Computational Medicinal Chemistry for Drug Discovery edited by Patrick Bultinck Ghent University Ghent, Belgium Hans De Winter W i Ifried Langenaeker Johnson & Johnson Pharmaceutical Research and Development A Division of Janssen Pharmaceutica N V: Beerse, Belgium Jan P Tollenaere Utrecht University Utrecht, The Netherlands m MARCEL DEKKER MARCEL DEKKER, INC NEW YORK: BASEL Although great care has been taken to provide accurate and current information, neither the author(s) nor the publisher, nor anyone else associated with this publication, shall be liable for any loss, damage, or liability directly or indirectly caused or alleged to be caused by this book The material contained herein is not intended to provide specific advice or recommendations for any specific situation Trademark notice: Product or corporate names may be trademarks or registered trademarks and are used only for identification and explanation without intent to infringe Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the Library of Congress ISBN: 0-8247-4774-7 This book is printed on acid-free paper Headquarters Marcel Dekker, Inc., 270 Madison Avenue, New York, NY 10016, U.S.A tel: 212-696-9000; fax: 212-685-4540 Distribution and Customer Service Marcel Dekker, Inc., Cimarron Road, Monticello, New York 12701, U.S.A tel: 800-228-1160; fax: 845-796-1772 Eastern Hemisphere Distribution Marcel Dekker AG, Hutgasse 4, Postfach 812, CH-4001 Basel, Switzerland tel: 41-61-260-6300; fax: 41-61-260-6333 World Wide Web http://www.dekker.com The publisher offers discounts on this book when ordered in bulk quantities For more information, write to Special Sales/Professional Marketing at the headquarters address above Copyright n 2004 by Marcel Dekker, Inc All Rights Reserved Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microfilmimg, and recording, or by any information storage and retrieval system, without permission in writing from the publisher Current printing (last digit): 10 PRINTED IN THE UNITED STATES OF AMERICA Preface Computational approaches to medicinal chemical problems have developed rapidly over the last 40 years or so In the late 1950s and early 1960s, gigantic mainframe computers were used to perform simple HMO (Huckel molecular orbital) and PPP (Pariser-Parr-Pople) calculations on aromatic compounds such as substituted benzenes, naphthalenes, anthracenes, etc., to explain their UV spectral properties In the early 1960s, stand-alone programs became available to simulate NMR spectra With the advent of Hansch-type analysis of structure-activity relationships (SAR), computers were used to solve multiple regression equations In 1963 the Quantum Chemistry Program Exchange (QCPE) started distribution of programs such as Extended Huckel Theory (EHT) and early versions of Complete Neglect of Differential Overlap (CNDO), which to the delight of theoretical chemists eventually made it possible to perform conformational analyses on nonaromatic molecules However scientifically exciting, all these computations involved quite some expertise in mastering the computer’s operating system as well as manual labor punching cards and hauling boxes of punched cards to and from the mainframe computer center Of greater concern, however, was the fact that real-life molecules such as those routinely synthesized by medicinal chemists were most often too big to be treated theoretically using the computers of those days This resulted in a situation in which the contribution of a theoretical chemist was, at best, politely tolerated but in general considered irrelevant to the work of a classically trained medicinal chemist All this changed, although slowly, in the 1970s, with improvements in the speed, manageability, and availability of computer technology A considerable impediment in the late 1970s and early 1980s was the lack of proper visualization of the theoretical results Indeed, it was discouraging to discuss theoretical results with a suspicious chemist on the basis of pages and pages of computer output This obstacle was dramatically removed with the advent of graphics computers able to depict HOMOs, LUMOs, MEPs (molecular electrostatic potential), dipole moment vectors, etc, superimposed on a 3D representation of the molecule(s) of interest By the early 1990s graphics workstations linked to multiprocessor machines were powerful enough to perform reliable calculations on real-life molecules in a time frame sufficiently small to keep the interest of the medicinal chemist alive and to show the results in an understandable and appealing way iii iv Preface Nowadays, one can safely state that the computational chemist has become a respectable member of a drug (ligand) design team, standing on an equal footing with the synthetic chemists, pharmacologists, and others at the beginning of the long and arduous path of ligand creation aimed toward bringing a medicine to the market The title of this book refers to two topics, namely, Computational Medicinal Chemistry and Drug Design It unites these topics by giving an overview of the main methods at the disposal of the computational chemist and to highlight some applications of these methods in drug design Although drug and ligand appear to be synonymous in this volume, they most definitely are not Notwithstanding ‘‘drug design’’ in the title, this volume essentially deals with methods that can be applied to molecules that may possibly become drugs Whether, when, and how a molecule may acquire the status of a drug or a medicine is investigated and decided by, among others, toxicologists, pharmacists, and clinicians and is therefore explicitly outside the scope of this volume Similarly, a choice had to be made regarding the topics covered in this volume For example, molecular dynamics (MD) based free-energy changes in solution calculations are not treated, because these are not yet a day-to-day practice in actual ligand design due to the very high computational demands for the long MD simulations required This book starts with seven chapters devoted to methods for the computation of molecular structure: molecular mechanics, semiempirical methods, wave function– based quantum chemistry, density-functional theory methods, hybrid methods, an assessment of the accuracy and applicability of these methods, and finally 3D structure generation and conformational analysis In the next chapters, one or several of those formalisms are used to describe some aspects of molecular behavior toward other molecules in terms of properties such as electrostatic potential, nonbonded interactions, behavior in solvents, reactivity and behavior during interaction with other molecules, and finally similarity on the basis of nonquantum and quantum properties Before addressing some aspects of, broadly speaking, ligand-receptor interactions, a critical evaluation of protein structure determination was felt in order This is then followed by accounts of docking and scoring, pharmacophore identification 3D searching, substructure searching, and molecular descriptors The following chapters address 2D and 3D models using classical molecular and quantum-based descriptors and models derived from data mining techniques as well as library design Given the increasing demand for enantiomerically pure drugs, vibrational circular dichroism (VCD) will become a standard technique in the medicinal chemical laboratory The VCD chapter illustrates the use of high-level quantum chemical calculations and conformational analysis discussed in previous chapters Similarly, the chapter on neuraminidase highlights the combined use of protein crystallography, ligand receptor interaction theory, and computational methods Finally, this volume ends with a concise glossary Thanks are due to Anita Lekhwani, who initially suggested this project, and to Lila Harris, who helped in realizing the project Each individual chapter was reviewed by at least three editors During monthly editorial meetings reviews were critically compared Preface v The editors are grateful to those authors who strictly adhered to the time schedule Finally, it is hoped that this volume may give the reader a useful overview of the main computational techniques that are currently in use on a day-to-day basis in modern ligand (drug) design, both in academia and in an industrial pharmaceutical environment Johnson & Johnson Pharmaceutical Research and Development–Beerse (Belgium) is gratefully acknowledged for financial and logistic support for this project Patrick Bultinck Hans De Winter Wilfried Langenaeker Jan P Tollenaere Contents Preface Contributors iii xi Molecular Mechanics and Comparison of Force Fields Tommy Liljefors, Klaus Gundertofte, Per-Ola Norrby, and Ingrid Pettersson Semiempirical Methods Thomas Bredow 29 Wave Function–Based Quantum Chemistry Trygve Helgaker, Poul Jørgensen, Jeppe Olsen, and Wim Klopper 57 Density-Functional Theory Paul W Ayers and Weitao Yang 89 Hybrid Quantum Mechanical/Molecular Mechanical Methods Jean-Louis Rivail Accuracy and Applicability of Quantum Chemical Methods in Computational Medicinal Chemistry Christopher J Barden and Henry F Schaefer III 119 133 3D Structure Generation and Conformational Searching Jens Sadowski, Christof H Schwab, and Johann Gasteiger 151 Molecular Electrostatic Potentials Peter Politzer and Jane S Murray 213 Nonbonded Interactions Steve Scheiner 235 vii viii Contents 10 Solvent Simulation Peter L Cummins, Andrey A Bliznyuk, and Jill E Gready 259 11 Reactivity Descriptors P K Chattaraj, S Nath, and B Maiti 295 12 Transition States and Transition Structures Orlando Acevedo and Jeffrey D Evanseck 323 13 Molecular Similarity, Quantum Topology, and Shape Paul G Mezey 345 14 Quantum Similarity and Quantitative Structure–Activity Relationships Ramon Carbo´-Dorca and Xavier Girone´s 15 Protein Structures: What Good Is Beauty If It Cannot Be Seen? Sander B Nabuurs, Chris A E M Spronk, Elmar Krieger, Rob W W Hooft, and Gert Vriend 365 387 16 Docking and Scoring Ingo Muegge and Istvan Enyedy 405 17 Pharmacophore Discovery: A Critical Review John H Van Drie 437 18 Use of 3D Pharmacophore Models in 3D Database Searching Re´my D Hoffmann, Sonja Meddeb, and Thierry Langer 461 19 Substructure and Maximal Common Substructure Searching Lingran Chen 483 20 Molecular Descriptors Geoff M Downs 515 21 2D QSAR Models: Hansch and Free–Wilson Analyses Hugo Kubinyi 539 22 3D QSAR Modeling in Drug Design Tudor I Oprea 571 23 Computational Aspects of Library Design and Combinatorial Chemistry Valerie J Gillet 24 Quantum-Chemical Descriptors in QSAR Mati Karelson 617 641 Contents ix 25 Data Mining Applications in Drug Discovery Michael F M Engels and Theo H Reijmers 26 Vibrational Circular Dichroism Spectroscopy: A New Tool for the Sterochemical Characterization of Chiral Molecules Philip J Stephens 27 Sialidases: Targets for Rational Drug Design Jeffrey C Dyason, Jennifer C Wilson, and Mark von Itzstein Glossary Index Ed E Moret and Jan P Tollenaere 669 699 727 747 769 Index Frozen orbitals, 123–124, 125 Fukui function, 112–113, 295, 299 nomenclature, 304 types, 304 Full configuration interaction calculation (FCI), 134 Fully automated pharmacophore discovery, 445–448 Functional form data mining methods, 680 Fungicidal activity QSAR, 658 GABA receptors and 3D pharmacophore, 475 GALOPED program, 630 Gambler, GEP, 412–413 GAMMA (Genetic Algorithm for Multiple Molecule Alignment), 197 Gauche-anti energy differences, Gauge-invariant atomic orbitals (GIAOs), VCD, 705 Gaussian, 105, 371, 590, 705 EFP approach, 285 Gaussian basis sets, 62–63 Gaussian output, 330 Gaussian vibrational analysis output, 328–329 Gauss theorem solvation energy, 267 solvation of molecule, 266 GB model, 269 GB/SA model, 16–17 General Interaction Properties Function (GIPF) descriptors, 651 procedure, 222–225 Generalized Born (GB) model, 269 Generalized effective potential (GEP) AUTODOCK, 412–413 methods, 412 Generalized hybrid orbital (GHO), 124 Generate, 153–154, 156, 158–159, 171–172, 182, 184–187, 190–193, 195, 198–199, 204–209, 353, 468, 470–471, 562 examples of models for peptide and peptidomimetic, 205 generate three-dimensional peptidic structures, 205 Genetic algorithm, 195, 197, 209 optimization cycle principles, 195 Genetic Algorithm for Multiple Molecule Alignment, 197 779 Genetic algorithms to conformational searching, 195–196 conformational search problems, 194–198 mutation and crossover, 197 Geometrical Similarity as Topological Equivalence, 354 Geometric hashing, 408 Geometry-determining torsion angles, peptide backbone, 203 Geometry optimization, 156, 162–163, 169, 182, 184, 190, 196, 198–199, 201, 207, 711–712 GEP AUTODOCK, 412–413 methods, 412 GERM software, 441 GHO, 124 GIAOs, VCD, 705 Gibbs free energy, 328 GIPF, see General Interaction Properties Function (GIPF) GLIDE, 407 Global reactivity descriptors, 296–300 Glutamine flipping, 396 Glycohydrolases rational drug design, 727–741 GOLD docking program, 407 GEP, 412–413 GPCRs, 448–449 G-protein-coupled receptors (GPCRs), 448–449 Gradient, 95, 102–103, 354 Graph, 164–165, 381, 477 Graphical analyses of CoMFA plots 3-D QSAR, 605–608 GREMAS code, 517 GRID, 182–186, 190, 192, 355–356, 562, 571, 587, 591, 609, 734, 736–737 search, 182–183, 186 sialidases drug design, 734–737 Grid-weighted holistic invariant molecular (G-WHIM) descriptors, 652 GRIND, 442 GROMOS (Groningen Molecular Simulation), 202 Groningen Molecular Simulation, 202 Ground-state electron density electronic systems, 92–93 variational principle, 94 GROW, 410 780 GSTE (Geometrical Similarity as Topological Equivalence), 354 Guanine electrostatic potentials, 218 Guenoche average linkage clustering, data mining clusters, 682 G-WHIM descriptors, 652 Halogenated methanes, Vs(r), 226 Halogen bonding, 225 Hamiltonian, 89–92, 95–98, 105–107, 109, 135, 347, 366 equation, 59 integrals, 64 operator, 31, 36, 366 zero-order, 77 Hammerhead, 410 Hammett, 365, 382, 540–542 Hansch, 382, 539–561, 571, 576, 584, 597, 609 method, 437, 438 model, 554 Hansch and Free-Wilson analyses, 539–563 application, 541–545 Hard and soft acids and bases definition, 298–299 Hard-hard interactions, 312 Hardness chemical reaction, 295 definition, 310–311 qualitative concepts, 309–312 Hardness kernel definition, 306 Hard-soft acid-base (HSAB) principle, 295, 299, 310 local version, 313 Hard spheres, 250 Hartree-Fock (HF), 13 approximation, 135 calculations DNA base guanine, 47 EFP methods, 283 level, 12 method limitations, 69 model, 64–66 performance, 68 theory, 30 accuracy and applicability, 138–139 utilizing the self-consistent-field procedure, 137–140 VCD, 705 V(r), 216 Hashed methods, 620 Hashing scheme, 409 Index Heisenberg, 346 Hellmann-Feynman theorem, MEP, 214 Hemagglutinin, 727 Heptane conformation, 184 HF, see Hartree-Fock (HF) Hierarchical cluster analysis, data mining example, 683 Hierarchical clustering, 471 data mining clusters, 682 Hierarchical tree substructure search (HTSS), 493–494 Higher-order term, 252 Highest occupied molecular orbital (HOMO), 300 energy average, 302 High throughput screening (HTS), 405, 669 Histidine flipping, 396 HIV-integrase inhibitors, 473–474 HMO method, 32 Hohenberg-Kohn paradigm, 136 Hohenberg-Kohn theorem, 93, 345, 347 ground-state electron density, 114 MEP, 214 thermodynamic analogies, 114 Hologram, 562 Holographic Electron Density Principle, 347–350 Holographic Electron Density Theorem, 345, 348 for Latent Molecular Properties, 349 recognition process, 360 HOMO, 300, 302 Homology models, 406 Hooke potential, Hooke’s law, Hosoya index, 526 HQ link, 121 HQSAR, 562 HSAB, see hard-soft acid-base (HSAB) principle HT3 antagonist examples of database hits, 464 HTS, 405, 669 HTSS, 493–494 Huckel MO (HMO) method, 32 ă HYBOT, 595 Hybrid frozen orbital, 124 Hybridization, 154, 161, 166–167, 174, 185, 466 Hybrid quantum mechanical/molecular mechanical methods, 119–128 accuracy and applicability, 142–144 Index Hydration energies, dependence, different charge sets, 18–19 Hydration free energy sensitivity, 18 Hydrogen bonding, 5, 465, 473, 559, 575, 591–593, 730, 740 molecular electrostatic potentials, 219–220 molecular surfaces, 219 Hydrophobicity, 575–576, 584, 594–595, 597 evaluation impact, 576 Hyperbolic cotangent, 263 HyperChem, 202 Hypersurface, 346, 348 ICRN, 395 ID descriptor, 528 IMAP, 590 IMOMM method, 126 Implicit modeling, intramolecular as intermolecular interactions, 204 Implicit solvent methods, 261–272 Incremental construction, 409 Incremental construction algorithms, 409– 410 Independent variables justification, 545 selection, 545 Indeterminant alignment problem, 3-D QSAR, 589 Indinavir molecule, electronic structure, 80 INDO, 40–41 active site of enzyme, 46–47 method, 39–41 Indole derivatives antagonists of benzodiazepine receptor, 381 plots, 380 structures and inhibitor constants, 379 Induction energy, 253 Inflammation targets, 450–451 Influenza disease, new drug development, 728 Influenza virus A and B sialidase, see sialidase Influenza virus sialidase, 727 Information map (IMAP), 590 Infrared (IR) spectra, 700–701, 706–707, 711–716, 718, 720–721 applications, 711–714 Integrated Molecular Transform, 659 781 Integrated MO+MM (IMOMM) method, 126 Intensity, 593, 700 Interaction energy, 94, 734, 738–739 electrostatic component, 237 exchange repulsion, 248–250 Interconformational distances, ConFirm, 186 Intermediate Neglect of Differential Overlap (INDO), 40–41 active site of enzyme, 46–47 Fock operator, 39 method, 39–41 Intermolecular ES energy, 243 Intermolecular interactions, 1–23, 14–15, 15 electrostatic and van der Waals, 14 Internal contraction, 79 Inverted key format example, 493 Ion channels, integral membrane proteins, 449 Ionization, 552–554 Ionization energy, 644, 648, 651 IR, see Infrared (IR) spectra Isodensity, 346, 351 Jacobian, 44 Kainate, conformational equilibrium, 19 KDD, 671 Key file generation, 492 Key search purpose, 492–493 Key selection, 491 KH modules of Vigilin solution structure, 393 Kinetic energy, 91, 97, 104, 108 Knowledge base, 172, 176 Knowledge-based scoring, 416–417 Knowledge discovery in database (KDD), 671 Kohn-Sham algorithm, divide-and-conquer method, 104–106 Kohn-Sham chemical potential, 98 Kohn-Sham equations, 96–99, 301 Kohn-Sham Hamiltonian, 107 Kohn-Sham method, 99 linear-scaling methods, 103–108 Kohn-Sham orbitals, 106, 115 Kohn-Sham potential, 104 linear-scaling methods, 108–110 Kohn-Sham theory, 304 Koopmans theorem, 35, 65 electronegativity, 302 782 Kroenecker delta, 356 Kubinyi paradox, 452–453 Lagrange multiplier, 300 Langevin dipoles (LD) method, 263 Large rings, 3D structure generators, 170 Latent properties of molecules, 348–349 LCAO (Linear Combination of Atomic Orbitals), 350 MO theory electronic exchange energy, 643 LD method, 263 Lead identification docking techniques, 405– 413 Lead optimization docking techniques, 405– 413 Lead structure discovery, 3D pharmacophores, 470–472 Least-cost path, 187 COBRA, 187 Lennard Jones, 170, 590 empirical potentials dispersion energy, 254 function, 414–415 Level of theory, 330 LHASA, 160–161 Liaison, 407 Library design, computational aspects, 617– 634 LIE, sialidases drug design, 738 Ligand binding, free energy and solvation effects, 274–277 Ligand conformation ensembles, 410 LigandFit, 407 Linear Combination of Atomic Orbitals, 350, 643 Linear Interaction Energy (LIE), sialidases drug design, 738 Linear response approximation (LRA), 275–277 implicit (dielectric continuum) solvation models, 276 Linear scaling method, Hartree-Fock methods, 66–67 Linear sequence fragment examples, 518 Link atoms, 121–122 Link atom semiempirical methods, 121–127 Lipinski properties molecular descriptor, 516 Lipophilic acids and bases, absorption, pH shift, 553 Index Lipophilicity, 365, 539–545, 548–552, 556, 558–562 LMCS, 207 LMO overlap, EFP approach, 285 Localization, 106 Local quantities reactivity and site selectivity, 312–315 Local reactivity descriptors, 303–306 Local self-consistent field (LSCF) method, 123 Local softness, 295 Log P, 382, 541, 545, 549–558 London dispersion, London forces, 253 Long-range interaction and boundary effects, explicit solvent molecules, 286–287 Lowest unoccupied molecular orbital (LUMO), 300 energy average, 302 Low-throughput mode, 405 LRA, 275–277 LRA method, free energy of solvation, 287 LSCF method, 123 LUMO, 300 energy average, 302 MACC, 471 MACC-2 method, 592 Macrocyclical molecule, corresponding superstructure, 169 MacroModel evaluation, 207–208 generate three-dimensional peptidic structures, 205 MAE, 12–13, 45 Many-particle quantum system characterization, 312 Mathematical modeling, data mining, 671 Matriptase, 420 benzamidine inhibitors, 421 binding mode, 423, 424 homology model, 420–421 Maximal common substructure search (MCSS), 197–198, 483–508, 496–508 algorithms, 496–497 clique-detection, 497–500 applications, 507–508 backtracking, 500–507 clique-detection algorithm, 498 problem, 484 Index Maximal similarity rule (MSR), 371 Maximum auto-and-cross-correlation (MACC), 471 Maximum auto-and-cross-correlation (MACC)-2 method, 592 Maximum-cost manner, COBRA, 187 Maximum hardness principle, 295, 311 Maxwell relation, 112 application, 304 Mayer, Naylor, Motoc, and Marshall (MNMM) depiction of algorithm, 445 method, 440 GPCRs, 448 McGregor algorithm, backtracking algorithm to MCSS, 500–501 MCM, generate 3D structures of peptides, 204 MCMM, 194 MCSCF, see Multiconfigurational self-consistent field (MCSCF) MCSS, see Maximal common substructure search (MCSS) MD, see Molecular dynamics (MD) Mean absolute error (MAE) AM1, ground state properties, 45 CFF, 13 CHARMm force fields, 13 force field, 12 Medicinal chemistry, 3-D QSAR, 575–576 MEDLA, 345 MEP, see Molecular electrostatic potential (MEP) Metal complexes, 3D structure generators, 170 Methoxy-tetrahydropyrane, equatorial-axial conformational energy differences, Methylacetamide, calculated energy differences, 10 Methylcyclohexane, axial and equatorial, calculated conformational energy differences, 11 Methylcyclohexylketone subproblems, 173 analogies, 174 Methyl oxirane, rotational strengths, 710 Methylpiperidine, calculated conformational energy differences axial-equatorial, 10 783 Metropolis, 194, 201, 204, 207 MHP, validity, 312 Microwave spectroscopy, 3D structure, 151 MIDCO (molecular isodensity contour) concept, 351–358 MIF filtering step, ALMOND, 592 MIMUMBA, 163, 171, 187, 189–190, 192 conformational analysis, 187–190 MINDO, see Modified Neglect of Diatomic Overlap (MNDO) Minimal basis sets, 62–63 Minimization, 90, 106, 108, 154, 166, 169, 176, 182, 185–186, 194, 199, 201, 204, 206, 590 Minimum polarizability principle (MPP), 295 validity, 312 MIR, 389 MK, 252 MK scheme, approaches to partitioning total interaction energy, 253 MM, see Molecular mechanics (MM) MMI, sialidases drug design, 738 MNMM, see Mayer, Naylor, Motoc, and Marshall (MNMM) MO, see Molecular orbital (MO) Model building, MQSM, 372 Model building stage, data mining, 672 Model representation, data mining methods, 680 Modified Hooke’s law, Modified Neglect of Diatomic Overlap (MNDO) MAE bond lengths, 46 ground state properties, 45 heats of formation, 45 method, 42 structure optimization, 47–48 MOGA, 633 Molconn-Z, 619 Molecular alignment, MQSM, 371 Molecular complementarity, 359–363 Molecular connectivity indices, 525 Molecular databases, 465–466 Molecular descriptors, 515–532 applications, 515 atom, bond, and feature counts, 516 3D fragments, 521–524 selection, 528–531 types, 516 784 Molecular dynamics (MD), 199, 201–202, 737 and explicit solvent models, 261 methodology, 16 sialidases drug design, 737–738 simulation, 199–201 sampling of conformations, 201 Molecular Electron Density Lego Approach (MEDLA), 345 Molecular electronegativity, 309 Molecular electrostatic potential (MEP), 67, 213–226, 314 applications, 219–226 features, 215 Molecular flexibility, 467 Molecular informatics fundamental law, 347–350 Molecular isodensity contour concept, 351–358 Molecular isodensity contour surface concept, 351–358 Molecular mechanical solvation model biomolecules, 277–283 Molecular mechanics (MM), 152, 159, 161–166, 176, 197, 473, 585, 590, 737–739 definition, energies, 22 principles, 2–6 quantum mechanics comparison, 12 rate-determining transition state peptide hydrolysis, 128 sialidases drug design, 737–738 Molecular mechanics force field, 3, 152, 160, 202, 205–207, 721 accuracy range, 13 correlated methods, 12 COSMO calculations, 266 definition, in different software packages, 6–23 generate three-dimensional peptidic structures, 205 Molecular mechanics force field, 3, 4, 194, 197, 207 accuracy range, 13 in different software packages, 6–23 Molecular mechanics force field, 3, 4, 207 in different software packages, 6–23 MAE, 13 Molecular Mechanics Interaction (MMI), sialidases drug design, 738 Molecular modeling, MQSM, 371 Index Molecular orbital (MO), 64, 112 related descriptors, 652–653 definition, 649–650 QSARs, 660 theory, 29 Molecular plane, contour plot, 246–247 Molecular property calculations, 67–69 Molecular quantum similarity measures (MQSM), 366, 371 Molecular recognition, 359–363 shape, 468–469 Molecular shape analysis, visualization, 354 Molecular shape complementarity analysis, Centrally Inverted Map Method, 358 Molecular similarity, 366, 467 quantum mechanical basis, 366–370 quantum mechanical concepts, 345–363 topological representative of shape, 346 Molecular simulations and ligand binding, 273 Molecular skeleton, 372 Molecular surfaces, 217–218 Molecules charge distribution, 643 curvature-based shape analysis, 353 heat of formation, 643 minimum and maximum partial charges, 650–651 selection of candidates, 469 shape description, 352–353 topological shape characterization, 353 uniqueness and similarity, 359–363 Molecules interaction, assignment of parameters, 245–247 MOLGEO, 176–177, 179 evaluation, 177–179 Moller-Plesset (MP2) energy, 77 Moller-Plesset Perturbation Theory (MPPT), 77–78, 136 Moller-Plesset theorem V(r), 216 Monte Carlo, 194, 199, 201, 204–205, 209, 738–739 conformational searches, 205 evaluations of thermodynamic properties, 121 free-energy perturbation, 17 methodology, 16 Monte Carlo Multiple Minimum (MCMM) package, 194 Index Monte Carlo plus minimization method (MCM), generate 3D structures of peptides, 204 Monte Carlo random search techniques, generate 3D structures of peptides, 204 Monte Carlo simulation, 199–201 docking program techniques, 412 and explicit solvent models, 261 Morokuma and Kitaura (MK), 252 Morse potential, MoSELECT program, 633 Mossbauer eect, 138 ă MP2 energy, 77 MPP, 295 validity, 312 MPPT, 77–78, 136 MQSM, 366, 371 MRA, 530 MRCI methods, 78 MRPT, 78 MRSDCI method, 79 MSINDO, 41 adsorption phenomena surface reactions, 47 MAE bond lengths, 46 ground state properties, 45 heats of formation, 45 MSR, 371 Mulliken approximation, 41 Mulliken atomic partial charges, 650 Mulliken charge partitioning method, 243–245 Mulliken charges, 67 Mulliken electronegativity scale, 296–297 Mulliken-like partitioning function, 106 Mulliken’s definition of electronegativity, 111 Mulliken’s population analysis scheme, 304 MULTIC, 184 Multiconfigurational self-consistent field (MCSCF), 69, 70, 642 theory of complete active space, 70–72 Multilayer perceptrons, data mining, 686 MultiObjective Genetic Algorithm (MOGA), 633 Multiobjective library design, 631–634 Multiple isomorphous replacement (MIR), 389 Multiple regression analysis (MRA), 530 785 Multiple ring conformations, 3D structure generators, 170–171 Multipoint pharmacophore approaches, 631 Multipoint pharmacophore fingerprints, 623 Multipole expansion, 109 electrostatic energy, 242 Multireference configuration interaction (MRCI) methods, 78 Multireference perturbation theory (MRPT), 78 Multireference singles-and-doubles configuration interaction (MRSDCI) method, 79 Multireference systems, dynamical correlation, 78–79 Muscarinic M3 receptor antagonists, 474– 475 Mutation, 198 NDDO level, link atoms, 122 method, 41–43 Nearest neighbor, 689 Neglect of Diatomic Differential Overlap (NDDO) level, link atoms, 122 method, 41–43 N-electron expansions, Slater determinants, 59–62 N-electron hierarchy, 81 Neural network, 576 Neuraminidases, rational drug design, 727– 741 Nitrogen-containing compounds, evaluated force fields, 8–9, 22–23 Nitrogen fixation, ZINDO calculations, 46 N-methylpiperidine, NMR spectroscopy, 3D structure, 151 Nonbonded energy, discontinuities, 286–287 Nonbonded interactions, 4, 235–255, 272 assignment of parameters, 245–247 exchange repulsion energy, 248–250 multipole approximation, 239 Noncovalent interactions, 235 strength, 236 Nonelectrostatic contribution, 270–271 Nonelectrostatic solvation free energy, linear relationship, 271 Nonelectrostatic terms, 98 Nonempirical, wave function-based quantum chemical methods, 58 Nonlinear QSAR models, 548–552 786 Nonpolar interaction energy, 270–271 Nonpolarization QM/MM model, solvation free energy, 281 Non-Quantum Similarity approach, 346 Normalized Molecular Moment Structure Descriptors, 659 Nuclear charge of nucleus, 122 Nuclear magnetic resonance (NMR) spectroscopy, 3D structure, 151 Nuclear repulsion, 29, 60, 310, 644 Nucleophilic addition, chemical reactivity, 314 Numerical descriptors, 619 Numerical integration, linear-scaling methods, 108–110 Numerical methods, 3D structure generation, 159–160 Numerical triangle smoothing, distance geometry, 198 OM1, 42, 48 OM2, 42, 48 OMEGA evaluation, 207–208 One-electron hierarchy, 81 One-electron integral, 41 ONIOM principle, 126–127 Onsager equation, 283 Onsager formula, 267 OPLS, 738 OPLS_AA force fields in different software packages, 6–23 Optimization algorithms, drawback, 156 Optimization cycle, 195 Optimization methods, 43–44 Orbitals, 59–63, 60 Organic reactions, chemical reactivity, 314 Organizational databases and data warehouse differentiating between, 675 Orthogonalization process, DFT, 125 Out-of-plane bending, Overfitting, 686 Overlap matrix, 64 Overlapping sphere triplet matching, 408 Overlap QSM, 368 Oxazolidinone antibiotics pharmacophore, 450 Oxygen-containing compounds, evaluated force fields, 8, 22–23 Parabolic Hansch model, 549 Parabolic model, 551 example, 551 Index Parallel processing methods, 495 Parameterization, 43–45 Parameters classification, 43 Parametric Model (PM3), 42, 642 Pareto optimization, 198 Pariser-Parr-Pople method, 36–37 PARM, 441 Parsimony principle, 545 Partial charge, 17, 245, 273, 656 Partial least squares (PLS) analysis, 548 MQSM, 372 Partitioning method, 622 Partitioning-relaxation-based substructure matching algorithms, 489–491 PASA, 371 Pauling’s electronegativity values, 296 Pauli principle, 60 Pauli repulsion, 40 PCA, see Principal component analysis (PCA) PCM, 138 activation enthalpy method, 337 effects of solvent, 335 PD, 263 PDB, see Protein Data Bank (PDB) PD basis sets, 705 PDBFINDER database, 395 Pearson’s theory, reactions in acid-base equilibrium, 299 Pentapeptide Leu-enkephalin, 203 Peptide and peptidomimetic units, examples of models, 205 Peptide structures, 202–206 Peptidomimetics, 202 Pericyclic transition structure geometries, 331 Perturbation, 194, 704–705, 738 Perturbation-dependent (PD) basis sets, 705 Perturbation theory, V(r), 215 Perturbed one-electron Fock matrix elements, 281 PES, see Potential energy surface (PES) Pharmacological activity, quantumchemical molecular descriptors, 656–659 Pharmacophore, 152, 185, 197, 562, 588, 590, 594, 600, 603–604 conformational analysis, 452 features, 467–468 for 5-HT3 antagonists, 463 Index [Pharmacophore] inclusion of sterically forbidden regions, 452 origins and characteristics, 462 Pharmacophore discovery, 437–455 analysis of methods, 442–448 applications, 448 computational controls, 453–454 dataflow, 438 datasets, 454 feature detection, 451–452 future, 451–455 historical development, 439–442 link to 3D searching, 451 retrospective predictivity, 452–453 Phosphate, threefold axis of symmetry, 392 Physicochemical properties, molecular descriptor, 516 Physiochemical property space, distribution of activities, 576–584 Physiochemical property space and biological activity relationships, 578 PICCOLO program, 631 Place and join, 409 Planar conformation, CORINA, 190 Plane waves use, 144 PLS analysis, 548 MQSM, 372 PLUMS, 631 PM3, 42, 137, 642 accuracy, 14 drug design, 48 link atoms, 122 MAE, ground state properties, 45 PMF scoring function, 416 Poisson-Boltzmann equation, 16, 17 Poisson or Poisson-Boltzmann equation, 267 Poisson’s equation linear-scaling techniques, 109 MEP, 213 Polarizability, 113, 356, 365, 595, 597 Polarizability kernel, 113 Polarizable Continuum Model (PCM), 138 activation enthalpy method, 337 effects of solvent, 335 Polarization, 252 and electrostatic energies differences, 282 Polarization energy, 252 Polarization functions, 63 787 Poling, 199–200 for conformational sampling application, 200 Poling algorithm, 199 Pose clustering, 409 Post Hartree-Fock, 125 Potential energy, 99, 156, 189, 192, 346, 348, 350, 363, 473, 703, 711 Potential energy surface (PES), 323 schematic, 325 thermodynamic quantities, 326 transition structures, 324 Potential pharmacophore point (PPP) Fock matrix elements, 36 pairs and triangles, 524 PPP Fock matrix elements, 36 method, 36–37 pairs and triangles, 524 Predictive data mining, 679 Principal component analysis, 548 Principal component analysis (PCA), 548, 594–597, 600, 652 scores from SaSA, 595–597 PROCHECK, 394 PRODOCK, 412 Product-based selection, 628–629 techniques, 627 PRO-LEADS, 413 Promolecular atomic shell approximation, MQSM, 371 Protein Data Bank (PDB), 151, 188, 190, 192, 206, 207, 209, 387, 406 Brookhaven, 151, 206 3D structure, 151 database generation, 395 manual inspection entry, 393 nomenclature errors, 396 types of errors, 396–400 Protein dipoles (PD), 263 Protein-ligand docking, 406–413 computational, 406 flowchart, 422 software, 407 Protein-ligand van der Waals energy, 413 Protein structures, 387–401 characteristics, 394 cope with errors, 389–390 detecting errors, 391–401 docking techniques, 406–408 errors alternate atoms and residues, 397–398 788 [Protein structures] errors over years, 398–401 examples of errors, 397 origin of errors, 388–389 types of errors, 396–400 validation, 394 water molecules, 398 water-related problems, 398 Proton transfer, 129, 311 Pseudoreceptor, 572 Pseudoreceptor models, 406 Pseudospectral method, 81 Puckered, 712 QCISD(T), 331 QM, see Quantum mechanics (QM) QMC, 58 QQ link, 121 QSAR, see Quantitative structure-activity relationship (QSAR) QSM, see Quantum similarity measure (QSM) QSPR, see Quantitative structure-property relationship (QSPR) QSTR, 365–382 Quadratic configuration interaction method QCISD(T), 331 Qualitative docking, 14 Quality Indicators for Crambin (ICRN), 395 Quantitative structure, 365–382 Quantitative structure activity models for acids and bases, 552–554 Quantitative structure-activity relationship (QSAR), 363, 365–382, 370, 372, 438, 530 analyses applications, 554–562 scope and limitations, 554–562 antibacterial activity, 658 anti-HIV drugs, 658 antiviral activities, 657 backward elimination, 547 capabilities of MQSM, 370–381 enzymatic reactions, 654–656 fungicidal activity, 658 history, 539–541 HQSAR binary QSAR similarity, 562–563 pharmacological activities, 656 validation and selection models, 545–548 Index Quantitative structure-property relationship (QSPR), 365–382, 530, 641 pharmacological activity, 656 Quantitative structure-toxicity relationships (QSTR), 365–382 Quantum-chemical descriptors antiviral activities, 657 QSAR, 641–662 Quantum chemical methods, computational medicinal chemistry, accuracy and applicability, 133–146 Quantum chemical molecular descriptors, 642–654 QSARs, 654 Quantum mechanical molecular electrostatic potentials, 655–656 Quantum mechanical solvation models, biomolecules, 277–283 Quantum mechanics (QM) energies, 22 interpolation scheme, method definition, rate-determining transition state, peptide hydrolysis, 128 Quantum mechanics (QM)/MM computational biochemistry application, 127–128 interaction energy, 278 methods ab initio, 282–283 chemical reactivity, 332 conformational transitions, 332 semiempirical, 279–281 studies of macromolecules, 121–127 studies of solutions, 120–121 system Hamiltonian, 278 Quantum Monte Carlo (QMC), 58 Quantum object, 367–370 ordering, 369 Quantum QSAR in biological systems, 654–662 Quantum quantitative structure activity relationships equation, 370 Quantum similarity, 345–346, 346, 363, 365– 382, 562 approach, 346 Quantum similarity measure (QSM), 367– 369 framework, 370 similarity indices, 369 Quantum thermodynamic definition of electronegativity, 298 Index Ramachandran plot, 203 of protein, 203 Random Incremental Pulse Search system, 194 Random methods conformational searching, 193–194 RAR ligands, 469 Ray-Kirsch algorithm, 486–488 Rayleigh-Schrodinger perturbation theory, ă 77 Reaction in solution study, 120 Reaction pathway, 325 Reactive behavior, 215–216 Reactivity descriptors, 295–315 global and local, 295 theoretical treatment of qualitative concepts, 300–303 Reagent-based selection, 626, 628 Reagent selection approaches, 626 Real physical phenomena vs charges, 246 vs dipoles, 246 Regression analysis to select descriptors, 530–531 Regression-based scoring, 415–416 Regression coefficients, 581–583 descriptive statistics, 580 distribution, 580 Relaxation, 197, 199, 204–205, 381 REPE, 35 Representation, pharmacophore discovery methods, 442–443 Repulsive part of energy, 283 Resolution-of-identity MP2 (RI-MP2), 80 Resonance energies calculation, 35 Resonance energy per electron (REPE), 35 Resonance integrals, 33, 643, 645 Restricted Hartree-Fock (RHF) activation energies, 331 calculations, 66 water, 66 Restricted tournament selection, 196 Retinoic acid receptor (RAR) ligands, 469 Reverse transcriptase (RT) inhibitors antiHIV agents, 225 RGB, 595 RHF activation energies, 331 calculations, 66 water, 66 Rigid bonds (RGB), 595 Rigid docking, 408–409 789 Rigid overlapping fragment, 410 RI-MP2, 80 Ring closure, 3D structure generation, 155 Ring descriptors examples, 518 Ring systems conformational searching, 183–184 Ring templates 3D structure generation, 155 RIPS (Random Incremental Pulse Search) system, 194 RMS CORINA models, 172 deviations, 389 Robust optimizers conformational search problems, 194–198 Roothaan equations, 31 Root-mean-square (RMS) CORINA models, 172 deviations, 389 Rotatable bonds (RTB), 595 ROTATE, 190, 192–193 and CORINA superimposition, 193 3D structure generator, 190–192 Rotational strengths comparison, 710 RTB, 595 RT inhibitors anti-HIV agents, 225 Rule-based and data-based methods 3D structure generation, 158, 186–193 and conformational searching, 163–171 Rule-based force field, 14 Rule-of-Five, 625–626 S4, 494–495 Saddle point, 323, 325, 332–333 SAM1, 42, 49 Sampling methods data mining, 686–687 docking program, 407 Sanderson’s electronegativity, 297, 307 Sanderson’s equalization, 307 Sanderson’s geometrical mean law, 307 SAR, 437 data mining, 687 SaSA descriptors, 595–597 SCA (systematic conformational analysis), 162–163, 187 for cyclical systems, 162–164 SCAMPI, 441 SCF calculation, 70–72, 281, 331 SCF procedure, 31, 124 Schrodinger equation, 29, 31, 58, 133134, ă 135, 366 Scoring applications, 420–428 790 Scoring functions affinity prediction and ranking, 418–419 binding modes prediction, 418 classes, 414 comparison, 417–419 data mining methods, 680 Scoring method docking program, 407 Scoring techniques, 413–428 Screening selection, 491 substructure matching algorithm selection, 491 valence angle and torsion angle, 523 Screening keys generation, 492 SCRF, 138 SCRF-SCIPCM method, 140 SCRIPT, 161–162 Searching molecular databases, 466–467 three dimension (3D) pharmacophores for, 470 Search or optimization method data mining, 681 Search trees, 182–183, 186–187 reordering of branches MCSS, 503 SELECT program, 630 Self-consistent field (SCF) calculation, 70–72, 281, 331 Self-consistent field (SCF) procedure, 31, 124 Self-Consistent Reaction Field (SCRF), 138 Self-organizing map (SOM) data mining, 682–684, 691 example, 684 Semi-Ab initio Model (SAM1), 42 vibrational frequencies, 49 Semiautomated, 440 Semiautomated pharmacophore discovery, 444–445 Semiempirical methods, 29–51 accuracy and applicability, 141–142 applications, 45–49 approximation, 30–32 combinations, 49 hybrid approaches, 51 parameters, 43–45 perspectives, 49–51 Semiempirical MNDO, AM1, and PM3 approximations, 279–281 Semiempirical solvation model parameterization, 281 Sequential key format example, 492 Index Serine protease, AM1 geometry optimization, 141 Shape, molecular similarity, 345–363 Shape analysis approaches, 355 Shape groups method, 350–358 molecular shape analysis, 353 Shrink-wrap algorithm, 451 Shrink-wrap surfaces, 468 Sialidase computational techniques, 733–740 drug design, AUTODOCK, 739 electron micrograph experiments, 729 GRID results, 736 ligplot diagram, 731 mechanism of action, 735 molscript diagram, 730 rational drug design, 727–741 x-ray crystal structure, 729 Similarity analysis, 350–358 Similarity matrix MQSM, 372 quantum object set properties, 368 Simulated annealing, 199, 201–202, 204 predict 3D structures of peptide, 204 trajectory, 202 Simulation experiments predict 3D structures of peptide, 204 Simulation methods, 199–202 for docking, 412 SINDO1 (symmetrically orthogonalized INDO/1), 41 SINDO (symmetrically orthogonalized INDO), 41, 50 Single-configurational and multiconfigurational Hartree-Fock theory, 63–72 Site changes, chemical reactions, 314 Six-membered rings conformational analysis, 160–161 Slater determinants, 37, 59–63, 60–61, 64, 69, 98 Slater functions, 35 SLBO, 123 Smallest set of smallest rings, 167, 190 Soft acid metal ions, 310 Soft modeling technique, model evaluation, 573–575 Softness definition, 310–311 qualitative concepts, 309–312 Softness kernel definition, 305 Index Softron substructure search system (S4), 494–495 Soft-soft interactions, 312 Solubility, 365, 473, 539, 549, 576, 578–580, 584, 595, 597 Solute and solute-solvent interactions, 282 Solute Hamiltonian operator, 278 Solvation, 205, 587, 738 continuum models, 270 Solvation energy definition, 265 electrostatic component, 262–270 nonelectrostatic contribution, 270–271 Solvation free energy, 262 calculations, 16–17 continuum methods for computing electrostatic contribution, 271 MM computations, 266 Solvation models explicit and implicit, 15–16 calculation comparison, 17–18 Solvent accessible surface, 16, 21, 277 Solvents, butadiene and acrolein, reactions, 337–338 Solvent simulation, 259–288 explicit solvent methods, 272–283 implicit solvation methodology, 261–272 limitations of methods, 283–287 methods based on division of solvation energy by atom, 271–272 SOM data mining, 682–684, 691 SPARTAN, 197 Spectator solvent molecules, 120 Spectroscopy, 151, 199 Spectrum, unpolarized absorption, 702 Spin density, 67 Spin density-functional theory, 99–100 SPINE, 676 Spin orbitals, 60 SSS, see Substructure searching (SSS) SSSR, 167, 190 Starting atom pair selection, 502–503 Stationary points, 323, 325, 326, 329, 333 computational chemistry, 330 Steepest descent, 329 Stereochemical, 154, 160, 351, 699, 721 Steric energy, 154 Stochastic, 193, 369–370 Stochastic transformation, 369–370 Stored and accessed data, data mining, 681 791 Strictly localized bond orbital (SLBO), 123 Structural analyses, molecular descriptors, 515 Structural anomalies, 391 Structure(s) importance of correct, 387 origin of errors, 388–389 Structure-activity relationships (SAR), 437 data mining, 687 Structure-based drug design, 387 Structure generation, automatic, 153 Structure isomorphism problems, 484–485 Structure of Crambin, geometry optimization, 125 Structure validation software, 390–394 Substructure, 164, 175, 197–198, 372, 465– 466, 468, 594, 600, 607 Substructure isomorphism, finding, 488 Substructure matching algorithms matching smaller to larger structure, 486–491 Substructure matching techniques for searching large databases, 491–495 Substructure searching (SSS), 483–508 methods, 486–491 techniques for improving, 495 Supramolecular Holographic Electron Density Theorem, 360 Swain-Lupton resonance, 657 Sybyl5.21 force fields in different software packages, 6–23 Symmetrically orthogonalized INDO, 41, 50 Symmetrically orthogonalized INDO/1, 41 Systematic conformational analysis, 162– 163, 187 for cyclical systems, 162–164 Systematic conformational search representation, 183 Systematic searches, 182–186 acyclical portions, 182–183 ring structures, corner flapping procedure, 185 Tabu search, 413 TAE method, 643 Tagged set, 367 Tanimoto coefficient, 621 Target structures based on selected properties, 490 Taylor expansion, 308 Taylor series expansion of energy, 302 TCDD, 221 TD-DFT, 140 792 Terminating conditions, MCSS, 503 Tetrachlorodibenzo-p-dioxin (TCDD), 221 TGSA, 372–373 TGSA, MQSM, 371–372 Thermal corrections, computed internal energy, 326 Thermodynamic cycle for binding of ligands, 260 for change of state of system, 260 Thermodynamic integration (TI) formula, 274–275 free energy of solvation, 287 Thermodynamic quantities, 326–329 Thermolysin, 128 Thomas-Fermi type models, 97 Three-bonded atoms, 523 3DFEATURES program, 524 Three dimension (3D) database searching 3D pharmacophore models, 461–476 selection of candidates, 469 fragments example, 523 molecular descriptors, 521–524 model building AIMB technique, 171–175 automatic, 158 molecular models automatic generation, 154–158 pharmacophore for BDZR/GABA receptors, 475 concept, 462–465 models 3D database searching, 461–476 QSAR balance, 594–597 Three-dimensional geometry, transition structure, 329 Three-dimensional molecular database, pharmacophore searching, 465–469 Three-dimensional (3D) quantitative structure-activity relationship (3D QSAR), 439 assumptions, 584–586 example, 597–608 fundamental hypothesis, 573 graphical analyses of CoMFA plots, 605– 608 history, 571–573 indeterminant alignment problem, 589 and medicinal chemistry, 575–576 methods, 598–600 set of assumptions, 584–585 models Index [Three-dimensional (3D) quantitative structure-activity relationship (3D QSAR)] drug design, 571–609 evaluation, 573–575 statistical methods, 598–600 statistical results, 600–605 Three-dimensional surfaces, 218 Three dimension (3D) maximum common substructure, 197 Three dimension (3D) pharmacophores BDZR/GABA receptors, 475 for focusing and profiling virtual combinatorial libraries, 470–472 lead structure discovery, 470–472 for searching molecular databases, 470 Three dimension (3D) structure generation automatic methods, 158–160 complications, 154–158 concept classification, 158–160 conformational analysis methods, 159 conformational flexibility, 155 conformational searching, 151–209 manual methods, 158 methods and programs, 160–176 program, 153 evaluation, 176–181 3DSEARCH program, 523 Three-point pharmacophore limitation, 620 Thrombin benzamidine inhibitors, 421 binding mode, 423, 424 Thrombin docking, 421–425 Thrombin/matriptase inhibitors selectivity, 420–426 TI formula, 274–275 free energy of solvation, 287 Time-Dependent DFT (TD-DFT), 140 Topo-geometrical superposition algorithm (TGSA), MQSM, 371–372 Topological and topographical indices, 524–526 Topological molecular shape, 350–358 Topology, 729 molecular similarity, 345–363 Torsion angles, conformations, 196 3D structure generation, 155 patterns, angle distributions, 188 Index Torsion fragment, torsion angle distribution, 189 Toxicity QSARs, 659–662 quantum-chemical descriptors, 659–662 Transferable atom equivalent (TAE) method, 643 Transition state, 103, 323–340, 731–732 computational approaches, 329–334 environment perturbing, 334–340 issues and conceptions, 325–326 schematic, 325 structures, 326 Transition state theory (TST), 325 Transition structure, 323–340 art of locating, 329–330 binding, 339 computational approaches, 329–334 evaluation calculations, 333 geometries, 331 issues and conceptions, 324–325 microsolvation effect, 339 schematic, 325 Transporters, integral membrane proteins, 449 Tree search, 166 Tree-structured fragment searching, 493 Triangle smoothing, 176 Triatomics-in-molecules (TRIM) method, 79 Trimacrocyclical bridged system, 156 Trimacrocyclical system, 3D structure generation, 155 TRIM method, 79 Triple-zeta basis sets, 63 Tripos force field, 14, 207, 465 Trypsinlike serine protease, 420 TST, 325 Two dimension (2D) fragments molecular descriptors, 516–529 QSAR, 539–563 balance, 594–597 Two dimension (2D)-to-3D conversion program, 154 UFF force fields, 14 and Dreiding force fields, UFF1.1 force fields in different software packages, 6–23 Ullmann algorithm, 489 Undirected graph, 497 793 Uniqueness Theorem of Molecular Recognition, 363 Universal functionals, density-functional theory, 94 Unrestricted Hartree-Fock (UHF) calculations, 65 dissociation, 66 V(r), 215–216 approximate evaluation, 217 formula, 216 noncovalent interactions, 217 rigorous evaluation of, 216–217 Valence angle and torsion angle fragments example, 522 Van der Waals energy, 270–271 Van der Waals interactions, Van der Waals radii, 263 Variational Transition State Theory (VTST), 138 Vector representation example, 677 Vibrational circular dichroism (VCD), 699– 702, 706–715, 717–721 experiment, 700–702 spectroscopy, 699–721 absolute configuration (AC), 721 liquid solutions, 721 spectrum, 702 applications, 711–714 illustrations, 706–709 using DFT methodology, 719 theory, 702–711 Vibrational dipole, 705 Virtual excitations, 73 Virtual library, size, 628 Virtual orbital excitations, 72–75 Virtual receptor site (VRA) concept, 591 Virtual screening, 153, 470, 472, 618–625, 740 3D descriptors, 620 designing focused libraries, 625 evaluation of methods, 624–625 flowchart, 426 Visualization, sialidases drug design, 734 VRA concept, 591 Vs(r), quantitatively characterizing features, 222–223 VTST, 138 Walter Reed Army Institute of Research (WRAIR), 519 Ward clustering, data mining, 682 ... ax–eq trans-1,2-diF, ax,ax-eq,eq trans-1,2-diCl, ax,ax-eq,eq trans-1,2-diBr, ax,ax-eq,eq trans-1,4-diF, ax,ax-eq,eq trans-1,4-diCl, ax,ax-eq,eq trans-1,4-diBr, ax,ax-eq,eq Butadiene, s-cis–s-trans... 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