Reviews in Computational Chemistry Volume 18

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CHAPTER 1 Clustering Methods and Their Uses in Computational Chemistry Geoff M. Downs and John M. Barnard Barnard Chemical Information Ltd., 46 Uppergate Road, Stannington, Sheffield S6 6BX, United Kingdom INTRODUCTION Reviews in Computational Chemistry, Volume 18 Edited by Kenny B. Lipkowitz and Donald B. Boyd Copyr ight © 2002 John Wiley & Sons, I nc. ISBN: 0-471-21576-7 Clustering is a data analysis technique that, when applied to a set of heterogeneous items, identifies homogeneous subgroups as defined by a given model or measure of similarity. Of the many uses of clustering, a prime motivation for the increasing interest in clustering methods is their use in the selection and design of combinatorial libraries of chemical structures pertinent to pharmaceutical discovery. One feature of clustering is that the process is unsupervised, that is, there is no predefined grouping that the clustering seeks to reproduce. In contrast to supervised learning, where the task is to establish relationships between given inputs and outputs to enable prediction of the output from new inputs, in unsupervised learning only the inputs are available and the task is to reveal aspects of the underlying distribution of the input data. Clustering is thus complemented by the related supervised process of classification, in which items are assigned labels applied to predefined groups: examples include recursive partitioning, naïve Bayesian analysis, and K nearest-neighbor selection. Clustering is a technique for exploratory data analysis and is used increasingly in preliminary analyses of large data sets of medium and high dimensionality as a method of selection, diversity analysis, and data reduction. This chapter reviews the main clustering methods that are used for analyzing chemical 1
2 Clustering Methods and Their Uses in Computational Chemistry data sets and gives examples of their application in pharmaceutical companies. Compared to the other costs of drug discovery, clustering can add significant value at minimal cost. First, we provide an outline of clustering as a discipline and define some of the terminology. Then, we give a brief tutorial on clustering algorithms, review progress in developing the methods, and offer some example applications. Clustering methodology has been developed and used in a variety of areas including archaeology, astronomy, biology, computer science, electronics, engineering, information science, and medicine. Good, general introductory texts on the topic of clustering include those by Sneath and Sokal, 1 Kaufmann and Rousseeuw, 2 Everitt, 3 and Gordon. 4 The main text that is devoted to clustering of chemical data sets is by Willett, 5 with review articles by Bratchell, 6 Barnard and Downs, 7 and Downs and Willett. 8 The present chapter is a complement and update to the latter article. In a previous volume of this series, Lewis, Pickett, and Clark 9 reviewed the use of diversity analysis techniques in combinatorial library design. As will be shown in the section on Chemical Applications, the current main uses of clustering for chemical data sets are to find representative subsets from high throughput screening (HTS) and combinatorial chemistry, and to increase the diversity of in-house data sets through selection of additional compounds from other data sets. Methods suitable for compound selection are the main focus of this chapter. The methods must be able to handle large data sets of high-dimensional data. For small, low-dimensional data sets, most clustering methods are applicable, and descriptions in the standard texts and implementations available in standard statistical software packages 10,11 suffice. Implementations designed for use on chemical data sets are available from most of the specialist software vendors, 12–17 the majority of which were reviewed by Warr. 18 The overall process of clustering involves the following steps: 1. Generate appropriate descriptors for each compound in the data set. 2. Select an appropriate similarity measure. 3. Use an appropriate clustering method to cluster the data set. 4. Analyze the results. This chapter focuses on step 3. For step 1, descriptors may include property values, biological properties, topological indexes, and structural fragments. The performance of these descriptors and forms of representation have been analyzed by Brown 19 and Brown and Martin. 20,21 Similarity searching for step 2 has been discussed by Downs and Willett; 22 characteristics of various similarity measures have been discussed by Barnard, Downs, and Willett. 23,24 For step 4, little has been published specifically about visualization and analysis of results for chemical data sets. However, most publications that focus on implementing systems that utilize clustering do provide details of how the results were displayed or analyzed.
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Page 3 and 4: Kenny B. Lipkowitz Department of Ch
Page 5 and 6: vi Preface three-dimensional struct
Page 7 and 8: viii Preface some descriptors and i
Page 9 and 10: Epilogue and Dedication My associat
Page 11 and 12: Contents 1. Clustering Methods and
Page 13 and 14: Contents xv Electron Transfer in Po
Page 15 and 16: Contributors John M. Barnard, Barna
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52 The Use of Scoring Functions in
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CHAPTER 3 Potentials and Algorithms
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Vn (1 + cos(nω + γ)) 2 K θ (θ
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are modified by their environment w
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Table 1 Polarizability Parameters f
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The polarizable point dipole models
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two to three orders of magnitude sl
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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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