{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,3]],"date-time":"2026-03-03T06:27:17Z","timestamp":1772519237284,"version":"3.50.1"},"reference-count":39,"publisher":"Oxford University Press (OUP)","issue":"12","license":[{"start":{"date-parts":[[2016,10,2]],"date-time":"2016-10-02T00:00:00Z","timestamp":1475366400000},"content-version":"vor","delay-in-days":480,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2015,6,15]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Motivation: Time-series observations from reporter gene experiments are commonly used for inferring and analyzing dynamical models of regulatory networks. The robust estimation of promoter activities and protein concentrations from primary data is a difficult problem due to measurement noise and the indirect relation between the measurements and quantities of biological interest.<\/jats:p>\n               <jats:p>Results: We propose a general approach based on regularized linear inversion to solve a range of estimation problems in the analysis of reporter gene data, notably the inference of growth rate, promoter activity, and protein concentration profiles. We evaluate the validity of the approach using in silico simulation studies, and observe that the methods are more robust and less biased than indirect approaches usually encountered in the experimental literature based on smoothing and subsequent processing of the primary data. We apply the methods to the analysis of fluorescent reporter gene data acquired in kinetic experiments with Escherichia coli. The methods are capable of reliably reconstructing time-course profiles of growth rate, promoter activity and protein concentration from weak and noisy signals at low population volumes. Moreover, they capture critical features of those profiles, notably rapid changes in gene expression during growth transitions.<\/jats:p>\n               <jats:p>Availability and implementation: The methods described in this article are made available as a Python package (LGPL license) and also accessible through a web interface. For more information, see https:\/\/team.inria.fr\/ibis\/wellinverter.<\/jats:p>\n               <jats:p>Contact: \u00a0Hidde.de-Jong@inria.fr<\/jats:p>\n               <jats:p>Supplementary information: Supplementary data are available at Bioinformatics online.<\/jats:p>","DOI":"10.1093\/bioinformatics\/btv246","type":"journal-article","created":{"date-parts":[[2015,6,13]],"date-time":"2015-06-13T17:12:36Z","timestamp":1434215556000},"page":"i71-i79","source":"Crossref","is-referenced-by-count":21,"title":["Robust reconstruction of gene expression profiles from reporter gene data using linear inversion"],"prefix":"10.1093","volume":"31","author":[{"given":"Valentin","family":"Zulkower","sequence":"first","affiliation":[{"name":"1 INRIA Grenoble\u2014Rh\u00f4ne-Alpes, 655 Avenue de l\u2019Europe, Montbonnot, 38334 Saint-Ismier Cedex, France, 2IAE Grenoble, Universit\u00e9 Pierre-Mend\u00e8s-France, Domaine universitaire BP 47, Grenoble Cedex 9, 38040 Saint Martin d\u2019H\u00e8res, France and 3Laboratoire Interdisciplinaire de Physique (CNRS UMR 5588), Universit\u00e9 Joseph Fourier, 140 Avenue de la physique BP 87, 38402 Saint Martin d\u2019H\u00e8res, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michel","family":"Page","sequence":"additional","affiliation":[{"name":"1 INRIA Grenoble\u2014Rh\u00f4ne-Alpes, 655 Avenue de l\u2019Europe, Montbonnot, 38334 Saint-Ismier Cedex, France, 2IAE Grenoble, Universit\u00e9 Pierre-Mend\u00e8s-France, Domaine universitaire BP 47, Grenoble Cedex 9, 38040 Saint Martin d\u2019H\u00e8res, France and 3Laboratoire Interdisciplinaire de Physique (CNRS UMR 5588), Universit\u00e9 Joseph Fourier, 140 Avenue de la physique BP 87, 38402 Saint Martin d\u2019H\u00e8res, France"},{"name":"1 INRIA Grenoble\u2014Rh\u00f4ne-Alpes, 655 Avenue de l\u2019Europe, Montbonnot, 38334 Saint-Ismier Cedex, France, 2IAE Grenoble, Universit\u00e9 Pierre-Mend\u00e8s-France, Domaine universitaire BP 47, Grenoble Cedex 9, 38040 Saint Martin d\u2019H\u00e8res, France and 3Laboratoire Interdisciplinaire de Physique (CNRS UMR 5588), Universit\u00e9 Joseph Fourier, 140 Avenue de la physique BP 87, 38402 Saint Martin d\u2019H\u00e8res, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Delphine","family":"Ropers","sequence":"additional","affiliation":[{"name":"1 INRIA Grenoble\u2014Rh\u00f4ne-Alpes, 655 Avenue de l\u2019Europe, Montbonnot, 38334 Saint-Ismier Cedex, France, 2IAE Grenoble, Universit\u00e9 Pierre-Mend\u00e8s-France, Domaine universitaire BP 47, Grenoble Cedex 9, 38040 Saint Martin d\u2019H\u00e8res, France and 3Laboratoire Interdisciplinaire de Physique (CNRS UMR 5588), Universit\u00e9 Joseph Fourier, 140 Avenue de la physique BP 87, 38402 Saint Martin d\u2019H\u00e8res, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Johannes","family":"Geiselmann","sequence":"additional","affiliation":[{"name":"1 INRIA Grenoble\u2014Rh\u00f4ne-Alpes, 655 Avenue de l\u2019Europe, Montbonnot, 38334 Saint-Ismier Cedex, France, 2IAE Grenoble, Universit\u00e9 Pierre-Mend\u00e8s-France, Domaine universitaire BP 47, Grenoble Cedex 9, 38040 Saint Martin d\u2019H\u00e8res, France and 3Laboratoire Interdisciplinaire de Physique (CNRS UMR 5588), Universit\u00e9 Joseph Fourier, 140 Avenue de la physique BP 87, 38402 Saint Martin d\u2019H\u00e8res, France"},{"name":"1 INRIA Grenoble\u2014Rh\u00f4ne-Alpes, 655 Avenue de l\u2019Europe, Montbonnot, 38334 Saint-Ismier Cedex, France, 2IAE Grenoble, Universit\u00e9 Pierre-Mend\u00e8s-France, Domaine universitaire BP 47, Grenoble Cedex 9, 38040 Saint Martin d\u2019H\u00e8res, France and 3Laboratoire Interdisciplinaire de Physique (CNRS UMR 5588), Universit\u00e9 Joseph Fourier, 140 Avenue de la physique BP 87, 38402 Saint Martin d\u2019H\u00e8res, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hidde","family":"de Jong","sequence":"additional","affiliation":[{"name":"1 INRIA Grenoble\u2014Rh\u00f4ne-Alpes, 655 Avenue de l\u2019Europe, Montbonnot, 38334 Saint-Ismier Cedex, France, 2IAE Grenoble, Universit\u00e9 Pierre-Mend\u00e8s-France, Domaine universitaire BP 47, Grenoble Cedex 9, 38040 Saint Martin d\u2019H\u00e8res, France and 3Laboratoire Interdisciplinaire de Physique (CNRS UMR 5588), Universit\u00e9 Joseph Fourier, 140 Avenue de la physique BP 87, 38402 Saint Martin d\u2019H\u00e8res, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2015,6,10]]},"reference":[{"key":"2023020115202715600_btv246-B1","doi-asserted-by":"crossref","first-page":"2705","DOI":"10.1093\/bioinformatics\/bts422","article-title":"BasyLiCA: a tool for automatic processing of a bacterial live cell array","volume":"28","author":"A\u00efchaoui","year":"2012","journal-title":"Bioinformatics"},{"key":"2023020115202715600_btv246-B2","doi-asserted-by":"crossref","first-page":"6361","DOI":"10.1128\/JB.181.20.6361-6370.1999","article-title":"Growth phase-dependent variation in protein composition of the Escherichia coli nucleoid","volume":"181","author":"Azam","year":"1999","journal-title":"J. Bacteriol."},{"key":"2023020115202715600_btv246-B3","doi-asserted-by":"crossref","first-page":"2725","DOI":"10.1109\/ACC.2012.6314940","article-title":"Determining transcription factor profiles from fluorescent reporter systems involving regularization of inverse problems","volume-title":"Proceedings of 2012 American Control Conference (ACC 2012)","author":"Bansal","year":"2012"},{"key":"2023020115202715600_btv246-B4","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1038\/msb4100120","article-title":"How to infer gene networks from expression profiles","volume":"3","author":"Bansal","year":"2007","journal-title":"Mol. Syst. Biol."},{"key":"2023020115202715600_btv246-B5","doi-asserted-by":"crossref","first-page":"e164","DOI":"10.1093\/nar\/gkt655","article-title":"A genome-wide screen for identifying all regulators of a target gene","volume":"41","author":"Baptist","year":"2013","journal-title":"Nucleic Acids Res."},{"key":"2023020115202715600_btv246-B6","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0065-2539(08)60946-4","article-title":"Linear inverse and ill-posed problems","volume":"75","author":"Bertero","year":"1989","journal-title":"Adv. Electron. Electron Phys."},{"key":"2023020115202715600_btv246-B7","doi-asserted-by":"crossref","first-page":"634","DOI":"10.1038\/msb.2012.70","article-title":"Shared control of gene expression in bacteria by transcription factors and global physiology of the cell","volume":"9","author":"Berthoumieux","year":"2013","journal-title":"Mol. Syst. Biol."},{"key":"2023020115202715600_btv246-B8","doi-asserted-by":"crossref","first-page":"1262","DOI":"10.1093\/bioinformatics\/btq016","article-title":"WellReader: a MATLAB program for the analysis of fluorescence and luminescence reporter gene data","volume":"26","author":"Boyer","year":"2010","journal-title":"Bioinformatics"},{"key":"2023020115202715600_btv246-B9","doi-asserted-by":"crossref","first-page":"2922","DOI":"10.1099\/mic.0.2007\/008565-0","article-title":"Effects of Fis on Escherichia coli gene expression during different growth stages","volume":"153","author":"Bradley","year":"2007","journal-title":"Microbiology"},{"key":"2023020115202715600_btv246-B10","volume-title":"Introduction to Linear System Theory","author":"Chen","year":"1970"},{"key":"2023020115202715600_btv246-B11","doi-asserted-by":"crossref","first-page":"1103","DOI":"10.1152\/physrev.00038.2009","article-title":"Fluorescent proteins and their applications in imaging living cells and tissues","volume":"90","author":"Chudakov","year":"2010","journal-title":"Physiol. Rev."},{"key":"2023020115202715600_btv246-B12","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1186\/1752-0509-4-55","article-title":"Experimental and computational validation of models of fluorescent and luminescent reporter genes in bacteria","volume":"4","author":"de Jong","year":"2010","journal-title":"BMC Syst. Biol."},{"key":"2023020115202715600_btv246-B13","doi-asserted-by":"crossref","first-page":"851","DOI":"10.1016\/S0005-1098(96)00254-3","article-title":"Nonparametric input estimation in physiological systems: problems, methods, and case studies","volume":"33","author":"de Nicolao","year":"1997","journal-title":"Automatica"},{"key":"2023020115202715600_btv246-B14","doi-asserted-by":"crossref","first-page":"717","DOI":"10.1038\/nrmicro2419","article-title":"Advantages and limitations of current network inference methods","volume":"8","author":"de Smet","year":"2010","journal-title":"Nat. Rev. Microbiol."},{"key":"2023020115202715600_btv246-B15","doi-asserted-by":"crossref","first-page":"639","DOI":"10.1128\/MMBR.68.4.639-668.2004","article-title":"Control of rRNA synthesis in Escherichia coli: a systems biology approach","volume":"68","author":"Dennis","year":"2004","journal-title":"Microbiol. Mol. Biol. Rev."},{"key":"2023020115202715600_btv246-B16","doi-asserted-by":"crossref","first-page":"820","DOI":"10.3390\/metabo3030820","article-title":"Physiological and molecular timing of the glucose to acetate transition in Escherichia Coli","volume":"3","author":"Enjalbert","year":"2013","journal-title":"Metabolites"},{"key":"2023020115202715600_btv246-B17","doi-asserted-by":"crossref","first-page":"2901","DOI":"10.1093\/bioinformatics\/btn562","article-title":"Reconstruction of transcriptional dynamics from gene reporter data using differential equations","volume":"24","author":"Finkenst\u00e4dt","year":"2008","journal-title":"Bioinformatics"},{"key":"2023020115202715600_btv246-B18","doi-asserted-by":"crossref","first-page":"658","DOI":"10.1038\/msb.2013.14","article-title":"Dissecting specific and global transcriptional regulation of bacterial gene expression","volume":"9","author":"Gerosa","year":"2013","journal-title":"Mol. Syst. Biol."},{"key":"2023020115202715600_btv246-B19","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1126\/science.1124618","article-title":"The fluorescent toolbox for assessing protein location and function","volume":"312","author":"Giepmans","year":"2006","journal-title":"Science"},{"key":"2023020115202715600_btv246-B20","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1080\/00401706.1979.10489751","article-title":"Generalized cross-validation as a method for choosing a good Ridge parameter","volume":"21","author":"Golub","year":"1979","journal-title":"Technometrics"},{"key":"2023020115202715600_btv246-B21","doi-asserted-by":"crossref","first-page":"3516","DOI":"10.1128\/JB.186.11.3516-3524.2004","article-title":"Transcriptome analysis of Crp-dependent catabolite control of gene expression in Escherichia coli","volume":"186","author":"Gosset","year":"2004","journal-title":"J. Bacteriol."},{"key":"2023020115202715600_btv246-B22","doi-asserted-by":"crossref","first-page":"561","DOI":"10.1137\/1034115","article-title":"Analysis of discrete ill-posed problems by means of the L-curve","volume":"34","author":"Hansen","year":"1992","journal-title":"SIAM Rev."},{"key":"2023020115202715600_btv246-B23","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1128\/MMBR.66.3.373-395.2002","article-title":"Signal transduction and regulatory mechanisms involved in control of the \u03c3S (RpoS) subunit of RNA polymerase","volume":"66","author":"Hengge-Aronis","year":"2002","journal-title":"Microbiol. Mol. Biol. Rev."},{"key":"2023020115202715600_btv246-B24","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1080\/00401706.1970.10488634","article-title":"Ridge regression: biased estimation for nonorthogonal problems","volume":"12","author":"Hoerl","year":"1970","journal-title":"Technometrics"},{"key":"2023020115202715600_btv246-B25","volume-title":"SciPy: Open Source Scientific Tools for Python","author":"Jones","year":"2001"},{"key":"2023020115202715600_btv246-B26","doi-asserted-by":"crossref","first-page":"36079","DOI":"10.1074\/jbc.M508202200","article-title":"A global regulatory role of gluconeogenic genes in Escherichia coli revealed by transcriptome network analysis","volume":"280","author":"Kao","year":"2005","journal-title":"J. Biol. Chem."},{"key":"2023020115202715600_btv246-B27","doi-asserted-by":"crossref","first-page":"701","DOI":"10.1038\/msb.2013.59","article-title":"Promoters maintain their relative activity levels under different growth conditions","volume":"9","author":"Keren","year":"2013","journal-title":"Mol. Syst. Biol."},{"key":"2023020115202715600_btv246-B28","doi-asserted-by":"crossref","first-page":"6043","DOI":"10.1073\/pnas.0606717104","article-title":"Combinatorial transcriptional control of the lactose operon of Escherichia coli","volume":"104","author":"Kuhlman","year":"2007","journal-title":"Proc. Natl. Acad. Sci. U.S.A."},{"key":"2023020115202715600_btv246-B29","doi-asserted-by":"crossref","first-page":"4125","DOI":"10.1016\/S0021-9258(19)85642-9","article-title":"The relative rates of protein synthesis and degradation in a growing culture of Escherichia coli","volume":"255","author":"Larrabee","year":"1980","journal-title":"J. Biol. Chem."},{"key":"2023020115202715600_btv246-B30","doi-asserted-by":"crossref","first-page":"6752","DOI":"10.1128\/JB.183.23.6752-6762.2001","article-title":"Predictive and interpretive simulation of green fluorescent protein expression in reporter bacteria","volume":"183","author":"Leveau","year":"2001","journal-title":"J. Bacteriol."},{"key":"2023020115202715600_btv246-B31","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1186\/1472-6750-14-11","article-title":"Unmixing of fluorescence spectra to resolve quantitative time-series measurements of gene expression in plate readers","volume":"14","author":"Lichten","year":"2014","journal-title":"BMC Biotechnol."},{"key":"2023020115202715600_btv246-B32","doi-asserted-by":"crossref","first-page":"2529","DOI":"10.1109\/CDC.2010.5717922","article-title":"Structural identification of unate-like genetic network models from time-lapse protein concentration measurements","volume-title":"Proceedings of 49th IEEE Conference on Decision and Control (CDC 2010), Atlanta, GA, USA","author":"Porreca","year":"2010"},{"key":"2023020115202715600_btv246-B33","doi-asserted-by":"crossref","first-page":"10555","DOI":"10.1073\/pnas.152046799","article-title":"Assigning numbers to the arrows: parameterizing a gene regulation network by using accurate expression kinetics","volume":"99","author":"Ronen","year":"2002","journal-title":"Proc. Natl. Acad. Sci. U.S.A."},{"key":"2023020115202715600_btv246-B34","doi-asserted-by":"crossref","first-page":"e1004028","DOI":"10.1371\/journal.pcbi.1004028","article-title":"Inference of quantitative models of bacterial promoters from time-series reporter gene data","volume":"11","author":"Stefan","year":"2015","journal-title":"PLoS Comput. Biol."},{"key":"2023020115202715600_btv246-B35","first-page":"157","article-title":"DNA supercoiling: a global transcriptional regulator for enterobacterial growth? Nat","volume":"3","author":"Travers","year":"2005","journal-title":"Rev. Microbiol."},{"key":"2023020115202715600_btv246-B36","doi-asserted-by":"crossref","first-page":"20130505","DOI":"10.1098\/rsif.2013.0505","article-title":"Reverse engineering and identification in systems biology: strategies, perspectives and challenges","volume":"11","author":"Villaverde","year":"2014","journal-title":"J. R. Soc. Interface"},{"key":"2023020115202715600_btv246-B37","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611970128","volume-title":"Spline Models for Observational Data","author":"Wahba","year":"1990"},{"key":"2023020115202715600_btv246-B38","doi-asserted-by":"crossref","first-page":"2017","DOI":"10.1529\/biophysj.107.122200","article-title":"Mathematical analysis and quantification of fluorescent proteins as transcriptional reporters","volume":"94","author":"Wang","year":"2008","journal-title":"Biophys. J."},{"key":"2023020115202715600_btv246-B39","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1128\/MMBR.69.1.12-50.2005","article-title":"The acetate switch","volume":"69","author":"Wolfe","year":"2005","journal-title":"Microbiol. Mol. Biol. Rev."}],"container-title":["Bioinformatics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/bioinformatics\/article-pdf\/31\/12\/i71\/49013941\/bioinformatics_31_12_i71.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/bioinformatics\/article-pdf\/31\/12\/i71\/49013941\/bioinformatics_31_12_i71.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,2,2]],"date-time":"2023-02-02T00:03:41Z","timestamp":1675296221000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/bioinformatics\/article\/31\/12\/i71\/216045"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,6,10]]},"references-count":39,"journal-issue":{"issue":"12","published-print":{"date-parts":[[2015,6,15]]}},"URL":"https:\/\/doi.org\/10.1093\/bioinformatics\/btv246","relation":{},"ISSN":["1367-4811","1367-4803"],"issn-type":[{"value":"1367-4811","type":"electronic"},{"value":"1367-4803","type":"print"}],"subject":[],"published-other":{"date-parts":[[2015,6,15]]},"published":{"date-parts":[[2015,6,10]]}}}