Reviews in Computational Chemistry Volume 18

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Scoring Functions for Receptor–Ligand Interactions 57 distributions for a data set of interacting molecules can thus be converted to sets of atom-pair potentials that are straightforward to evaluate. The first applications of knowledge-based scoring functions in drug research 164–166 were restricted to small data sets of HIV protease–inhibitor complexes and did not result in generally applicable scoring functions. Recent publications 82–86,92,93 have shown that useful general scoring functions can be derived with this method. The de novo design program SMoG 82,83 contained the first general-purpose implementation of such a potential. The ‘‘PMF’’ function by Muegge 86 consists of a set of distancedependent atom-pair potentials EijðrÞ that are written as EijðrÞ ¼ kT ln½ fjðrÞr ij ðrÞ=r ij Š ½4Š Here, r is the atom pair distance, and rijðrÞ is the number density of pairs ij that occur in a given radius range around r. The term rij in the denominator is the average density of receptor atoms j in the whole reference volume. The number density is calculated in the following manner. A maximum search radius is defined. This radius describes a reference sphere around each ligand atom j, in which receptor atoms of type i are searched, and which is divided into shells of a specified thickness. The number of receptor atoms i found in each spherical shell is divided by the volume of the shell and averaged over all occurrences of ligand atoms i in the database of protein–ligand complexes. Muegge argues that the spherical reference volume around each ligand atom needs to be corrected by eliminating the volume of the ligand itself, because ligand–ligand interactions are not regarded. This correction is done by the volume correction factor fjðrÞ that is a function of the ligand atom only and gives a rough estimate of the preference of atom j to be solvent exposed rather than buried within the binding pocket. Muegge could show that the volume correction factor contributes significantly to the predictive power of the PMF function. 90 Also, a relatively large reference radius of at least 7–8A˚ must be applied to implicitly include solvation effects, particularly the propensity of individual atom types to be located inside a protein cavity or in contact with solvent. 89 For docking calculations, the PMF scoring function is evaluated in a grid-based manner and combined with a repulsive van der Waals potential at short distances and minima extended slightly toward shorter distances. The DrugScore function created by Gohlke, Hendlich, and Klebe 92 is based on roughly the same formalism, albeit with several differences in the derivation leading to different potential forms. Most notably, the statistical distance distributions rijðrÞ=rij for the individual atom pairs ij are divided by a common reference state that is simply the average of the distance distributions of all atom pairs rðrÞ ¼ P P i j rijðrÞ=imax jmax , where the product in the denominator yields the total number of pair functions. Furthermore, no
58 The Use of Scoring Functions in Drug Discovery Applications volume correction term is used, and the sampling cutoff (the radius of the reference sphere) is set to only 6 A ˚ . The individual potentials have the form EijðrÞ ¼ kTðln½r ij ðrÞ=r ij Š ln½rðrÞŠÞ ½5Š The pair potentials in Eq. [5] are used in combination with other potentials, depending on one (protein or ligand) atom type only, that express the propensity of an atom type to be buried within a lipophilic protein environment upon complex formation. Contributions of these surface potentials and the pair potentials are weighted equally in the final scoring function. DrugScore was developed with the aim of differentiating between correctly docked ligand structures versus decoy (arbitrarily placed) structures for the same protein– ligand pair. A different type of reference state was chosen by Mitchell et al. 85 The pair interaction energy is written as EijðrÞ ¼kT ln½1 þ m ij sŠ kT ln½1 þ m ij sr ij ðrÞ=rðrÞŠ Here, the number density r ij ðrÞ is defined as in Eq. [4], but it is normalized by the number density of all atom pairs at this same distance instead of by the number of pairs ij in the whole reference volume. The variable m ij is the number of atom pairs ij found in the data set of protein–ligand complexes, and s is an empirical factor that defines the weight of each observation. This potential is combined with a van der Waals potential as a reference state to compensate for the lack of sampling at short distances and for certain underrepresented atom pairs. Apart from data on 90 protein–ligand complexes used in the original validation, no further application has been published. CRITICAL ASSESSMENT OF CURRENT SCORING FUNCTIONS Influence of the Training Data All fast scoring functions share a number of deficiencies that one should be aware of for any application. First, most scoring functions are in some way fitted to or derived from experimental data. The resulting functions necessarily reflect the accuracy of the data that were used in their derivation. A general problem with empirical scoring functions is the fact that the experimental binding energies are compiled from many different sources and therefore form inconsistent data sets containing systematic experimental errors. Scoring functions not only reflect the quality, but also the type of experimental data on which they are based. Most scoring functions are still derived from data on mostly high-affinity receptor–ligand complexes. Moreover, many of these
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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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4 Clustering Methods and Their Uses
Page 35 and 36: 6 Clustering Methods and Their Uses
Page 37 and 38: 8 Clustering Methods and Their Uses
Page 39 and 40: 10 Clustering Methods and Their Use
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
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Page 131 and 132: Shell Models 103 on estimates of sh
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for all i ði:e:; 8 iÞ: @U @qi l
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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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Reviews in Computational Chemistry Volume 18

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