{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T08:13:03Z","timestamp":1775808783115,"version":"3.50.1"},"reference-count":34,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2016,6,15]],"date-time":"2016-06-15T00:00:00Z","timestamp":1465948800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2016,6,15]],"date-time":"2016-06-15T00:00:00Z","timestamp":1465948800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Sci Rep"],"abstract":"<jats:title>Abstract<\/jats:title><jats:p>High-throughput <jats:italic>in vitro<\/jats:italic> screening experiments can be used to generate concentration-response data for large chemical libraries. It is often desirable to estimate the concentration needed to achieve a particular effect, or potency, for each chemical tested in an assay. Potency estimates can be used to directly compare chemical profiles and prioritize compounds for confirmation studies, or employed as input data for prediction modeling and association mapping. The concentration for half-maximal activity derived from the Hill equation model (i.e., <jats:italic>AC<\/jats:italic><jats:sub><jats:italic>50<\/jats:italic><\/jats:sub>) is the most common potency measure applied in pharmacological research and toxicity testing. However, the <jats:italic>AC<\/jats:italic><jats:sub><jats:italic>50<\/jats:italic><\/jats:sub> parameter is subject to large uncertainty for many concentration-response relationships. In this study we introduce a new measure of potency based on a weighted Shannon entropy measure termed the weighted entropy score (<jats:italic>WES<\/jats:italic>). Our potency estimator (Point of Departure, <jats:italic>POD<\/jats:italic><jats:sub><jats:italic>WES<\/jats:italic><\/jats:sub>) is defined as the concentration producing the maximum rate of change in weighted entropy along a concentration-response profile. This approach provides a new tool for potency estimation that does not depend on the assumption of monotonicity or any other pre-specified concentration-response relationship. <jats:italic>POD<\/jats:italic><jats:sub><jats:italic>WES<\/jats:italic><\/jats:sub> estimates potency with greater precision and less bias compared to the conventional <jats:italic>AC<\/jats:italic><jats:sub><jats:italic>50<\/jats:italic><\/jats:sub> assessed across a range of simulated conditions.<\/jats:p>","DOI":"10.1038\/srep27897","type":"journal-article","created":{"date-parts":[[2016,6,15]],"date-time":"2016-06-15T16:31:22Z","timestamp":1466008282000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Estimating Potency in High-Throughput Screening Experiments by Maximizing the Rate of Change in Weighted Shannon Entropy"],"prefix":"10.1038","volume":"6","author":[{"given":"Keith R.","family":"Shockley","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2016,6,15]]},"reference":[{"key":"BFsrep27897_CR1","doi-asserted-by":"publisher","first-page":"11473","DOI":"10.1073\/pnas.0604348103","volume":"103","author":"J Inglese","year":"2006","unstructured":"Inglese, J. et al. Quantitative high-throughput screening: a titration-based approach that efficiently identifies biological activities in large chemical libraries. Proc Natl Acad Sci USA 103, 11473\u201311478 (2006).","journal-title":"Proc Natl Acad Sci USA"},{"key":"BFsrep27897_CR2","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1007\/s00439-014-1482-9","volume":"134","author":"WC Reinhold","year":"2015","unstructured":"Reinhold, W. C. et al. Using drug response data to identify molecular effectors and molecular \u201comic\u201d data to identify candidate drugs in cancer. Hum Genet 134, 3\u201311 (2015).","journal-title":"Hum Genet"},{"key":"BFsrep27897_CR3","doi-asserted-by":"publisher","first-page":"1643","DOI":"10.1021\/tx500145h","volume":"27","author":"H Zhu","year":"2014","unstructured":"Zhu, H. et al. Big data in chemical toxicity research: the use of high-throughput screening assays to identify potential toxicants. Chem Res Toxicol 27, 1643\u20131651 (2014).","journal-title":"Chem Res Toxicol"},{"key":"BFsrep27897_CR4","doi-asserted-by":"publisher","first-page":"756","DOI":"10.1289\/ehp.1205784","volume":"121","author":"RR Tice","year":"2013","unstructured":"Tice, R. R., Austin, C. P., Kavlock, R. J. & Bucher, J. R. Improving the human hazard characterization of chemicals: a Tox21 update. Environ Health Perspect 121, 756\u2013765 (2013).","journal-title":"Environ Health Perspect"},{"key":"BFsrep27897_CR5","first-page":"1000121","volume":"5","author":"A Beam","year":"2014","unstructured":"Beam, A. & Motsinger-Reif, A. Beyond IC : Towards Robust Statistical Methods for Association Studies. J Pharmacogenomics Pharmacoproteomics 5, 1000121 (2014).","journal-title":"J Pharmacogenomics Pharmacoproteomics"},{"key":"BFsrep27897_CR6","doi-asserted-by":"publisher","first-page":"887","DOI":"10.1177\/1087057115581317","volume":"20","author":"JH Hsieh","year":"2015","unstructured":"Hsieh, J. H., Sedykh, A., Huang, R., Xia, M. & Tice, R. R. A Data Analysis Pipeline Accounting for Artifacts in Tox21 Quantitative High-Throughput Screening Assays. J Biomol Screen 20, 887\u2013897 (2015).","journal-title":"J Biomol Screen"},{"key":"BFsrep27897_CR7","doi-asserted-by":"publisher","first-page":"344","DOI":"10.1177\/1087057113505325","volume":"19","author":"KR Shockley","year":"2014","unstructured":"Shockley, K. R. Using weighted entropy to rank chemicals in quantitative high-throughput screening experiments. J Biomol Screen 19, 344\u2013353 (2014).","journal-title":"J Biomol Screen"},{"key":"BFsrep27897_CR8","doi-asserted-by":"publisher","first-page":"398","DOI":"10.1093\/toxsci\/kfs159","volume":"128","author":"RS Thomas","year":"2012","unstructured":"Thomas, R. S. et al. A comprehensive statistical analysis of predicting in vivo hazard using high-throughput in vitro screening. Toxicol Sci 128, 398\u2013417 (2012).","journal-title":"Toxicol Sci"},{"key":"BFsrep27897_CR9","first-page":"4","volume":"40","author":"AV Hill","year":"1910","unstructured":"Hill, A. V. The possible effects of the aggregation of the molecules of haemoglobin on its dissociation curves. J Physiol 40, 4\u20137 (1910).","journal-title":"J Physiol"},{"key":"BFsrep27897_CR10","doi-asserted-by":"publisher","first-page":"296","DOI":"10.1016\/j.drudis.2014.10.005","volume":"20","author":"KR Shockley","year":"2015","unstructured":"Shockley, K. R. Quantitative high-throughput screening data analysis: challenges and recent advances. Drug Discov Today 20, 296\u2013300 (2015).","journal-title":"Drug Discov Today"},{"key":"BFsrep27897_CR11","doi-asserted-by":"publisher","first-page":"2808","DOI":"10.1021\/ci200210d","volume":"51","author":"C Bergeron","year":"2011","unstructured":"Bergeron, C., Moore, G., Krein, M., Breneman, C. M. & Bennett, K. P. Exploiting domain knowledge for improved quantitative high-throughput screening curve fitting. J Chem Inf Model 51, 2808\u20132820 (2011).","journal-title":"J Chem Inf Model"},{"key":"BFsrep27897_CR12","doi-asserted-by":"crossref","unstructured":"Fujii, Y., Narita, T., Tice, R. R., Takeda, S. & Yamada, R. Isotonic Regression Based-Method in Quantitative High-Throughput Screenings for Genotoxicity. Dose Response 13, 10.2203\/dose-response.13-045.Fujii (2015).","DOI":"10.2203\/dose-response.13-045.Fujii"},{"key":"BFsrep27897_CR13","doi-asserted-by":"publisher","first-page":"151","DOI":"10.1093\/toxsci\/kfh007","volume":"77","author":"RB Conolly","year":"2004","unstructured":"Conolly, R. B. & Lutz, W. K. Nonmonotonic dose-response relationships: mechanistic basis, kinetic modeling and implications for risk assessment. Toxicol Sci 77, 151\u2013157 (2004).","journal-title":"Toxicol Sci"},{"key":"BFsrep27897_CR14","doi-asserted-by":"publisher","first-page":"342","DOI":"10.2203\/dose-response.003.03.005","volume":"3","author":"SD Peddada","year":"2005","unstructured":"Peddada, S. D. & Haseman, J. K. Analysis of nonlinear regression models: a cautionary note. Dose Response 3, 342\u2013352 (2005).","journal-title":"Dose Response"},{"key":"BFsrep27897_CR15","unstructured":"EPA (Environmental Protection Agency). ToxCast\u2122 Data. The ToxCast Analysis Pipeline: An R package for processing and modeling chemical screening data. https:\/\/www.epa.gov\/sites\/production\/files\/2015-08\/documents\/pipeline_overview.pdf (2016)(Date of access: March 25, 2016)."},{"key":"BFsrep27897_CR16","doi-asserted-by":"publisher","first-page":"854","DOI":"10.1016\/0272-0590(84)90107-6","volume":"4","author":"KS Crump","year":"1984","unstructured":"Crump, K. S. A new method for determining allowable daily intakes. Fundam Appl Toxicol 4, 854\u2013871 (1984).","journal-title":"Fundam Appl Toxicol"},{"key":"BFsrep27897_CR17","doi-asserted-by":"publisher","first-page":"697","DOI":"10.1016\/S0278-6915(01)00015-1","volume":"39","author":"RA Woutersen","year":"2001","unstructured":"Woutersen, R. A., Jonker, D., Stevenson, H., te Biesebeek, J. D. & Slob, W. The benchmark approach applied to a 28-day toxicity study with Rhodorsil Silane in rats. the impact of increasing the number of dose groups. Food Chem Toxicol 39, 697\u2013707 (2001).","journal-title":"Food Chem Toxicol"},{"key":"BFsrep27897_CR18","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","volume":"27","author":"CE Shannon","year":"1948","unstructured":"Shannon, C. E. A mathematical theory of communication. Bell Syst Techn J. 27, 1\u201355 (1948).","journal-title":"Bell Syst Techn J."},{"key":"BFsrep27897_CR19","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1016\/S0303-2647(99)00077-5","volume":"55","author":"S Fuhrman","year":"2000","unstructured":"Fuhrman, S. et al. The application of shannon entropy in the identification of putative drug targets. Biosystems 55, 5\u201314 (2000).","journal-title":"Biosystems"},{"key":"BFsrep27897_CR20","doi-asserted-by":"publisher","first-page":"R33","DOI":"10.1186\/gb-2005-6-4-r33","volume":"6","author":"J Schug","year":"2005","unstructured":"Schug, J. et al. Promoter features related to tissue specificity as measured by Shannon entropy. Genome Biol 6, R33 (2005).","journal-title":"Genome Biol"},{"key":"BFsrep27897_CR21","doi-asserted-by":"publisher","first-page":"e58","DOI":"10.1093\/nar\/gkr053","volume":"39","author":"Y Zhang","year":"2011","unstructured":"Zhang, Y. et al. QDMR: a quantitative method for identification of differentially methylated regions by entropy. Nucleic Acids Res 39, e58 (2011).","journal-title":"Nucleic Acids Res"},{"key":"BFsrep27897_CR22","doi-asserted-by":"crossref","unstructured":"Cover, T. M. & Thomas, J. A. Elements of information theory. (John Wiley & Sons, 1991).","DOI":"10.1002\/0471200611"},{"key":"BFsrep27897_CR23","doi-asserted-by":"publisher","first-page":"5664","DOI":"10.1038\/srep05664","volume":"4","author":"R Huang","year":"2014","unstructured":"Huang, R. et al. Profiling of the Tox21 10K compound library for agonists and antagonists of the estrogen receptor alpha signaling pathway. Sci Rep 4, 5664 (2014).","journal-title":"Sci Rep"},{"key":"BFsrep27897_CR24","doi-asserted-by":"publisher","first-page":"275","DOI":"10.1385\/ENDO:22:3:275","volume":"22","author":"A Vivacqua","year":"2003","unstructured":"Vivacqua, A. et al. The food contaminants bisphenol A and 4-nonylphenol act as agonists for estrogen receptor alpha in MCF7 breast cancer cells. Endocrine 22, 275\u2013284 (2003).","journal-title":"Endocrine"},{"key":"BFsrep27897_CR25","doi-asserted-by":"publisher","first-page":"188","DOI":"10.1038\/nrd3368","volume":"10","author":"R Macarron","year":"2011","unstructured":"Macarron, R. et al. Impact of high-throughput screening in biomedical research. Nat Rev Drug Discov 10, 188\u2013195 (2011).","journal-title":"Nat Rev Drug Discov"},{"key":"BFsrep27897_CR26","doi-asserted-by":"publisher","first-page":"906","DOI":"10.1126\/science.1154619","volume":"319","author":"FS Collins","year":"2008","unstructured":"Collins, F. S., Gray, G. M. & Bucher, J. R. Toxicology. Transforming environmental health protection. Science 319, 906\u2013907 (2008).","journal-title":"Science"},{"key":"BFsrep27897_CR27","doi-asserted-by":"publisher","first-page":"557","DOI":"10.1177\/1087057105276989","volume":"10","author":"D Kevorkov","year":"2005","unstructured":"Kevorkov, D. & Makarenkov, V. Statistical analysis of systematic errors in high-throughput screening. J Biomol Screen 10, 557\u2013567 (2005).","journal-title":"J Biomol Screen"},{"key":"BFsrep27897_CR28","doi-asserted-by":"publisher","first-page":"167","DOI":"10.1038\/nbt1186","volume":"24","author":"N Malo","year":"2006","unstructured":"Malo, N., Hanley, J. A., Cerquozzi, S., Pelletier, J. & Nadon, R. Statistical practice in high-throughput screening data analysis. Nat Biotechnol 24, 167\u2013175 (2006).","journal-title":"Nat Biotechnol"},{"key":"BFsrep27897_CR29","doi-asserted-by":"publisher","first-page":"705","DOI":"10.1177\/1087057112441623","volume":"17","author":"PE Ilouga","year":"2012","unstructured":"Ilouga, P. E. & Hesterkamp, T. On the prediction of statistical parameters in high-throughput screening using resampling techniques. J Biomol Screen 17, 705\u2013712 (2012).","journal-title":"J Biomol Screen"},{"key":"BFsrep27897_CR30","doi-asserted-by":"publisher","first-page":"1107","DOI":"10.1289\/ehp.1104688","volume":"120","author":"KR Shockley","year":"2012","unstructured":"Shockley, K. R. A three-stage algorithm to make toxicologically relevant activity calls from quantitative high throughput screening data. Environ Health Perspect 120, 1107\u20131115 (2012).","journal-title":"Environ Health Perspect"},{"key":"BFsrep27897_CR31","doi-asserted-by":"crossref","unstructured":"Marsden, J. & Weinstein, A. Calculus I. (Springer-Verlag New York Inc., 1985).","DOI":"10.1007\/978-1-4612-5026-5"},{"key":"BFsrep27897_CR32","unstructured":"Lynch, D. R. Numerical partial differential equations for environmental scientists and engineers. (Springer, 2005)."},{"key":"BFsrep27897_CR33","doi-asserted-by":"publisher","first-page":"298","DOI":"10.1136\/bmj.310.6975.298","volume":"310","author":"DG Altman","year":"1995","unstructured":"Altman, D. G. & Bland, J. M. Statistics notes: the normal distribution. BMJ 310, 298 (1995).","journal-title":"BMJ"},{"key":"BFsrep27897_CR34","unstructured":"R: A language and environment for statistical computing (R Foundation for Statistical Computing, Vienna, Austria, URL http:\/\/www.R-project.org\/\u2032\u2032, 2012)."}],"container-title":["Scientific Reports"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.nature.com\/articles\/srep27897","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/srep27897.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/srep27897.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,1,4]],"date-time":"2023-01-04T16:38:01Z","timestamp":1672850281000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.nature.com\/articles\/srep27897"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,6,15]]},"references-count":34,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2016,9,13]]}},"alternative-id":["BFsrep27897"],"URL":"https:\/\/doi.org\/10.1038\/srep27897","relation":{},"ISSN":["2045-2322"],"issn-type":[{"value":"2045-2322","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,6,15]]},"assertion":[{"value":"4 April 2016","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 May 2016","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 June 2016","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The author declares no competing financial interests.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"27897"}}