Index

504

Boundary element method, 99, 141–142 Bovine pancreatic trypsin inhibitor (BPTI),

2, 382, 383

Bovine protein tyrosine phosphate, 230 Brain lipid-binding protein (BLBP), 296–298 Branch-and-bound algorithm, 257, 267 Brownian

dynamics, 57, 452 rotational motion, 491

Canonical partition function, 41 CAP-DNA complex, 3 Cartesian coordinate, 115 CASP, 294

CATH, 277–278

CFF (consistent force field), 14 CHARMM, 12, 14, 17, 21, 141, 283, 289,

294, 399, 443, 450, 497 Chemical informatics, 363 Chemical library design, 364 Chemical reaction, 417 Chemical reactivity, 222 Chemical shifts, 254

Chemoinformatics (or cheminformatics), 363 Chromosome, 449

Citrate synthase, 231 Cluster

analysis, 85–86 sampling methods, 364

Coarse-grain potentials, 65 Combinatorial chemical synthesis, 363 Combining rules, 11

Comparative field analysis (CoMFA), 351, 353, 359

Comparative modeling (homology modeling), 3, 275–312

alignment, 279–280 errors, 290–294 evaluation, 294–295

identifying related proteins, 277–279 loop modeling, 285–286

model building, 280–289 side chain modeling, 286–289

COMPASS, 14 COMPOSER, 278, 280–281

Computer aided drug design (CADD), 351 Condensed phase spectroscopy, 222 Configuration interaction, 395, 421 Conformational analysis, 69–90

cluster analysis, 85–86

principal component analysis (PCA), 86– 89, 384

Index

[Conformational analysis]

principal coordinate analysis (PCoorA), 86–89, 384

side chain, 314, 321, 339–344 similarity measures, 84

Conformational constraints, 187 energy surface, 153 equilibrium, 427 flexibility, 222 restraints, 184 transitions, 2–3

Conformation sampling, 70–77, 286 distance geometry, 75–76 enumeration, 70, 75, 286

genetic algorithms, 73–74, 286

high temperature molecular dynamics, 70– 71, 286

J-walking, 74, 76

minimum perturbation method, 286 Monte Carlo simulations (MC), 71–73,

286

multiple copy simultaneous search (MCSS), 286

parallel tempering, 74, 76–77 Conformation

minimization, 77–82 optimization, 77–83 simulated annealing, 82–83

space, 70–71, 76, 86, 87–89, 289, 373–374 CONGEN, 278

Conjugated gradients minimization (CG), 79–81, 82, 284 (see also Minimization)

Conservation

angular momentum, 43, 51 energy, 43, 51

linear momentum, 43, 49, 51 Constant-pressure simulation, 53, 60 Constant-temperature (isothermal) simula-

tion, 53, 58 Constraint, 53, 62

dynamics, 122 Lagrange multipliers, 63 RATTLE, 50

SHAKE, 50, 63 Continuum

boundary conditions, 98 electrostatic approximation, 140 model, 94, 417, 459 Poisson–Laplace equation, 418 reaction field, 170

treatment of solvation, 94

Index

Convergence, 457 Coordinate frame global, 119

local, 119 Correlation function, 54

auto-correration function, 54 cross-correlation function, 54

pair correlation function, 421, 423 Coulomb’s law (see Electrostatics) Coupled cluster, 421

Covariance matrix, 87, 156 Crambin, 384 Creutzfeldt–Jakob disease, 372 CRYSTAL, 34

CURVES, 458 Cystic fibrosis, 372 Cytochrome c, 384

Cytosine-5-methyltransferase, 3

DALI, 277–278 Databases

mining, 363, 364

sequence and structure, 277–279 Daunomycin, 446

Debye model, 491

Debye–Huckel approximation, 143 Debye–Waller factor, 161, 249, 480, 489 Density function method, 222, 395

Kohn–Sham orbital, 223, 417 Detailed balance, 70

DIALS & WINDOWS, 458 Dielectric

boundaries, 22, 141 constant, 22, 417 continuum, 94, 170, 188 distance-dependent, 442, 450 effective, 98

permittivity of a vacuum, 92 R-dependent, 22

reaction field, 188 Diffusion

constant, 485 equation method, 290

Dihydrofolate reductase, 24 Dipalmitoylphosphatidylcholine (DPPC), 465 Direct sampling methods, 364

Dirichlet

distribution, 324, 327–329 mixture priors, 330–332

DISCO, 364

Dispersion (see van der Waals)

505

Distance geometry, 75–76, 258, 281, 359 bound smoothing, 258

embedding, 260 metric matrix, 259 refinement, 260

self-correction method, 264 Distance matrix, 84, 85, 87 Diversity analysis, 363 DNA, 1–3, 222, 441

2′-5′-phosphodiester, 448 B, 127, 442

base sequence, 444 base stacking, 447

environmental influence, 444 helicoidal parameters, 458 hydration, 458

iDNA, 449

peptide nucleic acids, 448 phase transition, 448 phosphoramidate, 448 polymerase III, 298 quadraplex, 449 ribbonlike model, 451 segmented rod model, 452 triplex, 443

water activity, 444, 458 Z, 442, 449

DOCK, 365 Docking, 296, 353

flexible docking, 69, 74, 76 ligand-receptor, 361

Donor-acceptor energetic interaction, 393 Dopaminergic ligand-receptor system, 352 Downhill simplex minimization, 79 DRAGON, 278

DREIDING, 14 Drew dodecamer, 443 Drug

computational screening, 69 computer-aided drug discovery, 69 discovery and design, 4, 85, 363 structure-based drug discovery, 69 therapy, 448

Dummy atoms, 177

Dynamic average, 41, 42, 270 Dynamicin, 446

Dynamic structure factor, 478

ECEPP (empirical conformational energy program for peptides), 15, 289

EcoRI, 445

Einstein relation, 485

506

Elastic incoherent structure factor, 479 Electron transfer

properties, 393, 404 protein, 393

rate, 394, 408 Electrostatics, 91

Coulomb’s law, 93, 95

Coulombic interactions, 96, 97, 105 electric field, 92

Ewald (see Ewald) potential, 92

Empirical force fields (see Potential energy function)

Empirical valence bond method, 222 Energy barriers, 70, 71, 76, 83, 86, 383–388 Energy basins, 86

Energy landscape, 71, 82–83, 373–374, 383–388

Ensemble average, 41, 270

canonical, 41, 58, 70 isobaric–isoenthalpic, 61 isothermal–isobaric, 58, 62, 470 microcanonical, 58, 127, 470 structure, 270

Entropy distance, 329 Enzyme, 221, 222

-catalyzed reactions, 222 Eosinophil neurotoxin, 291 Equipartition theorem, 49, 155 Erabutoxin, 293

Ergodic hypothesis, 42, 70, 76 ERRAT, 278

ESP (electrostatic potential), 21 Esperamicin, 446

Estrogen receptor, 445 Evolutionary algorithms, 360

Ewald, 105, 188, 191, 443, 447, 455 conducting boundary conditions, 106 particle mesh Ewald (PME), 27, 111, 188,

443

particle mesh (PM3), 110 summation, 105, 170, 399, 469

tinfoil boundary conditions, 192 (see also Ewald conducting boundary conditions)

Exchange repulsion (see van der Waals) Extended electrostatics, 454

FastA, 278–279

Fast multipole (FMA), 99, 103, 110, 454 Field integrated electrostatic approach, 142 Finite-difference relaxation algorithm, 141

Index

Finite difference, 99 Flavodoxin, 276, 282

Flexibility (see Molecular flexibility) Fluorescence spectroscopy, 238 Fock operator, 417

Folding simulations, 382–383 Folding temperature, 373

Folds, structural, 275, 279–280, 298, 371 Force field, 4, 71, 283

Formamide, 431

Frank–Condon

ionization potential, 400 transition, 408

Free energy, 137 absolute binding, 172 alchemical, 170 cavity formation, 139

charging free energy, 140 component analysis, 181 conformational, 184 coupling coordinates, 176 difference, 169, 417

dual topology, 180 endpoint corrections, 177 λ-Dynamics, 194

Gibbs, 58

Helmholtz, 58, 172, 421 hybrid energy function, 176 landscape, 388

perturbation formula/theory, 172, 174, 403, 449

simulations, 362, 403, 407 single topology, 180

slow growth method, 403 solvation, 141, 459 standard binding, 181

thermodynamic coupling, 137 thermodynamic cycle, 170, 362 thermodynamic integration, 137, 177, 185,

403

weighted histogram analysis method (WHAM), 186

FREEHELIX, 458

Frequentist probability theory, 317–322 FSSP database, 332

Funnel, energy, 373

Gaussian distribution, 54

GAUSSIAN, 21

Gauss’s law, 93, 97

GenBank, 277, 313

GeneCensus, 278

Index

Generalized born, 98, 142

Genetic algorithms (GA), 73–74, 257, 286, 290, 360

crossover operation, 73–74 migration operator, 73 mutation operator, 73–74

Gibbs sampling, 327–329 Glass temperature, 373 Global minimum, 82, 289 Global optimization, 82–83 Glucocorticoid receptor, 445

3-Glycerophosphate synthase, 291 Go model, 378, 380

G-protein coupled receptors, 353 Gradient RMS (GRMS), 82 Graph theoretic indicies, 359 Grid

-based sampling, 364 GRID, 365

Search, 78 GROMOS, 12, 450, 497

Hamiltonian, 41, 43 Hammett

equation, 358

σ parameter, 359 Hansch

Corwin, 351

π parameter, 358 Harmonic

analysis, 153 approximation, 118 potential, 71

HARMONY, 295 Hartree–Fock, 232, 395, 421

Heisenberg uncertainty principle, 95 Helmholtz (see Free energy) Hemoglobin, 2

Hessian matrix, 81

High throughput screening, 363 HIV protease, 4

HMG-D chromosomal, 445

Holonomic distance constraints, 122 Homeodomain, 445

Homology modeling, (see Comparative modeling)

Hoogsteen, 451 HP model, 378

HSSP database, 332

Hybrid QM–MM method (see Quantum mechanical/molecular mechanical)

507

Hydrocarbon chain dynamics, 488 Hydrophobic, 139

container, 100 Hydrogen bond

CEH O, 447

Hypernetted chain approximation, 420

ICM, 278

Ileal lipid-binding protein, 293 Image approximation, 100 Immunoglobulin fold, 285

Implicit solvent method (see Solvent) Infrared spectroscopy, 491

InsightII, 278 Insulin, 2

Integral equation, 170 Integrators

integration time step, 49 leapfrog, 45, 46, 123 Runge–Kutta, 123 stability, 50

Sto¨rmer–Verlet-leapfrog, 123 time reversibility, 43, 51 velocity Verlet, 45, 47 Verlet, 123

Interleukin 1β, 44, 293 Internal coordinate

molecular dynamics (ICMD), 115, 269 simulation, 115, 452

Ion channel, 467 Ionic

product, 424 strength, 142

J-walking, 74, 76 JUMNA, 452

Jumping among minima model (JAM), 165, 384

Karmers theory, 438 Kinematics equation, 120 Kinetic rate constant, 200

Knowledge-based potentials, 135, 147 (see also Coarse-grain potentials)

Kohn, W., 7

Kullback–Leibler divergence (see Entropy distance)

Kurtosis, 54

Lac repressor, 445 Lagrange–Hamilton formalism, 122

508

Lambda (λ) dynamics, 194 (see also Free energy)

λ repressor, 288 Lanczos algorithm, 157 Lattice models, 376–379 Langevin

dipole method, 399 equation, 56 generalized, 438 mode analysis, 163

Lattice summation methods (see Ewald) Leapfrog (see Integrators)

Legendre polynomial, 491 Lennard–Jones (see van der Waals) Levinthal paradox, 371

Lid method, 386

Linear free energy relationship (LFER), 358 Linear response approximation, 176, 239 Liouville formulation, 63

Liouville operator, 63 Lipid

bilayer structure, 465, 471

neutron scattering measurements, 477 polar group, 473

-soluble protein, 465

London’s dispersion interactions (see van der Waals)

LOOK, 278

Lysozyme, 2, 243, 372, 384

Marcus Theory, 394, 408

Markov chain Monte Carlo (MCMC), 322, 326–327

Master equation, 375 Maxwell’s equations, 93

Mean force field approximation, 145 Membranes, 3

molecular dynamics, 476 Methotrexate, 24 Methylamine, 428

Metric tensor, 118

Metropolis algorithm, 72, 76, 326 Metropolis–Hastings method, 326–327 Minimally frustrated random energy model,

374–376

Minimum perturbation method, 286 Minimization, 71, 77–82

adopted basis Newton–Raphson (ABNR), 81–82

conjugated gradients (CG), 79–81, 82, 116 downhill simplex method, 79

energy gradients, 121

Index

[Minimization]

gradient RMS (GRMS), 82 grid search, 78 minimization protocol, 82 Newton–Raphson (NR), 81

steepest descent (SD), 79–80, 82

MMFF (Merck molecular force field), 14, 21 ModBase, 278, 282–285, 299

MODELLER, 278–279, 292

Modeling, 3, 69, 275–312

ab initio modeling, 289–290

homology modeling (see Comparative protein structure modeling)

Models lattice, 289

simplified, 289 Molar refractivity, 359 Molecular

descriptors, 364 orbital theory, 417 polarization, 422 shape analysis, 359 similarity, 364

surface, 141 (see also Solvent accessible surface area)

trees, 123

Molecular dynamics (MD), 2, 39, 69, 74, 76, 83, 247, 261, 284, 286, 290, 361, 380, 384, 407, 418

high temperature MD, 70–71, 76, 77 simulation practice, 48

simulation protocol, 51 Molecular flexibility, 2–4, 69 MOLSCRIPT, 287

Monte Carlo simulations (MC), 39, 71, 74, 76, 77, 83, 115, 117, 257, 286, 290, 418 (see also Conformation sampling)

Markov chain Monte Carlo, 322, 326–327 metropolis algorithm, 72

trial move, 72–73 Mossbauser spectroscopy, 238 MP2 method, 232

Mulliken population analysis, 397

Multiple copy simultaneous search (MCSS), 286

Multiple linear regression (MLR), 358 Multiple time step method (MTS), 53, 63 Multipole expansion, 100

Myoglobin, 2, 382, 383

Nanotechnology, 441, 449

Nernst equation, 394

Index

Neural network artificial, 360

Neutron scattering, 239, 244

coherent inelastic neutron scattering, 245 elastic incoherent structure factor, 248 incoherent neutron scattering, 246 inelastic incoherent scattering intensity,

248

Newton, Sir Isaac, 169 Newton

equation of motion, 42 -Euler analysis, 124

-Raphson minimization (NR), 81 second law of motion, 42

Newtonian dynamics, 123 Nitrous acid, 446

Non-bond interactions (see Potential energy) Nonuniform charge distribution, 138 Normal mode analysis, 115, 153, 237

anharmonicity, 163 anharmonicity factor, 164

dihedral angle space normal mode analysis, 156, 158

refinement, 160

single parameter model, 159 Nuclear hormone receptors, 445

Nuclear magnetic resonance (NMR), 238, 253

spectroscopy, 3, 69, 76, 84, 294, 295, 314 structure determination, 254

Nuclear Overhauser effect (NOE), 253 ambiguity, 255, 265

assignment method (ARIA), 262, 265 automatic assignment, 265

intensity, 255 spin diffusion, 267

structural restraints, 255

Off-lattice models, 379–381 Oligonucleotide, 441

123D, 278

Onsager–Kirkwood parameter, 432 Onsager’s reaction field, 417

OPLS (optimized potential for liquid simulations), 17, 21

Optical tweezers, 441

Overhauser spectroscopy (NOSEY), 161 Oxidoreductase, 287

PAM matrix, 335, 336

Parallel tempering, 74, 76–77

Partial least squares (PLS), 359

509

Particle mesh Ewald (PME) (see Ewald) Pauli exclusion principle, 10, 138, 224

PDB (protein data bank), 277–278, 313, 336 Peptide bond

cis–trans transition, 71 Percus–Yevick approximations, 420

Periodic boundary conditions, 53, 96, 104, 401, 454

Pharmacophore, 351, 353

modeling by distance geometry, 76 prediction, 364

Phase space, 41 PhD, 278

Phosphoglycerate Kinase, 248 PIR database, 277

Poisson’s

-Boltzmann equation, 100, 139, 143, 189, 398, 403

equation, 93, 98, 140 Pople, J.A., 7

Pores, 467 Potential energy

electrostatic (see Electrostatics) force field, 16, 41, 468 function, 8, 95

hybrid (see Free energy) non-bond pairs, 96 optimization, 27 parameters, 8

shifting, 105

spherical truncation, 447 switching, 105, 447 transferability, 16

truncation methods, 97, 105, 454 twin-range approach, 100

Potential of mean force (PMF), 55, 134, 135, 136, 184, 289, 427, 447 (see also Umbrella sampling; Free energy)

PRESAGE, 278

Principal component analysis (PCA), 86–89 Principal coordinate analysis (PCoorA), 86–

89

Prion protein, 384–385 PrISM, 278 PROCHECK, 278, 294 PROCHECKNMR, 294 ProCyon, 278 PROFIT, 278

PROSAII, 278, 295, 298, 299, 300 Protein: characteristic motion, 40 Protein folding, 69, 289–290, 371–391

atomistic models, 382–388

510

[Protein folding] energy basins, 384

energy landscape, 373–376, 383–388 folding simulations, 382–383 folding temperature, 373

free energy landscape, 388 funnel, 373–374, 386–388 go model, 378, 380

HP model, 378

lattice models, 376–379

minimally frustrated model, 374–376 off-lattice models, 379–381

reaction coordinate, 373–374 simple models, 374–376 topological mapping, 385–388 unfolding simulations, 382–383

PROVE, 278 PSI-BLAST, 279, 300

Quantitative structure-activity relationship (QSAR), 351, 358

nonlinear, 360 Quantum dispersion, 138

Quantum mechanical/molecular mechanical (QM/MM), 3, 196, 222, 419, 446

boundary, 226

frozen orbital approach, 226 generalized hybrid orbital, 226 link atom approach, 226

local self-consistent field, 226 Quantum mechanics, 221 Quasi-harmonic analysis, 86, 154, 164 Quaternion, 119

Radial distribution function, 421, 474 Ramachandran map, 2, 321, 341 Random number generator, 73

Rare events, 199 RASMOL, 299 Rate equations, 200

Rational library design, 363 Reaction coordinate, 184, 199

Reaction field methods, 105, 140, 145, 454 Reaction path

conjugate peak refinement, 217 construction, 214

cost function, 211 diffusional path, 213

dominant reaction pathway, 209 Elber and Larplus paths, 211 MaxFlux reaction path, 212 Onsager–Machlup path, 213 variational method, 211

Index

Receptor essential volume, 357 Receptor excluded volume, 357 Redox potentials, 399

Reference interaction site model (RISM), 144, 163, 419

Reorganization energy inner shell, 395 outer shell, 395

RESP (restrained electrostatic potential), 21 Restriction endonuclease (see also EcoRI),

445

Retinoic acid binding protein I, 291 R-factor, 161

Ribonuclease A, 2, 291 Ribozyme, 447

Rigid body dynamics, 122

RMS distance (RMSD), 84, 276, 287–289 RNA, 2, 441

messenger, 446 tetraloop, 446 transfer, 441, 446 TRNA-Asp, 447

Rotamers, side chain, 278, 286–289, 321, 339–344

Rotational dynamics, 491 Rubredoxin, 401, 410 Runge–Kutta (see Integrators)

Salt effect, 398 Scalar couplings, 254

Scaled particle theory (SPT), 139 Scattering

Intensity, 240

Intermediate scattering function, 478 Schro¨dinger equation, 95, 223

SCOP, 277–278 Screening

broad, 363 target, 363

Secondary structure α-helix, 2, 281 β-sheet, 2

prediction by Bayesian methods, 338–339 SEGMOD, 281

Semiempirical method, 222, 225 Sequence alignment

Bayesian (see also Bayesian), 322–336 multiple, 332

Sequence comparison, 279 Sequence profiles, 330–332

Sequence-structure alignment, 336–338 Side chain conformational analysis, 314,

321, 339–344

Index

Similarity metric, 264 Simplectic, 123

Simplex minimization, 79

Simulated annealing, 71, 82–83, 117, 257, 261, 284, 360, 380, 417

Skewness, 54

Slater determinant, 223

Slow growth method (see Free energy) SN2 Reaction, 226, 433 Solution-phase reaction, 222 Solvation, 222, 442

inducible mulipole solvation model, 142 Solvatochromism, 426

Solvent

accessible surface area (SASA), 135, 138, 141, 146

boundary potential, 135, 145 effect, 133, 417

implicit, 133

implicit and explicit mix, 145 SPC/E (see Water models)

Spherical truncation (see Potential energy) SQUID, 278, 294

Staphylococcal nuclease, 249 Staphylococcal protein A, 388 Statistical analysis

standard error, 457

Steepest descent minimization (SD), 79–80, 82 Stochastic

boundary conditions, 100 dynamics, 56

Sto¨rmer–Verlet-leapfrog (see Integrators) Streptococcal protein G, 388

Structural genomics, 298–300 Superposition principle, 93 Surface

accessibility, 338–339 constrained all-atom solvent, 145 tension, 139

SWISS-MODEL, 278, 300

SWISS-PROT, 277, 300 Switching (see Potential energy) SYBYL, 278, 356

Symmetrical oligomers, 266 Symplectic, 123

TATA box, 3, 444 binding protein, 445

Tautomerization, 432 Telomeres, 449 Thermodynamic

average, 41, 42

cycle (see Free energy)

511

[Thermodynamic]

integration (see Free energy) perturbation theory (see Free energy)

THREADER, 278 Threading, 3, 280, 314 Through-bond couplings, 254 TIP3P (see Water models) TOPITS, 278

Torsion angle dynamics, 261 Trajectory analysis

mean-square displacement, 485 root-mean-square average, 54 time series, 53

Transcription factor, 445 Transition state, 199

energy barrier, 199 surfaces, 199

Transition state theory (TST), 201 corrections, 204

dynamic recrossings, 207 interstate dynamics, 201 rate constant, 201, 204 reactive flux method, 205

Transmembrane potential, 143 Transmission coefficient, 208 TrEMBL, 277–278 Triosephosphate isomerase, 3, 228 TRP operator, 446

Umbrella potentials, 194

sampling, 184, 187, 194, 410, 447 Unfolding simulations, 382–383

van der Waals, 10, 96 dispersion, 96 exchange repulsion, 96 Lennard–Jones, 10, 97

Variational principles, 421 VERIFY3D, 278, 295 Verlet (see Intergrators) Verlet neighbor list, 52 Verloop, 358

Vibrational spectra, 30 Villin, 382

Virtual molecular library, 69 Voronoi techniques, 359

Water

SPC, 399

SPC/E, 22, 399

TIP3P, 22, 399, 450

TIP4P, 399

512

Watson and Crick, 441, 451 Weighted histogram analysis method

(WHAM) (see Free energy) WHATCHECK, 278, 294 WHAT IF, 278

Wigner self energy, 109

X-ray Bragg diffraction, 241

Index

X-ray crystallography, 1–2, 3, 69, 84, 275, 281, 294, 295, 314

X-ray diffuse scattering, 242 X-ray scattering, 239, 240

Zero point energy, 119

ZIF268, 446

Zinc finger proteins, 445