iCliff Taylor's Version: Robust and Efficient Activity Cliff Determination

Abstract

Activity cliffs represent an important challenge to tackle in cheminformatics and drug design. One of the most common indicators to quantify them is the Structure-Activity Landscape Index (SALI). Here, we expose the mathematical limitations of SALI's formulation, the most evident: it is undefined in instances where the similarity between two molecules is one. We show how using a simple Taylor's series can aid this main problem, yielding a defined expression that can capture the ranking information from the original SALI. The second issue to solve is the quadratic complexity of using SALI to describe the roughness of the activity landscape of a set. Here, we propose iCliff, an indicator that can quantify the roughness in linear complexity. For this, we leverage the iSIM framework to obtain the average similarity of the set and a rearrangement to obtain the average of the squared property differences. The calculations for 30 different AC-focused databases suggest that there is a strong correlation between iCliff and the average pairwise of SALI's pairwise Taylor Series. To further explore the individual effects of removing each molecule in the activity landscape, we propose complementary iCliff. With this tool, we were able to identify the molecules that have a high number of activity cliffs with the rest of the molecules in the set.

Figure 1.

Activity cliff example for a pair of molecules with peroxisome proliferator-activated receptor delta (PPARδ) activity. Tanimoto similarity calculated from RDKIT binary fingerprints (2048 bits).

Figure 2.

Kendall’s tau correlations between the SALI and TS_SALI values for different truncation orders over the 30 studied libraries represented with ECFP4 (1024 bits), MACCS (166 bits), and RDKIT (2048 bits) binary fingerprints. In A) SALI is defined as in Eq. 1, in B) we use SALI with the squared property difference.

Figure 3.

Distribution of pairwise TS_SALI values using 3^rd order truncation for the A) ChEMBL264 and B) ChEMBL2835 libraries represented with ECFP4 fingerprints.

Figure 4.

Relationship between the average TS SALI value (from the TS SALI pairwise matrix) and the iCliff value for the 30 ChEMBL’s databases represented with ECPF4 fingerprints (1024 bits). The tendency line is shown in gray.

Figure 5.

iCliff values for the ChEMBL databases studied before and after removing activity cliffs (molecules in pairs with TS₃_SALI > the 99^th percentile). Molecules represented ECFP4 (1024-bit) fingerprints. The number of molecules annotated over the bars.

Figure 6.

Kendall’s tau correlations between the cTS_SALI and iCliff values over the 30 studied libraries using ECFP4 fingerprints.

Figure 7.

Variation of the Jaccard similarity between the ranking of cTS_SALI and complementary iCliff, when varying the fraction of molecules. A) CHEMBL2835_Ki and B) CHEMBL1862_Ki. Horizontal lines at 0.8 and 0.9, vertical line at 10% of the size of each set.

Figure 8.

iCliff values for the studied ChEMBL databases before and after removing activity cliffs (5% of molecules with lowest complementary iCliff). Molecules are represented with ECFP4 (1024-bit) fingerprints.

Figure 9.

Examples of separated pairs by the removal of the top 5% molecules with the lowest complementary iCliff values. Structures, pKi, and Tanimoto similarities between the pairs are shown. Molecules were represented using ECFP4 (1024-bit) fingerprints.