Skip to main content
SpringerLink
Log in

Extended continuous similarity indices: theory and application for QSAR descriptor selection

  • Published:
Journal of Computer-Aided Molecular Design Aims and scope Submit manuscript

Abstract

Extended (or n-ary) similarity indices have been recently proposed to extend the comparative analysis of binary strings. Going beyond the traditional notion of pairwise comparisons, these novel indices allow comparing any number of objects at the same time. This results in a remarkable efficiency gain with respect to other approaches, since now we can compare N molecules in O(N) instead of the common quadratic O(N2) timescale. This favorable scaling has motivated the application of these indices to diversity selection, clustering, phylogenetic analysis, chemical space visualization, and post-processing of molecular dynamics simulations. However, the current formulation of the n-ary indices is limited to vectors with binary or categorical inputs. Here, we present the further generalization of this formalism so it can be applied to numerical data, i.e. to vectors with continuous components. We discuss several ways to achieve this extension and present their analytical properties. As a practical example, we apply this formalism to the problem of feature selection in QSAR and prove that the extended continuous similarity indices provide a convenient way to discern between several sets of descriptors.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

Data availability

Data is available from the authors upon reasonable request. Python code for calculating the extended similarity measures is freely available at: https://github.com/ramirandaq/MultipleComparisons

References

  1. Bajusz D, Rácz A, Héberger K (2017) Chemical data formats, fingerprints, and other molecular descriptions for database analysis and searching. In: Chackalamannil S, Rotella DP, Ward SE (eds) Comprehensive medicinal chemistry III. Elsevier, Oxford, pp 329–378

    Chapter  Google Scholar 

  2. Bender A, Glen RC (2004) Molecular similarity: a key technique in molecular informatics. Org Biomol Chem 2:3204–3218

    Article  CAS  Google Scholar 

  3. Bajusz D, Rácz A, Héberger K (2015) Why is Tanimoto index an appropriate choice for fingerprint-based similarity calculations? J Cheminform 7:20. https://doi.org/10.1186/s13321-015-0069-3

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  4. Saxena A, Prasad M, Gupta A et al (2017) A review of clustering techniques and developments. Neurocomputing 267:664–681. https://doi.org/10.1016/J.NEUCOM.2017.06.053

    Article  Google Scholar 

  5. Geppert H, Vogt M, Bajorath J (2010) Current trends in ligand-based virtual screening: molecular representations, data mining methods, new application areas, and performance evaluation. J Chem Inf Model 50:205–216. https://doi.org/10.1021/ci900419k

    Article  CAS  PubMed  Google Scholar 

  6. Eckert H, Bajorath J (2007) Molecular similarity analysis in virtual screening: foundations, limitations and novel approaches. Drug Discov Today 12:225–233. https://doi.org/10.1016/j.drudis.2007.01.011

    Article  CAS  PubMed  Google Scholar 

  7. Willett P (2009) Similarity methods in chemoinformatics. Annu Rev Inf Sci Technol 43:1–117. https://doi.org/10.1002/aris.2009.1440430108

    Article  Google Scholar 

  8. Willett P (2006) Similarity-based virtual screening using 2D fingerprints. Drug Discov Today 11:1046–1053. https://doi.org/10.1016/j.drudis.2006.10.005

    Article  CAS  PubMed  Google Scholar 

  9. Willett P (2013) Fusing similarity rankings in ligand-based virtual screening. Comput Struct Biotechnol J 5:e201302002. https://doi.org/10.5936/csbj.201302002

    Article  PubMed  PubMed Central  Google Scholar 

  10. Willett P (2013) Combination of similarity rankings using data fusion. J Chem Inf Model 53:1–10. https://doi.org/10.1021/ci300547g

    Article  CAS  PubMed  Google Scholar 

  11. Todeschini R, Consonni V, Xiang H et al (2012) Similarity coefficients for binary chemoinformatics data: overview and extended comparison using simulated and real data sets. J Chem Inf Model 52:2884–2901. https://doi.org/10.1021/ci300261r

    Article  CAS  PubMed  Google Scholar 

  12. Rácz A, Andrić F, Bajusz D, Héberger K (2018) Binary similarity measures for fingerprint analysis of qualitative metabolomic profiles. Metabolomics. https://doi.org/10.1007/s11306-018-1327-y

    Article  PubMed  PubMed Central  Google Scholar 

  13. Rácz A, Bajusz D, Héberger K (2018) Life beyond the Tanimoto coefficient: similarity measures for interaction fingerprints. J Cheminform 10:48. https://doi.org/10.1186/s13321-018-0302-y

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  14. Miranda-Quintana RA, Bajusz D, Rácz A, Héberger K (2021) Differential consistency analysis: which similarity measures can be applied in drug discovery? Mol Inform 40:2060017. https://doi.org/10.1002/minf.202060017

    Article  CAS  Google Scholar 

  15. Miranda-Quintana RA, Bajusz D, Rácz A, Héberger K (2021) Extended similarity indices: the benefits of comparing more than two objects simultaneously. Part 1: theory and characteristics. J Cheminform 13:32. https://doi.org/10.1186/s13321-021-00505-3

    Article  PubMed  PubMed Central  Google Scholar 

  16. Miranda-Quintana RA, Rácz A, Bajusz D, Héberger K (2021) Extended similarity indices: the benefits of comparing more than two objects simultaneously. Part 2: speed, consistency, diversity selection. J Cheminform 13:33. https://doi.org/10.1186/s13321-021-00504-4

    Article  PubMed  PubMed Central  Google Scholar 

  17. Dunn TB, Seabra GM, Kim TD et al (2021) Diversity and chemical library networks of large data sets. J Chem Inf Model. https://doi.org/10.1021/ACS.JCIM.1C01013

    Article  PubMed  Google Scholar 

  18. Chang L, Perez A, Miranda-Quintana RA (2021) Improving the analysis of biological ensembles through extended similarity measures. BioRxiv. https://doi.org/10.1101/2021.08.08.455555

    Article  PubMed  PubMed Central  Google Scholar 

  19. Flores-Padilla A, Eurídice Juárez-Mercado K, Naveja JJ et al (2021) Chemoinformatic characterization of synthetic screening libraries focused on epigenetic targets. ChemRxiv. https://doi.org/10.33774/CHEMRXIV-2021-0PQ98

    Article  Google Scholar 

  20. Bajusz D, Miranda-Quintana RA, Rácz A, Héberger K (2021) Extended many-item similarity indices for sets of nucleotide and protein sequences. Comput Struct Biotechnol J 19:3628–3639. https://doi.org/10.1016/j.csbj.2021.06.021

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  21. Cherkasov A, Muratov EN, Fourches D et al (2014) QSAR modeling: where have you been? Where are you going to? J Med Chem 57:4977–5010. https://doi.org/10.1021/jm4004285

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  22. Piir G, Kahn I, García-Sosa AT et al (2018) Best practices for QSAR model reporting: physical and chemical properties, ecotoxicity, environmental fate, human health, and toxicokinetics endpoints. Environ Health Perspect 126:126001. https://doi.org/10.1289/EHP3264

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  23. Algamal ZY, Qasim MK, Lee MH, Mohammad Ali HT (2020) High-dimensional QSAR/QSPR classification modeling based on improving pigeon optimization algorithm. Chemom Intell Lab Syst 206:104170. https://doi.org/10.1016/J.CHEMOLAB.2020.104170

    Article  CAS  Google Scholar 

  24. Gaulton A, Bellis LJ, Bento AP et al (2012) ChEMBL: a large-scale bioactivity database for drug discovery. Nucleic Acids Res 40:D1100–D1107. https://doi.org/10.1093/nar/gkr777

    Article  CAS  PubMed  Google Scholar 

  25. Bolton EE, Wang Y, Thiessen PA, Bryant SH (2008) Chapter 12—PubChem: integrated platform of small molecules and biological activities. Annual reports in computational chemistry. Elsevier, Amsterdam, pp 217–241

    Google Scholar 

  26. Andersen CM, Bro R (2010) Variable selection in regression—a tutorial. J Chemom 24:728–737. https://doi.org/10.1002/cem.1360

    Article  CAS  Google Scholar 

  27. Leardi R (2007) Genetic algorithms in chemistry. J Chromatogr A 1158:226–233. https://doi.org/10.1016/J.CHROMA.2007.04.025

    Article  CAS  PubMed  Google Scholar 

  28. Goodarzi M, Dejaegher B, Vander HY (2012) Feature selection methods in QSAR studies. J AOAC Int 95:636–651. https://doi.org/10.5740/JAOACINT.SGE_GOODARZI

    Article  CAS  PubMed  Google Scholar 

  29. Eklund M, Norinder U, Boyer S, Carlsson L (2014) Choosing feature selection and learning algorithms in QSAR. J Chem Inf Model 54:837–843. https://doi.org/10.1021/CI400573C

    Article  CAS  PubMed  Google Scholar 

  30. National Center for Biotechnology Information. PubChem Database. Source=NCGC, AID=1851

  31. Rácz A, Bajusz D, Miranda-Quintana RA, Héberger K (2021) Machine learning models for classification tasks related to drug safety. Mol Divers 25:1409–1424. https://doi.org/10.1007/s11030-021-10239-x

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  32. Mauri A, Consonni V, Pavan M, Todeschini R (2006) Dragon software: an easy approach to molecular descriptor calculations. MATCH Commun Math Comput Chem 56:237–248

    CAS  Google Scholar 

  33. (2018) Dragon 7.0, Kode Cheminformatics. Dragon 70, Kode Cheminformatics

  34. Rácz A, Bajusz D, Héberger K (2019) Intercorrelation limits in molecular descriptor preselection for QSAR/QSPR. Mol Inform 38:1800154. https://doi.org/10.1002/minf.201800154

    Article  CAS  PubMed Central  Google Scholar 

  35. Bajusz D, Ferenczy GG, Keserű GM (2015) Property-based characterization of kinase-like ligand space for library design and virtual screening. Med Chem Commun 6:1898–1904. https://doi.org/10.1039/C5MD00253B

    Article  CAS  Google Scholar 

  36. Kelemen AA, Ferenczy GG, Keserű GM (2015) A desirability function-based scoring scheme for selecting fragment-like class A aminergic GPCR ligands. J Comput Aided Mol Des 29:59–66. https://doi.org/10.1007/s10822-014-9804-5

    Article  CAS  PubMed  Google Scholar 

  37. Héberger K (2010) Sum of ranking differences compares methods or models fairly. TrAC Trends Anal Chem 29:101–109. https://doi.org/10.1016/j.trac.2009.09.009

    Article  CAS  Google Scholar 

  38. Sipos L, Gere A, Popp J, Kovács S (2018) A novel ranking distance measure combining Cayley and Spearman footrule metrics. J Chemom 32:e3011. https://doi.org/10.1002/cem.3011

    Article  CAS  Google Scholar 

  39. Héberger K, Kollár-Hunek K (2011) Sum of ranking differences for method discrimination and its validation: comparison of ranks with random numbers. J Chemom 25:151–158. https://doi.org/10.1002/cem.1320

    Article  CAS  Google Scholar 

  40. Héberger K, Kollár-Hunek K (2019) Comparison of validation variants by sum of ranking differences and ANOVA. J Chemom 33:e3104. https://doi.org/10.1002/CEM.3104

    Article  Google Scholar 

  41. Lourenco JM, Lebensztajn L (2018) Post-Pareto optimality analysis with sum of ranking differences. IEEE Trans Magn 54:1–10. https://doi.org/10.1109/TMAG.2018.2836327

    Article  Google Scholar 

  42. Gere A, Rácz A, Bajusz D, Héberger K (2021) Multicriteria decision making for evergreen problems in food science by sum of ranking differences. Food Chem 344:128617. https://doi.org/10.1016/j.foodchem.2020.128617

    Article  CAS  PubMed  Google Scholar 

  43. Saratxaga CL, Bote J, Ortega-Morán JF et al (2021) Characterization of optical coherence tomography images for colon lesion differentiation under deep learning. Appl Sci 11:3119. https://doi.org/10.3390/APP11073119

    Article  CAS  Google Scholar 

  44. Sziklai BR (2021) Ranking institutions within a discipline: the steep mountain of academic excellence. J Informetr 15:101133. https://doi.org/10.1016/J.JOI.2021.101133

    Article  Google Scholar 

  45. West C (2018) Statistics for analysts who hate statistics, part VII: sum of ranking differences (SRD). LCGC North Am 36:2–6

    Google Scholar 

Download references

Funding

National Research, Development and Innovation Office of Hungary (OTKA), contracts K_20 134260 (KH) and PD_20 134416 (AR). University of Florida: startup grant: RAMQ. Hungarian Academy of Sciences: János Bolyai Research Scholarship: DB. Ministry for Innovation and Technology of Hungary: ÚNKP-21-5 New National Excellence Program: DB.

Author information

Author notes

  1. Anita Rácz and Timothy B. Dunn have contributed equally to this work.

Authors and Affiliations

  1. Plasma Chemistry Research Group, Research Centre for Natural Sciences, Magyar Tudósok Krt. 2, 1117, Budapest, Hungary

    Anita Rácz & Károly Héberger

  2. Department of Chemistry, University of Florida, Gainesville, FL, 32611, USA

    Timothy B. Dunn, Taewon D. Kim & Ramón Alain Miranda-Quintana

  3. Medicinal Chemistry Research Group, Research Centre for Natural Sciences, Magyar Tudósok Krt. 2, 1117, Budapest, Hungary

    Dávid Bajusz

  4. Quantum Theory Project, University of Florida, Gainesville, FL, 32611, USA

    Ramón Alain Miranda-Quintana

Authors
  1. Anita Rácz
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Timothy B. Dunn
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Dávid Bajusz
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Taewon D. Kim
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Ramón Alain Miranda-Quintana
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Károly Héberger
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Ramón Alain Miranda-Quintana or Károly Héberger.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary Information

Below is the link to the electronic supplementary material.

Supplementary file1 (DOCX 4056 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Rácz, A., Dunn, T.B., Bajusz, D. et al. Extended continuous similarity indices: theory and application for QSAR descriptor selection. J Comput Aided Mol Des 36, 157–173 (2022). https://doi.org/10.1007/s10822-022-00444-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10822-022-00444-7

Keywords

Search

Navigation