from secondary structure
277(3)
10.2 A Fourier analysis of symmetry
280(13)
10.2.1 Internal protein structure comparison
281(1)
10.2.2 Smoothing the score matrix
282(1)
10.2.3 Fourier transform
283(2)
10.2.4 Visualizing repeats
285(1)
10.2.5 Analysis of total power
286(2)
10.2.6 Removing expected symmetries
288(1)
10.2.7 Assessment of the Fourier approach
289(1)
10.2.8 Origin of structural symmetry
290(3)
11 Evolution and origins
293(15)
11.1 Evolution of structure and function
293(10)
11.1.1 Gene duplication and fusion
294(1)
11.1.2 Introns and exons
295(2)
11.1.3 Models of structure evolution
297(3)
11.1.4 Evolution of function
300(1)
11.1.5 Selection on random folds
301(2)
11.2 The origins of proteins
303(3)
11.2.1 The emergence of proteins in an RNA world
303(1)
11.2.2 Functions for protoproteins
304(2)
11.3 The secret of life
306(2)
References 308(17)
Contents 325

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