Schlick T. Molecular Modeling and Simulation: An Interdisciplinary Guide
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List of Figures
1.1 Crystal structure of two eubacterial ribosomal subunits solved
bytheYonathgroup........................ 4
1.2 Cryo-EM view of 70S ribosome complex solved by the Frank group 5
1.3 Simulation evolution (3D version) ................ 15
1.4 Simulation evolution (2D version) ................ 16
1.5 The progress of DNA sequencing technology. .......... 34
2.1 Sequence and structure data .................... 44
2.2 Paracelsus’ Janus ......................... 47
2.3 GroEL/GroES chaperonin/co-chaperonin complex ........ 51
2.4 Prion protein ........................... 57
2.5 AIDS drugs ............................ 59
3.1 An amino acid ........................... 79
3.2 Water clusters ........................... 81
3.3 Dipeptide formation ........................ 82
3.4 Peptide formula .......................... 84
3.5 Aspartame ............................. 84
3.6 The amino acid repertoire ..................... 86
3.7 Amino acids structures ...................... 87
3.8 Amino acid frequencies ...................... 89
3.9 Fibrous proteins .......................... 91
3.10 Rop ................................ 93
3.11 EF proteins ............................ 95
xxxiv List of Figures
3.12 Protein-structure variants ..................... 96
3.13 Gauche and trans orientations ................... 97
3.14 Dihedral angle ........................... 98
3.15 Rotations in polypeptides ..................... 99
3.16 Lysine rotamers .......................... 99
3.17 Amino acids rotamers ....................... 100
3.18 Ramachandran plots ........................ 101
3.19 Further study of Ramachandran plots ............... 102
4.1 The α-helix and β-sheet motifs .................. 107
4.2 α-helical proteins (a) ....................... 108
4.3 α-helical proteins (b) ....................... 109
4.4 β-helical proteins (a) ....................... 111
4.5 β-helical proteins (b) ....................... 112
4.6 α/β proteins ............................ 120
4.7 α + β proteins ........................... 121
4.8 Multi-domain proteins ...................... 122
4.9 Membrane and cell surface proteins ............... 123
4.10 Other proteins ........................... 124
4.11 Tomato bushy stunt virus ..................... 125
5.1 The DNA double helix ...................... 136
5.2 Nucleic acid components ..................... 137
5.3 Watson-Crick base pairing .................... 138
5.4 The polynucleotide chain and labeling .............. 139
5.5 Sugar envelope and twist puckers ................. 143
5.6 Sugar pseudorotation cycle .................... 144
5.7 Common sugar puckers ...................... 145
5.8 Sugar pucker clustering ...................... 146
5.9 Torsion angle wheel ........................
147
5.10 Deoxyadenosine adiabatic map .................. 149
5.11 Base-pair coordinate system ................... 153
5.12 Base-pair step and base pair parameters ............. 155
5.13 Model A, B, and Z-DNA ..................... 158
5.14 Model A, B, and Z-DNA, stereo side ............... 159
5.15 Model A, B, and Z-DNA, stereo top ............... 160
6.1 Bending in long DNA ....................... 171
6.2 Net DNA bending examples ................... 172
6.3 A-tract DNA dodecamer ..................... 173
6.4 Sequence-dependent local DNA hydration ............ 179
6.5 DNA/protein binding motifs ................... 183
6.6 Interwound and toroidal supercoiling ............... 184
6.7 Schematic view of DNA levels of folding ............ 187
6.8 Nucleosome core particle ..................... 189
List of Figures xxxv
6.9 Tetranucleosome and other solved nucleosomes ......... 190
6.10 Chromatin fiber models ...................... 191
6.11 Mesoscale chromatin model ................... 192
6.12 Polynucleosome modeling .................... 195
6.13 Supercoiling topology and geometry ............... 196
6.14 Brownian dynamics snapshots of DNA .............. 202
6.15 Site juxtaposition measurements ................. 203
7.1 Various hydrogen-bonding schemes ............... 208
7.2 DNA/protein complex with Hoogsteen bp ............ 209
7.3 Oligonucleotide analogues .................... 212
7.4 Various nucleotide-chain folding motifs ............. 218
7.5 RNA pseudoknot motif ...................... 219
7.6 RNAs with pseudoknots ...................... 220
7.7 Examples of solved riboswitches. ................. 224
7.8 Seven major motifs of tertiary interactions in RNA ....... 226
7.9 RNA structure annotation ..................... 227
7.10 RNA junctions annotation ..................... 228
7.11 RNA as graphs .......................... 230
7.12 RAG segments .......................... 232
7.13 Candidate RNA motifs ...................... 233
7.14 In silico pool selection ...................... 234
8.1 QM/MM concept ......................... 245
8.2 DNA quantum-mechanically derived electrostatic potentials ... 248
8.3 Enolase active site ......................... 249
8.4 DNA pol β chemical synthesis reaction ............. 250
8.5 Molecular geometry ........................ 251
8.6 CHARMM atom types ...................... 257
9.1 Normal modes of a water molecule. ............... 269
9.2 Computed protein and water spectra ............... 271
9.3 Vibrational modes types ...................... 272
9.4 Bond-length potentials ...................... 275
9.5 Bond angles ............................ 278
9.6 Bond-angle potentials
....................... 279
9.7 Stretch/bend cross terms ..................... 280
9.8 Butane torsional orientations ................... 280
9.9 Torsion-angle potentials ...................... 284
9.10 Model compounds for torsional parameterization ........ 285
9.11 Wilson angle ........................... 287
9.12 Van der Waals potentials ..................... 291
9.13 Coulomb potentials ........................ 294
xxxvi List of Figures
10.1 CPU time for nonbonded calculations .............. 302
10.2 Cutoff schemes .......................... 306
10.3 Switch and shift functions ..................... 309
10.4 Periodic domains ......................... 312
10.5 Various periodic domains ..................... 313
10.6 Space-filling polyhedra ...................... 313
10.7 Ewald’s trick of Gaussian masking ................ 319
10.8 CPU time for PME vs. fast multipole ............... 324
10.9 Fast multipole schemes ...................... 326
10.10 Screened Coulomb potential ................... 341
10.11 Poisson-Boltzmann rendering of the 30S ribosome ........ 343
11.1 One-dimensional function ..................... 351
11.2 2D Contour curves for quadratic functions ............ 354
11.3 3D curves for quadratic functions ................. 355
11.4 Sparse Hessians .......................... 357
11.5 Sparse Hessians, continued .................... 358
11.6 Line search minimization ..................... 360
11.7 Newton’s method, simple illustration ............... 365
11.8 Newton’s method, quadratic example output ........... 367
11.9 Newton’s method, cubic example output ............. 368
11.10 Minimization paths ........................ 377
11.11 Minimization progress ...................... 381
12.1 Lattice structure for simple random number generators ..... 396
12.2 Structures for linear congruential generators ........... 397
12.3 MC computation of π ....................... 407
12.4 Boltzmann probabilities ...................... 413
12.5 MC moves for DNA ........................ 416
12.6 MC and BD DNA Distributions .................. 417
12.7 Bad MC protocol ......................... 417
13.1 Sampling methods ......................... 430
13.2 Equilibration ........................... 439
13.3 Chaos in MD ........................... 441
13.4 Butane’s end-to-end distance ................... 442
13.5 Butane’s end-to-end distance convergence
............ 444
13.6 Energy drift ............................ 446
14.1 Effective Verlet phase space rotation ............... 470
14.2 Verlet resonance for a Morse oscillator ............. 472
14.3 Extrapolative vs. Impulse MTS .................. 474
14.4 Impulse vs. extrapolative force splitting ............. 476
14.5 Resonance from force splitting .................. 477
14.6 Harmonic oscillator Langevin trajectories ............ 481
List of Figures xxxvii
14.7 BPTI means and variances by Langevin and Newtonian MTS .. 483
14.8 LN algorithm ........................... 484
14.9 Manhattan plots for polymerase/DNA .............. 486
14.10 Polymerase/DNA system ..................... 487
14.11 BPTI spectral densities ...................... 487
14.12 Polymerase/DNA spectral densities ................ 488
14.13 Polymerase/DNA geometry .................... 488
14.14 Cholesky vs. Chebyshev approaches for random force ...... 496
14.15 Implicit and explicit Euler .................... 498
14.16 Verlet and implicit-midpoint energies ............... 500
14.17 PCA examples ........................... 506
14.18 Pol β’s Closing Pathway. ..................... 512
14.19 Pol β Kinetic Profile. ....................... 513
15.1 Sample drugs ........................... 525
15.2 Related pairs of drugs ....................... 527
15.3 Chemical library .......................... 533
15.4 SVD/refinement performance ................... 547
15.5 SVD-based database projection in 2D and 3D .......... 548
15.6 Cluster analysis .......................... 549
15.7 PCA projection in 2D, with similar pairs ............. 550
15.8 PCA projection in 2D, with diverse pairs ............. 551
D.1 Sample histogram for protein/DNA interaction analysis. ..... 587
D.2 Biphenyl. ............................. 608
D.3 Structure for linear congruential generators ........... 613
D.4 Hydrogen bond geometry ..................... 620
List of Tables
1.1 Structural biology chronology ................... 7
1.2 Biomolecular simulation evolution ................. 9
2.1 Protein databases .......................... 45
3.1 Amino acid frequency ....................... 90
5.1 Genetic code ............................ 132
5.2 Nucleic acid torsion angle definitions. ............... 142
5.3 Mean properties of representative DNA forms. .......... 151
5.4 Selected parameters for model DNA helices ........... 152
6.1 Base-pair step parameters for free and protein-bound DNA .... 167
6.2 Protein/DNA complexes ...................... 181
6.3 DNA content of representative genomes. ............. 185
7.1 Some classes of non-coding RNA (ncRNA). ............ 217
8.1 Some CHARMM atom types .................... 256
9.1 Characteristic stretching vibrational frequencies .......... 270
9.2 Characteristic bending and torsional vibrational frequencies ... 270
9.3 Examples of torsional potentials .................. 286
10.1 CPU time for nonbonded calculations ............... 303
xl List of Tables
11.1 Optimization software ....................... 378
11.2 Minimization comparisons ..................... 382
12.1 MC calculations for π ....................... 408
13.1 Biomolecular sampling methods .................. 428
13.2 High-frequency modes ....................... 434
13.3 Biomolecular timescales ...................... 434
14.1 Verlet timestep restriction timescales ................ 468
14.2 Stability limits ........................... 473
Acronyms, Abbreviations, and Units
A
A adenine (purine nitrogenous base)
˚
A angstrom (10
−10
m)
AdMLP adenovirus major late promoter (protein)
AIDS acquired immune deficiency syndrome
Ala (A) alanine
Arg (R) arginine
Asn (N) asparagine
Asp (D) aspartic acid
AS Altona/Sundaralingam (sugar description)
ATP adenosine triphosphate (energy source)
AZT zidovudine (AIDS drug)
B
bp base pair
bps base pairs
BAC bacterial artificial chromosome
BOES Born-Oppenheimer energy surfaces
BPTI bovine pancreatic trypsin inhibitor
BSE bovine spongiform encephalopathy (‘mad cow disease’)
C
cm centimeter (10
−2
m)
C cytosine (pyrimidine nitrogenous base)
xlii Acronyms, Abbreviations, and Units
CAP catabolite gene activator protein
CASP Critical Assessment of Techniques for Protein Structure Prediction
CG Conjugate gradient method (for minimization)
CJD Creutzfeld-Jakob disease (brain disorder, human version of BSE)
CN Crigler-Najjar (debilitating disease, gene therapy applications)
CP Cremer/Pople (sugar description)
CPU central processing units
Cys (C) cysteine
D
DFT density functional theory (quantum mechanics approach)
DH Debye-H¨uckel
DNA deoxyribonucleic acid (also A-, B-, C-, D-, P-, S-, T-, and Z-DNA)
DOE Department of Energy
E
erg energy unit (10
−7
J)
EM electron microscopy
F
fs femtosecond (10
−15
s)
FFT Fast Fourier Transforms
G
G guanine (purine nitrogenous base)
Gln (Q) glutamine
Glu (E) glutamic acid
Gly (G) glycine
GSS Gerstmann-Straussler-Scheinker disease (brain disorder similar
to CJD)
H
HDV hepatitis delta helper virus
His (H) histidine
HIV human immunodeficiency virus
HMC hybrid Monte Carlo
HTH helix/turn/helix (motif)
Hz hertz (inverse second)
I
Ile (I) isoleucine
IHF integration host factor (protein)
Acronyms, Abbreviations, and Units xliii
K
kbp kilobase pairs
kcal/mol kilocalories per mole (energy unit)
kDa kilodaltons (mass unit used for proteins)
KR Kirkwood-Riseman
L
Leu (L) leucine
Lys (K) lysine
LCG linear congruential generator
M
m meter
mgr minor groove
ms millisecond (10
−3
s)
μs microsecond (10
−6
s)
mm millimeter (10
−3
m)
MAD multiple isomorphous replacement (crystallography technique)
MC Monte Carlo
MD molecular dynamics
Met (M) methionine
Mgr major groove
MIR multiwavelength anomalous diffraction (crystallography technique)
MLCG multiplicative linear congruential generator
MTS multiple-timestep methods (for MD)
N
nm nanometer (10
−9
m)
ns nanosecond (10
−9
s)
NCBI National Center for Biotechnology Information
NASA National Aeronautics and Space Administration
NDB nucleic acid database
NIH National Institutes of Health
NMR nuclear magnetic resonance
NSF National Science Foundation
O
OTC ornithine transcarbamylase (chronic ailment, gene therapy
applications)
P
pn picoNewton (force unit)
ps picosecond (10
−12
s)