Reviews in Computational Chemistry Volume 18

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structures are peptidic in nature, whereas interesting lead molecules in pharmaceutical research are usually nonpeptidic. This influence of peptides is reflected in the relatively high contributions of hydrogen bonds in the total score. The balance between hydrogen bonding and hydrophobic interactions is a critical issue in scoring, and its consequences are especially obvious in virtual screening applications, as will be illustrated in the later section on Hydrogen Bonding versus Hydrophobic Interactions. Molecular Size Critical Assessment of Current Scoring Functions 59 The simple additive nature of most fast scoring functions often leads to large molecules being assigned high scores. Although it is true that small molecules with a molecular weight below 200–250 are rarely of very high affinity, there is no guarantee that larger compounds are more active. When it comes to comparing scores of two compounds of different size, it therefore makes sense to include a penalty term that diminishes the dependence of the score on molecular size. In some applications, a constant penalty value has been added to the score for each heavy atom. 167 Alternatively, a penalty term proportional to the molecular weight has been used. 168 The scoring function of the docking program FLOG, which contains force field and empirical terms, has been normalized to remove the linear dependence of the crude score on the number of ligand atoms that was found in a docking study of a 7500 compound database. 59 Entropy terms designed to estimate the restriction of conformational mobility upon ligand binding also help to eliminate overly large and flexible molecules, although they were originally introduced to improve the correlation between experimental and calculated affinities. 56,71 The size of the solvent-accessible surface of the ligand within the protein-binding pocket is also a useful penalty term because it helps avoid excessively large ligands that cannot fit completely into the binding site. Note, however, that all these approaches are very pragmatic in nature and do not solve the problem of size dependence, which is closely linked to the understanding of cooperativity effects. 125 Other Penalty Terms Scoring functions in general reward certain favorable interactions such as hydrogen bonds, but rarely penalize unfavorable interactions. Since scoring functions are derived from experimentally determined crystal structures, ‘‘unnatural’’ and energetically unfavorable orientations of a ligand within the receptor cavity are rarely observed and therefore cannot be accounted for by the scoring function. Knowledge-based scoring functions try to capture such effects indirectly by making those interactions repulsive that are not observed in crystal structures. It seems, however, that the statistical difference
60 The Use of Scoring Functions in Drug Discovery Applications between what is not observed and what is to be expected on average is often not significant enough to form reliable repulsive interactions. Furthermore, the neglect of angular terms in the derivation of knowledge-based scoring functions leads to average pair potentials that cannot discriminate well enough between different binding geometries. In the derivation of regression-based empirical scoring schemes, on the other hand, penalty terms have traditionally not been included. However, some situations like obvious electrostatic and steric clashes can be avoided by guessing reasonable penalty terms or by importing them from molecular mechanics force fields. An example of this is the ‘‘chemical scoring’’ function available in the docking program DOCK. 94–99 This function is a modified van der Waals potential made to be attractive or repulsive between particular groups of donor, acceptor, and lipophilic receptor atoms and ligand atoms. 169,170 Other unacceptable binding orientations cannot be avoided by simple clash terms, but instead require a more refined analysis of binding geometry. Among the causes for poor results are an imperfect steric fit ofthe ligand within the cavity, an unnaturally high degree of solvent-accessible ligand surface in the complex or the formation of voids at the receptor–ligand interface. Possible remedies are empirical filters that measure such fit parameters and remove docking solutions above a user-specified threshold. 171 A promising approach along these lines is the inclusion of artificially generated, erroneous, decoy solutions in the optimization of scoring functions. In the process of deriving weights for individual terms of the scoring function, the decoy solutions should always obtain lower ranks than the correct solutions, and thus suitable penalty terms could be derived automatically. Such a procedure was first reported for the scoring function of a flexible ligand superposition algorithm. 172,173 Specific Attractive Interactions Another general deficiency of scoring functions stems from the simplified description of attractive interactions. Molecular recognition is not based only on classical hydrogen bonds and hydrophobic contacts. Many researchers, especially those active in host–guest chemistry, are making use of other specific types of interactions. For example, hydrogen bonds that are formed between acidic protons and p systems. 174 These bonds can substitute for conventional hydrogen bonds in both strength and specificity, as has been noted, for example, in protein–DNA recognition 175 and as can be observed in serine protease complexes deposited in the PDB. 161 Another class of ‘‘unconventional’’ interactions is the cation–p interaction, which is especially important at the surface of proteins. 176,177 Current empirical scoring functions do not model these interactions and mostly disregard the directionality of, for example, interactions between aromatic rings. 178,179 In the derivation of empirical scoring functions, one thus implicitly attributes some of the binding energy arising
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Reviews in Computational Chemistry
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Kenny B. Lipkowitz Department of Ch
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vi Preface three-dimensional struct
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viii Preface some descriptors and i
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Epilogue and Dedication My associat
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Contents 1. Clustering Methods and
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Contents xv Electron Transfer in Po
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Contributors John M. Barnard, Barna
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Contributors to Previous Volumes *
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Volume 3 (1992) Tamar Schlick, Opti
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Volume 7 (1996) Geoffrey M. Downs a
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Volume 11 (1997) Mark A. Murcko, Re
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T. Daniel Crawford* and Henry F. Sc
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Topics Covered in Volumes 1-18 * Ab
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Reviews in Computational Chemistry
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2 Clustering Methods and Their Uses
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Page 37 and 38: 8 Clustering Methods and Their Uses
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Page 71 and 72: 42 The Use of Scoring Functions in
Page 79 and 80: Table 1 Reference List for the Most
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Page 117 and 118: CHAPTER 3 Potentials and Algorithms
Page 119 and 120: Vn (1 + cos(nω + γ)) 2 K θ (θ
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Page 123 and 124: Table 1 Polarizability Parameters f
Page 125 and 126: The polarizable point dipole models
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Page 131 and 132: Shell Models 103 on estimates of sh
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where we have used q Cl ¼ qNa. The
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Electronegativity Equalization Mode
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Electronegativity Equalization Mode
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of N molecules is taken as a Hartre
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is treated using variable charges.
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water have been developed, includin
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Applications 123 classical and rigi
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developing polarizable models. A va
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Comparison of the Polarization Mode
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negligible errors in such propertie
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ecome significant at field strength
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noteworthy in this regard because t
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References 135 9. P. Cieplak and P.
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References 137 48. E. L. Pollock an
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References 139 Computational Chemis
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References 141 139. J. Hinze and H.
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References 143 178. J. J. P. Stewar
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References 145 216. M. W. Mahoney a
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CHAPTER 4 New Developments in the T
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Introduction 149 applications). For
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FCWD(∆E ) FCWD(0) ∆E = 0 ∆E
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Introduction 153 Equations [6]-[12]
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Paradigm of Free Energy Surfaces 15
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Paradigm of Free Energy Surfaces 15
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In Eqs. [18] and [19], F0i is the e
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where ‘‘þ’’ and ‘‘ ’
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is, however, small for the usual co
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solute-solvent coupling through the
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where Z is the electrode overpotent
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energy surfaces of ET. 33,50-56 It
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This result indicates a fundamental
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βF i (X ) 40 20 0 −20 1 2 βλ 1
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Table 1 Main Features of the Two-Pa
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and Hss ¼ U rep ss 1 2 X j;k ðmj
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λ i /eV 4 3 2 1 0 0 10 20 30 40 Bo
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the width/Stokes shift relation (Eq
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Table 3 Mapping of the Q Model on S
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This situation is of course not sat
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F ± (Y ad )/λ I 0.8 0.4 0 −0.4
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it by choosing the GMH basis set 7
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Anharmonic higher order terms gain
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of the radiation is the perturbatio
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individual vibrational excitations
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m 12 /D 6 5.5 5 4.5 4 3.5 17 18 19
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In Eq. [144], the coordinates Y km
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ε/M −1 cm −1 4000 2000 0 analy
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βσ 2 /10 3 cm −1 14 12 10 8 Opt
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0.2 0.1 0 12 16 20 24 28 32 The app
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References 207 7. M. D. Newton, Adv
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References 209 59. R. Kubo and Y. T
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