{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,14]],"date-time":"2026-03-14T05:48:52Z","timestamp":1773467332736,"version":"3.50.1"},"reference-count":66,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2020,4,22]],"date-time":"2020-04-22T00:00:00Z","timestamp":1587513600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002322","name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior","doi-asserted-by":"publisher","award":["88881.062174\/2014-01"],"award-info":[{"award-number":["88881.062174\/2014-01"]}],"id":[{"id":"10.13039\/501100002322","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001807","name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo","doi-asserted-by":"publisher","award":["2012\/24962-3"],"award-info":[{"award-number":["2012\/24962-3"]}],"id":[{"id":"10.13039\/501100001807","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100007386","name":"Pro-Reitoria de Pesquisa, Universidade de S\u00e3o Paulo","doi-asserted-by":"publisher","award":["18.5.245.86.7"],"award-info":[{"award-number":["18.5.245.86.7"]}],"id":[{"id":"10.13039\/501100007386","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000002","name":"National Institutes of Health","doi-asserted-by":"publisher","award":["R35 GM122561"],"award-info":[{"award-number":["R35 GM122561"]}],"id":[{"id":"10.13039\/100000002","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The promoter state of a gene and its expression levels are modulated by the amounts of transcription factors interacting with its regulatory regions. Hence, one may interpret a gene network as a communicating system in which the state of the promoter of a gene (the source) is communicated by the amounts of transcription factors that it expresses (the message) to modulate the state of the promoter and expression levels of another gene (the receptor). The reliability of the gene network dynamics can be quantified by Shannon\u2019s entropy of the message and the mutual information between the message and the promoter state. Here we consider a stochastic model for a binary gene and use its exact steady state solutions to calculate the entropy and mutual information. We show that a slow switching promoter with long and equally standing ON and OFF states maximizes the mutual information and reduces entropy. That is a binary gene expression regime generating a high variance message governed by a bimodal probability distribution with peaks of the same height. Our results indicate that Shannon\u2019s theory can be a powerful framework for understanding how bursty gene expression conciliates with the striking spatio-temporal precision exhibited in pattern formation of developing organisms.<\/jats:p>","DOI":"10.3390\/e22040479","type":"journal-article","created":{"date-parts":[[2020,4,23]],"date-time":"2020-04-23T10:46:22Z","timestamp":1587638782000},"page":"479","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Binary Expression Enhances Reliability of Messaging in Gene Networks"],"prefix":"10.3390","volume":"22","author":[{"given":"Leonardo R.","family":"Gama","sequence":"first","affiliation":[{"name":"Departamento de Radiologia e Oncologia &amp; Instituto do C\u00e2ncer do Estado de S\u00e3o Paulo\u2014Faculdade de Medicina, Universidade de S\u00e3o Paulo, S\u00e3o Paulo CEP 05403-911, SP, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4002-7083","authenticated-orcid":false,"given":"Guilherme","family":"Giovanini","sequence":"additional","affiliation":[{"name":"Escola de Artes, Ci\u00eancias e Humanidades, Universidade de S\u00e3o Paulo, Av. Arlindo B\u00e9ttio, 1000, S\u00e3o Paulo CEP 03828-000, SP, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6865-5818","authenticated-orcid":false,"given":"G\u00e1bor","family":"Bal\u00e1zsi","sequence":"additional","affiliation":[{"name":"The Louis and Beatrice Laufer Center for Physical and Quantitative Biology, Stony Brook University, Stony Brook, NY 11794, USA"},{"name":"Department of Biomedical Engineering, Stony Brook University, Stony Brook, NY 11794, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4681-3069","authenticated-orcid":false,"given":"Alexandre F.","family":"Ramos","sequence":"additional","affiliation":[{"name":"Departamento de Radiologia e Oncologia &amp; Instituto do C\u00e2ncer do Estado de S\u00e3o Paulo\u2014Faculdade de Medicina, Universidade de S\u00e3o Paulo, S\u00e3o Paulo CEP 05403-911, SP, Brazil"},{"name":"Escola de Artes, Ci\u00eancias e Humanidades, Universidade de S\u00e3o Paulo, Av. Arlindo B\u00e9ttio, 1000, S\u00e3o Paulo CEP 03828-000, SP, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,4,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"120","DOI":"10.1063\/1.1750549","article-title":"Statistical fluctuations in autocatalytic reactions","volume":"8","year":"1940","journal-title":"J. Chem. 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