Reviews in Computational Chemistry Volume 18

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difference in conformational energy between the global minimum structure and the current conformation of the ligand in the complex. However, force field estimates of energy differences between individual conformations are not reliable for all systems. In practice, better correlations with experimental binding data are obtained when strain energy is used as a filter to weed out unlikely binding geometries rather than when strain energy is added to the final score. Estimation of ligand strain energy based on force fields can be time consuming, and so alternatives such as empirical rules derived from small-molecule crystal structure data are often employed. 144 Conformations generated by such programs are, however, often not strain free, because only one torsional angle is treated at a time. Some strained conformations can be excluded when two consecutive dihedral angles are simultaneously taken into account, however. 78 Empirical Scoring Functions The underlying idea of empirical scoring functions is that the binding free energy of a noncovalent receptor–ligand complex can be interpreted as a sum of localized, chemically intuitive interactions. Such energy decompositions can be a useful tool to understand binding phenomena even without analyzing 3D structures of receptor–ligand complexes. Andrews, Craik, and Martin 126 calculated average functional group contributions to binding free energy from a set of 200 compounds whose affinity to a receptor had been experimentally determined. These average functional group contributions can then be used to estimate a receptor-independent binding energy for a compound that can be compared to experimental values. If the experimental value is approximately the same as or higher than the calculated value, one can infer a good fit between receptor and ligand and essentially all functional groups of the ligand are involved in protein interactions. If the experimental energy is significantly lower, one can infer that the compound can not fully form its potential interactions with the protein. Experimental binding affinities have also been analyzed on a per atom basis in quest of the maximal binding affinity of noncovalent ligands. 145 It was concluded that for the strongest binding ligands, each nonhydrogen atom on average contributes 1.5 kcal/mol to the total binding energy. With 3D structures of receptor–ligand complexes at hand, the analysis of binding phenomena can of course be much more detailed. The binding affinity G binding can be estimated as a sum of interactions multiplied by weighting coefficients Gi Scoring Functions for Receptor–Ligand Interactions 53 G binding X i Gi fiðr l; rpÞ ½2Š where each fi is a function of the ligand coordinates r l and the protein receptor coordinates rp, and the sum is over all atoms in the complex. Scoring schemes
54 The Use of Scoring Functions in Drug Discovery Applications that use this concept are called ‘‘empirical scoring functions.’’ Several reviews summarize details of individual parameterizations. 17,146–151 The individual terms in empirical scoring functions are usually chosen so as to intuitively cover important contributions of the total binding free energy. Most empirical scoring functions are derived by evaluating the functions fi for a set of protein– ligand complexes and fitting the coefficients Gi to experimental binding affinities of these complexes by multiple linear regression or by supervised learning techniques. The relative weight of the individual contributions depends on the training set. Usually, between 50 and 100 complexes are used to derive the weighting factors, but in a recent study it was shown that many more than 100 complexes were needed to achieve convergence. 75 The reason for this large number is probably due to the fact that the publicly available protein–ligand complexes fall in a few heavily populated classes of proteins, such that in small sets of complexes few interaction types dominate. Empirical scoring functions usually contain individual terms for hydrogen bonds, ionic interactions, hydrophobic interactions, and for binding entropy. Hydrogen bonds are typically scored by simply counting the number of donor–acceptor pairs falling within a given distance and angle range considered to be favorable for hydrogen bonding, weighted by penalty functions for deviations from preset ideal values. 56,71,73 The amount of error-tolerance in these penalty functions is critical to the success of scoring methodology. When large deviations from ideality are tolerated, the scoring function may be unable to discriminate between different orientations of a ligand. Contrarily, small tolerances lead to situations where many structurally similar complex structures result in very similar scores. Attempts have been made to reduce the localized nature of such interaction terms by using continuous modulating functions on an atom-pair basis. 69 Other workers have avoided the use of penalty functions altogether and introduced separate regression coefficients for strong, medium, and weak hydrogen bonds. 75 For example, at Agouron a simple four-parameter potential, which is called the piecewise linear potential (PLP), was developed that is an approximation of a potential well without angular terms. 62 Most empirical scoring functions treat all types of hydrogenbond interactions equally, but some attempts have been made to distinguish between different donor–acceptor functional group pairs. Hydrogenbond scoring in the docking program GOLD, 60,61 for example, is based on a list of hydrogen-bond energies for all combinations of 12 defined donor and 6 acceptor atom types derived from ab initio calculations of model systems incorporating those atom types. A similar differentiation of donor and acceptor groups is made in the hydrogen-bond functions in the program GRID, 152 a program commonly used for the characterization of binding sites. 115–117 The inclusion of such lookup tables in scoring functions is presumed to avoid errors originating from the oversimplification of individual interactions. Reducing the weight of hydrogen bonds formed at the outer surface of the binding site is a useful measure for reducing the number of false positive
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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
Page 31 and 32: 2 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
Page 81: 52 The Use of Scoring Functions in
Page 117 and 118: CHAPTER 3 Potentials and Algorithms
Page 119 and 120: Vn (1 + cos(nω + γ)) 2 K θ (θ
Page 121 and 122: are modified by their environment w
Page 123 and 124: Table 1 Polarizability Parameters f
Page 125 and 126: The polarizable point dipole models
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Page 129 and 130: M i z i + q i d i k i and shell cha
Page 131 and 132: Shell Models 103 on estimates of sh
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minimization can be replaced by mor
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The energy required to create a cha
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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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