Normal Mode Analysis: Theory and Applications to Biological and Chemical Systems (Chapman & Hall/CRC Mathematical & Computational Biology)

Front cover......Page 1
Foreword......Page 6
Preface......Page 12
Acknowledgments......Page 16
Editors......Page 18
Contributors......Page 20
Contents......Page 24
1.1 Introduction......Page 26
1.2 PotentialWells......Page 27
1.3 Normal Modes......Page 30
1.3.1 Vibrational Modes......Page 32
1.3.2 Langevin and Brownian Modes......Page 34
1.4 Interpretation and Analysis of Normal Modes......Page 36
1.5 Conclusion......Page 40
References......Page 41
2.1 Introduction......Page 42
2.2 Normal Mode Theory......Page 44
2.3.1 Methods Based on the Rayleigh Quotient......Page 46
2.3.2 Perturbation Method......Page 47
2.4 The DIMB Method......Page 48
2.4.3 Convergence Criteria......Page 49
2.5.1 Neocarzinostatin......Page 52
2.5.2 Hemoglobin......Page 57
2.6 Concluding Remarks......Page 58
A.1 Initial Guess Vectors......Page 59
References......Page 61
3.1 Introduction......Page 66
3.1.2 Functional Motions of Proteins Are Cooperative Fluctuations Near the Native State......Page 68
3.2.2 GNM Assumes Fluctuations Are Isotropic and Gaussian......Page 69
3.2.3 Statistical Mechanics Foundations of the GNM......Page 71
3.2.4 Influence of Local Packing Density......Page 73
3.3.1 Equilibrium Fluctuations......Page 74
3.3.2 GNM Mode Decomposition: Physical Meaning of Slow and Fast Modes......Page 75
3.3.3 What Is ANM? How Does GNM Differ from ANM?......Page 78
3.3.4 Applicability to Supramolecular Structures......Page 80
3.3.5 iGNM: A Database of GNM Results......Page 83
3.4 Future Prospects......Page 84
References......Page 86
4.1 Introduction......Page 90
4.2 Basic Theories and Implementations......Page 91
4.2.1 NMA with Hybrid QM/MM Potentials......Page 92
4.2.2 Coarse-Grained NMA with Physical Potentials......Page 94
4.3.1 Active Site of Mb–CO......Page 96
4.3.2 Flexibility of Molecular Machines — Comparison between BNM and ANM......Page 100
4.4 Conclusions and Future Perspectives......Page 108
References......Page 109
5.1 Introduction......Page 116
5.2.1 Standard Normal Mode Calculation......Page 118
5.2.2 Comparison with the Conformational Change......Page 119
5.2.3 Effective Number of Modes Required for the Description......Page 120
5.2.4 RTB Approximation......Page 121
5.2.5 Tirion’s Approach......Page 123
5.2.6 Description of the Conformational Change with Approximate Modes......Page 126
5.3 Conformational Change of DHFR and NMA......Page 128
5.4 Applications......Page 130
References......Page 131
Unveiling Molecular Mechanisms of Biological Functions in Large Macromolecular Assemblies Using Elastic Network Normal Mode Analysis......Page 136
6.1 Introduction......Page 137
6.2.1 Normal Mode Theory......Page 138
6.2.2 Multi-Scale Energy Functions Using Elastic Networks......Page 139
6.2.3 Rotation–Translation Block Method......Page 140
6.2.5 Mapping the Pathway of Conformational Change Using NMA......Page 142
6.3 Applications......Page 144
6.3.1 Unveiling Molecular Mechanisms of Conformational Changes of Large Macromolecular Assemblies......Page 145
6.3.2 Exploration of Global Distortions and Interpretation of Low-Resolution Structural Information......Page 153
Acknowledgments......Page 158
References......Page 159
7.1 Introduction......Page 162
7.2.1 Basic Theory of NMA......Page 163
7.2.2 Elastic NMA......Page 164
7.3.1 NMA Based on Low-Resolution Density Maps......Page 165
7.3.2 QEDM-Assisted Cryo-EM Structural Refinement......Page 169
7.4.1 NMA at Length Scales of Several Microns......Page 171
7.4.2 Fiber Diffraction Refinement Based on Long-Range Normal Modes......Page 173
Acknowledgments......Page 175
References......Page 176
8.1 Introduction......Page 180
8.2 Comparison of Theory and Diffraction Experiment......Page 184
8.3 Effect of Displacements on the Bragg Peaks......Page 186
8.3.1 Normal Mode Predictions of X-Ray Diffuse Scattering......Page 188
8.4 Complete Refinement Strategies......Page 189
References......Page 190
9.1 Introduction......Page 196
9.2.1 Proteins......Page 197
9.2.2 Gaussian Network Model......Page 198
9.2.3 Spring Constants......Page 200
9.3.1 Conformational Changes......Page 201
9.3.2 Pair Distribution Functions......Page 202
9.3.4 Correlation Coefficients at Different Cutoff Distances and Spring Constants......Page 203
9.3.5 Cases of Highest Correlations......Page 205
9.3.7 Comparison of Fluctuations for Different Spring Constants......Page 206
References......Page 210
Effects of Sequence, Cyclization, and Superhelical Stress on the Internal Motions of DNA......Page 212
10.1 Introduction......Page 213
10.2.1 Molecular Representation......Page 214
10.2.2 DNA Force Field......Page 215
10.2.3 Kinetic Energy......Page 216
10.2.5 Imposed Superhelical Stress......Page 217
10.3.2 Linear DNA......Page 218
10.3.3 Circular DNA......Page 219
10.4.1 Intrinsic Bending and Single-Molecule Stretching......Page 220
10.4.2 Intrinsic Curvature and DNA Ring Puckering......Page 222
10.4.3 Intrinsic Curvature and Enzyme Cutting Patterns......Page 223
10.5.1 Dimer Deformability and Large-Scale Anisotropy of Linear DNA......Page 225
10.5.2 Dimer Deformability and Rotational Positioning of Circular DNA......Page 226
10.6.1 Roll–Slide Interdependence and Supercoiling of Circular DNA......Page 227
10.6.2 Twist–Rise Coupling and Overstretching of Linear DNA......Page 229
10.7 Summary......Page 231
References......Page 232
11.1 Introduction......Page 238
11.2.1 Theory......Page 240
11.2.2 Calculation Details......Page 243
11.3.1 (Dialanine)......Page 244
11.3.2 Poliovirus......Page 245
11.3.3 Rhinovirus and CCMV......Page 252
11.4 Discussion......Page 253
References......Page 255
12.1 Introduction......Page 258
12.2 Collective-Mode Description of Protein Dynamics......Page 259
12.3 Principal Component Analysis......Page 260
12.4 Langevin Mode......Page 263
12.5 Conservation and Convergence of Collective Variables......Page 264
12.6 Anharmonicity of Energy Landscape and JAM Model......Page 266
12.7 Application of JAM Concept......Page 268
12.8 Application of the Normal Mode Concept to the Dynamics Crystallographic Refinement......Page 271
12.9 Neutron Scattering......Page 272
References......Page 274
Imaginary-Frequency, Unstable Instantaneous Normal Modes, the Potential Energy Landscape, and Diffusion in Liquids......Page 278
13.1 Introduction......Page 279
13.2 Unstable Modes and Diffusion......Page 281
13.2.1 Statistical Mechanics on the PEL......Page 282
13.2.2 The Random EnergyModel......Page 291
13.3 Diffusive and Nondiffusive Unstable Modes......Page 295
13.3.1 Potential EnergyPr ofile Based Methods......Page 296
13.3.2 Landscape Based Methods......Page 297
13.4 Summary and Conclusions......Page 300
References......Page 301
14.1 Introduction......Page 306
14.2.1 Theory......Page 308
14.3.1 The Harmonic Limit: Trp-Cage......Page 310
14.3.2 Beyond the Harmonic Limit: Dialanine......Page 317
14.4 Summary and Conclusions......Page 321
References......Page 323
15.1 Introduction......Page 326
15.2 Cytochrome c......Page 327
15.3 QCF Approach......Page 328
15.3.1 Fermi’s Golden Rule......Page 329
15.3.2 Quantum Correction Factor......Page 330
15.3.3 NM Calculations for Cyt c......Page 331
15.3.4 Application to VER of the CD Bond in Cyt c......Page 332
15.3.5 Fluctuation of the CD Bond Frequency......Page 333
15.4 Reduced Model Approach......Page 334
15.4.1 Reduced Model for a Protein......Page 335
15.4.2 Maradudin–Fein Formula......Page 336
15.4.3 Third-Order Coupling Elements......Page 337
15.4.4 Width Parameter......Page 338
15.5.1 Comparison with Experiment......Page 340
15.5.2 Validity of Fermi’s Golden Rule......Page 341
15.5.3 Higher-Order Coupling Terms......Page 342
15.6 Summary......Page 343
References......Page 345
16.1 Introduction......Page 350
16.2 Computation of Vibrational Lifetimes......Page 353
16.3.1 Cytochrome c......Page 355
16.3.2 Photoactive Yellow Protein......Page 360
16.4 Concluding Remarks......Page 364
Acknowledgments......Page 366
Appendix: Force Field for Chromophore......Page 367
References......Page 369
17.1 Introduction......Page 374
17.2.1 Principal Component Analysis......Page 375
17.2.2 Constraint Method......Page 377
17.2.4 Principal Component Restraints......Page 379
17.3.2 Rapid Conformational Sampling......Page 384
17.3.3 Large Conformational Motions: Allosteric Transitions, Unfolding, Folding......Page 386
References......Page 388
Using Collective Coordinates to Guide Conformational Sampling in Atomic Simulations......Page 392
18.1.2 A Qualitative Picture of the Conformational Energy Landscape......Page 393
18.1.3Objecti ves and Basic Strategies for Enhanced Conformation Sampling......Page 394
18.2.1 Collective Coordinate Descriptions of Protein Dynamics......Page 395
18.2.2 Enhanced Sampling Methods Employing Collective Coordinates......Page 396
18.3.1 The Weak Coupling Method for Constant Temperature MD Simulations......Page 397
18.3.2 The ACM Scheme......Page 398
18.3.3 Using ANM to Guide Atomic Simulations in the ACM Scheme......Page 400
18.3.4 The Amplified Collective Motion-Assisted Minimum Escaping (ACM-AME) Scheme......Page 401
18.4.1 Interdomain Motions of Bacteriophage T4 Lysozyme......Page 403
18.4.2 Folding of an S-Peptide Analog......Page 405
18.4.3A CM-AME Sampling of Peptide Conformations......Page 408
18.5 Summary......Page 409
References......Page 410
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E......Page 418
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I......Page 421
L......Page 422
M......Page 423
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S......Page 427
T......Page 429
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Z......Page 431
Back cover......Page 448