Molecular similarity in medicinal chemistry.

Perspective pubs.acs.org/jmc

Molecular Similarity in Medicinal Chemistry Miniperspective Gerald Maggiora,*,†,‡ Martin Vogt,§ Dagmar Stumpfe,§ and Jürgen Bajorath*,§ †

College of Pharmacy and BIO5 Institute, University of Arizona, 1295 North Martin, P.O. Box 210202, Tucson, Arizona 85721, United States ‡ Translational Genomics Research Institute, 445 North Fifth Street, Phoenix, Arizona 85004, United States § Department of Life Science Informatics, B-IT, LIMES Program Unit Chemical Biology and Medicinal Chemistry, Rheinische Friedrich-Wilhelms-Universität, Dahlmannstrasse 2, D-53113 Bonn, Germany ABSTRACT: Similarity is a subjective and multifaceted concept, regardless of whether compounds or any other objects are considered. Despite its intrinsically subjective nature, attempts to quantify the similarity of compounds have a long history in chemical informatics and drug discovery. Many computational methods employ similarity measures to identify new compounds for pharmaceutical research. However, chemoinformaticians and medicinal chemists typically perceive similarity in different ways. Similarity methods and numerical readouts of similarity calculations are probably among the most misunderstood computational approaches in medicinal chemistry. Herein, we evaluate different similarity concepts, highlight key aspects of molecular similarity analysis, and address some potential misunderstandings. In addition, a number of practical aspects concerning similarity calculations are discussed.

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INTRODUCTION Molecular similarity is one of the most heavily explored and exploited concepts in chemical informatics and is also a central theme in medicinal chemistry.1−3 Many computational similarity methods have been (and continue to be) introduced.1,2 Why do we apparently care so much about similarity in the molecular world? Simply put, comparing compounds and their properties, especially activity, is one of the most frequent exercises in chemical and pharmaceutical research but often for rather different reasons. In medicinal chemistry, questions are asked such as the following: Can a similar follow-up candidate compound be identified for a liability-associated lead? Is a candidate too similar to a competitor’s compound to establish an intellectual property position? How can we complement our compound collection with different (i.e., dissimilar) compounds?” Providing answers to these and other questions requires the assessment of similarity (or dissimilarity) in one way or another. As will be discussed throughout this review, three basic components are required to construct suitable computational measures of molecular similarity: (1) a representation whose components encode the molecular and/or chemical features relevant for similarity assessment, (2) a potential weighting of representation features, and (3) a similarity function (also called a similarity coefficient) that combines the information contained in the representations to yield an appropriate similarity. This value usually lies between ‘0’ and ‘1’, where ‘1’ results from the complete identity of the molecular representations (but not necessarily the compounds). Repre© XXXX American Chemical Society

sentation features typically are different types of molecular descriptors. A weighting scheme will be required if contributions of these features should be differently prioritized for similarity assessment (otherwise, if all selected features should be equally considered, no weighting is required). Applications in chemical informatics that involve systematic comparisons of compounds and the quantification of their similarity provide a stimulating intellectual setting for method development. Quantitative readouts of similarity are also of practical relevance in, for example, the identification of new candidate compounds on the basis of known actives via virtual screening,4,5 for which similarity searching is one of the most popular approaches.6,7 Why is similarity assessment a complicated problem? Two compounds that share a common substructure can be detected unambiguously, or all compounds sharing this substructure can be retrieved from a compound database. However, as illustrated in Figure 1, it cannot be said with certainty if two compounds are similar to each other, what their degree of similarity might be and how similarity should be assessed. In this case, the catch is that it is difficult to rationalize relationships that are principally subjective in nature. First and foremost, similarity like beauty is more or less in the eye of the beholder. The difficulty of the problem increases further when attempting to describe similarity relationships in a formally consistent manner and to quantify them with aid of computational methods, as Received: September 12, 2013

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dx.doi.org/10.1021/jm401411z | J. Med. Chem. XXXX, XXX, XXX−XXX

Journal of Medicinal Chemistry

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Figure 1. Similarity perception and concepts. Two exemplary vascular endothelial growth factor receptor 2 ligands are shown, and different ways to assess their similarity are illustrated.

problem is the requirement to clearly define and consistently account for similarity. As illustrated in Figure 2, compounds that might not be considered similar often share similar activity (horizontal compound relationship) or other property values. In contrast, compounds that likely would be considered very similar might not do so (vertical compound relationship), clearly illustrating the limitations of the SPP. Structure−activity relationship (SAR) discontinuity, i.e., small chemical modifications that lead to significant changes in biological activity, represents a major limitation of the SPP. The extreme form of SAR discontinuity is provided by “activity cliffs”.9−11 A key aspect associated with the SPP that strongly influences nearly all considerations of similarity in chemical informatics and medicinal chemistry is that molecular similarity values are rarely of interest per se. Rather, they are used as a basis for correlating similarity, however assessed, with compounddependent properties such as biological activity. Despite its fundamental importance, this aspect is surprisingly often not considered in computational similarity analysis.

further detailed below. Although similarity is difficult to rationalize and quantify, computational decision support in similarity assessment is nevertheless often requested in medicinal chemistry; unfortunately, it fails more often than not. Why is this so? Herein, different similarity concepts and computational approaches for similarity assessment are discussed. In addition, an attempt is made to rationalize why there is often a discrepancy between computational and medicinal chemical views of similarity and address some common misunderstandings. Finally, the use and interpretation of similarity calculations in the practice of medicinal chemistry are discussed.

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DO SIMILAR STRUCTURES HAVE SIMILAR PROPERTIES? In the context of a seminal book publication8 that appeared in the early 1990s when molecular similarity analysis first became popular, the similarity property principle (SPP) emerged, which stated that similar compounds should have similar properties, the most frequently studied property being biological activity. Although this fundamental principle sounds simple enough, it is very difficult to capture methodologically. At the heart of the B



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Figure 2. Similarity versus activity. Three vascular endothelial growth factor receptor 2 ligands are shown that represent different (vertical vs horizontal) similarity−activity (potency) relationships.

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SIMILARITY HAS MANY DIFFERENT MEANINGS It is evident that similarity is a widely used concept that is of relevance for recognizing and organizing all components of the physical environment as well as many other aspects of life. However, even in the more narrowly confined molecular world, similarity may have many different meanings or interpretations depending on our individual perspective. Hence, if the ultimate aim is to formally describe similarity in a consistent manner despite its intrinsic limitations, it is of critical importance to first distinguish between different similarity criteria and concepts, as illustrated in Figure 1. Chemical or Molecular Similarity? Although the terms chemical and molecular similarity are often used synonymously, this may not be entirely accurate. Chemical similarity is based primarily on the physicochemical characteristics of compounds (e.g., solubility, boiling point, log P, molecular weight, electron densities, dipole moments, etc.) while molecular similarity focuses primarily on the structural features (e.g., shared substructures, ring systems, topologies, etc.) of compounds and their representation. Physicochemical properties and structural features are typically accounted for by different types of descriptors. Such descriptors are generally defined as mathematical functions or models of chemical properties or molecular structure. For chemical similarity assessment, reaction information and different functional groups can also be considered. In the current work, the focus is more on molecular than chemical similarity. 2D versus 3D Similarity. Similarity can be evaluated on the basis of 2D and 3D molecular representations. 2D similarity methods rely on information deduced from molecular graphs. Direct graph comparisons12 and graph similarity calculations are computationally demanding and not widely applied in molecular similarity analysis at present. By contrast, molecular descriptors that capture graph information such as fragment13 or topological atom environment fingerprints14 are very popular. Fingerprints are generally defined as bit string13 or feature set14 representations of molecular structure and properties. Such molecular representations can be efficiently compared computationally, thus enabling similarity calculations on a large scale. Because compounds are inherently threedimensional and their molecular conformations have generally

higher information content than their corresponding molecular graphs, one might anticipate that 3D similarity, which involves the comparison of molecular conformations and associated properties,15,16 should be generally preferred to 2D similarity. However, this is not the case for two principal reasons. First, chemists are trained on the basis of molecular graphs (i.e., 2D structural representations) and in general are more comfortable with basing their considerations on graphs than on the 3D structures of compounds. Molecular graphs typically used by chemists often also contain conformational and stereochemical information. Second, given the uncertainties associated with identifying biologically active conformations in vast conformational ensembles of test compounds, 2D approaches are typically more robust, despite their relative simplicity, and often yield superior results in SAR analysis and activity prediction.17,18 Many current similarity methods preferentially utilize 2D molecular representations; most, however, do not contain any stereochemical information, which limits their ability to properly treat enantiomeric compounds. Since such compounds have identical atom connectivity, their similarity values will be unity if stereoinsensitive molecular representations are used. Furthermore, as will be discussed below in detail, similarity calculations on the basis of 2D molecular representations have a number of other intrinsic limitations. In the following, we will base our discussion of similarity calculations and similarity measures on 2D approaches, in particular, fingerprint similarity searching, for several reasons. As pointed out above, chemists are generally more familiar with 2D than 3D representations of compounds and consider similarity mostly on the basis of 2D molecular graphs. Furthermore, many of the conclusions drawn from the analysis of simple similarity searching readily apply to more complex similarity methods. In this context, our preference for 2D similarity assessment should not be interpreted as a disregard of 3D similarity concepts and methods. Given the medicinal chemistry focus of our presentation, we mostly adhere to 2D similarity considerations herein. Molecular versus Biological Similarity. Another similarity concept that requires consideration is the biological similarity of compounds, which departs from the conceptual framework of the SPP. Instead, the usual structural or physicochemical property descriptors are replaced by the C



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Figure 3. Complex similarity relationships. Cyclooxygenase (COX) inhibitors and their activity profiles are compared. HSL stands for hormonesensitive lipase.

to a medicinal chemist’s perspective in this context. Consider, for example, the set of well-known cyclooxygenase (COX) inhibitors compared in Figure 3. All of these inhibitors are approved drugs except lumiracoxib, which lost its United States approval in 2007. If we apply a whole-compound view, compounds such as the ibuprofen enantiomers, ibuprofen and paracetamol, or diclofenac and lumiracoxib, appear visibly similar. From a medicinal chemistry point of view, however, this assessment may not be generally agreed upon since small chemical differences can lead to important changes in specificity profiles (e.g., diclofenac vs lumiracoxib) or compounds containing different functional groups can be synthesized or derivatized in different ways (e.g., ibuprofen vs paracetamol). Hence, a medicinal chemist’s view of similarity might again be more local in nature and/or take chemical reaction information directly into account. Moreover, these COX inhibitors are involved in highly complex similarity−activity relationships that also cannot easily be separated from a medicinal chemistry perspective. For example, the (R)-(−)-enantiomers of ibuprofen and naproxen are inactive, but under physiological conditions the (R)-(−)-enantiomer of ibuprofen is converted into the active (S)-(+)-enantiomer by the enzyme 2arylpropionyl-CoA epimerase. Furthermore, paracetamol and lumiracoxib are selective for COX-2, but the other inhibitors are active against both COX-1 and COX-2, the former activity giving rise to gastrointestinal side effects. Moreover, naproxen alone is also active against hormone-sensitive lipase. Such examples illustrate that considerations of chemical and functional criteria might readily alter the perception of global molecular resemblance. Clearly, such similarity considerations fall into a gray zone, as they are influenced by subjective criteria as well as the experience of the investigator, and hence, there is no generally accepted way to judge such similarity relationships. Accordingly, relations between the cognitive and computational aspects of molecular similarity are discussed in more detail in the following section.

activities of the compounds against a panel of reference targets, generally proteins, that provide “biological signatures”19,20 analogous to the structure- or property-based representations extensively discussed herein. In this case, the activity profiles corresponding to the biological signatures of the compounds are compared using an appropriate similarity function as a measure of pairwise similarity, irrespective of the structural features of the compounds. Hence, in this case, biological similarity is assessed in target space rather than chemical space. For SAR analysis and medicinal chemistry programs, biological similarity is generally more difficult to implement than structure- or property-based representations because specific activity values might not be available for compounds of interest. In addition to their use as molecular similarity measures, biological signatures can also provide an approximate measure of compound promiscuity.21 For example, summing the individual values in a binary biological signature (active = 1 or inactive = 0) yields the number of targets against which the associated compound exhibits activity. Global versus Local Similarity. A very important criterion for similarity analysis is distinguishing between global and local similarity views. For example, the comparison of pharmacophore models in drug design focuses only on selected atoms, groups, or functionalities that are known or hypothesized to be responsible for activity. This represents a local view of similarity, in contrast to the more global view typically found in chemical informatics, where compounds are considered in their entirety. In the latter case, the calculated property or structural descriptors typically used to compute molecular similarities are generally derived from structural information associated with entire compounds. For example, if we translate the structural information of a compound into a fragment fingerprint, a global molecular representation is obtained. This whole-compound view of similarity is characteristic of the perspective of chemoinformaticians. Medicinal Chemistry Perspective. In addition to local and global views, however, special attention must also be paid D



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Figure 4. Similarity assessment through pattern recognition. Exemplary computer- and human-based pattern recognition processes for similarity assessment are illustrated.

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COGNITIVE VERSUS COMPUTATIONAL ASPECTS OF MOLECULAR SIMILARITY While similarity as perceived by trained medicinal chemists is decidedly not the same as similarity obtained by computational means, there are some aspects of the two that are comparable. For example, in both cases, some type of symbolic representation is required to characterize the structural information of the compounds being compared, although in the former case the representation is not explicitly stated. Regardless of their details, however, both types of symbolic representation must make molecular information comprehensible in such a way that structural/feature patterns can be identified and recognized. In general terms, pattern recognition refers to the ability to detect recurrent themes, organization principles, relationships, and rules in large data sets,22 an essential requirement for decision making by humans as well as for computational learning.22,23 The identification of patterns within data forms a basis for classification and directly applies to our molecular world. More than anything else, the recognition of molecular patterns, based on human or computational exploration, provides a basis for arriving at decisions as to whether two compounds are similar to each other or not. Since data complexity generally scales with the number of patterns that can be discovered, it quickly becomes impossible for humans to consider them in a comprehensive manner. Therefore, humans intuitively, and often unconsciously, reduce patterns to simpler ones that contain the essential feature(s) of the original pattern. But unlike applications of computational pattern recognition, the precise nature of these key patterns in human pattern recognition is unknown. For instance, to cross a road safely, we need to recognize patterns associated with moving objects and/or engine noise but are not required to understand which type of car or motorbike is approaching. This intuitive reductionist approach to pattern recognition is clearly reflected by decision-making by medicinal chemists, as further discussed below. Selecting key patterns regardless of whether they are mathematically defined or expressed in terms of vague

conscious or subconscious mental constructs is the most crucial element in any assessment of molecular similarity. The key patterns used by humans or computers will generally vary from individual to individual or from algorithm to algorithm, a situation that most likely will yield results with varying degrees of agreement for the same set of data. This follows because the representations used by humans and by computers, which most likely are significantly different, are crucial components in determining what can be understood about relationships of objects to each other, whether they are physical objects, concepts, ideas, or compounds. Despite the common search for key patterns, the use of representations to determine similarity in machine computation compared to human perception of similarity by medicinal chemists differs significantly,2 as schematically illustrated in Figure 4. In the case of machine computation, algorithms have been developed for constructing suitable representations of the structural information in compounds and for evaluating similarity functions or coefficients associated with these representations.4,24,25 However, since there is no unique or invariant way to represent molecular and chemical information, constructing representations suitable for a given task or goal depends on what is the task or goal. As noted earlier and discussed further below, mathematical functions that are designed to reflect the degree of molecular similarity typically yield values that lie on the unit interval [0, 1] of the real line. But as is also discussed below, the form of these functions also influences the similarity values because they usually differ even when identical representations are used, although in some cases they are linearly or monotonically related.2 Role of Chemical Intuition and Experience. Although well-defined, computed values may not account for the degree of similarity in a way that is consistent with the perceptions of medicinal chemists because human perception of similarity is a much more complicated, varied, and subtle task (vide supra). Moreover, the “cognitive algorithms” by which medicinal chemists perceive similarity are largely unknown, although some recent work has begun to address this question.26−28 These studies clearly show that chemical intuition and E



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(such as statistics, ecology, and psychology), have also been used to compare specific molecular representations. The Tanimoto coefficient is generally defined by c Tc(A, B) = (1) a+b−c

experience play major roles in decision making in medicinal chemistry. Surprisingly, there is typically little consensus between experienced medicinal chemists in judging preferred compounds and assessing favorable or unfavorable molecular features.26−28 Furthermore, it has been shown that perception of molecular structures is strongly context-dependent; i.e., depending on the order in which we view compounds and how they are grouped, different conclusions are drawn.27 This points to a potential advantage of computational similarity assessment because compound representations or patterns are constant and context-independent. It has also been shown that medicinal chemists often have difficulties comprehending the nature and meaning of the parameters they might have considered and the scientific criteria upon which decisions on compounds are based.28 Medicinal chemists typically base their compound decisions on very few patterns or parameters, fewer than they believe,28 a fact that clearly reflects the pattern-reduction approach referred to above. Decision parameters generally result from feature reduction and pattern reduction, which also provides a foundation of machine learning approaches.22,23 Computational methods such as neural networks,29 or support vector machines,30 are essentially designed for pattern-based similarity assessment, which requires training data the use of which also renders these computational modeling efforts context-dependent. The resulting computational models have the often cited “box black character”, which means that they cannot be interpreted in chemical terms. In some ways, this provides an interesting analogy to medicinal chemists who do not realize upon which parameters their compound decisions might be based.28 Although it may not be possible to rationalize our judgments, we are typically more content with our own decisions than those obtained computationally that, in many cases, can be difficult to interpret. Accordingly, machine learning methods such as decision trees31 or emerging chemical patterns32 are often favored in practice because they yield interpretable patterns, even though they may be based on rather abstract representations of molecular and chemical information. In light of the above, it is clear that judgments of molecular similarity can be influenced by a number of cognitive aspects. Lastly, with regard to the SPP, it should be re-emphasized that mere assessment of molecular similarity is generally not the ultimate goal. Rather, in many cases, it is the identification of similar compounds that, based on the SPP, are presumed to have similar properties (especially biological activities) to known reference or target compounds. This adds additional layers of complexity to our perception of similarity and can further complicate our judgments. Similarity Coefficients. The question then arises as to whether it is reasonable to assume that any “rationalization” of similarity, or that any consistent computational representation and comparison of compounds that yields a numerical readout, will increase our own consensus and be superior to subjective decisions. The Tanimoto coefficient (Tc)24,33 is introduced to help answer this and related questions and to provide an illustration of how molecular similarity can be quantified. Although it may not be the best procedure, it is by far the most popular and, because of its ease of implementation and speed, is in widespread use today in chemical informatics and computational medicinal chemistry. As detailed in the sequel, a variety of other similarity measures,24,25 most of which did not originate in chemical informatics but in other scientific fields

where a and b are the number of features present in compounds A and B, respectively, and c is the number of features shared by A and B. Hence, Tc quantifies the fraction of features common to A and B to the total number of features of A or B, where the c term in the denominator corrects for double counting of the features. Another perhaps more intuitive way to interpret Tanimoto similarity is based on an alternative form of the denominator on eq 1, i.e., a + b − c = (a − c) + (b − c) + c

(2)

Here the terms (a − c) and (b − c) are the number of features unique to A or B, respectively. Substituting eq 2 into eq 1 yields the numerically equivalent form of Tc, c Tc(A, B) = (a − c) + (b − c) + c (3) Dividing numerator and denominator by (a − c) + (b − c) gives Tc(A, B) =

R (a , b , c ) 1 + R (a , b , c )

(4)

where R (a , b , c ) =

c (a − c) + (b − c)

(5)

which can be interpreted as the ratio of the number of features shared by A and B to the number of their unique features. As A and B become more similar, the number of shared features approaches the number of features in A and B (i.e., c → a,b) and the number of unique features in both compounds approaches zero (i.e., (a − c) → 0 and (b − c) → 0) because in the limit the number of shared features and number of features in A and B become equal (i.e., a = b = c). Thus, their ratio goes to infinity, (i.e., R(a,b,c) → ∞), which in the limit gives Tc(A,B) = 1. Conversely, as A and B become less similar, the number of shared features approaches zero and consequently all of the features of A and B are unique, and thus, the ratio of these features also goes to zero (i.e., c → 0, (a − c) → a, (b − c) → b, and R(a,b,c) → 0); thus, in the limit, Tc(A,B) = 0. In the intermediate region where the number of shared features is greater than zero but less than the lesser of the number of features in A and B (i.e., 0 < c < min(a,b)) and where the number of unique features is less than the total number of possible features (i.e., (a − c) + (b − c) < a + b), the Tanimoto similarity will lie between the extremes of the unit interval of the real line, i.e., 0 < Tc(A,B) < 1. One way to think about this is to note that as the number of shared features between two compounds increases, their number of unique features must correspondingly decrease. Thus, there is interplay between the number of shared features and the number of unique features exemplified by their ratio R(a,b,c). The calculation of Tanimoto similarity is typically based on representations called “molecular fingerprints”,4,6,7 which can be viewed as classical sets or binary vectors whose elements have values of “1” or “0” corresponding, respectively, to the presence or absence of specific features (e.g., molecular F



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fragments). In some cases, elements with value “1” are called “on-bits“ and those with value “0” are called “off-bits“, hence, the description of molecular fingerprints as “bit strings” or “bit vectors”. Note that the molecular fingerprints described above do not account for multiple occurrences of the different features, only whether they occur at least once in a given compound. However, feature counts can be added to fingerprints by using integer values to represent features instead of a binary format. Fingerprints of different design and complexity are available,7 as further discussed below. For similarity searching, fingerprints are among the original and to this date most popular descriptors. Dissimilarity can be quantified in a complementary manner such that small values indicate similarity and large values dissimilarity. Accordingly, a dissimilarity measure can be derived from the Tc by taking the appropriate complement known as the Soergel distance (Sg),24 i.e., Sg(A, B) = 1 − Tc(A, B) = 1 −

c a+b−c

written here in a form that clearly shows that the denominator is the arithmetic mean of the number of features in A and B. Since 1/2(a + b) ≤ (a + b) − c, it follows that Tc(A,B) ≤ Dc(A,B), as illustrated by the distributions depicted in Figure 6. Both similarity coefficients are symmetric, since the similarity of A with respect to B is the same as the similarity of B with respect to A. In fact, any Tv in which α = β yields a symmetric similarity coefficient such that Tvα=β(A,B) = Tvα=β(B,A). Tversky similarity coefficients with two unequal weighting factors (α ≠ β) are, on the other hand, asymmetric, their degree of asymmetry depending on the relative magnitudes of the weighting factors. Similarity coefficients can be classified according to their compound ranking characteristics. Coefficients that always produce the same ranking of compounds, although their absolute similarity values might differ, are said to be monotonic. For example, Tvα,β(A,B) and Tvα′,β′(A,B) are monotonically related if the parameters have the same ratio so that α′ = kα and β′ = kβ. These coefficients can be converted into each other by the monotonic function

(6)

that can be rewritten as (a + b − c ) − c c = a+b−c a+b−c ( a − c ) + (b − c ) = a+b−c

Tvα′, β′(A, B) =

Sg(A, B) = 1 −

c α(a − c) + β(b − c) + c

(7)

(8)

Tvα = 1, β = 1(A, B) = Tc(A, B) ≤ Tvα = 1/2, β = 1/2(A, B) = Dc(A, B)

+ b)

(12)

An extreme form of Tv occurs when the reference compound A is weighted (α = 1) and the database compound is not (β = 0), in which case eq 8 becomes c Tvα = 1, β = 0(A, B) = (13) a In this case, the Tversky similarity coefficient provides a measure of how similar A is to B, which can be interpreted as the fraction of the features in the reference compound A that are matched by database compound B. Interchanging the values of the weighting factors so that now α = 0 and β = 1 places the entire weighting on the database compound B and gives c Tvα = 0, β = 1(A, B) = (14) b which in this case can be interpreted as the fraction of the database compound B that is similar to the reference compound A. These two forms of Tv represent extreme forms of Tversky similarity coefficients.

c 1 (a 2

(10)

Thus, Tversky similarity now only depends on the single parameter α. Note that differences in the numerical distribution of the normalized Tv and Tc are to a large extent due to the fact that the Tc corresponds to a non-normalized Tv under the condition α + β = 2. Furthermore, as clearly shown in Figure 6,

The denominator is closely related to that given for Tanimoto similarity in eq 3 except for the two parameters α and β that weight the number of features unique to A or B, (a − c) and (b − c), respectively. As defined by Tversky,34 α and β are nonnegative. In chemical informatics and computational medicinal chemistry applications, these parameters are typically chosen to lie within the unit interval [0, 1] of the real line. In either case, zero and unity bound the value of Tv. The larger α is compared to β, the more weight is put on the unique features of reference compound A and the less on database compound B and vice versa. Thus, in the case of Tv, whose values also range from 0 to 1, the similarity values change as the two weights vary. This makes it possible to study the relative importance of common and unique features for compound ranking with respect to the reference and database compounds. As discussed further below, the weighting scheme can be applied to introduce asymmetry into similarity calculations. For the special case α = β = 1, where the unique features of both compounds are weighted equally, Tv is identical to Tc. In the case where α = β = 0.5, Tv is identical to the Dice coefficient (Dc)24 Dc(A, B) =

+1−k

which can be verified by elementary algebraic transformations. Thus, normalization of the parameters imposes no restriction on the ranking and, hence, the generality of Tv. In the following, the sum of the weighting parameter values is restricted to unity, i.e., α + β = 1. Replacing β in eq 8 by 1 − α yields c Tvα(A, B) = α(a − c) + (1 − α)(b − c) + c c = αa + (1 − α)b (11)

As noted above, the denominators in eqs 1 and 3, a + b − c and (a − c) + (b − c) + c, respectively, represent the number of features that occur in either A or B, and the Tc can then be rationalized as the percentage of shared features, whereas the Soergel distance corresponds to the percentage of features unique to A or B given by (a − c) and (b − c), respectively. Another similarity measure that is growing in usage is the Tversky coefficient (Tv),34 which is given by Tvα , β(A, B) =

1 k Tvα , β(A, B)

(9) G



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intuitive perspective. Tversky similarity, which originated in psychology (not informatics), is conceptually based on a number of asymmetric characteristics that are associated with human perceptions of similarity. An example given by Tversky involves a comparison of Korea and China; the similarity of Korea to China is usually considered to be greater than the similarity of China to Korea. This view, which is rather general, suggests that relative size, however accounted for, has a significant influence on the perceived asymmetry of the similarity of entities, including compounds, when compared by humans. Moreover, this can also be interpreted in terms of eqs 13 and 14, since the “fraction” of Korea that is similar to China is definitely not the same as the “fraction” of China that is similar to Korea. Often it is not considered that the Tversky similarity coefficient is parametrized to account for asymmetric aspects of similarity by capturing the asymmetric characteristics inherent in many different types of objects under comparison. To understand, in light of the above, how human perception of the similarity of two compounds might be asymmetric, it is necessary to distinguish the compounds being compared. Let us consider an ordered pair in which A is a reference compound and B a database compound. If the reference A is a small compound and a substructure of a larger compound, A is rather similar to B. This follows because A is a close match to a part of B. However, if the situation is reversed, i.e., B is now used as the reference and A is the database compound, the similarity will be lower because most of B differs from A. This is a molecular example of the size effect described above in the case of the perceived asymmetric similarity comparisons of Korea and China. Equations 13 and 14 and the accompanying discussion fully support this analysis. In Tc calculations, this perceived asymmetric similarity relationship is not reflected, but Tv calculations offer this possibility as a consequence of appropriate weighting. Importantly, perceived relative size-dependent asymmetric similarity is distinct from representation-dependent molecular size or complexity effects mentioned above, which systematically bias similarity calculations by producing large values for larger and topologically more complex compounds. Human Perception. The assessment of similarity on the basis of human perception is considerably more complicated than reflected by the examples given above because a number of other conscious and subconscious factors also play a role. For example, a key factor in similarity assessment is the ability of humans, in general, and medicinal chemists, in particular, to intuitively reduce the complexity of the problem at hand (vide supra). This need to reduce complexity largely depends on the fact, as pointed out by numerous psychologists, that humans can only hold a relatively small number of things in their working memory at any point in time.40,41 Working memory is that part of memory that actively holds multiple pieces of transitory information that can be manipulated by verbal and nonverbal tasks, such as reasoning and comprehension, and makes the results of these tasks available for further information-processing. In the case of medicinal chemists this means that only structural features perceived to be most essential, or some simplified representation of them, might be retained and considered for similarity assessment, very consistent with the results obtained by Kutchukian et al.,28 indicating the partly unconscious use of only one or two chemical parameters by medicinal chemist in compound evaluation and decision making. Understanding these criteria, which will undoubtedly differ from medicinal chemist to

Increasing molecular size or complexity generally leads to increasing fingerprint bit densities, which are defined for a given compound A as ρFP (A) =

number of on‐bits total number of fingerprint bits

(15)

Such increases in the bit density ρFP(A) have a statistical tendency to yield higher similarity values for larger compounds,35 a well-known complication in similarity searching7 and a cause of apparent asymmetry in distributions of similarity values.36 Molecular complexity effects can be balanced or eliminated in different ways, for example, by equally taking into account bits that are set on or off in similarity calculations37,38 or by combining binary fingerprint representations with their complements, i.e., adding the complement to the original bit string, thereby producing a constant fingerprint bit density for compounds of any size.39 Calculating Tanimoto, Tversky, or Dice similarity has an assumed advantage that numerical values can now be used to distinguish similarity relationships in a consistent manner. How does this numerical approach from chemical informatics relate to, and perhaps influence, the more subjective assessment of similarity in medicinal chemistry? Are calculated similarity values suitable to replace chemical intuition and judgment? Computed versus Intuitive Similarity. There are a number of issues that arise when comparing computed similarity values with those assigned by medicinal chemists. One issue is that the similarity scale employed by medicinal chemists is not uniform. The following argument, which depends on the complementary nature of similarity and dissimilarity, illustrates this point. In computations the degree of dissimilarity is typically taken as the complement of similarity: dissimilarity = 1 − similarity

Hence, the more dissimilar two compounds are, the less similar they are to each other and vice versa. Importantly, such complementary behavior between computed similarity and dissimilarity values does not, however, apply in the case of human perception. For example, humans can better assess similarity the more similar compared objects are to each other. By contrast, as objects become less and less similar, a point is reached where it is generally difficult for humans to assess their degree of similarity or dissimilarity. Recall that in the former case one is dealing with features that are common to both compounds, whereas in the latter case one is dealing features that are unique to each of the compounds. This follows from the basic psychophysics of human perception because it is easier for humans to make comparative judgments of objects with common features than between objects whose features are unique. Since computed similarity values do not suffer from these problems, a divergence between human perceptions and computed values of similarity likely arises. In most cases, this is not a problem for medicinal chemists who typically want to synthesize and test compounds that are similar to known actives. Then, high calculated similarity values have an intuitive meaning. However, if similarity values are decreasing in size, boundaries between similarity and dissimilar become rather diffuse and one is often unable to interpret such values. The question of symmetry vs asymmetry of similarity, as formally discussed above, should also be considered from an H



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Figure 5. Frequency of fingerprint features. The relative frequency of occurrence of the 150 most frequent features of (a) MACCS and (b) ECFP4 is calculated for a random subset of 1 million ZINC database compounds.

using their in-house fingerprints and sets of active compounds, that a Tc value of 0.85 reflected a high probability that two compounds shared the same activity.43 For more than 15 years, this Tc value has propagated in the literature as a general threshold for bioactivity and has been applied in many practical applications, although the value is not reliable when other molecular representations are used for similarity calculations.4,7,44 Neighborhood behavior and calculated similarity values are strongly dependent on chosen molecular representations and similarity measures.4 While this is generally wellknown, it is often underappreciated in medicinal chemistry even today. The often-observed use of putative Tc threshold values of biological activity reflects common misunderstandings of similarity calculations. In the following, we present and discuss exemplary similarity calculations to highlight several characteristic features. Fingerprints of Different Design. In the following, two conceptually different fingerprints are compared that are popular in computational medicinal chemistry. The molecular access system (MACCS) fingerprint,13 also termed MACCS structural keys, is a prototypic fragment-based fingerprint that consists of 166 structural fragments with 1−10 non-hydrogen atoms and is one of the original and most popular similarity search tools.6,7 Its design is simple. Each bit position is assigned to one particular structural fragment or key and its presence or absence in a compound is detected. By contrast, we use the extended connectivity fingerprint (ECFP) with bond diameter four (ECFP4) that currently is one of the most popular fingerprints for similarity searching.14 ECFPs account for the local bond topologies, which describe the connectivity of atoms in the neighborhood of each nonhydrogen atom in a molecule. The size of the neighborhood depends on the so-called bond diameter given by the maximum number of bonds considered. The ECFP design is much more complex than MACCS because many different atom environment features can be generated. Different from MACCS, ECFP4 consists of sets of compound-specific features whose overlap is quantified as a measure of molecular similarity. Although many different atom environments can in principle exist, feature sets derived for individual compounds are often relatively small (e.g., containing less than 100 features), depending on their topology. Similarity Value Distributions. Although the definition of Tc yields an interpretable value as “the percentage of fingerprint features shared between two compounds”, it is very difficult to judge whether a given Tc value indicates the

medicinal chemist, is a nontrivial task. Thus, computed similarity values and judgments by medicinal chemists are both influenced by dependencies on molecular size and complexity, but the effect is much more pronounced and difficult to predict in the case of medicinal chemists’ assessments of similarity. The inconsistency of humans when confronted with complex decision tasks42 is well reflected by generally observed changes in medicinal chemists’ judgment about the quality of the same compounds when presented in different orders (vide supra).27 It is evident that medicinal chemists are often left with conscious or subconscious “impressions”, which they fold into their assessments of similarity in some implicit way, being intuitively aware of the complexity of the problem at hand, which then automatically leads to a reductionist approach in decision making. It is therefore not surprising that similarity calculations are attractive in medicinal chemistry because they reduce complex molecular comparisons to a simple numerical readout. Then, however, the key question becomes what such computed values actually mean.

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CHARACTERISTICS OF SIMILARITY CALCULATIONS In the following section, we highlight opportunities and limitations of similarity calculations in light of the above discussion. Thereby, we evaluate the apparent attractiveness of numerical similarity measures as a complement, or replacement, of human perception and study relationships between calculated and perceived similarities. Similarity Property Principle Revisited. A critically important aspect to realize is that most similarity methods do not explicitly take biological activity into account. Thus, similarity values generally reflect the similarity of chosen molecular representations. Yet this is hardly of interest in medicinal chemistry. Instead, chemoinformaticians and medicinal chemists typically attempt to bridge between calculated similarity and biological activity, well in accord with the SPP discussed above. In fact, the key question asked in this context typically is “Which Tc value reliably indicates that compound B has the same activity as reference compound A?” In other words, “How similar must A and B be to have the same activity?” This is the major attraction of reducing complex similarity relationships to simple numbers and the source of some profound misunderstandings of similarity calculation. The 0.85 Myth. In a seminal study quantifying chemical neighborhood behavior, investigators from Tripos established, I



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Figure 6. Similarity coefficient distributions. Distributions of similarity values resulting from 10 million comparisons of randomly chosen ZINC compounds are reported for the Tanimoto and Dice coefficient and the (a) MACCS and (b) ECFP4 fingerprint.

Figure 7. Comparison of similarity coefficients. For two thrombin inhibitors Dice, Tanimoto, and Tversky coefficients are compared using MACCS and ECFP4. Tversky similarity calculations were carried out using different parameter settings.

presence of “significant similarity” or not. This is the case because the coefficient value does not tell us anything about the specific features under comparison. For instance, many MACCS bit positions refer to structural features that are often found in compounds, whereas ECFP4 systematically encodes atom environments, many of which are infrequently found in compound data sets. For this reason, ECFP4 Tc values are generally smaller than MACCS Tc values. This difference in feature frequencies is illustrated in Figure 5 that reports the relative frequencies of the 150 most frequently detected MACCS and ECFP4 features in 1 000 000 compounds randomly selected from the ZINC (version 12) database.45 MACCS and ECFP4 fingerprints were calculated with the Molecular Operating Environment (MOE).46 Overall the ZINC subset contained 183 476 different ECFP4 features, but only 632 of these features occurred in more than 1% of the compounds. Considering the sparseness of most ECFP4 features, it is not surprising that some molecules that are structurally similar contain a significant number of unique

features. Importantly, the differences in feature distribution between MACCS and ECFP4 lead to very different distributions of similarity coefficient values. To illustrate these differences 10 000 000 similarity values were calculated for randomly chosen pairs of ZINC compounds. The results are shown for MACCS and ECFP4 Tc and Dc calculations in Figure 6, where it is clear that the Dc distributions are shifted toward higher values and are less symmetrical than the comparable Tc distributions. These effects are due to the normalization (α + β = 1) of the Dc and can be rationalized based on the discussions associated with eqs 9 and 11. Similar effects are, in general, observed for Tv, yielding distributions very similar to those of the Dc, regardless of the value of the parameter α. The figure shows that different combinations of fingerprints and similarity coefficients produce different similarity value distributions, further emphasizing the critically important point that calculated similarity has no absolute meaning. J



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Figure 8. Similarity searching using different fingerprints and similarity coefficients. By use of compound A from Figure 7 as a reference, similarity values were calculated for 1 million ZINC compounds and 25 thrombin inhibitors (including compound B from Figure 7) using the Tanimoto and Tversky (α = 0.1 and α = 0.9) coefficients and the (a) MACCS and (b) ECFP4 fingerprints. The similarity coefficient is plotted as a function of the rank (reported on on a logarithmic scale). The positions of the 25 thrombin inhibitors are marked on each curve.

searched and ranked using different similarity coefficients. In Figure 8, the ranks are displayed on the x-axis from low to high ranks on a logarithmic scale. On the y-axis, the corresponding coefficient values are reported. For each similarity coefficient, the position of the 25 thrombin inhibitors is marked. The graphs illustrate that compound ranks significantly vary depending on the coefficient and representation used. In this example, MACCS in combination with Tv and α = 0.9 yields the largest number of thrombin inhibitors within the top 1000 database compounds (corresponding to 0.1% of the screened database). However, it is stressed that no general conclusions about the relative performance of individual coefficients and fingerprints can be drawn from a single example given the strong compound class dependence of similarity calculations (vide infra). Similarity Threshold Values. Considering the global distributions of similarity values, it is of interest to derive threshold values that indicate a statistically significant level of similarity. Significance analysis of similarity values can be used, for instance, to determine if similarities between compounds sharing a property like biological activity might simply occur by chance or if compound similarity is likely to be associated with the shared property. For this purpose, conventional p-values can be calculated. For example, a Tc threshold value at a significance level of p = 0.01 would indicate a probability of 1% that the Tc value calculated for two randomly chosen compounds meets or exceeds the threshold. Threshold values can be estimated from the distribution of a large sample of similarity values obtained by randomly selecting pairs of compounds and calculating their similarity coefficient. The cumulative distribution function F(t) of the values then relates a similarity value t to the ratio of similarity values less than or equal to t, and the significance is given by p = 1 − F(t). If such threshold values are generally applicable in the context of similarity searching, i.e., if a similarity value exceeding a threshold value is a rare event and thus indicates significant similarity, they must be largely independent of the selected reference compound. It is emphasized at this point that only calculated similarity values and their statistics are considered; accounting for compound activity according to the SPP is addressed in the next subsection.

Although the global distribution of Tv values does not significantly depend on the settings of α, this parameter determines how similarity relative to a given reference molecule is perceived. If more weight is put on features (bit settings) of the reference molecule (i.e., if α > 0.5), different similarity relationships evolve. Compounds that contain most of the reference features plus some additional ones are considered to be more similar to the reference molecule than compounds that contain fewer of the reference features but also fewer additional features, although the percentage of shared features might be the same for both molecules. How different representations and similarity coefficients affect computed similarity values is illustrated in Figure 7, using two exemplary thrombin inhibitors taken from the ChEMBL (version 15)47 database. Both molecules contain more ECFP4 features than MACCS features, but the number of shared features is lower for ECFP4, as expected on the basis of the feature distributions discussed above. Consequently, the different coefficients produce significantly lower similarity values for ECFP4. Dc is increased compared to Tc as shown in the discussions related to eqs 9 and 12. Because Dc is identical to normalized Tv with α = 1, its value can be numerically compared to the asymmetrical Tv values with parameters α = 0.1 and α = 0.9, respectively. It can be observed that Tv decreases for α = 0.1 and increases for α = 0.9. In the first case, more weight is put on the features exclusive to molecule B, and in the second case, less weight is put on these features. Thus, the influence of these features on the similarity value is either increasing or decreasing compared to Dc. Changing α has an effect on computed similarity values. More importantly, however, the parameter also influences how similarity is perceived in a search when database compounds are ranked in the order of decreasing similarity to a reference molecule. Here, the absolute value of similarity is not of interest, especially if the value cannot be interpreted in a meaningful way. Rather, the rank positions of compounds with the desired properties determine the usefulness of a similarity coefficient. Figure 8 illustrates the effect that the choice of different similarity coefficients has on the ranking of compounds in a similarity search. Molecule A in Figure 7 was taken as a reference, and 1 000 000 ZINC compounds together with molecule B and 24 other thrombin inhibitors were K



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Figure 9. Threshold values of similarity coefficients versus significance levels. Cumulative distribution functions were generated for different similarity coefficients and two fingerprints by selecting 100 random reference compounds from the ZINC database and calculating the similarity to the remaining ZINC compounds from the subset of selected compounds according to Figure 5. The graphs on the left show the median as well as first and third quartile cumulative distribution function F(t) derived from the 100 sampled distributions. On the right, threshold values (y-axis) are shown depending on different levels of significance (x-axis) on a logarithmic scale. The median threshold values as well as the first and third quartile threshold values are reported: (a) MACCS and Tc; (b) MACCS and Tv(α=0.9); (c) ECFP4 and Tc; (d) ECFP4 and Tv(α=0.9).

case, their similarity to all remaining ZINC compounds in a ZINC sample was calculated. Not surprisingly, search profiles for individual reference compounds generally differed. On the

To illustrate the influence of different reference compounds on similarity calculations, search profiles were generated for 100 compounds randomly chosen from the ZINC database. In each L



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Figure 10. Similarity value distributions for active compounds. The distribution of similarity coefficient values for compounds sharing the same activity is reported for 10 exemplary compound activity classes taken from the ChEMBL database. The boxplot representations provide quartile and median similarity values for all compound comparisons. The whiskers represent the most extreme data points within the 1.5 interquartile range for the lower and upper quartiles, respectively. Data points falling outside this range are not shown. On the x-axis, the ChEMBL target identifiers (Ids) are provided for each class: 11, thrombin; 43, β-2 adrenergic receptor; 72, dopamine D2 receptor; 86, monoamine oxidase A; 194, coagulation factor X; 214, muscarinic acetylcholine receptor M4; 10 498, cathepsin L;11 003, melanocortin receptor 3; 11 060, carbonic anhydrase VII; 11 627, acyl coenzyme cholesterol acyltransferase.

Do Activity-Relevant Similarity Threshold Values Exist? Although the above considerations highlight the principal limitations of similarity calculations from a statistical point of view, they do not consider similarity from the perspective of a medicinal chemist. In this case, the SPP takes center stage and raises the issue of whether calculated similarities can serve as indicators of activity similarity. This directly relates to the “0.85 myth” discussed above and represents one of the most important applications of quantitative molecular similarity analysis in medicinal chemistry. To address this question, similarity calculations must be carried out for compounds having different specific activities. Therefore, 10 exemplary compound activity classes were taken from ChEMBL (version 15).47 Each compound was required to have a pKi value of at least 7 for its designated target (thus limiting the analysis to potent compounds with available highconfidence activity measurements). Similarity values were then calculated for all pairs of compounds sharing the same activity. The results of these calculations are reported in Figure 10. Regardless of the fingerprint representations and similarity coefficients used, the observed similarity value distributions for active compounds strongly depended on the compound activity class. For example, median MACCS Tc values varied from ∼0.3 to ∼0.75 depending on the class. As shown in Figure 9a, a MACCS Tc threshold value of ∼0.65 corresponds to a statistically significant similarity at the level of p = 0.01. It follows that most compounds active against a given target

basis of these profiles, a significance level (p-value), given by the ratio of the number of compounds whose similarity values with respect to the reference compound exceed the given threshold, was assigned to every reference compound for each threshold value in the range 0−1. This yielded 100 curves relating threshold values to p-values. Figure 9 reports cumulative distribution functions and threshold values as a function of the significance level for different similarity coefficients with respect to the MACCS and ECFP4 fingerprints. The graphs on the left depict the median as well as first and third quartile sampled cumulative distribution functions, while the graphs on the right report the Tc threshold value as a function of the p-value. These graphs are obtained from the cumulative distribution function by exchanging the x- and y-axis and by plotting the p-values on a logarithmic scale in order to enhance the visual resolution for low p-values indicating high significance. Shown are the median threshold values and the interquartile ranges of the thresholds obtained from the original 100 curves. From the curves, it is apparent that statistically significant similarity threshold values strongly depend on the fingerprint representation and the similarity coefficient that are used. In addition, there are large variations in threshold value depending on the reference compounds. Thus, although threshold values might be associated with statistically significant similarity, without taking activity into account, they are not transferable and are associated with large margins of error, due to the dependence on reference compounds, as illustrated in Figure 9. M



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all combinations of fingerprints and similarity coefficients. These findings illustrate that generally applicable similarity threshold values as a potential indicator of activity similarity do not exist. Such values also cannot be derived with any certainty for individual compound classes, as revealed by the variability of similarity values and lack of general statistical significance.

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PRACTICAL CONSIDERATIONS Calculated similarities, regardless of how we perceive them from a medicinal chemistry perspective, strongly depend on the compound classes under study as well as the molecular representations (descriptors) and similarity measures used.48,49 If multiple reference compounds are employed, the results of similarity calculations must be combined in some ways, typically through the application of data fusion techniques,50 which further complicates matters. The results discussed above illustrate that calculated similarity values do not enable us to relate molecular and activity similarity in a meaningful way to each other and that it is impossible at present to establish generally applicable threshold values indicating that two compounds share the same activity. Does all this mean that similarity calculations have no utility in medicinal chemistry? The answer is no. The key issue is to understand what similarity calculations can and cannot provide for. As long as one believes that the magnitude of computed similarity measures has

Figure 11. Average Tc threshold values for scaffold recall rates. For MACCS (blue) and ECFP4 (red), the average Tc threshold value required to achieve a specified scaffold recall rate is reported. The variations of these Tc values across all trials are reported as error bars for recall rates of 25%, 50%, and 75%. Numbers next to the error bars give the median database selection set size for which the recall rate is achieved. The figure was adapted from ref 53.

yielded similarity values that varied greatly and were not statistically significant. Equivalent observations were made for

Figure 12. Early enrichment of active compounds with different scaffolds. Two exemplary reference compounds and a set of active compounds having different scaffolds are shown that were found in the 100 top-ranked database compounds (individual ranks are reported). At the top, κ opioid receptor ligands are shown and at the bottom human immunodeficiency virus type 1 protease inhibitors. N



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Figure 13. Compound ranks in virtual screening. Results from virtual screening trials are shown leading to the identification of new inhibitors of the Sec-7 domain of cytohesins (Secin 16, 87, and 144). Two reference compounds are shown. For each of the three hits, rank positions are reported for four alternative search strategies including support vector machine (SVM) calculations with two fingerprints (FP 1 and FP 2) as descriptors as well as similarity searching with two fingerprints using a single reference compound (FP 1, reference 1 and FP 3, reference 2).

elements corresponds to a high probability that reference and database compounds share the same activity. In contrast to pharmacophore-based searching, fingerprint similarity searching, which is based on a whole-molecule assessment of similarity, does not require pharmacophore hypotheses or specific knowledge about activity-relevant features of compounds. It is applicable when very little is known except the activities of the reference compound(s) used in the search. No activity information associated with specific substructural features in the fingerprints is required, only the assumption that the SPP is applicable. Importantly, similarity searching produces a ranking of database compounds in the order of decreasing computed similarity values relative to the reference compound(s). In this case, absolute similarity values are not relevant except on a relative scale for ranking of compounds. A database ranking starts with compounds that are most similar to the reference compound(s), typically closely related analogues, and as we proceed further down the ranking, database compounds become increasingly dissimilar but might nonetheless be active. In a study designed to assess the scaffold

immediate implications for activity and that their values scale, in one way or another, with a probability of activity, little can be expected. Meaningful applications of similarity calculations can, however, be considered if one is aware of these limitations. Computed Similarities on a Relative Scale. One of the major applications of similarity analysis is ligand-based virtual screening, where one or more active reference compounds are used to search databases to identify other compounds with similar structures and, by the SPP, hopefully, with similar activities.4−7 Such searches can be carried out on the basis of local or global similarity methods. For example, pharmacophore searching51 is based on local similarity and attempts to identify all database compounds that match a predefined pharmacophore query, regardless of the remaining substructures. Such calculations can be carried out to identify structurally diverse compounds having similar activities, a procedure commonly referred to as scaffold hopping.52 The horizontal compound relationship in Figure 2 represents an example of a scaffold hop. Pharmacophore searching typically produces a “pass−fail” readout and identifies a set of compounds that match the query. It is assumed that close resemblance of pharmacophore O



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hopping potential of similarity searching,53 it has been shown that Tc threshold values cannot be determined that indicate a significant enrichment of structurally diverse active compounds in database rankings. Figure 11 summarizes search results for MACCS and ECFP4 over different activity classes.53 Average Tc values are reported for the fraction of active database compound series with distinct scaffolds for which at least one active compound was detected. Error bars are shown for Tc values at which compounds represented by 25%, 50%, or 75% of all “active scaffolds” were detected. The numbers at the error bars indicate the median ranks of these active compounds. For example, to detect active compounds for 25% of all available scaffolds, ∼1% (5488) of all database compounds had to be selected on average for MACCS and ∼0.5% (2,360) for ECFP4. The large error bars indicate that it was not possible to define Tc threshold values for the retrieval of structurally diverse active compounds across different compound classes. In essentially all calculations, however, a few active compounds with scaffolds different from the reference compounds were found at relatively high rank positions, as shown in Figure 12. Thus, the calculations show that scaffold hops can be detected, although large numbers of other database compounds had to be selected to achieve a significant scaffold recall of 25% or more. These findings illustrate the resolution limits of whole-molecule similarity searching. Nevertheless, similarity searching is relevant for many practical applications. The attractiveness of similarity-based compound rankings in medicinal chemistry is that they provide a continuum of compound similarity relationships that can be intuitively assessed. Although we do not know precisely where active compounds with different scaffolds might be found in similarity-based ranked lists, inspecting the rankings enables compound selection on the basis of chemical intuition and experience. In this case, the chemical informatics and medicinal chemistry perspectives meet. Figure 13 shows the results of a practical virtual screening application54 that exemplifies the opportunities of similarity searching. The study was designed to identify new inhibitors of cytohesins,55 a family of small guanine nucleotide exchange factors, by virtually screening a large compound database containing 3.7 million compounds. Three newly discovered structurally diverse inhibitors54 and their database ranks produced by four related yet distinct search strategies are reported. The positions of the inhibitors in the database rankings show a remarkable spread. Two of these active compounds were highly ranked by one search strategy (ranks 7 and 35, respectively) but vanished in the database background when the others were applied. The highest rank obtained for the third inhibitor was 354, and this compound could only be selected on the basis of visual inspection of rankings and intuition because a total of only 145 compounds taken from different rankings were experimentally tested.54 Nearest Neighbor Analysis. Another application of similarity calculations that is relevant to medicinal chemistry and is also independent of absolute similarity values is the mapping of the chemical neighborhood of compounds. Similarity calculations can easily retrieve the k-nearest nearest neighbors, i.e., k most similar compounds, to a given compound from any collection.50 The similarity radius, i.e., the range of similarity values considered with respect to a specific reference compound, can be easily adjusted, thereby increasing or decreasing the number of compounds for inspection. Such nearest neighbor calculations enable chemical interpretation of

limited numbers of similarity relationships and are useful, for example, in support of hit expansion studies or in the generation of focused compound libraries. Since the mapping of chemical neighborhoods does not require sophisticated molecular representations, simple fragment-based fingerprints can be used effectively. Rendering Fingerprint Calculations Comparable. Although similarity threshold values of activity do not exist, it is possible to determine corresponding Tc or other related coefficient values for different fingerprints that are met or exceeded by the same proportion of compound pairs in large databases. For example, in systematic similarity-based search calculations on 128 compound data sets taken from ChEMBL, 12% of all possible compound pairs reached or exceeded a MACCS Tc value of 0.70.56 The same proportion of compound pairs was obtained for an ECFP4 Tc of 0.31, thus establishing an approximate correspondence of these Tc values for the two fingerprints. Following this approach, it is possible to map corresponding Tc values for different fingerprints that select the same percentage of compound pairs.56 Such correspondences depend to some extent on the composition of the compound collection under study. Figure 14 reports correspondence

Figure 14. Corresponding Tc values for MACCS and ECFP4. Distributions of MACCS and ECFP4 Tc values were determined by conducting 10 million comparisons between randomly selected ZINC compounds (according to Figure 6). Correspondence between MACCS and ECFP4 Tc values was established by relating those Tc values to each other that were met or exceeded by the same percentage of comparisons (indicated as labeled points on the curve).

between MACCS Tc and ECFP4 Tc values established on the basis of the randomly sampled distributions shown in Figure 6. Selected points on the curve are highlighted that correspond to certain fractions of compound comparisons meeting or exceeding the corresponding MACCS Tc (x-axis) or ECFP4 Tc (y-axis) values. The curve illustrates the representation dependence of similarity values. Furthermore, it provides a guideline for assessing the significance of similarity values obtained for a newly introduced fingerprint on the basis of a standard fingerprint (such as MACCS) with which many investigators are familiar. Dissimilarity Selection. The selection of compounds that are most dissimilar to those of an existing collection has a long history in compound acquisition in the pharmaceutical industry.57,58 It is also a meaningful application of similarity/ dissimilarity calculations. In this case, the interest is in the P



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whole-molecule view, as is often done in chemical informatics, or focuses on pharmacophores or functional groups (i.e., local molecular information), as is typically the case in medicinal chemistry. Furthermore, the modeling of activity landscapes, which integrates compound similarity and activity relationships,63 often leads to rather different interpretations by computational and medicinal chemists when calculated similarity values are used. Moreover, attempts to interpret calculated similarity values and differences between them in structural terms might often cause confusion. Similarity calculations are nevertheless of considerable interest in medicinal chemistry. In addition, because human assessment depends significantly on the knowledge and experience of medicinal chemists, it is not surprising that calculated similarity values are often seen as an attractive means of decision support. However, we also note that many similarity search and benchmark studies reported in the computational literature lack proper statistical assessment, which complicates the comparison and interpretation of calculated similarity values. Probably the largest conceptual roadblock to computational similarity analysis is that the quantitation of chemical or molecular similarity is generally not of interest per se but rather the extrapolation from calculated similarity values to other molecular properties, in particular, biological activity. There are no well-defined relationships between calculated similarity and activity similarity and no similarity threshold values that reliably indicate whether a test compound shares the activity of a reference compound, a situation that is further confounded by the presence, albeit rare, of activity cliffs.10,11 These issues frequently gives rise to misunderstandings in medicinal chemistry. Moreover, similarity calculations are strongly dependent on compound classes, molecular representations, and similarity measures, which complicates their interpretation and practical application. If one is aware of these caveats, computational similarity analysis provides a number of meaningful and useful medicinal chemistry-relevant applications. For example, similarity calculations often aid in compound selection if the focus is not on the absolute magnitude of the similarity values but rather on their relative magnitudes, which determines the ranking of compounds and is decidedly more robust to differences in similarity values that arise from the use of different similarity measures. Despite current limitations, computational similarity analysis has its place in drug development, if applied in a considerate manner, to complement and further expand medicinal chemists’ perception(s) of molecular similarity. For fundamental reasons, it is not possible to eliminate subjective elements from similarity assessments, which puts strong emphasis on the careful interpretation of computational results. The development of computational similarity methods with reduced compound class dependence will be an important topic for future research. In addition, the exploration of new concepts to account for biological similarity of small compounds will be equally attractive.

extreme values of a distribution of similarity values, not the largest ones as in the case of nearest neighbor analysis but rather the smallest ones because of the complementary relationship between similarities and dissimilarities. Different algorithms have been produced for dissimilarity selection.57,58 Regardless of their specific details, many of these methods are based upon pairwise similarity calculations of library and external candidate compounds.

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CONCLUDING REMARKS The present review provides an overview of the foundations of molecular similarity analysis and describes a number of different similarity-based concepts relevant to medicinal chemistry. As is well-known, the principal difficulty associated with similarity analysis is that similarity itself is an inherently subjective concept so that absolute standards do not exist. Nonetheless, a wide variety of computational approaches have been developed in an attempt to account for molecular similarity in a formally consistent and unbiased manner. Although this may be a daunting task, it remains a critically important endeavor because of the power that the concept of molecular similarity brings to the practice of chemistry in general and to medicinal chemistry in particular. Long before computational methods for treating molecular similarity were developed, chemists employed similarity in a number of areas of chemistry, a particularly noteworthy example being the development of the periodic table.59 The similarity concept provides a framework, albeit an imperfect one, for assessing the similarity of compounds, which is one of the central tasks in medicinal chemistry. Since an individual’s capacity to judge similarity relationships is limited to fairly small numbers of relatively simple compounds, computational approaches are indeed essential in modern medicinal chemistry, despite their limitations. This raises a key issue, namely, how medicinal chemists perceive molecular similarity and how this perception relates to similarity evaluated computationally. A brief discussion is provided here describing some of the cognitive aspects of similarity perception and its strong association with human pattern recognition and reduction because they affect the subjective decisions of medicinal chemists. Clearly, similarity considerations strongly influence which compounds are made, and these compounds then essentially reflect our views of similarity. This might often limit the spectrum of compounds that are considered and prevent the exploration of chemically unusual ones that fall outside our similarity perception. On the other hand, for many therapeutic targets there is a large number of structurally diverse active compounds available,60 a knowledge base that is often more considered in chemical informatics than medicinal chemistry. Given the medicinal chemistry focus of our presentation, we have based our methodological considerations on 2D similarity calculations. However, from a computational perspective, 3D similarity methods are of course equally relevant.61,62 Regardless of the methods used, however, 3D similarity assessment in drug design remains affected by the uncertainties associated with extrapolating from computed to often unknown bioactive compound conformations. Without doubt, similarity is often viewed differently in chemical informatics and medicinal chemistry. This is exemplified by global and local comparisons of compounds. We have rationalized that similarity relationships might fundamentally change depending on whether one applies a

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AUTHOR INFORMATION

Corresponding Authors

*G.M.: phone, 520-405-4736; e-mail, gerry.maggiora@gmail. com. *J.B.: phone, 49-228-2699-306; e-mail, [email protected]. de. Notes

The authors declare no competing financial interest. Q



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Biographies

(2) Medina-Franco, J. L.; Maggiora, G. M. Molecular Similarity Analysis. In Chemoinformatics for Drug Discovery; Bajorath, J., Ed.; John Wiley and Sons: Hoboken, NJ, in press. (3) Kubinyi, H. Similarity and Dissimilarity: A Medicinal Chemist’s View. Perspect. Drug Discovery Des. 1998, 9−11, 225−232. (4) Eckert, H.; Bajorath, J. Molecular Similarity Analysis in Virtual Screening: Foundations, Limitations and Novel Approaches. Drug Discovery Today 2007, 12, 225−233. (5) Koeppen, H. Virtual ScreeningWhat Does It give Us? Curr. Opin. Drug Discovery Dev. 2009, 12, 397−407. (6) Willett, P. Similarity-Based Virtual Screening Using 2D Fingerprints. Drug Discovery Today 2006, 11, 1046−1053. (7) Stumpfe, D.; Bajorath, J. Similarity Searching. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2011, 1, 260−282. (8) Johnson, M.; Maggiora, G. M., Eds. Concepts and Applications of Molecular Similarity; John Wiley & Sons: New York, 1990. (9) Maggiora, G. M. On Outliers and Activity CliffsWhy QSAR Often Disappoints. J. Chem. Inf. Model. 2006, 46, 1535−1535. (10) Stumpfe, D.; Bajorath, J. Exploring Activity Cliffs in Medicinal Chemistry. J. Med. Chem. 2012, 55, 2932−2942. (11) Stumpfe; D.; Hu,Y.; Dimova, D.; Bajorath, J. Recent Progress in Understanding Activity Cliffs and their Utility in Medicinal Chemistry. J. Med. Chem. [Online early access]. DOI: 10.1021/jm401120g. Published Online: Aug 27, 2013. (12) Raymond, J. W.; Willett, P. Maximum Common Subgraph Isomorphism Algorithms for the Matching of Chemical Structures. J. Comput.-Aided Mol. Des. 2002, 16, 521−533. (13) MACCS Structural Keys; Accelrys: San Diego, CA. (14) Rogers, D.; Hahn, M. Extended-Connectivity Fingerprints. J. Chem. Inf. Model. 2010, 50, 742−754. (15) Good, A. C.; Richards, W. G. Explicit Calculation of 3D Molecular Similarity. Perspect. Drug Discovery Des. 1998, 9−11, 321− 338. (16) Rush, T. S.; Grant, J. A.; Mosyak, L.; Nicholls, A. A Shape-Based 3-D Scaffold Hopping Method and Its Application to a Bacterial Protein−Protein Interaction. J. Med. Chem. 2005, 48, 1489−1495. (17) Brown, R. D.; Martin, Y. C. The Information Content of 2D and 3D Structural Descriptors Relevant to Ligand−Receptor Binding. J. Chem. Inf. Model. 1997, 37, 1−9. (18) McGaughey, G. B.; Sheridan, R. P.; Bayly, C. I.; Culberson, J. C.; Kreatsoulas, C.; Lindsley, S.; Maiorov, V.; Truchon, J.-F.; Cornell, W. D. Comparison of Topological, Shape, and Docking Methods in Virtual Screening. J. Chem. Inf. Model. 2007, 47, 1504−1519. (19) Fliri, A.; Loging, W.; Thadeio, P. F; Volkmann, R. Biological Spectra Analysis: Linking Biological Activity Profiles to Molecular Structure. Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 261−266. (20) Petrone, P. M.; Simms, B.; Nigsch, F.; Lounkine, E.; Kuthukian, P.; Cornett, A.; Deng, Z.; Davies, J. W.; Jenkins, J. L.; Glick, M. Rethinking Molecular Similarity: Comparing Compounds on the Basis of Biological Activity. ACS Chem. Biol. 2012, 7, 1399−1409. (21) Hu, Y.; Bajorath, J. Compound Promiscuity: What Can We Learn from Current Data? Drug Discovery Today 2013, 18, 644−650. (22) Duda, R. O.; Hart, P. E.; Stork, D. G. Pattern Classification; Wiley: New York, 2001. (23) Bishop, C. M. Pattern Recognition and Machine Learning; Springer: Berlin, 2006. (24) Willett, P.; Barnard, J. M.; Downs, G. M. Chemical Similarity Searching. J. Chem. Inf. Comput. Sci. 1998, 38, 983−996. (25) Maggiora, G. M.; Shanmugasundaram, V. Molecular Similarity Measures. Methods Mol. Biol. 2004, 275, 1−50. (26) Takaoka, Y.; Endo, Y.; Yamanobe, S.; Kakinuma, H.; Okubo, T.; Shimazaki, Y.; Ota, T.; Sumiya, S.; Yoshikawa, K. Development of a Method for Evaluating Drug-likeness and Ease of Synthesis Using a Dataset in Which Compounds Are Assigned Scores Based on Chemists’ Intuition. J. Chem. Inf. Comput. Sci. 2003, 43, 1269−1275. (27) Lajiness, M. S.; Maggiora, G. M.; Shanmugasundaram, V. Assessment of the Consistency of Medicinal Chemists in Reviewing Sets of Compounds. J. Med. Chem. 2004, 47, 4891−4896.

Gerald Maggiora studied chemistry and biophysics at the University of California at Davis, earning a Ph.D. in biophysics. He spent more than 20 years as Professor of Chemistry and Biochemistry, University of Kansas, and Professor of Pharmaceutical Sciences, University of Arizona. He spent an equal amount of time in the pharmaceutical industry as a Director of Computer-Aided Drug Discovery and Senior Research Scientist. His interests include molecular and mathematical modeling, scientific applications of computer-aided decision making, drug design, and applications of fuzzy mathematics and rough set theory to biological and medical problems. For more than 2 decades he has focused on chemical informatics and molecular similarity. In 2008 he received the Herman Skolnik Award, Division of Chemical Information of the American Chemical Society. Martin Vogt studied mathematics and computer science at the University of Bonn, Germany, and holds a degree in computer science. He currently is a Research Associate in the Department of Life Science Informatics at the University of Bonn where he also completed his doctoral thesis on Bayesian methods for virtual screening under the guidance of Prof. Jürgen Bajorath. Previously, he was employed at the Fraunhofer Institute for Applied Information Technology (FIT) where he worked on image recognition algorithms for bioinformatics applications. His research interests include algorithmic method development in chemoinformatics, especially focusing on data mining and machine learning methods. Dagmar Stumpfe studied biology at the University of Bonn, Germany. In 2006, she joined the Department of Life Science Informatics at the University of Bonn headed by Prof. Jürgen Bajorath for her Ph.D. thesis, where she worked on methods for computer-aided chemical biology with a focus on the exploration of compound selectivity. Since 2009, Dagmar has been working as a Postdoctoral Fellow in the department, and her current research interests include computational chemical biology and large-scale structure−activity relationship analysis. Jürgen Bajorath studied biochemistry at the Free University, Berlin. Beginning with postdoctoral studies in San Diego, CA, he spent more than 15 years in the United States. He currently is Professor and Chair of Life Science Informatics at the University of Bonn, Germany. He is also an Affiliate Professor in the Department of Biological Structure at the University of Washington, Seattle. His research interests include drug discovery, computer-aided medicinal chemistry and chemical biology, and chemoinformatics (http://www.lifescienceinformatics. uni-bonn.de).

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ACKNOWLEDGMENTS D.S. is supported by Sonderforschungsbereich 704 of the Deutsche Forschungsgemeinschaft.

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ABBREVIATIONS USED COX, cyclooxygenase; Dc, Dice coefficient; ECFP,extended connectivity fingerprint; FP, fingerprint; HSL, hormonesensitive lipase; MACCS, molecular access system; SAR, structure−activity relationship; Sg, Soergel distance; SPP, similarity property principle; SVM, support vector machine; Tc, Tanimoto coefficient; Tv, Tversky coefficient; 2D, twodimensional; 3D, three-dimensional

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REFERENCES

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Perspective

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