While the field of computational structural biology or structural bioinformatics is rapidly developing, there are few books with a relatively complete coverage of such diverse research subjects studied in the field as X-ray crystallography computing, NMR structure determination, potential energy minimization, dynamics simulation, and knowledge-based modeling. This book helps fill the gap by providing such a survey on all the related subjects. Comprising a collection of lecture notes for a computational structural biology course for the Program on Bioinformatics and Computational Biology at Iowa State University, the book is in essence a comprehensive summary of computational structural biology based on the author s own extensive research experience, and a review of the subject from the perspective of a computer scientist or applied mathematician. Readers will gain a deeper appreciation of the biological importance and mathematical novelty of the research in the field. Contents: X-ray Crystallography Computing NMR Structure Determination Potential Energy Minimization Molecular Dynamics Simulation Knowledge-based Protein Modeling Appendices: Design and Analysis of Computer Algorithms Numerical Methods.
Author(s): Zhijun Wu
Publisher: World Scientific Publishing Company
Year: 2008
Language: English
Pages: 243
Tags: Биологические дисциплины;Матметоды и моделирование в биологии;
Contents......Page 12
Preface......Page 8
1.1 Protein Structure......Page 14
1.1.1. DNA, RNA, and protein......Page 15
1.1.2. Hierarchy of structures......Page 17
1.1.3. Properties of amino acids......Page 18
1.1.4. Sequence, structure, and function......Page 19
1.2.1. Experimental approaches......Page 22
1.2.2. Theoretical approaches......Page 23
1.2.3. Knowledge-based methods......Page 24
1.2.4. Structural refinement......Page 25
1.3 Dynamics Simulation......Page 26
1.3.1. Potential energy and force field......Page 27
1.3.2. Monte Carlo simulation......Page 28
1.3.3. Solution of equations of motion......Page 29
1.3.4. Normal mode analysis......Page 30
1.4 The Myth of Protein Folding......Page 31
1.4.1. Folding of a closed chain......Page 32
1.4.2. Biological and physical basis......Page 33
1.4.3. Computer simulation......Page 34
1.4.4. Alternative approaches......Page 36
Protein structure......Page 37
Protein folding......Page 38
2.1 The Phase Problem......Page 40
2.1.1. X-ray diffraction......Page 41
2.1.2. Electron scattering......Page 42
2.1.3. Atomic scattering factor......Page 45
2.1.4. Crystal lattice......Page 47
2.2 Least Squares Solutions......Page 50
2.2.1. Diffraction equations......Page 51
2.2.2. Sayre’s equations......Page 52
2.2.3. Cochran distributions......Page 54
2.2.4. Minimal principles......Page 57
2.3 Entropy Maximization......Page 59
2.3.1. Entropy vs. probability......Page 60
2.3.2. Maximizing entropy......Page 61
2.3.3. Newton method......Page 64
2.3.4. Fast Fourier transform (FFT) and discrete convolution......Page 65
2.4.1. Patterson function......Page 67
2.4.3. Molecular replacement......Page 69
2.4.4. Anomalous scattering......Page 71
The phase problem......Page 72
Least squares solutions......Page 73
Indirect methods......Page 74
3.1 Nuclear Magnetic Resonance......Page 76
3.1.1. Nuclear magnetic fields......Page 77
3.1.2. NMR spectra......Page 80
3.1.3. COSY experiment......Page 82
3.1.4. Nuclear Overhauser effect (NOE)......Page 84
3.2 Distance Geometry......Page 86
3.2.1. The fundamental problem......Page 87
3.2.2. Exact distances......Page 88
3.2.3. Sparse distances......Page 89
3.2.4. Distance bounds......Page 91
3.3.1. Embedding......Page 94
3.3.2. Least squares method......Page 95
3.3.3. Geometric buildup......Page 97
3.3.4. Potential energy minimization......Page 98
3.4 Structural Analysis......Page 100
3.4.1. The coordinate root mean square deviation......Page 101
3.4.2. NMR structure evaluation......Page 102
3.4.3. Ramachandran plot......Page 104
3.4.4. Structure refinement......Page 105
Distance geometry......Page 106
Distance-based protein modeling......Page 108
Structural analysis......Page 109
4 Potential Energy Minimization 99......Page 112
4.1.1. Quantum chemistry calculation......Page 113
4.1.2. Semiempirical approximation......Page 115
4.1.3. Protein energy landscape......Page 118
4.1.4. Implicit and explicit solvent effects......Page 119
4.2.1. Steepest-descent direction method......Page 120
4.2.2. Conjugate gradient method......Page 121
4.2.3. Newton method......Page 122
4.2.4. The quasi-Newton method......Page 123
4.3 Global Optimization......Page 124
4.3.2. Stochastic search......Page 125
4.3.3. Branch and bound......Page 127
4.3.4. Simulated annealing......Page 128
4.4.1. Integral transform......Page 129
4.4.3. Smoothing properties......Page 131
4.4.4. Computation of transformation......Page 132
Local optimization......Page 135
Function transformation......Page 136
5.1 Equations of Motion......Page 138
5.1.2. Principle of variation......Page 139
5.1.3. Equation for molecular motion......Page 140
5.1.4. Force field calculation......Page 141
5.2.1. Initial positions and velocities......Page 142
5.2.2. The Verlet algorithm......Page 143
5.2.3. Leap-frog algorithm......Page 147
5.2.4. Shake and Rattle......Page 148
5.3.1. Initial and ending positions......Page 151
5.3.2. Finite difference......Page 152
5.3.3. Stochastic path following......Page 153
5.3.4. Multiple shooting......Page 155
5.4 Normal Mode Analysis......Page 158
5.4.2. Normal modes......Page 159
5.4.3. Thermodynamic properties......Page 162
5.4.4. Gaussian network modeling......Page 163
Initial-value problem......Page 166
Boundary-value problem......Page 167
Normal mode analysis......Page 168
6.1. Sequence/Structural Alignment......Page 169
6.1.2. Shortest path problem......Page 171
6.1.3. Optimal alignment......Page 173
6.1.4. Structural alignment......Page 177
6.2.1. Fold recognition......Page 178
6.2.2. Inverse folding......Page 179
6.2.3. Scoring functions......Page 180
6.2.4. Complexities of threading......Page 181
6.3 Knowledge-based Structural Refinement......Page 182
6.3.2. Distance distributions......Page 183
6.3.3. Mean force potentials......Page 185
6.4 Structural Computing and Beyond......Page 186
6.4.1. Structural bioinformatics......Page 187
6.4.2. High-performance computing......Page 188
6.4.3. Structural genomics......Page 190
6.4.4. Biocomplexes and biosystems......Page 191
Fold recognition/threading......Page 192
Beyond structural computing......Page 193
Appendix A Design and Analysis of Computer Algorithms......Page 195
A.1.1. Computational model......Page 196
A.1.2. Computing time......Page 198
A.1.4. Example analysis......Page 199
A.2.1. NP-completeness......Page 201
A.2.2. Satis.ability problem......Page 202
A.2.4. Polynomial time reduction......Page 203
A.3.1. Lists......Page 205
A.3.3. Graphs......Page 206
A.3.4. Trees......Page 207
A.4.1. Sorting......Page 208
A.4.2. Searching......Page 211
A.4.3. Solution to the shortest path problem......Page 212
A.4.4. Minimal weight spanning tree......Page 213
Selected Further Readings......Page 214
B.1.1. Matrix–vector operations......Page 215
B.1.2. Matrix factorizations......Page 218
B.1.3. Linear systems of equations......Page 220
B.1.4. Singular value decomposition......Page 221
B.2 Numerical Optimization......Page 223
B.2.1. Steepest descent direction method......Page 224
B.2.2. Conjugate gradient method......Page 226
B.2.3. Newton method......Page 228
B.2.4. Quasi-Newton method......Page 229
B.3 Numerical Solutions to Initial-Value Problems......Page 231
B.3.2. Single-step method......Page 232
B.3.3. Multistep method......Page 233
B.3.4. Accuracy and convergence......Page 234
B.4 Numerical Solutions to Boundary-Value Problems......Page 235
B.4.2. Single shooting......Page 236
B.4.3. Multiple shooting......Page 238
B.4.4. Finite difference......Page 239
Selected Further Readings......Page 240
Index......Page 242
