Matched molecular pair analysis: significance and the impact of experimental uncertainty.

Article pubs.acs.org/jmc

Matched Molecular Pair Analysis: Significance and the Impact of Experimental Uncertainty Christian Kramer,*,† Julian E. Fuchs,† Steven Whitebread,‡ Peter Gedeck,§ and Klaus R. Liedl† †

Department of Theoretical Chemistry, Faculty for Chemistry and Pharmacy, Center for Molecular Biosciences Innsbruck (CMBI), Leopold-Franzens University Innsbruck, Innrain 80/82, A-6020 Innsbruck, Austria ‡ Preclinical Safety Profiling, Center for Proteomic Chemistry, Novartis Institutes for BioMedical Research, 250 Massachusetts Avenue, Cambridge, Massachusetts 02139, United States § Novartis Institute for Tropical Diseases, 10 Biopolis Road, No. 05-01 Chromos, Singapore 138670, Singapore S Supporting Information *

ABSTRACT: Matched molecular pair analysis (MMPA) has become a major tool for analyzing large chemistry data sets for promising chemical transformations. However, the dependence of MMPA predictions on data constraints such as the number of pairs involved, experimental uncertainty, source of the experiments, and variability of the true physical effect has not yet been described. In this contribution the statistical basics for judging MMPA are analyzed. We illustrate the connection between overall MMPA statistics and individual pairs with a detailed comparison of average CHEMBL hERG MMPA results versus pairs with extreme transformation effects. Comparing the CHEMBL results to Novartis data, we find that significant transformation effects agree very well if the experimental uncertainty is considered. This indicates that caution must be exercised for predictions from insignificant MMPAs, yet highlights the robustness of statistically validated MMPA and shows that MMPA on public databases can yield results that are very useful for medicinal chemistry.

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INTRODUCTION

seen across different chemotype series, the effects are more likely to be real and transferable. MMPA is also a prime example for the power within the “big data” movement7 that becomes more and more important in medicinal chemistry: The effects of specific molecular transformations on ADME/Tox and physicochemical properties can be predicted based on detailed statistics of the effects in past programs. By use of these statistics, clear design guidelines can be formulated and the number of design cycles in drug discovery projects can be reduced. For example, MMPA analyses have been published for target properties such as metabolic stability,8,9 hERG,10 melting point,11 inhibition of various CYP450 enzymes and membrane permeability,12 aqueous solubility, plasma protein binding, and oral exposure.4 MMPA becomes increasingly useful with increasing database sizes, since predictions can only be made for transformations whose effects have previously been observed several times. For this reason, most publications about MMPA emanate from pharmaceutical companies that possess huge databases and concentrate around context-independent ADME and toxicity

During the past years, matched molecular pair analysis (MMPA) has become a standard tool for the extraction of medicinal chemistry knowledge from large databases. The basic idea of MMPA is to search large chemical databases for sets of molecular pairs that are linked by identical chemical transformations.1−4 Predictions about the effect of the transformations are made based on an analysis of the past distribution of differences in biochemical or biophysical properties. The most promising modifications can then be used to prioritize synthesis and subsequent testing.5,6 The MMPA process is one of the simplest forms of generating chemical knowledge from biological assay data and mirrors basic medicinal chemical learning processes. Compared to other prediction approaches such as QSAR and QSPR models, MMPA’s power stems from the simplicity and tractability with which predictions are made. In terms of prediction accuracy, MMPA is motivated by the assumption that it is easier to predict differences in activity or a property value rather than the actual value. Within a broader framework of SAR analysis, MMPA can be seen as a special type of local QSAR. If the same effects due to specific transformations are © XXXX American Chemical Society

Received: January 17, 2014

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dx.doi.org/10.1021/jm500317a | J. Med. Chem. XXXX, XXX, XXX−XXX

Journal of Medicinal Chemistry

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properties.1,3,4,8,11−16 MMPA publications from academic groups exist17−21 but are relatively rare, most probably because of the limitations in data access. The current state of MMPA has very nicely been reviewed,5 and a future perspective has been given.6 MMPA results depend on both the transformation and the chemical environment. The chemical context of the anchoring atom can have a high impact on the effect of chemical transformations.10,14,22 For example, Papadatos et al. have shown that the effect of introducing of a methoxy group on hERG blockade depends on whether the methoxy group is added to an aliphatic group or an aromatic ring. While from a chemical point of view it is obvious that the chemical context of the transformation is important for the effect, Papadatos et al. systematically showed that manifestations of the chemical context can be statistically revealed using MMPA. With increasing data set sizes, more and more refined chemical environments can be analyzed, with the only real restriction being the number of pairs available for transformations in specific chemical environments. At the same time, the paucity of pairs for most transformations introduces the need for proper statistical analysis. MMPA does not yield a single absolute value but a distribution of differences for every transformation. If a large number of pairs is available, the distribution gets a characteristic shape (which may be Gaussian or multinomial, depending on the purity of the chemical environment of the transformation) for every property and transformation within a given chemical environment. Since there are only a few examples available for most transformations, reliability and transferability of the observed differences become critical. Those can be assessed using classical statistical methods. Only few published MMPA studies contain statistical estimates for the reliability of the observed differences (such as p-values), and there is even less detail on how they arrived at the significance estimates. Commendable exceptions include a study by Keefer et al. that uses Student’s t test,13 two studies by Papadatos et al. that both use a multinomial test for binned classes,10,22 and a study by Schultes et al. that combines the Shapiro−Wilk normality test with a subsequent paired t test (in case the distribution of differences is sufficiently normally distributed) or a Wilcoxon signed-rank test.11 In a 2008 study on the effects of chemical substitutions on ligand potency in general, Hajduk and Sauer found that most transformations they inspected failed normality tests, although the distribution plots visually appeared nearnormal and centered near zero.23 They applied 2 × 2 contingency tests on their data. Dossetter et al. visually inspected difference histograms for normality and calculated pvalues using Student’s t test.9 Gleeson et al. used a hard threshold of at least 20 pairs per transformation and at least five Daylight fingerprint clusters with a Tanimoto similarity of 0.7 to ensure chemical diversity and thus transferability of the knowledge gained from MMPA.12 The term of MMPA is relatively new and started showing up in the scientific literature around 2005.1,3,4 As with every new technique, there is a lively discussion about the usefulness and limitations of MMPA behind the scenes of official publications. We think that many questions about the applicability of MMPA results and the true value of MMPA can be answered if the statistics behind MMPA is understood and put on solid ground. In particular, it can be shown that all doubts revolving around issues such as the paucity of pairs for specific contexts, the experimental uncertainty and variability of the transformation

sets, the issue of mixing data from different laboratories, the influence of the chemical neighborhood, and the variability of the physical effect can be addressed within a common statistical framework. In this publication, we demonstrate how MMPA issues can be analytically understood using the equation for the paired t test. We show how the minimum number of pairs necessary to achieve significance can be calculated, and we describe the important difference between statistical significance and effect size estimation, i.e., the point when the estimate for the average chemical effect becomes acceptably reliable. All the statistical points are illustrated using hERG MMPA data from ChEMBL17. The connection between statistical analysis and the interpretation of the discovered rules in lead optimization are detailed using the hydrogen to chlorine, hydroxy, and phenyl transformation. Finally, we compare the transformation statistics from CHEMBL17 data to the Novartis in-house data and show that both agree extremely well if the transformations are significant. Before starting with the theoretical details, we want to add some notes on practical issues: In the remaining work, we will exclusively use the paired t test, since this allows sketching of mathematical relations between the involved effects in a clear and simple way. The paired t test only works for continuous data under the constraint that it is sufficiently normally distributed. If the target data are categorical, a multinomial test can be used. If the target data are continuous but clearly not normally distributed, a Wilcoxon signed-rank test can be used. Also, it is recommendable to analyze the data at hand for sufficient chemotype diversity in order to not inadvertently generalize trends for a single scaffold series.

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THEORY The paired t test is the appropriate statistical test for normally distributed activity or property differences between sets of pairs of molecules. Compared to the Z-test and Z-score, the t test corrects for the fact that the true average and standard deviation are not known but calculated from the samples. The test statistic t is calculated according to t=

ΔAct − μ0 σD

n

Here, n is the number of pairs, ΔAct is the average activity difference, σD is the standard deviation of the sample differences, and μ0 is the offset from the null hypothesis that is usually set to zero for MMPA. The calculated t-value can be compared against tabulated two-sided t-values, and the probability that the observed distribution would be observed by randomly drawing samples from a distribution with the average μ0 (usually 0.0) and standard deviation σD can be obtained. If the probability is below a given threshold (often 0.05), the observed distribution is called significantly different from zero. If the observed distribution is not significantly different from zero, the standard MMPA interpretation is that it is unclear whether the chemical transformation on average causes an increase or a decrease in activity. Statistical significance only indicates whether an average is above or below zero with a given certainty; significance itself does not tell anything about how much above or below zero the average effect is. A given chemical transformation with hundreds of thousands of pairs available could be extremely significantly different from zero but only have a very small B



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laboratories and different assays, they will be called heterogeneous pair. If homogeneous and heterogeneous pairs are to be pooled in MMPA, the equation for the pooled standard deviation can be used to estimate σexp:

average effect and thus be completely uninteresting for lead optimization. The average activity difference ΔAct , combined with the standard error of the mean (SEM) σ SEM ΔAct = D n is relevant for estimating the quantitative impact of a chemical transformation. Note that in the context of MMPA, SEM and σD quantify very different phenomena: SEM indicates how reliable the estimate for the average effect is (compared to the average effect calculated from an infinite number matched pairs with the same transformation and chemical context), whereas σD quantifies how similar the effect of the transformation on individual pairs is. Schoenbrodt and Perugini describe the corridor of stability as a threshold in number of samples starting from which statistical estimates have a smaller deviation than a given threshold.24 For MMPA, the corridor of stability for ΔAct can be calculated from the equation of SEM, since for normal distributions the 95% confidence interval (CI95) is always 1.96 times broader than the SEM. σ CI 95 = 1.96 SEM = 1.96 D n

σexp =

nhomo + nhetero − 2

Here, nhomo and σexp,homo correspond to the number and the experimental standard deviation of the pairs measured in the same laboratory and assay whereas nhetero and σexp,hetero represent the same for all other pairs. When searching for effects in databases and testing a series of transformations for significance, chances of finding random effects that appear significant increase with the number of transformations analyzed. This can be taken into account using corrections such as the Bonferroni correction for multiple testing.28 An important practical question for MMPA is the minimum number of pairs needed to achieve statistical significance. This can be answered by rearranging the equation for the t-value (which is a function of the significance level and the degrees of freedom) for ΔAct ,

The equations for SEM and CI95 only hold for large n, since for small samples the real σ is systematically underestimated, even using Bessel’s correction.25 For example, the true σ is on average underestimated by 20% for n = 2, by 6% for n = 5, and by 3% by n = 10. Nevertheless, the numbers calculated using the idealized equations (using the normal distribution) are sufficient to give an idea about critical numbers, even if caution should be used when interpreting the absolute numbers. Both SEM and t depend on the standard deviation σD of the activity differences. σD itself depends on two different factors: (1) the experimental uncertainty or comparability of the two activities within the pair (σexp) and (2) the true physical spread of the effect of the transformations (σtrue) according to σD =

(nhomo − 1)σexp,homo 2 + (nhetero − 1)σexp,hetero 2

ΔAct,min =

t(0.5 + p/2, df = n − 1)σD n

and repeatedly solving for various n, drawn from a normal distribution with σD. p is the significance level and df are the degrees of freedom, calculated as n − 1.

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HERG The human ether-a-go-go-related gene (hERG) product is a potassium channel that is responsible for repolarization of the cell membrane during the heart’s action potential.29−32 Blockade of this channel can lead to QT prolongation, which in turn increases the risk for potentially fatal torsades des pointes. The hERG channel is able to bind a variety of different chemotypes, and hERG blockade has been the reason for withdrawal of several drugs from different drug classes from the market.33−38 Since hERG is one of the major antitargets in drug design, there is plenty of biochemical data on hERG blockade in both public and company databases.39 The hERG data in CHEMBL have been measured in a number of different assays, including patch-clamp and radioligand displacement assays with different radioligands. The internal Novartis hERG data have been measured in a radioligand displacement assay, using terfenadine or E-4031 as reference ligand. The experimental uncertainties of the internal Novartis assay, calculated from repeated measurements for the reference ligands, are σexp = 0.32 log units for terfenadine and σexp = 0.39 log units for E-4031. The experimental uncertainties extracted from all double measurements of various ligands with terfenadine as reference ligand are σexp = 0.26 log units and σexp = 0.32 log units with E-4031 as reference ligand. Since most compounds are measured in duplicate or triplicate (uncertainty is reduced with approximately 1/√n) and the experimental uncertainties themselves vary, we use 0.2 log units as experimental uncertainty for the activity of individual Novartis hERG activities. There have been many different publications on models for hERG binding, including classic QSAR models, pharmacophore

2σexp2 + σtrue 2

The experimental uncertainty of the individual measurement has to be multiplied by 2 because MMPA analyzes the differences between two measurements that both contain experimental uncertainty. For highly context-specific matchedmolecular pairs, the transformation effect on affinity will always be very similar and σtrue will approximate zero with increasing levels of context refinement. σexp directly depends on the measurements. On the basis of a huge set of independent double measurements extracted from ChEMBL, Kramer et al. have recently estimated σexp = 0.54 log units for heterogeneous public pKi values.26 Using a similar methodology, Kalliokoski et al. have arrived at σexp = 0.69 log units for pIC50 values, measured in different laboratories.27 For two series of control measurements of the assay standards within Novartis, they have calculated σexp = 0.2 log units. From these values and the equations given above, it immediately follows that pairs measured in the same assays are to be preferred over pairs from different assays, since pairs from different assays have a higher σexp and thus a higher SEM and lower t-values. For the remaining document, we will use the following terminology: If two data points that form a pair have been measured in the same laboratory and the same assay, they will be called homogeneous pair. If they have been measured in different laboratories or different assays or both different C



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Table 1. Calculated Minimum Average Activity (pKi/ pIC50) Difference ΔAct,min Necessary To Achieve Statistical Significance at the p = 0.05 Levela heterogeneous pKi, σexp = 0.54 n 2 3 4 5 7 10 20 50 100

σtrue = 0.0 5.47 1.68 1.13 0.89 0.68 0.53 0.35 0.22 0.15

± ± ± ± ± ± ± ± ±

4.10 0.89 0.48 0.32 0.20 0.13 0.06 0.02 0.01

σtrue = 0.5 6.53 2.02 1.34 1.06 0.81 0.64 0.42 0.26 0.18

± ± ± ± ± ± ± ± ±

4.96 1.04 0.56 0.39 0.24 0.15 0.07 0.03 0.01

heterogeneous pIC50, σexp = 0.69 σtrue = 0.0 7.00 2.15 1.43 1.15 0.86 0.68 0.45 0.28 0.19

± ± ± ± ± ± ± ± ±

σtrue = 0.5

5.25 1.13 0.60 0.42 0.26 0.16 0.07 0.03 0.01

7.83 2.40 1.61 1.29 0.97 0.77 0.51 0.31 0.22

± ± ± ± ± ± ± ± ±

5.88 1.26 0.67 0.47 0.29 0.18 0.08 0.03 0.02

homogeneous pKi/pIC50, σexp = 0.2 σtrue = 0.0 2.02 0.62 0.42 0.33 0.25 0.20 0.13 0.08 0.06

± ± ± ± ± ± ± ± ±

1.54 0.32 0.17 0.12 0.07 0.05 0.02 0.008 0.004

σtrue = 0.5 4.12 1.27 0.84 0.67 0.51 0.40 0.27 0.16 0.11

± ± ± ± ± ± ± ± ±

3.09 0.66 0.36 0.24 0.15 0.10 0.04 0.02 0.008

Note that the values behind the plus−minus sign indicate the standard deviation of the simulated ΔAct,min , not the standard error of the mean. σexp denotes the experimental uncertainty or variability for the individual measurements. Values for σexp are taken from Kramer et al.26 and Kalliokoski et al.27 a

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models, homology models, and MMPA.40−62 The general hERG pharmacophore includes a positively ionizable nitrogen and two or three aliphatic or aromatic features distributed around the positively ionizable feature. It has been recognized that both log Pow and the pKa of the nitrogen are correlated with hERG binding.

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RESULTS Minimum Activity Difference To Achieve Significance. The minimum average activity difference ΔAct,min necessary in order to find that a chemical transformation has an effect that is significantly different from zero can be calculated for a given number of pairs n, σD, and a significance level p. Table 1 shows values for ΔAct,min , calculated for different values of n and σD at the p = 0.05 level. For two pairs of identical transformations, the minimum activity difference varies between 2.02 ± 1.54 and 7.83 ± 5.88 log units. This is a lot more than typically found for any transformation; therefore, it can safely be assumed that transformations with only two examples will never represent a statistically significant result. The standard deviations are quite high for small numbers; even for seven matched pairs, the standard deviation of ΔAct,min is between a third and a fourth of the total difference. This indicates that the significance estimates vary drastically and for small n should be interpreted with caution. With 10 pairs, the minimum activity difference to achieve significance varies between 0.2 ± 0.05 log units for homogeneous pairs and 0.77 ± 0.18 log units for heterogeneous IC50 pairs. Table 1 reveals that there is a big difference between homogeneous and heterogeneous pairs. For example, if there is no physical variation, i.e., the effect is highly similar as in the case of very context-sensitive matched pairs, four pairs are needed to identify a statistically significant effect with an average activity difference of 0.42 log units from homogeneous pairs. For heterogeneous pairs, it takes between 10 and 20 pairs for pKi data and more than 20 pairs for pIC50 data. If there is some variation in the true physical effect, i.e., σtrue = 0.5 log units, it takes between 7 and 10 homogeneous pairs but 20 heterogeneous pairs for pKi data and well between 20 and 50 heterogeneous pairs for pIC50 data. A larger variance for the true physical effect has a stronger effect on data from the same assay, since it proportionally adds more noise here. Therefore, it is highly desirable to only compare homogeneous matched pairs, if possible. Fortunately, matching pairs within the same assay and laboratory is easily possible because ChEMBL reports an assay identifier. Mixing Homogeneous and Heterogeneous Pairs. In some situations it might not be possible to always create homogeneous pairs or it may be possible to complement a small set of homogeneous pairs with heterogeneous pairs. Table

METHODS AND MATERIALS

All numerical simulations and calculations have been done using R63 and Python. For all values calculated from sampling, 10 000 repetitions have been used per setting. The scripts are available from the authors upon request. hERG MMPA based on all publicly available hERG data from ChEMBL17 and on the Novartis in-house database has been carried out in the following steps: (1) All available hERG IC50 and Ki data have been extracted from ChEMBL1764 and the Novartis in-house database. (2) Only hERG inhibition data with exact values (no qualifiers) between 1 mM and 0.1 pM and a CHEMBL target confidence score of at least 4 were used. We refrained from using only data with the highest possible confidence score (9), since earlier tests (details not shown) indicated that starting from a value of 4, the experimental variation for double measurements does not become smaller with increasing target confidence. We only considered compounds with up to 70 heavy atoms. All compounds where the difference between minimum and maximum measured value was larger than 2.5 log units were removed in order to filter out unreliable data.65,66 (3) After stripping off salts and checking for valid SMILES strings using RDKit,67 the RDKit implementation of the Hussain and Rea MMP algorithm15 was used to create the raw matched pair data set. We allowed maximally 10 heavy atoms to be exchanged for a valid matched pair. (4) The raw matched pairs were pooled across identical transformations, and the activity differences for each transformation were assigned. For each activity entry, ChEMBL17 supplies an assay identification. If both members of the pair were measured in the same assay and laboratory, the difference between these two measurements was assigned and all measured affinities from other assays were dropped (homogeneous). If there was no overlap between the assay identifications of both compounds forming the pair, the average activity for both was used to calculate the activity difference (heterogeneous). For all transformations, the results ( ΔAct , σD, n, p) were calculated for sets that only contain homogeneous pairs and sets that contain the maximum number of pairs (including both homogeneous and heterogeneous pairs). D



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Table 2. Calculated Minimum Average Activity Difference ΔAct,min Necessary to Achieve Statistical Significance at the p = 0.05 Level for Different Mixtures of Homogeneous Pairs (nhomo) and Heterogeneous Pairs (nhetero) with σtrue = 0.0 log Unitsa nhomo nhetero 0 2 3 5 10 20 50

0 7.00 2.15 1.15 0.68 0.45 0.28

± ± ± ± ± ±

2 5.25 1.13 0.42 0.16 0.07 0.03

2.02 1.06 0.95 0.78 0.58 0.42 0.27

± ± ± ± ± ± ±

1.54 0.44 0.34 0.23 0.12 0.07 0.03

3

5

10

20

50

0.62 ± 0.32 0.71 ± 0.26 0.72 ± 0.23 0.66 ± 0.18 0.53 ± 0.11 0.40 ± 0.06 0.26 ± 0.03

0.33 ± 0.12 0.45 ± 0.13 0.49 ± 0.13 0.50 ± 0.12 0.45 ± 0.09 0.37 ± 0.05 0.25 ± 0.02

0.20 ± 0.05 0.25 ± 0.06 0.29 ± 0.06 0.32 ± 0.06 0.33 ± 0.05 0.30 ± 0.04 0.23 ± 0.02

0.13 ± 0.02 0.15 ± 0.02 0.17 ± 0.03 0.20 ± 0.03 0.22 ± 0.03 0.23 ± 0.03 0.20 ± 0.02

0.08 ± 0.008 0.09 ± 0.009 0.09 ± 0.009 0.10 ± 0.01 0.12 ± 0.01 0.14 ± 0.01 0.14 ± 0.01

a

Note that the values behind the plus−minus sign indicate the standard deviation of the simulated ΔAct,min , not the standard error of the mean. Experimental variability used are σexp,homo = 0.2 log units and σexp,hetero = 0.69 log units. Cases where adding heterogeneous pairs increases (worsens) ΔAct,min are highlighted in bold.

Table 3. Number of Matched Pairs Necessary To Calculate the Average Effect within ±0.1 Log Unit

2 shows ΔAct,min necessary to achieve significance for pIC50 data and pooled homogeneous and heterogeneous pairs with p = 0.05, σtrue = 0.5 log units. Table 2 shows that starting from three matched homogeneous pairs, it only makes sense to add heterogeneous pairs if the number of heterogeneous pairs is much higher than the number of homogeneous pairs. Adding a smaller fraction of heterogeneous pairs adds more noise than information. For creating the results in Table 2, we have used parameters for σexp,homo, σexp,hetero, and σtrue, which we would consider typical for MMPA. Different parameters will yield slightly different distributions, but there will often be situations where adding few additional heterogeneous pairs is detrimental. Set aside scientific concerns about mixing IC50 data from different assays, a rule of thumb can be that for mixing pairs from the same assay with pairs of IC50 data from different assays, there have to be at least twice as many pairs from different assays in order not to deteriorate the overall statistics. Fortunately, this is not a problem for MMPA based on public data, since most similar pairs have been measured in the same assays and laboratories (as will be shown later). Number of Pairs Necessary for Effect Size Estimation. Apart from statistical significance, the absolute effect size is an interesting property, since it indicates the absolute activity difference to be expected from adding and removing specific functional groups. Statistical significance only indicates whether some effect is different from zero but not by how much. In order to illustrate the number of pairs needed for effect size estimation, we calculate the minimum number of samples necessary to reduce the CI95 for the estimation of the mean effect to ±0.1 log unit (which is chosen about as arbitrarily as the 0.05 p-level for significance estimation). The CI95 is independent of the average effect but depends on σexp and σtrue. In Table 3, we show the calculated number of pairs necessary for different settings with low and high experimental uncertainty and true physical variation. It takes many more pairs to estimate the average effect of chemical transformation within ±0.1 log units than it takes to identify significance. For example, even when using homogeneous pairs with zero physical variation between the pairs, it still takes 31 pairs to estimate the average effect. In contrast, five homogeneous pairs are sufficient to discover a statistically significant effect if the true average activity difference is at least 0.33 log units. If a little physical variation of 0.2 log units is added, 46 pairs are necessary to reliably estimate the average effect. If heterogeneous pairs are used, 224−462 pairs are

physical variation, σtrue [log units] experimental variability, σexp [log units] homogeneous heterogeneous Ki heterogeneous IC50

0.2 0.54 0.69

0.0 31 224 366

0.2 46 239 381

0.5 127 320 462

necessary to estimate the average physical effect. This is more than is usually available in any data set apart from the most common transformations like hydrogen → methyl or hydrogen → fluorine. While it may be sufficient to know the direction in which a chemical transformation will change activity in lead optimization, the above analysis shows that even with highly context-specific data sets the prediction of the absolute effect necessitates dozens or hundreds of pairs. This is not a problem if MMPA is used as an idea generator that gives a rough idea of the biochemical effect of the transformations, but it is problematic if quantitative predictions are sought. hERG MMPA. We extracted all hERG Ki and IC50 data from ChEMBL17 and performed MMPA on the data, as described in the Methods and Materials section. Significance at the p = 0.05 level has been calculated using the paired t test. On the basis of homogeneous pairs only, we found 296 different transformations with a significant effect on hERG binding. For some transformations with only few pairs available, the standard deviation σD of the differences is lower than 0.28, which is the lower threshold for σD if we assume an experimental uncertainty σexp for the individual measurement of 0.2 log units (√2 × 0.2 = 0.28). The low standard deviation is most probably an artifact from insufficient sampling. For those cases, we recalculated the t- and p-values using σD = 0.28 in the equation for the t test. This correction rendered 104 additional transformations insignificant. A comparison of the σD values against the number of pairs per transformation is shown in Figure 1. Transformations that become insignificant after correcting σD are highlighted in red. After correcting σD, 192 transformations with a significant effect remain. Figure 1 shows that only transformations with very few pairs have a σD lower than 0.3 log units. All transformations with more than 10 pairs have a σD higher than 0.28. The distribution of the number of pairs per transformation with a significant E



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constructed from simpler and more frequently occurring transformations. Therefore, the coverage evaluation by transformation type is arguably not very relevant in the end. The CHEMBL17 hERG data sets contains 15 651 pairs of molecules, which are connected by one or several transformations that exchange less than 11 heavy atoms. A total of 1853 pairs are connected by a transformation with a significant effect, corresponding to 12% of all pairs. Still, individual molecules may be part of several pairs. For predicting the activity of a new compound, it can be sufficient if the compound can be reached via one single transformation with a significant effect. Overall, there are 4633 different compounds in the CHEMBL17 hERG data set that we analyzed. Out of these, 1969 compounds are involved in at least one transformation that has a significant effect, corresponding to 42% of all compounds. So nearly half of all compounds used for the hERG analysis can be reached by a transformation with an effect that is significantly different from zero. The above analysis is not complete because it ignores some factors that are relevant for lead optimization: First, insignificant transformations with a small SEM, e.g., bioisosteric replacements,68 can also be very useful for predicting the activity of a new compound. This would increase the number of compounds for which MMPA is helpful. Second, significance does not necessarily mean that the effect size is well understood. Transformations with a significant effect can yield very inaccurate predictions where the sign of the predicted difference is correct, but the exact difference is highly variable. Third, MMPA would be applied prospectively in practice, but the above analysis does not take into account the order in which chemical series have been synthesized. The numbers calculated above indicate that the coverage of the CHEMBL17 hERG MMPA could be around 50% of the whole database, but a realistic coverage study that also takes into account effect size estimates and synthesis date is more complex and beyond the scope of this contribution. Most Frequent Transformations. The 21 most frequent transformations are listed in Table 4. A full list of all significant transformations can be found in the Supporting Information. The most frequent transformation is the addition of a methyl group. According to the analysis of all 405 transformations, adding a methyl on average increases hERG binding by 0.11 ± 0.03 log units. Analysis of the 390 homogeneous pairs only yields exactly the same numbers. For the hydrogen to chlorine transformations, there is one single example where both compounds that form the pair have been measured in different assays. The activity difference of this pair does not agree with the other pairs: The average increase in hERG binding according to the mixed set analysis is 0.41 ± 0.06 log units, whereas the average increase according to the homogeneous pairs is 0.44 ± 0.05. The standard deviation for the homogeneous set is smaller (0.48 vs 0.58) and the overall signal is stronger, indicating that the single heterogeneous pair is a strong outlier. Overall, the statistics for the most frequent transformations are very similar when analyzing homogeneous pairs only or mixed homogeneous and heterogeneous pairs. This is mainly due to the fact that homogeneous pairs are the major subset of the total set of pairs. In some cases, the standard deviation of the homogeneous pairs is a little bit lower (for example, for the hydrogen to trifluoromethyl transform and the hydrogen to methylhydroxy transform). In other cases, the average activity

Figure 1. Number of homogeneous pairs versus standard deviation for all transformations with a significant effect on hERG affinity. For each transformation, there are at least three pairs available. Transformations with a very low initial σD calculated from the pairs, which become insignificant when using σD = 0.28 log units in the t test, are colored in red.

effect on hERG binding (with corrected σD) are shown in Figure 2.

Figure 2. Number of pairs per transformation with an effect significantly different from zero found for all ChEMBL17 hERG Ki and IC50 data. Note that the x-axis is square root transformed. The total number of transformations is 192.

Figure 2 shows that there are very few transformations with many examples. Overall, there are 192 types of transformations found with a significant effect. For 38 of these, there are only three pairs available. For another 32 transformations, there are only four pairs available. MMPA Coverage. The usefulness of MMPA depends on the coverage of the data set. If MMPA is only applicable for a small fraction of all predictions to be made, it will be less useful overall. MMPA database coverage can be calculated in a number of different ways that yield different fractions of database coverage. Here, we calculate and discuss three different coverage metrics. A total of 192 of all 28 588 different transformation types that we extracted from CHEMBL17 hERG data have a significant effect, corresponding to 0.67% of the set of all transformation types. In the Hussain and Rea algorithm, there can be several transformation types per pair, each including a different amount of context specification. This leads to a large set of transformations that formally only occur once but can be F



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Table 4. 21 Most Common Chemical Transformations with a Significant Effect on hERG Activity Found in ChEMBL17a homogeneous and heterogeneous pairs

homogeneous pairs only

transformation

n

ΔAct ± SEM

σD

p

n

ΔAct ± SEM

σD

p

R-H → R-CH3 R-H → R-Cl R1-CH2-R2 → R1-C2H4-R2 R-CH3 → R-C2H5 R-F → R-Cl R-H → R−OH R-H → R-CF3 R-CH3 → R-CF3 R-CH3 → R-Cl o-R1,R2-phenyl → m-R1,R2-phenyl R-CH3 → R-isopropyl R-H → R-CH2OH R-F → R-CF3 R-CH3 → R-phenyl R-phenyl → R-(p-fluorophenyl) 1,2-R1,R2-ethan → 1,1-R1,R2-ethan R-OCH3 → R-Cl R-CH3 → R-cyclopropyl R-CH3 → R-phenyl 1,4-R1,R2-phenyl → 1,3,4-R1,Cl,R2-phenyl 4,5-R1,R2-oxazole → 2,5-R1,R2-quinoline

405 111 81 78 78 62 60 59 46 42 31 28 27 26 26 25 24 23 22 21 20

0.11 ± 0.03 0.41 ± 0.06 0.13 ± 0.06 0.24 ± 0.05 0.29 ± 0.04 −0.38 ± 0.07 0.35 ± 0.07 0.48 ± 0.07 0.17 ± 0.06 0.13 ± 0.06 0.29 ± 0.09 −0.30 ± 0.10 0.36 ± 0.11 0.51 ± 0.13 0.27 ± 0.06 −0.33 ± 0.10 0.34 ± 0.09 0.47 ± 0.08 0.64 ± 0.13 0.28 ± 0.07 0.32 ± 0.08

0.59 0.58 0.51 0.41 0.33 0.54 0.58 0.54 0.41 0.38 0.48 0.53 0.56 0.66 0.32 0.49 0.45 0.37 0.63 0.34 0.36

0.00018 2.6 × 10−11 0.024 1.7 × 10−06 2.8 × 10−10 7.6 × 10−07 1.5 × 10−05 7.2 × 10−09 0.0068 0.026 0.0023 0.0055 0.0025 0.00054 0.00024 0.0029 0.0011 3.70× 10−06 0.00011 0.0013 0.00083

390 110 73 76 76 52 59 58 44 42 30 27 27 26 26 24 24 22 22 19 19

0.11 ± 0.03 0.44 ± 0.05 0.14 ± 0.06 0.24 ± 0.05 0.29 ± 0.04 −0.40 ± 0.08 0.37 ± 0.07 0.48 ± 0.07 0.17 ± 0.06 0.13 ± 0.06 0.30 ± 0.09 −0.27 ± 0.10 0.36 ± 0.11 0.51 ± 0.13 0.27 ± 0.06 −0.36 ± 0.10 0.34 ± 0.09 0.48 ± 0.08 0.64 ± 0.13 0.28 ± 0.07 0.33 ± 0.08

0.59 0.48 0.53 0.41 0.33 0.57 0.57 0.54 0.42 0.38 0.48 0.51 0.56 0.66 0.32 0.48 0.45 0.39 0.63 0.34 0.37

0.00026 5.1 × 10−16 0.022 1.8 × 10−06 1.6 × 10−10 5.3 × 10−06 5.2 × 10−06 7.7 × 10−09 0.013 0.026 0.002 0.011 0.0025 0.00054 0.00024 0.0013 0.0011 1.60 × 10−05 0.00011 0.0013 0.00096

a

Analysis based on all pairs found and analysis based on only those pairs that have been measured in the same assays are shown side by side. The pvalue is calculated using Student’s t-test.

anchoring atom, and context-sensitive MMPA10,14,22 would probably reveal different subgroups within these sets. Only for four out of the first five transformations (hydrogen → methyl, hydrogen → chlorine, methyl → ethyl, fluorine → chlorine) the CI95 (1.96 × SEM) is smaller than 0.1 log units, and thus, the average effect size can be estimated at a very accurate level. For all other transformations, more examples are needed in order to fully characterize the average affinity difference to be expected. From a statistical point of view, the fluorine → chlorine transform is especially interesting because it is the only nearly fully characterized transformation. It has an average affinity difference of 0.28 log units and a very low standard deviation (σD = 0.33 log units) close to the standard deviation that can be explained by experimental noise only, this indicates that there is almost no context-sensitive effect visible from the available CHEMBL data. Additionally, the CI95 is below 0.1 log units, indicating that the effect size estimate is very stable. Interestingly, the difference of the AlogP increments between fluorine and chlorine is 0.27,72 very close to the hERG affinity difference of 0.28 log units. Clarifying whether or not there really is no context-dependency for this transform will, however, need more data and detailed studies. Assuming that the lipophilicity as measured by log P scales 1:1 with hERG binding (which is indicated in studies by Kawai et al.73 and assumed in the lipophilic ligand efficiency index74), the observed difference in hERG affinity due to changing fluorine to chlorine can purely be assigned to the difference in lipophilicity as the major driving force for hERG binding. However, it needs to be noted that scaling factors of 0.5 and less have also been indicated in the literature.12,69 For all other transformations, more pairs and context-sensitive analysis are needed in order to fully statistically characterize the effect. Where Does the Spread in Differences Come From? An Analysis of the Extreme Cases of the Hydrogen to

difference is slightly larger for the homogeneous set (for example, for the hydrogen to hydroxy transform or the methyl to isopropyl transform). However, these are minor effects. In order to avoid adding pairs that introduce more noise than signal, we recommend to only analyze pairs that have been measured in the same assay. This is obviously easy for MMPA based on large company databases, but according to the analysis shown here, it is also possible for literature-based MMPA (e.g., on CHEMBL data). For the most frequent transformations shown in Table 4, 96% of the pairs that are amenable for MMPA have been measured in the same assay anyway. In general, the effects of the transformations identified are in agreement with prior chemical hERG knowledge: Most of the transformations in Table 4 add lipophilic groups and increase hERG binding.40,69−71 For example, the introduction of chlorine adds 0.44 ± 0.05 log units in hERG affinity. Adding a hydroxyl function on average decreases hERG binding by 0.40 log units, and a methylhydroxy group on average decreases hERG binding by 0.27 log units. Interestingly, moving one carbon atom out of a linker into a terminal methyl group on average decreases hERG binding by 0.36 log units. This is a nonstandard modification with respect to hERG affinity, indicating that branching or introducing a bend in the structure can be favorable for reducing hERG affinity. The standard deviation of the effects seems to be loosely correlated with the differences in size introduced in the transformation. The lowest standard deviations σD are found for the fluorine to chlorine transform (0.33) and the benzene to p-fluorobenzene transform (0.32). Assuming a contribution of √2 × 0.2 log units from the experimental uncertainty, there is almost no physical variation in the effect of these transforms. The largest standard deviations are found for the methyl to benzene transform (0.66) and the hydrogen to benzene transform (0.63). The large standard deviations indicate that the effect strongly depends on the chemical environment of the G



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Chlorine, Hydroxy, and Phenyl Transformations. Hydrogen to Chlorine. Overall, there are 110 pairs of compounds available that have been measured in the same hERG assay where hydrogen has been replaced by chlorine. The effects of the transformation on hERG have an average of 0.44 log units and σD = 0.48 log units. Inspection of the pairs with the most extreme effects revealed that they included four errors (wrong stereochemistry, wrong values copied from other publication, wrong value entered into CHEMBL) in the database. After removal of the erroneous pairs, the average effect is 0.41 log units with σD = 0.43 log units. We decided to nevertheless keep these pairs as a known bias in the overall statistics shown in Table 4, since it is impossible to inspect all pairs of all transformations and fully remove the bias. Figure 3 shows a histogram of the distribution of the hERG affinity differences for the hydrogen to chlorine transformation.

respectively. The common pattern here is the rather electron rich aromatic systems onto which chlorine is attached. Whether or not there is a specific pattern yielding a strong increase in hERG affinity through the addition of chlorine to an electron rich aromatic ring has to be determined in further studies. In all cases, the chlorine is added to an aromatic ring. A simple context description according to the nature of the anchoring atom would not help to distinguish between the different cases. The rather rare cases where the addition of chlorine reduces hERG affinity can be explained by special effects, such as conformational changes and modified acidity. In standard cases, addition of chlorine can be expected to increase hERG affinity. Hydrogen to Hydroxy. In CHEMBL17, there are 52 pairs of compounds that have been measured in the same hERG assay and are connected by the hydrogen to hydroxy transformation. The transformation effects span from −1.82 to 1.11 log units in hERG affinity difference with an average effect of −0.40 log units and σD = 0.57 log units. Inspection of the pairs with the strongest effects revealed three database errors (% efflux mistaken with Ki, wrongly copied value from older publication, and copy-and-paste error into CHEMBL). If these are removed, the average effect of the transformation is −0.38 log units with σD = 0.52 log units. The distribution of affinity differences is shown in Figure 4. The compounds where the hydrogen to hydroxy transformation has the least and the most beneficial effect on hERG affinity (excluding database errors) are shown in Table 6. In pair 7, introduction of the hydroxy group causes a decrease in hERG affinity of 1.84 log units.80 In the words of the authors of the original publication, “This is a dramatic example of the effect of polarity on hERG inhibition as the incorporation of the tertiary alcohol decreased hERG inhibition almost 70-fold ...”. This is certainly the most extreme example in the CHEMBL database: the affinity decrease is 4.5 times stronger than would normally be expected. In pairs 881 and 9,82 the additional hydroxy group causes a decrease in hERG affinity of 1.42 and 1.11 log units, respectively. In all three pairs 7−9, the hydroxy is added as a secondary or tertiary hydroxy group on an aliphatic ring. This might be a pattern that leads to very strong decrease in hERG binding, but our data with n = 6 (including the next three pairs) are too little to draw strong conclusions from. This has to be verified with additional pairs but is beyond the scope of this contribution. In pairs 10,83 11,84 and 12,47 addition of a hydroxy group increases hERG affinity by 0.46, 0.50, and 1.07 log units. This is counterintuitive; one would usually expect polar groups to decrease hERG binding. For compounds 10 and 11, there can be tautomeric forms. In the Cambridge Crystallographic Database, the pure hydroxyisoquinoline of 11 is crystallized as the isoquinolinone tautomer. Tautomerism could strongly affect hERG binding and explain the observed differences. In addition, the reliability of the published affinity values of pair 10 are doubtful, since 196 and 67 μM are at the low affinity end of the assay. In pair 11, both values have been measured with n = 1, so this could also be random outliers. We recommend retesting these two. For pair 12, there are not many experimental details given in the original publication, and we did not find any clear reason to discard the values. It would be interesting to independently remeasure pair 12: If this addition of a hydroxy group really turns out to increase hERG binding

Figure 3. Distribution of hERG affinity differences for the hydrogen to chlorine transformation.

The distribution looks very normal, with the average effect on hERG affinity at 0.4 log units and maxima and minima of −0.76 and 1.9 log units. These two, however, are erroneous entries in the CHEMBL database (original publication copies wrong values from older publication, and “>” sign ignored). The compounds where the hydrogen to chlorine transformation really (excluding database errors) has the least and the most beneficial effect on hERG affinity are shown in Table 5. In pair 1, introduction of the chlorine reduces hERG affinity by 0.66 log units.75 Since the chlorine is in ortho position of two other large groups, this could be a steric effect causing a conformational change of the ligand upon introduction of the chlorine. Introduction of bromine in the same position also reduces hERG affinity by 0.84 log units. In pair 2, the hERG affinity is reduced by 0.49 log units upon introduction of the chlorine.76 This is most probably also due to a steric effect, since the chlorine is added in ortho position to the linker. Introducing fluorine in the same position also reduces hERG affinity by 0.68 log units. In pair 3, introduction of the second chlorine on the ring reduces hERG affinity by 0.43 log units.77 The authors of the original publication argue that the second chlorine increases the acidity of the aromatic hydroxy group and thereby reduces the overall lipophilicity of the compound. This inductive effect of the chlorine is to be expected, but it will only make a difference if there is another group whose acidity can be modified. In pairs 4,78 5,79 and 679 introduction of the chlorine increases hERG affinity by 1.40, 1.52, and 1.73 log units, H



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Table 5. Pairs with the Most Extreme Effects on hERG Affinity Due to Hydrogen → Chlorine Transformationa

a

The introduced chlorine is highlighted.

average effect of the transformation is 0.58 log units with σD = 0.61 log units. The distribution of affinity differences is shown in Figure 5. This distribution does not look Gaussian. However, it consists of rather few underlying examples plus some database errors, so there are too little data for drawing statistical conclusions about different underlying effects. The compounds where the addition of a phenyl group has the largest effects on hERG affinity in both directions (excluding database errors) are shown in Table 7.

so strongly, several hERG pharmacophores would have to be revised. Hydrogen to Phenyl. In CHEMBL17, there are 22 pairs of compounds that have been measured in the same hERG assay and are connected by the hydrogen to phenyl transformation. The transformation effects span from −0.50 to 1.54 log units in hERG affinity difference with an average effect of 0.64 log units and σD = 0.63 log units. Inspection of the pairs with the strongest effects revealed two database errors (CHEMBL transcription error and inadvertent conversion of single % efflux value from older publication into Ki). If these are removed, the I



Article

variability of the effect of specific transformations: Chlorine usually increases hERG affinity, but if added to the appropriate aromatic system with two hydroxy groups, it can also decrease hERG affinity by increasing the acidity of the hydroxy groups. These effects have to be separated with context-specific MMPA, but for the statistical identification of most of these effects databases probably have to grow more. A simple aromatic/ aliphatic anchor differentiation will not help in the majority of cases we identified. Validation with Novartis Data. In order to test the robustness of the MMPA statistics, we compared the average activity differences of the transformations with significant effects in CHEMBL17 with the average activity differences of the same transformations from Novartis in-house hERG data. Overall, we found 69 transformations that have a statistically significant effect in both databases. Sixteen additional transformations were initially significant in both databases but became insignificant in at least one database when calculating the t test with σD = 0.28 log units. A plot of the average effect sizes of all transformations that were initially significant in both databases is shown in Figure 6. A plot of the average effect sizes of all transformations that are insignificant in both databases is shown in Figure 7. Note that it is indeed the average effects of the transformations that we want to compare, so there is no artificial correlation inflation effect92 created here. The full statistics about all transformations that are covered with at least two pairs in both databases is given in the Supporting Information. The average activity differences for transformations that are significant in databases agree very well with an R2 of 0.83. Both databases perfectly agree on the sign of the average activity difference of all 69 transformations that are significant in both databases. The initial set of differences had an unrealistically low σD for some transformations due to insufficient sampling. After correction of the t and p values with σD = 0.28 log units, 16 transformations become insignificant in at least one of the databases. For 3 of the 16 transformations that we discard because of insignificance, the sign between the CHEMBL MMPA set and the Novartis in-house set does not agree. This shows that it is important to calculate the t test based on a realistic estimate for σD. The average activity differences for insignificant transformations show almost no correlation (R2 = 0.11). For many insignificant transformations, the MMPA results from the two databases do not even agree on the sign. This clearly shows that the statistics must not be ignored if transferable MMPA results are expected. MMPA results based on too few pairs are not reliable. The effect of the transformations tends to be stronger in CHEMBL, which can be seen from the slope of 1.22. Possible explanations for this effect are a publication bias (only the modifications with a stronger effect are published) and different chemical space covered in ChEMBL and the Novartis database. Also, the standard deviations of the transformation effects are systematically larger by roughly 0.1 log units in the CHEMBL data (details not shown). This can most probably be explained with a larger number of errors that cause extreme effects in the CHEMBL database. Overall, the predictions of the effect of specific molecular transformations on hERG affinity turn out to be highly reliable and transferable, if sufficient prior data are available and the statistics indicate significant effects. There is no single significant transformation where both databases disagree on

Figure 4. Distribution of hERG affinity differences for the hydrogen to hydroxy transformation.

In pairs 1385 and 14,86 addition of a phenyl ring decreases hERG affinity by 0.50 and 0.21 log units, respectively. This is counterintuitive, since additional hydrophobic groups usually increase hERG binding. However, the molecules of both groups are already quite large, and the introduced phenyl groups might cause unfavorable steric repulsions with the hERG channel. This would be in line with findings from a hERG model by Zachariae et al.91 The hERG channel has quite a large pore, but the additional phenyl rings might render the molecule slightly too large to fit the channel. In pair 15 the addition of the phenyl ring decreases hERG binding by 0.19 log units.87 The series that includes these two molecules has a very interesting SAR with respect to hERG, and the effect is most probably steric: With hydrogen only at the substitution position, the hERG affinity is 0.72 μM. With methyl, hERG affinity drops to >10 μM, and with ethyl it becomes 5 μM. The bulkier the substituent gets, the stronger is the hERG affinity. The substitution position is ortho to another aromatic ring on a double-ring system: With the hydrogen substituent, the other two aromatic systems can be coplanar. With larger substituents, this is not possible anymore and hERG affinity drops. In pairs 16,88 17,89 and 18,90 addition of a phenyl ring increases hERG affinity by 1.22, 1.52, and 1.54 log units. We did not find any particular pattern for these pairs. Overall, there are too little data for the hydrogen to phenyl transformation to create smaller subsets. A simple aliphatic/ aromatic anchoring environment differentiation cannot separate the two groups described above. The analysis of matched molecular pairs at the extreme ends of the hERG affinity difference distributions reveals that apart from experimental uncertainty, there are a number of factors that contribute to variability of the chemical effect for the same transformation: First, databases contain errors. We found wrongly assigned values, ignored qualifiers, % efflux values that were misread as Ki values, and wrong stereochemistry. The errors were introduced both when copying to CHEMBL and in QSAR publications that wrongly cite values from other publications. It appears that MMPA can be a very valuable tool for cleaning up databases. MMPA can identify surprising outcomes of specific transformations, and these often turn out to be database errors. Second, we found that steric effects that most probably change the ligand conformation can also play a role for hERG inhibition; for example, it can counterintuitively lead to decreased hERG affinity upon introduction of a phenyl ring. There are also other chemical effects that increase the J



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Table 6. Pairs with the Most Extreme Effects on hERG Affinity Due to Hydrogen → Hydroxy Transformationb

a

Stereochemistry not fully defined. bThe introduced hydroxy group is highlighted.

Joining CHEMBL and Novartis Data. A practically important question is whether joining pairs from CHEMBL with the more homogeneous set of Novartis in-house pairs increases the applicability domain of MMPA or rather destroys the in-house statistics by adding heterogeneous and noisy public data. In order to test this, we generated a joint data set

the directionality of the effect. The differences in the absolute effects are to be expected from both the example calculations of the CI95 and the differences between the Novartis database and CHEMBL. Still, the analysis shows that the t test used to test for significance (affinity differences from zero) is able to extract highly trustworthy MMPA results. K



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effects either point to database issues or call for a deeper scientific analysis. The theoretical analysis presented here is based on the paired t test, which in turn depends on the assumption of normally distributed differences. Even if in reality this may not always be the case, the numbers that can be estimated using the analysis presented here give a rough estimate for the number of pairs necessary to achieve significance or even full effect size estimation. If normality can be assumed, the t test covers all data issues (experimental uncertainty, paucity of pairs, physical variability) that usually arise in MMPA, apart from the chemical diversity of the pairs.6 This issue is related to applicability domain questions and has to be established with different methods. In the past, MMPA has often been used to identify bioisosteres, i.e., molecular replacements that do not change the affinity.19,22 While we did not detail the statistical tools for bioisosterism tests, with some minor modifications the paired t test and the SEM considerations can also be used to statistically test for bioisosterism. Dossetter et al. have proposed MMPA as part of a medicinal chemistry expert system that proposes chemical modifications in lead optimization.5 This points in the direction where we expect MMPA to practically play a major role in the future. Since there are only few examples for most transformations available and MMPA is a purely statistical approach, proper statistical analysis of the knowledge gained from MMPA, as outlined in this contribution, will be very important for future MMPA and medicinal chemistry expert systems. If MMPA statistics is carried out appropriately, the results are very reliable and thus useful.

Figure 5. Distribution of hERG affinity differences for the hydrogen to phenyl transformation.

from Novartis and CHEMBL17 hERG data and recalculated the statistics as indicated above. In the Novartis data set, there are 286 transformation types with a significant effect on hERG affinity. In the joint data set, this number increases to 393 transformation types. This clearly shows that adding CHEMBL data to in-house data can increase the applicability domain of MMPA. A plot of the average effect on affinity for the transformations is shown in Figure 8. Both sets perfectly agree on the sign of the effects for all transformations. There are 25 transformation types whose effect becomes insignificant if the CHEMBL data are included (shown in red). For all of these transformations, the average affinity difference gets closer to zero due to adding CHEMBL data. In contrast, there are 132 transformation types that become significant due to adding CHEMBL data. The absolute value of the average affinity difference of these transformations tends to increase, but there are also a number of examples where the average affinity difference gets closer to zero. The transformation types whose effect gets closer to zero become more significant because there are more example pairs available. Outlook. The standard deviation of the activity differences gives a direct hint towards the matched pair sets that would benefit from further refinement based on the chemical context of the anchoring atom. Context-dependent MMPA is a very promising addition to standard MMPA. The main issue for context-sensitive MMPA is the arising paucity of pairs if the transformation sets are further divided according to their chemical context. In general, context-sensitive MMPA will deal with smaller standard deviations but also fewer pairs. The statistical issues arising from having less but more focused data can be handled using the statistical tools explained in this contribution. The practical implications of our analysis on molecular design are threefold: First, we have shown how to rigorously quantify promising transformations. This is important in a setting where synthesis or assays are expensive and resources need to be economically allocated. In such a setting, the appropriate statistics for MMPA helps to identify the most promising transformations. Second, our work paves the way to appropriately set expectations: If a transformation has never or only once or twice been observed before, estimations about the effects of such transformations are rather broad. Also, the experimental uncertainty has a significant impact on single observations. Third, statistical analysis of matched molecular pairs allows one to define normal and extreme effects. Extreme

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CONCLUSIONS We have analyzed the relation between experimental uncertainty and MMPA, described the statistical significance calculation for MMPA, and showed that the effects of molecular transformations on hERG affinity based on CHEMBL17 data agree very well with Novartis in-house data if both are statistically significant. By use of the paired t test, it is possible to calculate the number of pairs necessary to achieve statistical significance with a given average activity difference and vice versa. Using standard estimates for the experimental uncertainty of pairs measured in the same assay and pairs measured in different assay, we numerically demonstrate that it is highly desirable to build pairs from identical assays measured in the same laboratory. For normal effect sizes (activity differences of 0.5 log units), four pairs can be sufficient to identify significant differences if the pairs have been measured in the same assay and laboratory. If the pairs are assembled from different assays or laboratories, it takes at least 10−20 pairs to reach the same level of significance. Mixing heterogeneous pairs (assembled from different assays) among homogeneous pairs only makes sense if more than double the number of homogeneous pairs can be added. Otherwise, heterogeneous pairs will only add noise. For a quantitative estimation of the average effect size, we calculate that it takes at least 31 pairs in order to estimate the average activity difference with a 95% confidence interval lower than 0.1 log unit. We present a statistical analysis of matched molecular pairs extracted for all hERG Ki and IC50 data extracted from ChEMBL17. The most frequent pairs all fit to prior knowledge about hERG, e.g., the average effect of all transformations L



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Table 7. Pairs with the Most Extreme Effects on hERG Affinity Due to Addition of a Phenyl Groupa

a

The introduced phenyl is highlighted.

statistically robust MMPA results. In addition, we have shown that Novartis and CHEMBL data can be pooled and the gain from an increased coverage of transformation space is much larger than the loss due to an increase in noise. If only the transformations are published, MMPA offers a nice way of

agrees with lipophilicity. The average affinity differences we identified in the CHEMBL database are highly correlated with hERG affinity differences from MMPA on the internal Novartis database. Both databases perfectly agree on the sign of the effect, and the effects themselves are highly correlated. This shows that public databases can be sufficiently large to deliver M



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Figure 6. Comparison of MMPA average activity differences from CHEMBL17 and Novartis in-house data for all transformations that initially appear significant (at the 0.05 level) in both databases. Error bars indicate the SEM of the average activity difference. Transformations whose average activity difference becomes insignificant after correcting with σD = 0.28 log units are shown in red. This includes all three transformations where CHEMBL and the Novartis database initially disagree about the sign of the average effect. The correlation for the average effect of all transformations that remain significant is R2 = 0.83 with a slope of 1.22.

Figure 8. Comparison of MMPA average activity differences from Novartis in-house data and the joint Novartis/CHEMBL17 data set. Transformations are colored according to the data set in which they are significant: Transformations that are significant in both sets are colored in gray; transformations that are only significant in the Novartis set are colored in red. Transformations that become significant in the joint set are colored in blue. Error bars indicate the SEM of the average activity difference.

Detailed analysis of the pairs with very different effects on hERG affinity for the hydrogen to chlorine, hydroxy, and phenyl transformation revealed electronic and steric features that contribute to the variability of the effects. Inspection of the pairs with extreme effects gave insights into different molecular mechanisms that modulate hERG affinity, although based on the same molecular transformations. MMPA turns out to be a valuable tool for both predicting the effects of molecular transformations and fishing interesting SAR examples from databases that lead to a deeper understanding of medicinal chemistry principles. We thus conclude that MMPA is a very robust tool for lead optimization and will have growing importance in the daily medicinal chemistry practice with context-sensitive analysis based on growing bioactivity databases, if the statistics are appropriately carried out as outlined in this contribution.

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ASSOCIATED CONTENT

S Supporting Information *

All hERG transformations extracted from CHEMBL17 and the corresponding statistics from the Novartis in-house database, a Python program to generate the MMP analysis, and scripts to generate the plots of this publication. This material is available free of charge via the Internet at http://pubs.acs.org.

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Figure 7. Comparison of MMPA average activity differences from CHEMBL17 and Novartis in-house data for all transformations that are insignificant (at the 0.05 level) in both databases. Error bars indicate the SEM of the average activity difference. The correlation for the average effect of all transformations that are insignificant in both databases is R2 = 0.11 with a slope of 0.53.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +43 512 507 57103. Notes

sharing precompetitive information between companies and the public without exposing proprietary information.

The authors declare no competing financial interest. N



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ACKNOWLEDGMENTS The editors of the Journal of Medicinal Chemistry have granted a waiver on the proprietary data deposition requirements for the Novartis validation set.

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ABBREVIATIONS USED ADME, absorption, distribution, metabolism, excretion; CADD, computer-aided drug design; CI95, 95% confidence interval; hERG, human ether-a-go-go-related gene; MMPA, matched molecular pair analysis; QSAR, quantitative structure− activity relationship; QSPR, quantitative structure−property relationship; SAR, structure−activity relationship; SEM, standard error of the mean; σ, standard deviation

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