Reviews in Computational Chemistry Volume 18

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Scoring Functions for Receptor–Ligand Interactions 51 The appropriate statistical mechanics treatment has been reviewed elsewhere 118 and is not the topic of this chapter. Large-scale Monte Carlo or molecular dynamics (MD) simulations are necessary to derive reasonably accurate values of binding free energies. These computational methods are only suitable for small sets of compounds, since they require large amounts of computational resources. Moreover, even the most advanced techniques are reliable only for calculating binding free energy differences between closely related ligands. 119–122 However, a number of less rigorous but faster scoring schemes have been developed that should be amenable to larger numbers of ligands. For example, recent experience has shown that continuum solvation models can replace explicit solvent molecules, at least in the final energy evaluation of the simulation trajectory. 123 Another less expensive alternative for computing binding free energies is the use of linear reponse theory 109,110 in conjunction with a surface term. 112 Scoring functions that can be evaluated quickly enough to be practical in docking and virtual screening applications are very crude approximations to the free energy of binding. They usually take into account only one receptor– ligand complex structure and disregard ensemble averaging and properties of the unbound state of the binding partners. Furthermore, all scoring methods have in common the fact that the free energy is obtained from a sum of terms. In a strict physical sense, this is not possible, since the free energy of binding is a state function, but its components are not. 124 Furthermore, simple additive models cannot describe subtle cooperativity effects. 125 Nevertheless, it is often useful to interpret receptor–ligand binding in an additive fashion, 126–128 and estimates of binding free energy are available in this way at very low computational cost. Fast scoring functions can be categorized into three main classes: (1) force field-based methods, (2) empirical scoring functions, and (3) knowledge-based methods. Each of these is now discussed. Force Field-Based Methods An obvious idea to circumvent parameterization efforts for scoring is to use nonbonded energies of existing, well-established molecular mechanics force fields for the estimation of binding affinity. In doing so, one substitutes estimates of the free energy of binding in solution by an estimate of the gasphase enthalpy of binding. Even this crude approximation can lead to satisfying results. A good correlation was obtained between nonbonded interaction energies calculated with a modified MM2 force field and IC 50 values of 33 inhibitors of human immunodeficiency virus (HIV)-1 protease. 129 Similar results were reported in a study of 32 thrombin–inhibitor complexes with the CHARMM force field. 130 In both studies, however, experimental data represented rather narrow activity ranges and little structural variation. The AMBER 131,132 and CHARMM 133 nonbonded terms are used as a scoring function in several docking programs. Protein terms are usually
52 The Use of Scoring Functions in Drug Discovery Applications precalculated on a cubic grid, such that for each ligand atom only the interactions with the closest grid points have to be evaluated. 94 This leads to an increase in speed of about two orders of magnitude compared to traditional atom-by-atom evaluation. Distance-dependent dielectric constants are usually employed to approximate the long-range shielding of electrostatic interactions by water. 100 However, compounds with high formal charges still obtain unreasonably high scores due to overestimated ionic interactions. For this reason, it has been common practice in virtual screening to separate databases of compounds into subgroups according to their total charge and then to rank these groups separately. When electrostatic interactions are complemented by a solvation term calculated by the Poisson–Boltzmann equation 134 or faster continuum solvation models (as in Ref. 135), the deleterious effects of high formal charges are diminished. In a validation study on three protein targets, Shoichet et al. 103 observed a significantly improved ranking of known inhibitors after correction for ligand solvation. The current version of the docking program DOCK calculates solvation corrections based on the generalized Born 136 solvation model. 105 The method has been validated in a study where several peptide libraries were docked into various serine protease active sites. 137 In the context of scoring, the van der Waals term of force fields is mainly responsible for penalizing docking solutions with steric overlap between receptor and ligand atoms. The term is often omitted when only the binding of experimentally determined complex structures is analyzed. 102,138,139 A recent addition to the list of force field-based scoring methods has been developed by Charifson and Pearlman. Their so-called OWFEG (one window free energy grid) method 114 is an approximation to the expensive firstprinciples method of free energy perturbation (FEP). 140 For the purpose of scoring, an MD simulation is carried out with the ligand-free, solvated receptor site. The energetic effects of probe atoms on a regular grid are collected and averaged during the simulation. Three simulations are run with three different probes: a neutral methyl-like atom, a negatively charged atom, and a positively charged atom. The resulting three grids contain information on the score contributions of neutral, positively, and negatively charged ligand atoms located in various positions of the receptor site and can thus be used in a straightforward manner for scoring. The OWFEG approach seems to be successful for Ki prediction as well as for virtual screening applications. 113 Its conceptual advantage is the implicit consideration of entropic and solvent effects and the inclusion of some protein flexibility in the simulations. The calculation of ligand strain energy traditionally lies in the realm of molecular mechanics force fields. Although effects of strain energy have rarely been determined experimentally, 141 it is generally accepted that high-affinity ligands bind in low-energy conformations. 142,143 If a compound must adopt a strained conformation to fit into a receptor pocket, a less negative binding free energy should result. Strain energy can be estimated by calculating the
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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
Page 29 and 30: 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: Table 1 Reference List for the Most
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
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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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Reviews in Computational Chemistry Volume 18

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