Editing Quantitative structure–activity relationship (section)

{{Short description|Predictive chemical model}}

'''Quantitative structure–activity relationship''' models ('''QSAR''' models)  are [[regression analysis|regression]] or classification models used in the chemical and biological sciences and engineering. Like other regression models, QSAR regression models relate a set of "predictor" variables (X) to the potency of the [[response variable]] (Y), while classification QSAR models relate the predictor variables to a categorical value of the response variable.

In QSAR modeling, the predictors consist of physico-chemical properties or theoretical [[molecular descriptor]]s<ref>{{cite book |last1=Todeschini |first1=Roberto |last2=Consonni |first2=Viviana |title=Molecular Descriptors for Chemoinformatics |series=Methods and Principles in Medicinal Chemistry |year=2009 |volume=41 |publisher=Wiley |doi=10.1002/9783527628766 |isbn=978-3-527-31852-0 |url=https://onlinelibrary.wiley.com/doi/book/10.1002/9783527628766 |language=en}}</ref><ref>{{cite book |last1=Mauri |first1=Andrea |last2=Consonni |first2=Viviana |last3=Todeschini |first3=Roberto |title=Handbook of Computational Chemistry |publisher=Springer International Publishing |isbn=978-3-319-27282-5 |pages=2065–2093 |url=https://link.springer.com/referenceworkentry/10.1007/978-3-319-27282-5_51 |language=en |chapter=Molecular Descriptors|year=2017 |doi=10.1007/978-3-319-27282-5_51 }}</ref> of chemicals; the QSAR response-variable could be a [[biological activity]] of the chemicals. QSAR models first summarize a supposed relationship between [[chemical structure]]s and [[biological activity]] in a data-set of chemicals.  Second, QSAR models [[predictive inference|predict]] the activities of new chemicals.<ref>{{cite book |last1=Roy |first1=Kunal |last2=Kar |first2=Supratik |last3=Das |first3=Rudra Narayan | name-list-style = vanc | chapter = Chapter 1.2: What is QSAR? Definitions and Formulism |title=A primer on QSAR/QSPR modeling: Fundamental Concepts |date=2015 |publisher=Springer-Verlag Inc |location=New York |isbn=978-3-319-17281-1 |pages=2–6 |chapter-url=https://books.google.com/books?id=FFcSCAAAQBAJ&pg=PA4 }}</ref><ref>{{cite journal |last1=Ghasemi  |first1=Pérez-Sánchez|last2=Mehri |first2= Pérez-Garrido |year=2018 |title= Neural network and deep-learning algorithms used in QSAR studies: merits and drawbacks |journal=Drug Discovery Today |volume=23 |issue=10 |pages=1784–1790 |doi=10.1016/j.drudis.2018.06.016|pmid=29936244|s2cid=49418479}}</ref>

Related terms include ''quantitative structure–property relationships''  (''QSPR'') when a chemical property is modeled as the response variable.<ref name = "Nantasenamat_2009">{{cite journal | vauthors = Nantasenamat C, Isarankura-Na-Ayudhya C, Naenna T, Prachayasittikul V | title = A practical overview of quantitative structure-activity relationship | journal = Excli Journal | volume = 8 | pages = 74–88 | year = 2009 | doi = 10.17877/DE290R-690 }}</ref><ref name = "Nantasenamat_2010">{{cite journal | vauthors = Nantasenamat C, Isarankura-Na-Ayudhya C, Prachayasittikul V | title = Advances in computational methods to predict the biological activity of compounds | journal = Expert Opinion on Drug Discovery | volume = 5 | issue = 7 | pages = 633–54 | date = Jul 2010 | pmid = 22823204 | doi = 10.1517/17460441.2010.492827 | s2cid = 17622541 }}</ref>
"Different properties or behaviors of chemical molecules have been investigated in the field of QSPR. Some examples are quantitative structure–reactivity relationships (QSRRs), quantitative structure–chromatography relationships (QSCRs) and, quantitative structure–toxicity relationships (QSTRs), quantitative structure–electrochemistry relationships (QSERs), and quantitative structure–[[biodegradability]] relationships (QSBRs)."<ref name = "Yousefinejad and Hemmateenejad_2015">{{cite journal | vauthors = Yousefinejad S, Hemmateenejad B | title = Chemometrics tools in QSAR/QSPR studies: A historical perspective | journal = Chemometrics and Intelligent Laboratory Systems | volume =  149, Part B | pages = 177–204 | year = 2015| doi = 10.1016/j.chemolab.2015.06.016}}</ref>

As an example, biological activity can be expressed quantitatively as the concentration of a substance required to give a certain biological response.  Additionally, when physicochemical properties or structures are expressed by numbers, one can find a mathematical relationship, or quantitative structure-activity relationship, between the two.  The mathematical expression, if carefully validated,<ref name = "Tropsha_2003">{{cite journal | vauthors = Tropsha A, Gramatica P, Gombar VJ | author-link1 = Alexander Tropsha | title = The Importance of Being Earnest: Validation is the Absolute Essential for Successful Application and Interpretation of QSPR Models | journal = QSAR Comb. Sci. | volume = 22 | pages = 69–77 | year = 2003 | doi = 10.1002/qsar.200390007 }}</ref><ref name = "Gramatica_2007">{{cite journal | vauthors =  Gramatica P | title = Principles of QSAR models validation: internal and external | journal = QSAR Comb. Sci. | volume = 26 | issue = 5 | pages = 694–701| year = 2007 | doi = 10.1002/qsar.200610151 | hdl = 11383/1668881 | hdl-access = free }}</ref><ref>{{cite journal |last1=Ruusmann |first1=V. |last2=Sild |first2=S. |last3=Maran |first3=U. |date=2015 |title=QSAR DataBank repository: open and linked qualitative and quantitative structure–activity relationship models |journal=Journal of Cheminformatics |volume=7 |pages=32 | pmid=26110025 | doi=10.1186/s13321-015-0082-6|pmc=4479250 | doi-access=free}}</ref><ref name="Chirico_Gramatica_2012">{{cite journal | vauthors = Chirico N, Gramatica P | title = Real external predictivity of QSAR models. Part 2. New intercomparable thresholds for different validation criteria and the need for scatter plot inspection | journal = Journal of Chemical Information and Modeling | volume = 52 | issue = 8 | pages = 2044–58 | date = Aug 2012 | pmid = 22721530 | doi = 10.1021/ci300084j }}</ref> can then be used to predict the modeled response of other chemical structures.<ref name="Tropsha2010">{{cite journal|last1=Tropsha|first1=Alexander|author-link=Alexander Tropsha|title=Best Practices for QSAR Model Development, Validation, and Exploitation|journal=Molecular Informatics|volume=29|issue=6–7|year=2010|pages=476–488|issn=1868-1743|doi=10.1002/minf.201000061|pmid=27463326|s2cid=23564249}}</ref>

A QSAR has the form of a [[mathematical model]]:
* Activity = ''f''{{tsp}}(physiochemical properties and/or structural properties) + error

The error includes [[model error]] ([[bias of an estimator|bias]]) and observational variability, that is, the variability in observations even on a correct model.