J. Chem. Inf. Comput. Sci. 1998, 38, 497-505
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Rational Screening Set Design and Compound Selection: Cascaded Clustering Paul R. Menard,*,† Richard A. Lewis,‡ and Jonathan S. Mason† Computer-Assisted Drug Design, New Lead Generation, Rhoˆne-Poulenc Rorer, Collegeville, Pennsylvania 19426 and Dagenham, RM10 7XS, UK Received January 12, 1998
The use of cascaded clustering is reported. This technique was developed to permit the application of Jarvis-Patrick clustering based on structural fingerprints to large chemical databases, while keeping the maximum cluster size and the number of singletons produced at reasonable levels. The basis for the algorithm, its implementation, and validation are described. In the first part of the paper, the approach is used to create a representative subset of compounds for biological testing from the corporate compound repository. A variation of the method is then used for the comparison of relatively large databases. Finally, compound selection using cascaded clustering is shown to be complementary to the Diverse Property-Derived approach, which is based on partitioning by six molecular descriptors. INTRODUCTION
With the advent of high-throughput screening (HTS), many more compounds can be subjected to bioassay than was possible with traditional screening methods. Researchers must therefore identify more compounds for screening in order to satisfy this increased capacity. One of the best sources for screening candidates is the corporate compound repository. A second source is external compound collections: compounds different from those in the corporate repository can be identified and acquired. More recently, combinatorial chemistry techniques have allowed the production of large numbers of compounds both quickly and relatively inexpensively. One approach to screening is simply to schedule all available compounds for bioassay in random order or by some other arbitrary selection process. This may result in large batches of structurally similar but inactive compounds being screened sequentially, with little resultant return in terms of biological activity. A major goal of pharmaceutical research is to identify new biological leads as quickly and efficiently as possible. Furthermore, not all bioassays are appropriate for HTS methodology. In some cases, the assay cost may become prohibitive when dealing with large numbers of compounds. By identifying a small, structurally diverse or representative set of compounds for priority screening from a larger compound collection and by augmenting this set regularly with new dissimilar compounds, the chances of finding a lead quickly should be increased, and such a set should be relevant for both high-throughput and traditional screening methods. If such a method also defines relationships between similar compounds, this would facilitate the process of selecting compounds for lead follow-up.1 The cascaded clustering technique has been developed in order to address these needs. This approach is based on clustering using 2D structural fingerprints and incorporates novel methodology for dealing partially with clustering problems inherent to the † ‡
Collegeville, Pa. Dagenham, UK.
Jarvis-Patrick nonhierarchical method; such problems are too wide a range of cluster sizes, heterogeneous clustering, and excessive numbers of compounds which fail to cluster at all. The method is equally applicable to clustering based on other similarity metrics. Background. There is no universally agreed-upon definition of chemical diversity, and there are several approaches for identifying chemically diverse or representative collections of compounds. We therefore start by defining our terms: “diverse” will be defined as a compound collection spanning as wide a range of values as possible relative to some descriptor derived from a compound’s structure. “Representative” will mean a compound subset reflecting the distribution of values for some descriptor shown by the parent collection from which it is derived. Descriptors which can be used for diversity profiling can be derived from onedimensional chemical properties (1D, e.g., molecular weight), two-dimensional (2D, e.g., topological descriptors such as structural fingerprints or substructural keys, or physicochemical descriptors such as clogP), or three-dimensional (3D, e.g., shape indices or pharmacophoric keys). For a fuller review, see refs 2-9. Furthermore, either partitioning or clustering may be used to select compounds relative to a given descriptor. In partitioning, the descriptor must be capable of being defined by an absolute value such as a real number (e.g., clogP). The possible range of values for the descriptor is then typically broken down into subdivisions of equal size, and compounds are selected so as to fill each subdivision. Advantages are easy control of granularity, the ability to identify property space not represented by any structures in the set being considered, and straightforward comparison of compound populations. Partitioning is particularly useful in designing diverse collections. In clustering, compounds are grouped together based on their similarities, normally a distance-based calculation using some descriptor. Since results are relative to the compound collection being analyzed and not against absolute values as in partitioning, it is difficult to determine what property space is unrepresented or to
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498 J. Chem. Inf. Comput. Sci., Vol. 38, No. 3, 1998
Figure 1. Daylight fingerprint/clustering methodology
compare populations. However, the relative nature of the analysis is well suited to defining representative subsets.10 In an earlier paper in this series,11 the Diverse PropertyDerived (DPD) approach was presented. Briefly, the DPD approach involves partitioning compounds over a property space derived from six pairwise noncorrelated molecular and physicochemical descriptors. The descriptors used were hydrogen bond acceptor count, hydrogen bond donor count, flexibility index, clogP, aromatic density, and electrotopological index. These are intuitively satisfying to the pharmaceutical researcher, since they relate directly to factors important for ligand-receptor binding (electrostatics and shape) as well as to absorption/cell wall transport. This method was initially used to create a small diverse set (1000 compounds) for biological testing, and is currently being applied in lead follow-up studies and external compound acquisitions. In traditional pharmaceutical research, relatively large numbers of structurally related compounds may be made during the exploration of structure-activity relationships. On the other hand, externally purchased (or available) compounds may be quite different from those produced by inhouse research and may be the only representatives of their chemical families in the repository. However, compounds having widely different structures may have similar physicochemical properties, and using these properties alone to characterize and select compounds may fail to sample important chemical families or interesting structures. It was therefore decided to develop a topologically based method which would complement the DPD approach. This method would serve two critical needs: (1) the selection of structurally representative sets from compound collections and (2) the comparison of compound collections, with the capability of identifying compounds from a query collection which are structurally dissimilar to those in a reference collection. Daylight Fingerprints and Similarity. The approaches to be discussed are based on the Daylight Clustering Package12 which provides a full capability for clustering based on 2D structural descriptors. The strategy is outlined in Figure 1. Briefly, the Daylight fingerprint module generates a binary descriptor (fingerprint) representing the 2D structural characteristics of a molecule. All bond paths within the molecule containing typically between two and eight atoms are identified and converted to binary representations using a pseudorandom hashing algorithm, with each representation being added to the overall molecular finger-
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print. The resulting fingerprint is then folded by successively dividing it in half and ORing the fragments together until a sufficient information density is achieved (in this study, at least 30% of the bits set). A potential advantage that this method has over fingerprints that are based on substructural keys is that the fingerprint is based solely on the topology of the molecule, not on a predefined set of functional group keys that may not be entirely appropriate for the compound collection being analyzed. A possible disadvantage is that the hashing algorithm may cause different functionalities to set the same bits. Furthermore, fingerprint folding, although advantageous for increasing the efficiency of disk and CPU utilization, can cause a slight loss of information as the fingerprint halves are merged. In our experience, neither of these two factors appeared to cause any substantial misclustering. A nearest neighbors list is then generated based on the similarities of each molecule to all other molecules in the dataset. The Tanimoto metric is used to calculate similarity
T ) NA&B/(NA + NB - NA&B) where NA and NB are the number of bits set in fingerprints A and B, and NA&B is the number of bits common to A and B. Clustering Methods. Two methods were considered for clustering: a hierarchical method based on Ward’s algorithm13 and the nonhierarchical Jarvis-Patrick method14 provided by Daylight. In Ward’s method, relationships are maintained not only between compounds in clusters but also between clusters themselves, including singletons (structures which cluster alone). This simplifies the task of finding related structures for bioassay once an active compound is found. It is easy to vary the number of clusters produced by modulation of the clustering parameters. The clusters produced are generally intuitively sensible to the chemists, the ratio of singletons to clusters is low, and maximum cluster sizes, even under forcing conditions, are reasonable. The drawback is rather demanding in terms of disk space and CPU requirements. The dissimilarity matrix can require up to O(N2) disk space for storage, and the standard algorithm requires O(N3) time for the clustering process.15 Some workers have achieved improved performance by use of Murtagh’s Reciprocal Nearest-Neighbor algorithm, which requires only O(N) disk space and O(N2) time.16 With the implementation we had in our hands at the time, Ward’s method was best suited to the analysis of 10 000 structures or less, due to the time constraints imposed by our O(N2) implementation; the technique was therefore not used in this study. In fairness, it should be added that newer implementations can cluster up to 200K structures in a reasonable time.17 The Jarvis-Patrick algorithm clusters molecules using conditions which state that two structures will cluster together if (a) they are in each other’s list of K nearest neighbors and (b) they have some integer value J of their K nearest neighbors in common. Both J and K are user-defined parameters and can be varied to provide optimum results based on the chemical database being studied and on the clustering goals. In the Daylight nearest neighbors routine, if some integer value K of nearest neighbors is requested for each structure then that number will be found, regardless
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of how low a value of T is required to satisfy this criterion. If a subsequent clustering method is based solely on nearest neighbors data, this may cause structures which are in reality quite dissimilar to cluster together. The Jarvis-Patrick algorithm has several computational and practical advantages for clustering chemical structures. It is computationally efficient from both a CPU (O(N2) time) and a disk utilization perspective and therefore is suitable for very large databases ranging upward of a million structures. Our experiments on an SGI IndigoII R4000 running Irix5.3 gave an approximate formula of W/CPU s ) 1700*(N/10 000)∧2, where W is the run time, and N is the number of objects. For N ) 100 000, W ≈ 48 CPU h. A comparison by Willett of nonhierarchical clustering methods for the analysis of chemical datasets based on substructural features showed the relative superiority of this approach.18 Unfortunately, the method also has drawbacks. JarvisPatrick is nonhierarchical, and no relationship between clusters is obtained. If J ≈ K, then the condition for clustering is very stringent, and a significant fraction of the data remains unclustered (singletons). If J , K, the condition for clustering is less stringent, and a few, very large, clusters may form. A similar phenomenon occurs in hierarchical clustering as the fusion distance is increased; in this case, methods for determining the correct distance have been proposed.19 Unfortunately they are not applicable to the Jarvis-Patrick method. The Daylight Jarvis-Patrick implementation (v441) did not support a minimum similarity threshold in the nearest neighbors calculation; therefore, some heterogeneous clusters may result as described above. We speculate that the use of a sensible cutoff may improve the quality of clusters but that the issues posed by the presence of singletons will still exist. Alternative Methods for Set Design and Compound Selection. The selection of a method for set design or compound selection depends on a number of factors, such as the number of structures being analyzed, the size of the subset desired, available biological results and their possible correlation with a given descriptor, etc. Several studies have been published that look at the issues surrounding selection of representative/diverse compound subsets and comparison of compound collections; only a few will be mentioned here. Willett studied three nonhierarchical clustering methods based on 2D substructural fragments18 and found the JarvisPatrick approach the most effective for grouping structures with similar physical, chemical, or biological properties. Daylight fingerprints in conjunction with Jarvis-Patrick clustering, and readily calculated physicochemical descriptors such as partition coefficient and molar refractivity, were used by Shemetulskis to analyze and compare datasets.20 Both approaches were found to be practical for use on moderately sized datasets (approximately 100 000 structures). Pearlman has developed software21 to perform subset selection from large compound collections, using novel BCUT descriptors and more traditional structural fingerprints. An advantage to the BCUT approach is its applicability to very large datasets and its potential appeal to medicinal chemists (BCUT values are based on electronegativity, polarizability, hydrogen bond donor and acceptor ability, and other factors related to ligand-protein binding). Willett22 has developed a rapid method for comparing datasets based on descriptors calculated from pairwise intermolecular similarities within
each dataset, including but not limited to the number of heavy atoms, rotatable bonds or rings, or structural fingerprints. Each descriptor characterizes the dataset as a whole, not on a molecule-by-molecule basis, but is computationally efficient and also applicable to very large datasets. An extension of this method has been used to analyze the diversity of compound subsets relative to a parent database and thereby select a set of molecules representing much of the parent dataset’s diversity. More recently, Clark23 has described a stochastic algorithm (OptiSim) that uses dissimilarity to select molecules. There is an adjustable parameter that controls the subsample size and hence the balance between representativeness and diversity. However, this does require a comparison metric that is meaningful when measuring distance between quite dissimilar objects. Our anecdotal experience is that a measure of (1-T) is not suitable when folded Daylight fingerprints are used, as the distance can be affected by chance bit matches that are artifacts of the folding process.
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Objectives. The standard compound collections we wished to analyze ranged from a few hundred structures to several hundred thousand. The initial goal of our work was to develop a clustering approach based on the Jarvis-Patrick algorithm which would meet our needs, namely to produce homogeneous, limited-size clusters with a small (
