Similarity search profiles as a diagnostic tool for the analysis of virtual screening calculations

An analysis method termed similarity search profiling has been developed to evaluate fingerprint-based virtual screening calculations. The analysis is based on systematic similarity search calculations using multiple template compounds over the entire value range of a similarity coefficient. In graphical representations, numbers of correctly identified hits and other detected database compounds are separately monitored. The resulting profiles make it possible to determine whether a virtual screening trial can in principle succeed for a given compound class, search tool, similarity metric, and selection criterion. As a test case, we have analyzed virtual screening calculations using a recently designed fingerprint on 23 different biological activity classes in a compound source database containing approximately 1.3 million molecules. Based on our predefined selection criteria, we found that virtual screening analysis was successful for 19 of 23 compound classes. Profile analysis also makes it possible to determine compound class-specific similarity threshold values for similarity searching.     

Anatomy of fingerprint search calculations on structurally diverse sets of active compounds

Similarity searching using molecular fingerprints is a widely used approach for the identification of novel hits. A fingerprint search involves many pairwise comparisons of bit string representations of known active molecules with those precomputed for database compounds. Bit string overlap, as evaluated by various similarity metrics, is used as a measure of molecular similarity. Results of a number of studies focusing on fingerprints suggest that it is difficult, if not impossible, to develop generally applicable search parameters and strategies, irrespective of the compound classes under investigation. Rather, more or less, each individual search problem requires an adjustment of calculation conditions. Thus, there is a need for diagnostic tools to analyze fingerprint-based similarity searching. We report an analysis of fingerprint search calculations on different sets of structurally diverse active compounds. Calculations on five biological activity classes were carried out with two fingerprints in two compound source databases, and the results were analyzed in histograms. Tanimoto coefficient (Tc) value ranges where active compounds were detected were compared to the distribution of Tc values in the database. The analysis revealed that compound class-specific effects strongly influenced the outcome of these fingerprint calculations. Among the five diverse compound sets studied, very different search results were obtained. The analysis described here can be applied to determine Tc intervals where scaffold hopping occurs. It can also be used to benchmark fingerprint calculations or estimate their probability of success.     

Large-scale similarity search profiling of ChEMBL compound data sets

A large-scale similarity search investigation has been carried out on 266 well-defined compound activity classes extracted from the ChEMBL database. The analysis was performed using two widely applied two-dimensional (2D) fingerprints that mark opposite ends of the current performance spectrum of these types of fingerprints, i.e., MACCS structural keys and the extended connectivity fingerprint with bond diameter four (ECFP4). For each fingerprint, three nearest neighbor search strategies were applied. On the basis of these search calculations, a similarity search profile of the ChEMBL database was generated. Overall, the fingerprint search campaign was surprisingly successful. In 203 of 266 test cases (～76%), a compound recovery rate of at least 50% was observed with at least the better performing fingerprint and one search strategy. The similarity search profile also revealed several general trends. For example, fingerprint searching was often characterized by an early enrichment of active compounds in database selection sets. In addition, compound activity classes have been categorized according to different similarity search performance levels, which helps to put the results of benchmark calculations into perspective. Therefore, a compendium of activity classes falling into different search performance categories is provided. On the basis of our large-scale investigation, the performance range of state-of-the-art 2D fingerprinting has been delineated for compound data sets directed against a wide spectrum of pharmaceutical targets.     

Fingerprint scaling increases the probability of identifying molecules with similar activity in virtual screening calculations.

Results of systematic virtual screening calculations using a structural key-type fingerprint are reported for compounds belonging to 14 activity classes added to randomly selected synthetic molecules. For each class, a fingerprint profile was calculated to monitor the relative occupancy of fingerprint bit positions. Consensus bit patterns were determined consisting of all bits that were always set on in compounds belonging to a specific activity class. In virtual screening calculations, scale factors were applied to each consensus bit position in fingerprints of query molecules. This technique, called "fingerprint scaling", effectively increases the weight of consensus bit positions in fingerprint comparisons. Although overall prediction accuracy was satisfactory using unscaled calculations, scaling significantly increased the number of correct predictions but only slightly increased the rate of false positives. These observations suggest that fingerprint scaling is an attractive approach to increase the probability of identifying molecules with similar activity by virtual screening. It requires the availability of a series of related compounds and can be easily applied to any keyed fingerprint representation that associates bit positions with specific molecular features.     

Balancing the influence of molecular complexity on fingerprint similarity searching

Differences in molecular complexity and size are known to bias the evaluation of fingerprint similarity. For example, complex molecules tend to produce fingerprints with higher bit density than simple ones, which often leads to artificially high similarity values in search calculations. We introduce here a variant of the Tversky coefficient that makes it possible to modulate or eliminate molecular complexity effects when evaluating fingerprint similarity. This has enabled us to study in detail the role of molecular complexity in similarity searching and the relationship between reference and active database compounds. Balancing complexity effects leads to constant distributions of similarity values for reference and database molecules, independent of how compound contributions are weighted. When searching for active compounds with varying complexity, hit rates can be optimized by modulating complexity effects, rather than eliminating them, and adjusting relative compound weights. For reference molecules and active database compounds having different complexity, preferred parameter settings are identified.     

Analysis of a high-throughput screening data set using potency-scaled molecular similarity algorithms

Molecular similarity methods for ligand-based virtual screening (VS) generally do not take compound potency as a variable or search parameter into account. We have incorporated a logarithmic potency scaling function into two conceptually distinct VS algorithms to account for relative compound potency during search calculations. A high-throughput screening (HTS) data set containing cathepsin B inhibitors was analyzed to evaluate the effects of potency scaling. Sets of template compounds were randomly selected from the HTS data and used to search for hits having varying potency levels in the presence or absence of potency scaling. Enrichment of potent compounds in small subsets of the HTS data set was observed as a consequence of potency scaling. In part, observed enrichments could be rationalized as a result of recentering chemical reference space on a subspace populated by potent compounds. Our findings suggest that VS calculations using multiple reference compounds can be directed toward the preferential detection of potent database hits by scaling compound contributions according to potency differences.     

Introduction of the conditional correlated Bernoulli model of similarity value distributions and its application to the prospective prediction of fingerprint search performance

A statistical approach named the conditional correlated Bernoulli model is introduced for modeling of similarity scores and predicting the potential of fingerprint search calculations to identify active compounds. Fingerprint features are rationalized as dependent Bernoulli variables and conditional distributions of Tanimoto similarity values of database compounds given a reference molecule are assessed. The conditional correlated Bernoulli model is utilized in the context of virtual screening to estimate the position of a compound obtaining a certain similarity value in a database ranking. Through the generation of receiver operating characteristic curves from cumulative distribution functions of conditional similarity values for known active and random database compounds, one can predict how successful a fingerprint search might be. The comparison of curves for different fingerprints makes it possible to identify fingerprints that are most likely to identify new active molecules in a database search given a set of known reference molecules.     

Bounds and algorithms for fast exact searches of chemical fingerprints in linear and sublinear time

Chemical fingerprints are used to represent chemical molecules by recording the presence or absence, or by counting the number of occurrences, of particular features or substructures, such as labeled paths in the 2D graph of bonds, of the corresponding molecule. These fingerprint vectors are used to search large databases of small molecules, currently containing millions of entries, using various similarity measures, such as the Tanimoto or Tversky's measures and their variants. Here, we derive simple bounds on these similarity measures and show how these bounds can be used to considerably reduce the subset of molecules that need to be searched. We consider both the case of single-molecule and multiple-molecule queries, as well as queries based on fixed similarity thresholds or aimed at retrieving the top K hits. We study the speedup as a function of query size and distribution, fingerprint length, similarity threshold, and database size |D| and derive analytical formulas that are in excellent agreement with empirical values. The theoretical considerations and experiments show that this approach can provide linear speedups of one or more orders of magnitude in the case of searches with a fixed threshold, and achieve sublinear speedups in the range of O(|D|0.6) for the top K hits in current large databases. This pruning approach yields subsecond search times across the 5 million compounds in the ChemDB database, without any loss of accuracy.