Definitions and notations
In the present study, 3-D similarity computations that employ a single conformer per compound and multiple diverse conformers per compound are referred to as the “single-conformer approach” and the “multiple-conformer approach”, respectively. The multiple-conformer approach is further classified into two different approaches: the “best-conformer-pair” approach and the “all-conformer-pair” approach. In the best-conformer-pair approach, a similarity score between a single conformer and a compound (or between two compounds), where each compound has multiple diverse conformations, is represented by the greatest similarity score among all conformer pairs considered per conformer-compound pair (or compound-compound pair). In the all-conformer-pair approach, one may treat each of the individual conformer pairs as if it were a unique compound pair. These two different methods for the multiple-conformer approach were employed to help simulate different database search or analysis strategies using 3-D molecular similarity. The five different 3-D similarity usage scenarios considered in this study are summarized in Table .
Different 3-D similarity search (or analysis) scenarios considered
As described in the Methods section, the six different score types were considered: shape-Tanimoto (ST), color-Tanimoto (CT), and combo-Tanimoto (ComboT) for each of the ST- and CT-optimizations. For convenience, superscript “ST-opt” or “CT-opt” is used to indicate whether the similarity score is estimated in the ST-optimized alignment or in the CT-optimized alignment (i.e., STST-opt, CTST-opt, ComboTST-opt, STCT-opt, CTCT-opt, and ComboTCT-opt), and the similarity scores from the single-conformer and multiple-conformer approaches are denoted with subscripts “single” and “multi”, respectively. Similarly, subscripts “best” and “all” are used to indicate the best-conformer-pair approach and all-conformer-pair approach, respectively. For example, STbestCT-opt represents the CT-optimized ST score using the best-conformer-pair approach and CTallST-opt indicates the ST-optimized CT score using the all-conformer-pair approach. ComboTsingleST-opt indicates the ST-optimized ComboT score from the single-conformer-per-compound model. The word “XT” is used when we refer to any of the similarity measures (i.e., ST, CT, and ComboT), or to a similarity score in a general sense.
Similarity scores for the randomly selected conformer pairs
To investigate effects of employing multiple conformers per compound upon the 3-D similarity score between randomly selected biologically-tested compounds, the distributions of the 3-D similarity scores between the 10,000 compounds in the 10-K set were constructed using both the single-conformer and multiple-conformer approaches. The resulting 3-D similarity score distributions are shown in Figures , , , , and their averages and standard deviations are summarized in Table . For the single-conformer approach (Figure , corresponding to Scenario A
in Table ), the similarity score distributions for the unique conformer-conformer pairs and the unique compound-compound pairs are identical (since only one conformer per compound is considered). For the multiple-conformer approach, however, three different distributions were generated: the unique conformer-conformer pairs (Figure , Scenario B
), the unique conformer-compound pairs (Figure , Scenario D
), and the unique compound-compound pairs (Figure , Scenario E
). Note that the 3-D similarity scores for the unique conformer-compound pairs (in Figure ) and unique compound-compound pairs (in Figure ) were computed using the “best-conformer-pair” approach, meaning that only the greatest similarity score was chosen from all relevant conformer pairs [i.e.
, up to 10 (= 1
10) conformer-conformer pairs per conformer-compound pair and up to 100 (= 10
10) conformer-conformer pairs per compound-compound pair, because ten diverse conformers per compound were used].
Figure 1 Similarity distributions for “single-conformer” (Scenario A) approach. Binned distributions in 0.01 increments of the 3-D similarity scores for the unique “conformer-conformer” pairs arising from 10,000 randomly selected (more ...)
Figure 2 Similarity distributions for multi-conformer “all-conformer-pair” (Scenario B) approach. Binned distributions in 0.01 increments of the 3-D similarity scores for the unique “conformer-conformer” pairs arising from 10,000 (more ...)
Figure 3 Similarity distributions for multi-conformer “best-conformer-pair” (Scenario D) approach. Binned distributions in 0.01 increments of the 3-D similarity scores for the unique “conformer-compound” pairs arising from 10,000 (more ...)
Figure 4 Similarity distributions for multi-conformer “best-conformer-pair” (Scenario E) approach. Binned distributions in 0.01 increments of the 3-D similarity scores for the unique “compound-compound” pairs arising from 10,000 (more ...)
Similarity score distribution statistics for the random compound pairs
As shown in Table and Figure , when the single-conformer approach (Scenario A
) was employed, the average similarity score for the “unique” compound-compound pairs from the 10-K set was 0.54, 0.07, 0.62, 0.41, 0.18, and 0.59 for STST-opt
, and ComboTCT-opt
, respectively. These averages for the 10-K set are exactly identical to those for the 734-K set determined from the previous study [10
], reflecting the fact that 10-K set was constructed from random sampling of the 734-K set, and importantly suggesting that the 10-K set is representative of the 734-K set.
Perhaps surprising to some, the distributions (Figure ) and statistics (Table ) of the 3-D similarity scores from the “all-against-all” conformer comparison using multiple diverse conformers per compound (Scenario B) are essentially identical to those computed with a single conformer per compound (Figure ), showing that the single-conformer and multiple-conformer “all-against-all” comparisons yield near identical random distributions. This suggests that the 3-D similarity distributions for random conformer pairs of biologically tested chemicals, whether using a single conformer or multiple conformers, is a general result. It also suggests that further analysis of the 10-K set may be a reasonable representation of a much larger bioactivity data set corpus and that conclusions drawn from the 10-K set may be applicable in a more general sense as the 10-K set represents the 734-K set and is possibly extensible to or may otherwise represent the analysis of all biologically tested compounds in PubChem.
Comparison of Figure to Figure is rather telling. If one uses a single conformer query against a multi-conformer database (Scenario D
), as is often done in a similarity query of a 3-D database, e.g.
, for virtual screening purposes, the average random distribution values increase by 0.06, 0.05, 0.08, 0.09, 0.04, and 0.10 for STST-opt
, and ComboTCT-opt
, respectively, as a result from picking the best conformer pair out of the maximum of ten diverse conformers considered per database compound. By comparing Figure to Figure , one sees that, if a multi-conformer 3-D query is used against a multi-conformer 3-D database (Scenario E
), there is a further increase over the results of Scenario D
in that the average random distribution values increase by 0.05, 0.04, 0.07, 0.07, 0.03, and 0.08 for STST-opt
, and ComboTCT-opt
, respectively, as a result of an additional order of magnitude increase in diverse conformer pairs considered per compound query. One keen observation is that, as the conformer pair count considered per compound pair increases from 1 to a maximum of 100, the width of the distribution curves (i.e.
, the variation of the similarity scores) does not change very much, whereas the location of the distribution curves (i.e.,
the average of the similarity scores) does. Furthermore, the average similarity score differences between the potential maximums of 10 and 100 conformer pairs per compound pair (Figure vs.
Figure ) are smaller by 0.01-0.02 than those between 1 and a potential maximum of 10 conformer pairs per compound pair (Figure vs.
Figure ), indicating a decrease in the rate of the similarity score change as a function of the order of magnitude of the conformer pair count increase. [This observed reduction could also partially reflect an effective reduction in the average count of diverse conformer pairs per compound considered, because not every compound considered will have ten diverse conformers associated. However, considering the 10-K set averages 9.0 diverse conformers per compound, this effect should not be large but would be of increasing importance as the logarithmic count of diverse conformers per compound is further increased.] This reduction in the rate of the average similarity score increase as a function of the logarithm increase of conformer pairs suggests that the similarity score change will eventually plateau (i.e.
, at some point, consideration of additional diverse conformers per compound will cease to change the distribution average). This log/linear behavior is similar to that observed in our earlier work [8
], where a corresponding increase in the logarithmic number of conformers resulted in a linear increase of 3-D similarity neighbors. With that said, at ten diverse conformers per compound, there still seems to be additional room for further increases in the random distribution average if one was to consider using more diverse conformers per compound. It may be important to point out that, since PubChem samples conformers and then picks a diverse subset of these sampled conformers, if one was to use conformers without sampling or picking a non-diverse subset, there may be additional shifts or changes in these average random distributions.
Note that the CTST-opt
distribution in Figure has a second peak at CTST-opt
0. This bimodality is related to the definition of the CT
score. If none of the fictitious “feature” atoms used in the CT
score are proximate, it will result in a zero or near-zero CT
score. Whereas the CT-optimization maximizes the CT
score, the ST-optimization ignores it. Considering the shift in the CTST-opt
distributions is 0.11, the compound pairs with CTCT-opt
0.11 would have negative CTST-opt
scores, which is smaller than the smallest possible value of the CT score. [Note that the CT score ranges from 0 to 1 by definition.] This shift builds up the zero counts, thus forming a second peak at CTST-opt
To further demonstrate what one might find in various 3-D similarity search/analysis scenarios, the similarity score matrices generated for the 10-K set were used to investigate the average and standard deviation of the “per-query” similarity scores for the five different scenarios described in Table . Scenario A uses a single conformer for each of the “query” and “database” compounds, and the other four search scenarios employ up to ten diverse conformers for each “database” compound. The “query” in Scenario B and Scenario E is a compound that may have up to ten diverse conformers whereas Scenario C and Scenario D use a single conformer as a “query”. Scenario B and Scenario C use the “all-conformer-pair” approach, while Scenario D and Scenario E use the “best-conformer-pair” approach. The resulting distributions from the five search scenarios are shown in Figures , , for the ST, CT, and ComboT values, respectively.
Figure 5 Average and standard deviation distributions for shape-Tanimoto (ST), per “query”. Binned distributions in 0.01 increments of the average and standard deviation of the shape-Tanimoto (ST) scores per query-type for the five similarity search (more ...)
Figure 6 Average and standard deviation distributions for color-Tanimoto (CT), per “query”. Binned distributions in 0.01 increments of the average and standard deviation of the color-Tanimoto (CT) scores per query-type for the five similarity search (more ...)
Figure 7 Average and standard deviation distributions for combo-Tanimoto (ComboT), per “query”. Binned distributions in 0.01 increments of the average and standard deviation of the combo-Tanimoto (ComboT) scores per query-type for the five similarity (more ...)
Note that the “all-conformer-pair” approach effectively treats multiple conformers of a compound as individual compounds. For this reason, Scenario B and Scenario C, which adopt the all-conformer-pair approach, resulted in nearly identical average per-query similarity scores as Scenario A, which uses a single conformer per compound. These three search scenarios are conceptually identical to constructing the distribution curves for the unique compound-compound pair computed using the single-conformer approach (Figure ) and those for the unique conformer-conformer pair computed using the “all-conformer-pair” approach (Figure ). On the other hand, Scenario D and Scenario E, which use the “best-conformer-pair” approach, increased the per-query similarity scores. The averages for Scenario D and Scenario E were the same as those for conformer-compound pairs (Figure ) and the unique compound-compound pairs (Figure ), respectively, computed with multiple diverse conformers per compound.
The average per-query similarity scores in Figures , , are nearly identical to the averages found in Table , but the standard deviations for the per-query similarity scores tend to be about 0.01 less than the standard deviations in Table . The modes of the average values are generally greater by 0.02-0.04 than the overall average values for most ST and ComboT values. Figures , , suggest that some structures have smaller 3-D similarity search averages and greater standard deviations, yielding mode values that are shifted from the overall average values. This appears more pronounced in the case of ST-optimized similarity score values. So, depending on the mix of chemical structures being considered in an individual 3-D similarity search (and perhaps to the extent of their shape and feature uniqueness), there may be considerable volatility in the distribution of similarity scores between individual 3-D similarity queries. In the aggregate, however, most biologically considered chemicals in the 10-K set (and potentially PubChem in general) appear to have a limited range of variation in average 3-D similarity scores and standard deviation values.
Similarity scores for the non-inactive–non-inactive pairs
A. Summary statistics
In the second part of this study, the distributions of the 3-D similarity scores between non-inactive compounds for each of the considered 1,528 bioassays archived in PubChem were constructed using the 156-K set and both the single-conformer and multiple-conformer approaches, to address the question: how will employing multiple conformers per compound change the 3-D similarity scores between the non-inactive molecules for a given biological assay? In addition, the results from this section, in conjunction with the analyses for the random compound pairs in the previous section, provide clues to the question: does one see (greater) separation of active and inactive spaces when employing multiple conformers per compound, as opposed to a single conformer per compound?
The assay-type counts for these 1,528 bioassays are shown in Figure . The bioassays in the PubChem BioAssay database can be classified into four categories, according to PubChem depositor-assigned assay types: primary, confirmatory, summary, and other. Note that there is another category in Figure , “Unspecified”, because the assay-type attribute for AID records are optional, and not required. The per-AID average and standard deviation of the six 3-D similarity scores (i.e.
, and ComboTCT-opt
) for the NN pairs of each of the 1,528 AIDs are included in Additional file 3
, and their overall per-AID average and standard deviation (i.e.
)] and σ
)]; see the Methods section for the definition) are listed in Table and Table . The average and standard deviation of the differences in these per-AID values between the single-conformer and multiple-conformer approaches are summarized in Table . The distributions of the per-AID average similarity scores for the 1,528 AIDs are shown in Figures and .
Break down of assays by type. Assay-type counts for the 1,528 bioassays considered in the present study.
Summary statistics for per-AID shape-Tanimoto (ST)-optimized 3-D similarity
Summary statistics for per-AID color-Tanimoto (CT)-optimized 3-D similarity
Comparison of summary statistics of per-AID 3-D similarity
Figure 9 Per-AID shape-Tanimoto (ST)-optimized 3-D similarity average values. Binned distributions in 0.01 increments of the average 3-D similarity scores for non-inactive–non-inactive (NN) pairs of 1,528 AIDs in the PubChem BioAssay database, computed (more ...)
Figure 10 Per-AID color-Tanimoto (CT)-optimized 3-D similarity average values. Binned distributions in 0.01 increments of the average 3-D similarity scores for non-inactive–non-inactive (NN) pairs of 1,528 AIDs in the PubChem BioAssay database, computed (more ...)
As described in the Methods section, the same analyses were also performed for a subset of the 1,528 assays, which consists of 843 assays that have active compounds only (without any inconclusive or unspecified compounds), and the results are summarized in Additional file 4
. Note the minor peaks in the distributions for the best-conformer-pair approach in Figures , . These peaks arise from the 34 National Institutes of Neurological Disorders and Strokes (NINDS) approved drug screenings, in which the same set of non-inactive compounds were tested against different targets. Although they are different assays, they do have the same set of non-inactive compounds, yielding the minor peaks in Figures , . Because these 34 assays are not included in the 843 assays, the resulting similarity score distribution curves from the 843 assays are closer to the normal distribution than those from the 1,528 assays. However, the two assay sets have very similar averages and standard deviations to each other, and hence the analysis and discussion below, which are based on the 1,528 assay set, also hold for the 843 assay set.
Summarized in Table 6, the overall average and standard deviation of the per-AID average similarity score differences between the best-conformer-pair approach and single-conformer approach were 0.09 ± 0.03, 0.09 ± 0.04, 0.15 ± 0.06, 0.15 ± 0.04, 0.07 ± 0.03, and 0.18 ± 0.06 for μ(STbest−singleST-opt), μ(CTbest−singleST-opt), μ(ComboTbest−singleST-opt), μ(STbest−singleCT-opt), μ(CTbest−singleCT-opt), and μ(ComboTbest−singleCT-opt), respectively, indicating that the best-conformer-pair approach gives a statistically significant increase in 3-D similarity scores between the NN pairs, relative to those computed using a single conformer per compound. On the other hand, the overall averages and standard deviations for μ(STall−singleST-opt), μ(CTall−singleST-opt), μ(ComboTall−singleST-opt), μ(STall−singleCT-opt), μ(CTall−singleCT-opt), and μ(ComboTall−singleCT-opt) were −0.01 ± 0.03, −0.02 ± 0.06, −0.03 ± 0.09, −0.02 ± 0.04, −0.01 ± 0.05, and −0.03 ± 0.09, respectively, meaning that there were no statistically significant differences in the average 3-D similarity scores for the NN pair between the all-conformer-pair approach (Scenario B) and the single-conformer approach (Scenario A).
In general, as shown in Tables and , when going from primary screen assays to confirmatory assays to summary assays, the average similarity scores between the NN pairs increase, regardless of whether a single conformer or multiple conformers are used for each compound. However, these increases should not be considered as statistically meaningful because the standard deviations of the NN-pair 3-D similarity scores also become greater and these distributions significantly overlap.
Employing multiple conformers per compound (Scenario E as opposed to Scenario A) increases the NN-pair 3-D similarity scores by a similar amount for all of the primary, confirmatory, and summary assays. For example, the average and standard deviation of μ(ComboTbest−singleST-opt) were 0.16 ± 0.05, 0.15 ± 0.06, and 0.17 ± 0.06, for primary, confirmatory, and summary assays, respectively (Table ). Therefore, the multiple-conformer effects upon the 3-D similarity score of the NN pairs should be considered as independent of the assay category.
B. Comparison between the NN-pairs and randomly selected pairs
If one considers the data from Table (i.e.
, the rows labeled as “Random” in Table and Table ) and compares them to the per-AID results, one sees that for randomly selected biologically tested molecules the overall averages are consistently less than the per-AID values across all 3-D similarity optimization types and across both single-and multi-conformer approaches, with the notable exception of “Unspecified” assay types. This is a similar result found in the earlier study [10
] that used a single conformer per compound.
Table and Figures and summarize how distant the average NN-pair similarity scores for each of the bioassays considered are from those for randomly selected compound pairs (from Table ). Note that the per-AID NN-pair CT score average for a given assay are found as much as 14 standard deviation units away from the corresponding average for the random compound pairs, reflecting that the average and standard deviation of the CT scores for the random compound pair are less than those of the ST or ComboT scores.
The cumulative count of biological assays whose non-inactive–non-inactive (NN) pairs have the average 3-D similarity score smaller than a given threshold
Figure 11 Deviation from random of per-AID shape-Tanimoto (ST)-optimized 3-D similarity average values. Deviation of the ST-optimized 3-D similarity scores for non-inactive–non-inactive (NN) pairs of 1,528 AIDs from the corresponding average for the random (more ...)
Figure 12 Deviation from random of per-AID color-Tanimoto (CT)-optimized 3-D similarity average values. Deviation of the CT-optimized 3-D similarity scores for non-inactive–non-inactive (NN) pairs of 1,528 AIDs from the corresponding average for the random (more ...)
When averaged over the six different similarity score types, the single-conformer approach resulted in 1,279 AIDs (83.8%) with the NN-pair similarity scores equal to or greater than the corresponding average for the random compound pairs. The multiple-conformer approach reduced this number to 1,090 AIDs (71.4%) on average, implying a decrease in the distance of the NN-pair similarity from the random compound pair similarity in general. However, there is a minute difference between the ST scores and the CT and ComboT scores. When multiple conformers were used for each compound, there was a decrease in the difference between the ST scores of the NN-pairs and those of the random pairs for the entire range. On the other hand, as shown in Table 7, the multiple-conformer effect resulted in more bioassays that had NN-pair CT and ComboT score averages equal to or greater than the respective μ + 2σ thresholds. For example, when going from the single conformer per compound to ten diverse conformers per compound, the number of bioassays with μ(CTNN-pairST-opt) ≥ μ(CTrandomST-opt) + 2σ(CTrandomST-opt) increases from 144 (= 1,528 − 1,384) to 153 (=1,528 − 1,375), whereas the number of bioassays with μ(STNN-pairST-opt) ≥ μ(STrandomST-opt) + 2σ(STrandomST-opt) decreases from 38 (=1,528 − 1,490) to 28 (=1,528 − 1,500).
C. Examples of multiple-conformer effects in 3-D similarity computation
This section presents examples that show substantial multiple-conformer effects upon 3-D similarity between biologically similar molecules. An underlying assumption of these examples is that a similarity score at least two standard deviations above the average similarity score of the randomly selected conformers (i.e.
, greater than μ
) is statistically significant. For example, two compounds are considered to be structurally similar to each other when the ComboTST-opt
score between them is greater than 0.88 and 1.03 for the single-conformer and best-conformer-pair approaches, respectively (on the basis of the statistical parameters in Table ).
According to our supplementary computation, the average and standard deviation of the 2-D similarity scores between all compound pairs arising from the 10-K set, computed using the PubChem subgraph fingerprint [36
] and Tanimoto equation [37
], were 0.42 ± 0.13, and hence, a pair of molecules with the 2-D similarity score greater than 0.68 were considered to be structurally similar to each other under the same threshold (i.e.
) as used for 3-D similarity. Note that 2-D similarity methods do not always recognize structural similarity between biologically similar molecules that 3-D similarity methods readily do [8
In the examples below, each conformer of a given compound will be designated with a local conformer identifier (LID) [11
], which, in conjunction with CID, allows the user to uniquely identify each conformer in PubChem3D. For simplicity, a particular conformer of a compound is represented by combining the corresponding CID and LID. For example, conformer “60823.2” represents LID 2 of CID 60823, the default conformer of atorvastatin. The default conformer of a compound record in PubChem3D is the first diverse conformer, which is used when a single conformer is considered for a molecule. Note that LID 1 of a compound is not necessarily the default conformer, because the diverse conformer ordering of a compound may or may not begin with LID 1.
An example of substantial multiple-conformer effects upon 3-D similarity comparison can be found with the non-inactive compounds of AID 1033 [45
] (Figure ), an NMR-based screening to identify small molecules that target the chaperone DnaK in E.coli [46
]. As shown in the dendrograms produced by the PubChem Structure Clustering tool [11
] in Figure , whereas some compound pairs show 2-D similarity scores below 0.68, the 3-D ComboTST-opt
similarity scores computed using ten conformers per compound are all well above 1.03. For example, the 2-D similarity score between CIDs 668798 and 1246750 is 0.48, and the ComboTST-opt
score computed using a single default conformer is 0.53, implying that both the 2-D and single-conformer 3-D similarity cases cannot recognize structural similarity between the two molecules. However, when ten diverse conformers per compound are employed, the largest ComboTST-opt
score from all the conformer pairs is 1.21 [corresponding to the (668798.12, 1246750.25) pair], sufficiently high enough to consider them structurally similar to each other.
Figure 13 Demonstrated multi-conformer effects using AID 1033. Effects of employing multiple conformers per compound upon 3-D similarity of the non-inactive compounds tested in AID 1033. Eight compounds in panel (a) are non-inactive in AID 1033. Panel (b) depicts (more ...)
Another example in which the PubChem 3-D multi-conformer similarity method provides an improvement is AID 491 [48
] (Figure ), which contains in vitro affinity data extracted from the literature for small-molecule inhibitors tested against influenza A virus sialidase (also known as neuraminidase) [49
]. Figure shows the dendrograms for eight compounds selected from 60 non-inactive compounds in AID 491 for demonstration purposes. Although the eight compounds can be classified into two clusters of compounds at a 2-D similarity threshold of 0.5, the 3-D ComboTST-opt
similarity among them is greater than 1.03 across all eight structures when ten conformers are used for each compound. In other words, the two independent 2-D similarity clusters, each representing a different chemical series, are recognized as a single 3-D similarity cluster, which in part emphasizes the relative strengths of the PubChem 3-D similarity method over its PubChem 2-D similarity counterpart. The 3-D similarity single-conformer approach, however, cannot recognize the similarity between all eight compounds. CIDs 490518 and 505938 are the compound pair that shows the greatest difference between the 2-D similarity score and the 3-D CTST-opt
score (0.41 vs.
1.04). Note that the conformer superposition between 490518.39 and 505938.4 resulted in a substantial increase in the CTST-opt
score, compared to the superposition between the default conformers 490518.1 and 505938.1.
Figure 14 Demonstrated multi-conformer effects using AID 491. Effects of employing multiple conformers per compound upon 3-D similarity of non-inactive compounds tested in AID 491. Panel (a) shows the dendrogram based on 2-D similarity among eight compounds selected (more ...) D. Summary comparison of overall average similarity
Figure compares the overall average 3-D similarity scores for the random compound-compound pairs with the overall average μμ
)] values for the NN and NI pairs, computed in the present and previous studies [10
]. As shown in Figure , the single-conformer approach does not result in a noticeable difference between the average 3-D similarities for the NN pair and those for the random compound-compound pair, with distributions that considerably overlap. While there are individual assays where an improvement is found (e.g.
, more AIDs with the average similarity of the NN pairs 2σ
away from those of the random pairs in the case of CT and ComboT values), the use of the multiple-conformer approach does not make a noticeable improvement in the aggregate.
Figure 15 Summary comparison of overall average similarity. Comparison of the overall average 3-D similarity scores, μμ(XT)], for the non-inactive–non-inactive (NN) pairs with those for the non-inactive–inactive (NI) pairs and random (more ...)
Why is this so? The lack of a more noticeable difference between the NN pairs and random pairs can be attributed to an assumption used in the molecular similarity methods and the nature of typical biological assays. All molecular similarity methods exploit the so-called similarity principle, which states that “structurally similar molecules are likely to have similar biological and pharmacological properties” [51
]. An underlying assumption of the similarity principle is that structurally similar molecules tend to bind to a target macromolecule in a similar fashion. However, not all biological assays have a well-defined target macromolecule. For example, biological experiments may be designed to find molecules that target a whole cell or a whole organism, involving many different potential binding sites, modes of action, etc. Even when there is a well-defined target and carefully crafted assay, there is also no guarantee that the observed activity is real or manifested in an intended way, with the potential for molecules to bind irreversibly or otherwise denature the experiment by being cytotoxic, a chromophore at the detector wavelength, protein aggregator, etc. There is also no guarantee, after the activity observed is validated as being real, that the way in which two similar molecules bind will be identical (e.g.
, agonist vs
. antagonist vs
. partial-agonist vs
. partial-antagonist). Further confusing matters, there is no guarantee that the biologically inactive molecules are indeed not active for a given biological target with factors in how the assay is performed preventing or not registering such activity. The complications that one can imagine preventing accurate correlation of structural similarity with biological activity in one form or another are nearly limitless but one must try nevertheless to do the best they can with the data they have.
The 1,528 bioassays considered in this study were selected without considering any complexities, and therefore, there is no guarantee that the observed biological similarity between bioactive molecules in these assays arises from structural similarity. Without an assumption of correlation between structural and biological similarities for these bioactive molecules, expected structural similarity between bioactive molecules should not be very different from that between biologically (and structurally) unrelated molecules. This idea is consistent with the small difference in 3-D similarity scores between the NN-pairs and random compound-compound pairs, as depicted in Figure . In this context, the average similarity scores for the NI pairs should also be similar to those for the NN-pairs and the random pairs because the NI-pairs are biologically unrelated by nature, consistent with our previous study using a single conformer per compound (also compared in Figure ). The multiple-conformer approach would not make any noticeable difference of the NI-pair from the NN pair and random pair “on average”, although the present study did not consider the 3-D similarity score computation of the NI pairs using the multiple-conformer approach, as its proper treatment would require a tremendous amount of additional computational resources beyond our current means.