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Research Article

Activity-relevant similarity values for fingerprints and implications for similarity searching

[version 1; peer review: 3 approved]
PUBLISHED 06 Apr 2016
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Abstract

A largely unsolved problem in chemoinformatics is the issue of how calculated compound similarity relates to activity similarity, which is central to many applications. In general, activity relationships are predicted from calculated similarity values. However, there is no solid scientific foundation to bridge between calculated molecular and observed activity similarity. Accordingly, the success rate of identifying new active compounds by similarity searching is limited. Although various attempts have been made to establish relationships between calculated fingerprint similarity values and biological activities, none of these has yielded generally applicable rules for similarity searching. In this study, we have addressed the question of molecular versus activity similarity in a more fundamental way. First, we have evaluated if activity-relevant similarity value ranges could in principle be identified for standard fingerprints and distinguished from similarity resulting from random compound comparisons. Then, we have analyzed if activity-relevant similarity values could be used to guide typical similarity search calculations aiming to identify active compounds in databases. It was found that activity-relevant similarity values can be identified as a characteristic feature of fingerprints. However, it was also shown that such values cannot be reliably used as thresholds for practical similarity search calculations. In addition, the analysis presented herein helped to rationalize differences in fingerprint search performance.

Keywords

Bioactive compounds, molecular similarity, similarity-property principle, similarity searching, fingerprints, Tanimoto coefficient, activity similarity

Introduction

Calculation of molecular similarity is a central task in chemoinformatics14 for which a variety of methods, chemical descriptors, and similarity measures have been introduced17. A key aspect of the molecular similarity concept is that one often attempts to extrapolate from calculated similarity to activity similarity. In other words, it is assumed that increasing chemical similarity correlates with an increasing likelihood that two compounds share the same activity, in accord with the similarity-property principle (“similar compounds should have similar properties”)1; a major foundation of chemoinformatics. A methodological consequence of the molecular similarity concept and similarity-property principle was the introduction of similarity searching for active compounds2,6. Here, similarity values are calculated for known active reference and database compounds, which are then ranked in the order of decreasing similarity to the reference(s). Classical molecular descriptors for these search calculations include 2D-fingerprints, i.e. bit string representations of chemical structures and/or properties derived from molecular graphs2,8,9. The overlap between fingerprints is quantified as a measure of molecular similarity using metrics such as the Tanimoto coefficient (Tc)2,7; the gold standard in the chemoinformatics field. For a pair of compounds represented by fingerprints, its Tc value is calculated as the ratio between the number of features conserved in both fingerprints and the number of features present in either fingerprint. Accordingly, the Tc is a numerical measure of similarity ranging from zero (no fingerprint overlap) to one (fingerprint identity).

Similarity search calculations exemplify the similarity conundrum in chemoinformatics: the ultimate goal is the identification of new active compounds on the basis of similarity, but activity information is not used as a search parameter. It has been shown that generally applicable Tc threshold values as an indicator of activity similarity do not exist9. This is the case because similarity value distributions are compound class- and fingerprint-dependent. To further complicate matters, it has also been shown that 2D-fingerprints successfully detect structurally diverse active compounds at varying similarity levels9,10. In general, a continuum of similarity values is produced that may or may not indicate activity similarity, depending on the characteristics of active compounds.

A limited number of attempts have been made to associate calculated similarity with observed activity similarity. For example, early investigations of compound clustering, molecular diversity, and chemical neighborhood behavior using fingerprints have indicated that, on average, 85% of compounds that yielded a Tc value of 0.85 compared to a known active molecule were also active1113. These findings were based on MACCS keys14, a classical fingerprint in chemoinformatics consisting of a dictionary of 166 structural fragments, as well as UNITY fingerprints13 that assemble atom pathways of pre-defined lengths. However, using connectivity pathway fingerprints of different design and biological screening data to analyze the relationship between calculated similarity and observed activity similarity, it was concluded that there was only a likelihood of 30% that compounds yielding a Tc value of at least 0.85 shared the same activity15. In addition, Kullback-Leibler divergence analysis from information theory and Bayesian modeling were combined16 to predict the recall of active compounds from fingerprint similarity searching and a conditional correlated Bernoulli model of similarity value distributions was developed17 to predict database rankings. Furthermore, belief theory was applied to empirically derive probabilistic relationships between calculated similarity and activity on the basis of similarity search benchmark calculations18. In this study, MACCS keys and extended connectivity fingerprints (ECFPs)19 were used, among others. ECFPs capture layered atom environments in compounds up to a pre-determined bond diameter. When different fingerprints were compared in benchmark calculations ECFPs often yielded highest similarity search performance8,9. On the basis of probability assignment curves that related activity and similarity values for pairs of compounds to each other, it was shown, for example, that at a Tc value of 0.85 calculated with atom pathway fingerprints, ~30% of detected compound pairs shared the same activity18, consistent with earlier observations15. For an ECFP with bond diameter 6 (ECFP6), a Tc threshold of 0.42 yielded comparable results18.

Other types of fingerprints were generated exclusively on the basis of experimental activity observations, e.g. activities measured in panels of screening assays20, or by combining chemical and biological criteria21. These studies departed from the conceptual framework of the similarity-property principle by using activity data as descriptors and -completely or partly- circumventing similarity calculations on the basis of molecular structures.

Herein, we report an analysis designed to rationalize similarity searching on the basis of different molecular comparisons, carried out on a large scale, and determine similarity values across different compound activity classes. It is shown that similarity value ranges indicative of activity can be identified for different fingerprints. However, it is also shown that such similarity values cannot be reliably used as thresholds for similarity searching, given the ratio of different molecular comparisons that are involved.

Materials and methods

Compound classes

In a previous large-scale similarity search analysis of the ChEMBL database22, a variety of activity classes were identified for benchmarking that were “easy” (i.e. yielded generally high compound recall using different fingerprints), “preferred/intermediate” (moderate compound recall), or “difficult” (low compound recall)23. For our analysis, we have made use of this classification scheme and extracted these activity classes from ChEMBL version 20 if they contained at least 50 compounds with high-confidence assay data for human targets24 and a potency of at least 10 µM. In addition, a random sample of 10,000 compounds was drawn from ZINC25 representing assumed inactive database compounds. All randomly selected (“random”) compounds had a molecular weight of less than 550 Da. Accordingly, all compounds with a molecular weight exceeding 550 Da were also removed from activity classes, thus balancing the potential of molecular size effects in similarity searching26.

On the basis of these criteria, 22 easy, 50 intermediate, and 30 difficult activity classes were obtained covering a wide range of targets. Easy activity classes contained a total of 2967 compounds with, on average, 135 compounds per target; intermediate activity classes contained 25,175 compounds with a mean of 504 per target, and difficult activity classes 47,109 compounds with a mean of 1570 per target. The molecular weight distributions of compounds from all categories are reported in Figure 1. Compounds from ZINC had overall slightly lower weight than active compounds but the distributions of molecular weights of from different activity class categories were very similar.

52a9c30e-8ac7-4af0-89b0-a79c6e30c7dc_figure1.gif

Figure 1. Molecular weight ranges.

Density plots report the molecular weight (Da) distributions of compounds in all categories.

Similarity calculations

Two standard fingerprints of different design were used including MACCS and ECFP with bond diameter 4 (ECFP4). As a similarity metric, the Tc was calculated.

Systematic pairwise similarity calculations were carried out for all individual activity classes (active vs. active), the random category (random vs. random), and active vs. random compounds.

Results and discussion

Comparison of compounds belonging to different categories

During similarity searching, active reference compounds are compared to inactive database compounds or desired compounds having the same activity (“hits”). Thus, similarity searching can be mimicked by systematically comparing active compounds having the same activity with each other and active compounds to random database compounds. Comparison of random database compounds with each other is not carried out during traditional similarity searching, but the similarity value distribution resulting from this comparison can be monitored as an additional reference.

Distribution of combined similarity values

Figure 2 shows the distribution of Tc values from active vs. active, random vs. active, and random vs. random compound comparisons using MACCS and ECFP4. For this comparison, Tc values obtained for all activity classes were combined. Thus, the resulting distribution represented ~55 million Tc values for compounds active against 102 targets. Comparison of ZINC compounds yielded 50 million Tc values. Their distribution was regarded to represent global chemical similarity (although many ZINC compounds are considered “drug-like”) and thus termed “chemical similarity distribution”.

52a9c30e-8ac7-4af0-89b0-a79c6e30c7dc_figure2.gif

Figure 2. Distribution of combined similarity values.

Density plots of Tc values are shown for similarity comparison using (a) MACCS and (b) ECFP4. Compared were active compounds in each activity class (Act vs Act, purple), 10,000 random ZINC compounds with each activity class (Rand vs Act, maroon), and 10,000 random compounds (Rand vs Rand, green). Similarity values of all 102 activity classes were combined. Dashed vertical lines indicate the means of the distributions.

Figure 2a shows that global similarity values calculated using MACCS yielded a normal distribution, given its very large sample size, which was centered on a MACCS Tc value of 0.4. The comparison of random vs. active compounds using MACCS, resulting in a total of ~753 million Tc values, 50 million of which were randomly sampled for the generation of density plots, produced a nearly identical normal distribution, also reflecting randomness. By contrast, the distribution of Tc values from active compounds, albeit significantly overlapping with the reference distributions, was shifted to the right, centered on a MACCS Tc value of 0.47. This distribution was regarded to represent activity-relevant similarity, given that it originated from more than 100 qualifying activity classes.

Figure 2b shows that calculations using ECFP4 produced very different Tc value distributions. Compared to MACCS, ECFP4 Tc value distributions were shifted towards much lower Tc values and confined to small value ranges mostly falling within the interval [0.0, 0.2] (which should be known to similarity search practitioners). The chemical similarity distribution and random vs. active distribution were centered on an ECFP4 Tc value of 0.11. Also in this case, a slight shift of the activity-relevant distribution towards higher values was observed, centered on an ECFP4 Tc of 0.15. Hence, for both ZINC and ChEMBL compounds, ECFP4 calculations mostly covered only small Tc value ranges.

Distributions for different activity class categories

Figure 3 shows corresponding Tc value distributions that were separately generated for easy, intermediate, and difficult activity classes. Comparison of these value distributions nicely correlated with the different similarity search performance observed for these activity classes.

52a9c30e-8ac7-4af0-89b0-a79c6e30c7dc_figure3.gif

Figure 3. Distribution of similarity values for different activity class categories.

Density plots of Tc values are shown for similarity comparison using (a) MACCS and (b) ECFP4 according to Figure 2. In this case, Tc value distributions were separately recorded for each activity class category (easy, intermediate, and difficult). In addition, easy activity classes were compared to a reduced random set of 1000 ZINC compounds (reported in the upper right panels).

In Figure 3a, the chemical similarity and random vs. active distributions were again essentially identical and centered on a MACCS Tc value of 0.4, although the sample sizes of active compounds were smaller in this case. The random vs. active distribution did not change when the random sample was reduced in size from 10,000 to 1000 ZINC compounds, indicating that the distribution was stable. Equivalent observations were made for the distributions of ECFP4 values shown in Figure 3b.

However, for both MACCS and ECFP4, gradual shifts in the distributions of Tc values for different activity class categories were observed. From difficult over intermediate to easy activity classes, the activity-relevant distributions shifted towards higher Tc values. Thus, corresponding to increasing similarity search performance, the comparison of active compounds produced higher Tc values than random vs. active comparisons, leading to an enrichment of active compounds at higher positions in similarity-based rankings. For easy activity classes, the shape of the distributions departed from normal distributions and became multi-modal, probably reflecting activity class-dependent differences in Tc values. These distributions displayed a significant shift towards higher Tc values with a mean of 0.6 and 0.28 for MACCS and ECFP4, respectively.

Activity-relevant similarity

Comparison of the distributions in Figure 3 made it possible to delineate activity-relevant similarity value ranges. In Figure 3a, the chemical similarity and random vs. active distributions for MACCS matched the baseline at a value of ~0.8, whereas a significant proportion of Tc values of 0.8 or greater were observed for comparisons of active compounds, especially for easy activity classes. Equivalent observations were made for an ECFP4 Tc value of ~0.3 shown in Figure 3b. Thus, for MACCS and ECFP4, there was a much higher probability that comparison of active compounds yielded a Tc value of at least 0.8 and 0.3, respectively, than comparison of active vs. random (or random vs. random) compounds. Figure 4 reports for all activity class categories the percentages of Tc values of at least 0.8 (MACCS, Figure 4a) and 0.3 (ECFP4, Figure 4b). These percentages significantly increased for difficult over intermediate to easy activity classes, (again mirroring similarity search performance), reaching medians of 17.7% (MACCS) and 37.5% (ECFP4), with a significant spread of percentages among easy activity classes, as revealed by the box plot representations in Figure 4.

52a9c30e-8ac7-4af0-89b0-a79c6e30c7dc_figure4.gif

Figure 4. Distribution of similarity values in activity-relevant ranges.

Box plots report the distribution of the percentage of Tc values falling into activity-relevant ranges for each category of activity classes using (a) MACCS and (b) ECFP4. A box plot gives the minimum percentage of Tc values in the activity-relevant range per category (bottom line), first quartile (lower boundary of the box), median value (thick line), third quartile (upper boundary of the box), and highest percentage of Tc values (top line).

Taken together, these findings show that it was possible to detect activity-relevant Tc value ranges for different fingerprints by systematically comparing Tc value distributions for active and randomly selected compounds.

Implications for similarity searching

A key question was whether activity-relevant similarity values might also serve as threshold values for similarity searching, contrary to the conclusions drawn from earlier studies analyzing compound recall rates and rankings. In this context, the ratio of different compound comparisons involved in similarity search calculations must be considered, as discussed below. The activity-relevant Tc value ranges of ≥ 0.8 (MACCS) and ≥ 0.3 (ECFP4) derived from comparison of similarity value distributions are plausible likelihood estimates, as further supported by the data in Table 1. For example, for easy activity classes, 16% of MACCS Tc values for comparison of active compounds reached or exceeded 0.8, whereas this was only the case for 0.005% of random vs. active comparisons. For ECFP4, the corresponding percentages were 38.2% and 0.03%, respectively. However, in a typical similarity search trial, many more active vs. random compound comparisons are carried out than active vs. active comparisons, given that only small numbers of compounds with a specific activity are usually available in databases. For example, let us consider the most favorable case of easy activity classes, a search with MACCS using a single active reference compound, and a similarity threshold value of 0.8. If a database of 100,000 inactive and 50 active compounds were to be screened, eight active compounds would be detected together with five false-positives on the basis of the ratios given in Table 1. If 500,000 database compounds were to be screened, the number of false-positives would increase to 25 (given that the active vs. random distribution was normal). For ECFP4, applying a similarity threshold value of 0.3 under the same search conditions, screening a database with 50 active and 500,000 inactive compounds would result in 19 true- and 150 false-positives. Hence, even for easy activity classes, activity-relevant similarity values could not be reliably applied as thresholds in a typical similarity search scenario because of the large discrepancy in the number of different comparisons. Furthermore, for difficult search tasks, the number of true-positive detections would be reduced significantly and the number of false-positives would further increase (Table 1).

Table 1. Similarity values falling into activity-relevant ranges.

MACCS
Activity
Class
category
Number of Tc values ≥ 0.8
Act vs ActAct vs Rand (10000
compounds)
Easy39178 (16.0%)1613 (0.005%)
Intermediate538349 (5.0%)27423 (0.01%)
Difficult559442 (1.2%)70057 (0.01%)
ECFP4
Activity
Class
category
Number of Tc values ≥ 0.3
Act vs ActAct vs Rand (10000
compounds)
Easy93611 (38.2%)8282 (0.03%)
Intermediate1041694 (10.9%)104003 (0.04%)
Difficult1854822 (4.1%)233943 (0.05%)

Reported are the total number of pairwise compound comparisons and percentages of Tc values (bold) falling into activity-relevant ranges of similarity values identified for the MACCS and ECFP4 fingerprints. “Act” stands for active and “Rand” for random.

The percentages of compounds from different categories falling into activity-relevant similarity ranges reported in Table 1 also helped to rationalize the relative performance of fingerprints in benchmark calculations. Such retrospective calculations typically focus on easy or intermediate activity classes (otherwise, mostly “negative” results would be obtained). In benchmark settings, ECFPs are often superior to MACCS and other standard fingerprints. If compound recall rates are determined, which is usually the case, but only possible in retrospective applications, ECFP4 is clearly favored over MACCS, given the much larger percentage of true-positive detections according to Table 1. However, it should also be noted that even for easy activity classes, ECFP4 only detected less than 40% of active compounds at activity-relevant similarity values. Thus, the false-negative rate was high, even more so for MACCS, indicating that the sensitivity of these fingerprints to active compounds in a similarity search scenario is low. This again reflects the fact that structure-activity information is not explicitly used in a fingerprint search.

In a prospective similarity search application, when active compounds are sparse and unknown and source databases are large, it would be more difficult to draw a line between ECFP4 and MACCS, as discussed above. Then, the ability to identify novel hits will much depend on the specific features of active compounds and the capacity of different fingerprints to capture them.

A plus of activity-relevant similarity values, as determined herein, is that they have been derived over many different activity classes and are thus general in nature. As such, they become a characteristic feature of a given fingerprint, although their utility for practical similarity searching is limited.

Conclusion

In conclusion, in this study, we have addressed the issue of how, from a fundamental point of view, activity similarity might be related to molecular similarity calculated using fingerprints by focusing on systematic compound comparisons involved in similarity searching. The analysis has led to the introduction of activity-relevant similarity values as a characteristic feature of fingerprints of different design, which we consider useful as likelihood estimates. For example, given our ensemble of activity classes, the likelihood that a compound comparison yielded a Tc value of at least 0.8 for MACCS or 0.3 for ECFP4 was hundreds of times higher for compounds sharing the same activity than randomly selected or active vs. random compounds.

Data availability

ZENODO: Activity classes from different categories, doi: http://dx.doi.org/10.5281/zenodo.4731527

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Jasial S, Hu Y, Vogt M and Bajorath J. Activity-relevant similarity values for fingerprints and implications for similarity searching [version 1; peer review: 3 approved] F1000Research 2016, 5(Chem Inf Sci):591 (https://doi.org/10.12688/f1000research.8357.1)
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ApprovedThe paper is scientifically sound in its current form and only minor, if any, improvements are suggested
Approved with reservations A number of small changes, sometimes more significant revisions are required to address specific details and improve the papers academic merit.
Not approvedFundamental flaws in the paper seriously undermine the findings and conclusions
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Reviewer Report 12 Apr 2016
Wendy Warr, Wendy Warr & Associates, Holmes Chapel, UK 
Approved
VIEWS 29
This is a short but interesting paper and is extremely well written. I use the adjective “short” because the novel results occupy fewer than eight pages, if the figures and tables are ignored. Nevertheless, the results are interesting and well ... Continue reading
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Warr W. Reviewer Report For: Activity-relevant similarity values for fingerprints and implications for similarity searching [version 1; peer review: 3 approved]. F1000Research 2016, 5(Chem Inf Sci):591 (https://doi.org/10.5256/f1000research.8986.r13264)
NOTE: it is important to ensure the information in square brackets after the title is included in all citations of this article.
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Reviewer Report 12 Apr 2016
Peter Ertl, Novartis Institutes for Biomedical Research, CH-4056 Basel, Switzerland 
Approved
VIEWS 24
An interesting manuscript focusing on a relationship between molecule similarity and biological activity, one of the most important (and still not fully solved) problems of applied cheminformatics. The topic is therefore relevant to drug design.

The question the authors are trying ... Continue reading
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Ertl P. Reviewer Report For: Activity-relevant similarity values for fingerprints and implications for similarity searching [version 1; peer review: 3 approved]. F1000Research 2016, 5(Chem Inf Sci):591 (https://doi.org/10.5256/f1000research.8986.r13265)
NOTE: it is important to ensure the information in square brackets after the title is included in all citations of this article.
  • Author Response (F1000Research Advisory Board Member) 14 Apr 2016
    Jürgen Bajorath, Department of Life Science Informatics, B-IT, LIMES Program Unit Chemical Biology and Medicinal Chemistry, Rheinische Friedrich-Wilhelms-Universität, Bonn, Germany
    14 Apr 2016
    Author Response F1000Research Advisory Board Member
    Thank you for suggesting the follow-up investigation. We note that the results of the two most relevant investigations were discussed in the introduction.
    Competing Interests: No competing interests were disclosed.
COMMENTS ON THIS REPORT
  • Author Response (F1000Research Advisory Board Member) 14 Apr 2016
    Jürgen Bajorath, Department of Life Science Informatics, B-IT, LIMES Program Unit Chemical Biology and Medicinal Chemistry, Rheinische Friedrich-Wilhelms-Universität, Bonn, Germany
    14 Apr 2016
    Author Response F1000Research Advisory Board Member
    Thank you for suggesting the follow-up investigation. We note that the results of the two most relevant investigations were discussed in the introduction.
    Competing Interests: No competing interests were disclosed.
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Reviewer Report 07 Apr 2016
Georgia B. McGaughey, Vertex Pharmaceuticals, Boston, USA 
Approved
VIEWS 31
The authors summarize in detail the threshold between actives and inactives using 2D fingerprints for the MACCS and ECFP4 fingerprint methods using data derived from ChEMBL. The paper is well written and should be indexed.  A few suggestions are made, ... Continue reading
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McGaughey GB. Reviewer Report For: Activity-relevant similarity values for fingerprints and implications for similarity searching [version 1; peer review: 3 approved]. F1000Research 2016, 5(Chem Inf Sci):591 (https://doi.org/10.5256/f1000research.8986.r13263)
NOTE: it is important to ensure the information in square brackets after the title is included in all citations of this article.
  • Author Response (F1000Research Advisory Board Member) 14 Apr 2016
    Jürgen Bajorath, Department of Life Science Informatics, B-IT, LIMES Program Unit Chemical Biology and Medicinal Chemistry, Rheinische Friedrich-Wilhelms-Universität, Bonn, Germany
    14 Apr 2016
    Author Response F1000Research Advisory Board Member
    It is noted that the Muchmore et al. reference was already cited. In addition, 3D similarity measures were not considered herein. By design, the study did neither focus on compound ... Continue reading
COMMENTS ON THIS REPORT
  • Author Response (F1000Research Advisory Board Member) 14 Apr 2016
    Jürgen Bajorath, Department of Life Science Informatics, B-IT, LIMES Program Unit Chemical Biology and Medicinal Chemistry, Rheinische Friedrich-Wilhelms-Universität, Bonn, Germany
    14 Apr 2016
    Author Response F1000Research Advisory Board Member
    It is noted that the Muchmore et al. reference was already cited. In addition, 3D similarity measures were not considered herein. By design, the study did neither focus on compound ... Continue reading

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Alongside their report, reviewers assign a status to the article:
Approved - the paper is scientifically sound in its current form and only minor, if any, improvements are suggested
Approved with reservations - A number of small changes, sometimes more significant revisions are required to address specific details and improve the papers academic merit.
Not approved - fundamental flaws in the paper seriously undermine the findings and conclusions
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