{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T12:58:19Z","timestamp":1773665899150,"version":"3.50.1"},"reference-count":72,"publisher":"Public Library of Science (PLoS)","issue":"2","license":[{"start":{"date-parts":[[2011,2,3]],"date-time":"2011-02-03T00:00:00Z","timestamp":1296691200000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"DOI":"10.1371\/journal.pcbi.1001069","type":"journal-article","created":{"date-parts":[[2011,2,3]],"date-time":"2011-02-03T21:37:26Z","timestamp":1296769046000},"page":"e1001069","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":56,"title":["Gene Expression Noise in Spatial Patterning: hunchback Promoter Structure Affects Noise Amplitude and Distribution in Drosophila Segmentation"],"prefix":"10.1371","volume":"7","author":[{"given":"David M.","family":"Holloway","sequence":"first","affiliation":[]},{"given":"Francisco J. P.","family":"Lopes","sequence":"additional","affiliation":[]},{"given":"Luciano","family":"da Fontoura Costa","sequence":"additional","affiliation":[]},{"given":"Bruno A. N.","family":"Traven\u00e7olo","sequence":"additional","affiliation":[]},{"given":"Nina","family":"Golyandina","sequence":"additional","affiliation":[]},{"given":"Konstantin","family":"Usevich","sequence":"additional","affiliation":[]},{"given":"Alexander V.","family":"Spirov","sequence":"additional","affiliation":[]}],"member":"340","published-online":{"date-parts":[[2011,2,3]]},"reference":[{"key":"ref1","doi-asserted-by":"crossref","first-page":"798","DOI":"10.1038\/415798a","article-title":"Establishment of developmental precision and proportions in the early Drosophila embryo.","volume":"415","author":"B Houchmandzadeh","year":"2002","journal-title":"Nature"},{"key":"ref2","doi-asserted-by":"crossref","first-page":"1888","DOI":"10.1016\/j.cub.2005.09.046","article-title":"Bicoid determines sharp and precise target gene expression on the Drosophila embryo.","volume":"15","author":"O Crauk","year":"2005","journal-title":"Curr Biol"},{"key":"ref3","doi-asserted-by":"crossref","first-page":"2949","DOI":"10.1002\/dvdy.20940","article-title":"Analysis of pattern precision shows that <italic>Drosophila<\/italic> segmentation develops substantial independence from gradients of maternal gene products.","volume":"235","author":"DM Holloway","year":"2006","journal-title":"Dev Dynam"},{"key":"ref4","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1016\/j.cell.2007.05.025","article-title":"Probing the limits to positional information.","volume":"130","author":"T Gregor","year":"2007","journal-title":"Cell"},{"key":"ref5","doi-asserted-by":"crossref","first-page":"558","DOI":"10.1016\/j.devcel.2008.09.004","article-title":"Probing intrinsic properties of a robust morphogen gradient in <italic>Drosophila<\/italic>.","volume":"15","author":"F He","year":"2008","journal-title":"Dev Cell"},{"key":"ref6","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1016\/0092-8674(88)90183-3","article-title":"The <italic>bicoid<\/italic> protein determines position in the <italic>Drosophila<\/italic> embryo in a concentration-dependent manner.","volume":"54","author":"W Driever","year":"1988","journal-title":"Cell"},{"key":"ref7","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1016\/0092-8674(88)90182-1","article-title":"A gradient of <italic>bicoid<\/italic> protein in <italic>Drosophila<\/italic> embryos.","volume":"54","author":"W Driever","year":"1988","journal-title":"Cell"},{"key":"ref8","article-title":"Principles of development. 2nd ed","author":"L Wolpert","year":"2002"},{"key":"ref9","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1016\/S0092-8674(04)00037-6","article-title":"Seeing is believing: The bicoid morphogen gradient matures.","volume":"116","author":"A Ephrussi","year":"2004","journal-title":"Cell"},{"key":"ref10","doi-asserted-by":"crossref","first-page":"R249","DOI":"10.1016\/j.cub.2010.01.026","article-title":"The Bicoid morphogen system.","volume":"20","author":"A Porcher","year":"2010","journal-title":"Current Biology"},{"key":"ref11","doi-asserted-by":"crossref","first-page":"418","DOI":"10.1038\/448420a","article-title":"A ten percent solution.","volume":"448","author":"J Reinitz","year":"2007","journal-title":"Nature"},{"key":"ref12","doi-asserted-by":"crossref","first-page":"89","DOI":"10.3233\/ISB-00080","article-title":"Making the body plan: precision in the genetic hierarchy of Drosophila embryo segmentation.","volume":"3","author":"AV Spirov","year":"2003","journal-title":"In Silico Biol"},{"key":"ref13","doi-asserted-by":"crossref","first-page":"1134","DOI":"10.1038\/nature03509","article-title":"Dynamics of <italic>Drosophila<\/italic> embryonic patterning network perturbed in space and time using microfluidics.","volume":"434","author":"EM Lucchetta","year":"2005","journal-title":"Nature"},{"key":"ref14","doi-asserted-by":"crossref","first-page":"e3651","DOI":"10.1371\/journal.pone.0003651","article-title":"A precise Bicoid gradient is nonessential during cycles 11\u201313 for precise patterning in the <italic>Drosophila<\/italic> blastoderm.","volume":"3","author":"EM Lucchetta","year":"2008","journal-title":"PLoS ONE"},{"key":"ref15","doi-asserted-by":"crossref","first-page":"3823","DOI":"10.1073\/pnas.0807878105","article-title":"Anterior-posterior information in the absence of a strong Bicoid gradient.","volume":"106","author":"A Ochoa-Espinosa","year":"2009","journal-title":"Proc Nat Acad Sci USA"},{"key":"ref16","doi-asserted-by":"crossref","first-page":"4135","DOI":"10.1073\/pnas.71.10.4135","article-title":"Kinetic proofreading: a new mechanism for reducing errors in biosynthetic processes requiring high specificity.","volume":"71","author":"JJ Hopfield","year":"1974","journal-title":"Proc Nat Acad Sci USA"},{"key":"ref17","doi-asserted-by":"crossref","first-page":"1393","DOI":"10.1242\/dev.124.7.1393","article-title":"Drosophila embryonic pattern repair: how embryos respond to bicoid dosage alteration.","volume":"124","author":"R Namba","year":"1997","journal-title":"Development"},{"key":"ref18","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1242\/dev.02238","article-title":"The interpretation of morphogen gradients.","volume":"133","author":"HL Ashe","year":"2006","journal-title":"Development"},{"key":"ref19","doi-asserted-by":"crossref","first-page":"7148","DOI":"10.1073\/pnas.110057697","article-title":"Stochastic focusing: fluctuation-enhanced sensitivity of intracellular regulation.","volume":"97","author":"J Paulsson","year":"2000","journal-title":"Proc Nat Acad Sci USA"},{"key":"ref20","doi-asserted-by":"crossref","first-page":"1183","DOI":"10.1126\/science.1070919","article-title":"Stochastic gene expression in a single cell.","volume":"297","author":"MB Elowitz","year":"2002","journal-title":"Science"},{"key":"ref21","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1038\/nature01258","article-title":"Control, exploitation and tolerance of intracellular noise.","volume":"420","author":"CV Rao","year":"2002","journal-title":"Nature"},{"key":"ref22","doi-asserted-by":"crossref","first-page":"2943","DOI":"10.1016\/S0006-3495(02)75635-X","article-title":"Attenuation of noise in ultrasensitive signaling cascades.","volume":"82","author":"M Thattai","year":"2002","journal-title":"Biophys J"},{"key":"ref23","doi-asserted-by":"crossref","first-page":"636","DOI":"10.1038\/ng1807","article-title":"Noise in protein expression scales with natural protein abundance.","volume":"38","author":"A Bar-Even","year":"2006","journal-title":"Nat Genet"},{"key":"ref24","doi-asserted-by":"crossref","first-page":"510","DOI":"10.1038\/nature08150","article-title":"Partial penetrance facilitates developmental evolution in bacteria.","volume":"460","author":"A Eldar","year":"2009","journal-title":"Nature"},{"key":"ref25","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1186\/1752-0509-1-52","article-title":"Master equation simulation analysis of immunostained Bicoid morphogen gradient.","volume":"1","author":"YF Wu","year":"2007","journal-title":"BMC Sys Biol"},{"key":"ref26","doi-asserted-by":"crossref","first-page":"114","DOI":"10.1117\/12.497009","article-title":"Mesoscopic reaction-diffusion in intracellular signaling.","volume":"5110","author":"J Elf","year":"2003","journal-title":"Proc SPIE"},{"key":"ref27","doi-asserted-by":"crossref","first-page":"2923","DOI":"10.1093\/bioinformatics\/bti431","article-title":"Stochastic reaction-diffusion simulation with MesoRD.","volume":"21","author":"J Hattne","year":"2005","journal-title":"Bioinformatics"},{"key":"ref28","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1016\/0021-9991(76)90041-3","article-title":"A general method for numerically simulating the stochastic time evolution of coupled chemical reactions.","volume":"22","author":"D Gillespie","year":"1976","journal-title":"J Comput Phys"},{"key":"ref29","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1063\/1.481811","article-title":"The chemical Langevin equation.","volume":"113","author":"DT Gillespie","year":"2000","journal-title":"J Chem Phys"},{"key":"ref30","doi-asserted-by":"crossref","first-page":"e1000184","DOI":"10.1371\/journal.pcbi.1000184","article-title":"Spatial bistability generates <italic>hunchback<\/italic> expression sharpness in the <italic>Drosophila<\/italic> embryo.","volume":"4","author":"FJP Lopes","year":"2008","journal-title":"PLoS Comput Biol"},{"key":"ref31","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1038\/341335a0","article-title":"The products of the <italic>Drosophila<\/italic> gap genes <italic>hunchback<\/italic> and <italic>Kr\u00fcppel<\/italic> bind to the <italic>hunchback<\/italic> promoters.","volume":"341","author":"J Treisman","year":"1989","journal-title":"Nature"},{"key":"ref32","doi-asserted-by":"crossref","first-page":"138","DOI":"10.1038\/337138a0","article-title":"The Bicoid protein is a positive regulator of <italic>hunchback<\/italic> transcription in the early <italic>Drosophila<\/italic> embryo.","volume":"337","author":"W Driever","year":"1989","journal-title":"Nature"},{"key":"ref33","doi-asserted-by":"crossref","first-page":"855","DOI":"10.1016\/S0092-8674(94)90622-X","article-title":"Synergy between the Hunchback and Bicoid morphogens is required for anterior patterning in <italic>Drosophila<\/italic>.","volume":"78","author":"M Simpson-Brose","year":"1994","journal-title":"Cell"},{"key":"ref34","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1038\/340363a0","article-title":"Determination of spatial domains of zygotic gene-expression in the <italic>Drosophila<\/italic> embryo by the affinity of binding-sites for the <italic>Bicoid<\/italic> morphogen.","volume":"340","author":"W Driever","year":"1989","journal-title":"Nature"},{"key":"ref35","doi-asserted-by":"crossref","first-page":"e2774","DOI":"10.1371\/journal.pone.0002774","article-title":"The role of input noise in transcriptional regulation.","volume":"3","author":"G Tkacik","year":"2008","journal-title":"PLoS ONE"},{"key":"ref36","doi-asserted-by":"crossref","first-page":"e1000486","DOI":"10.1371\/journal.pcbi.1000486","article-title":"Stable, precise, and reproducible patterning of Bicoid and Hunchback molecules in the early <italic>Drosophila<\/italic> embryo.","volume":"5","author":"Y Okabe-Oho","year":"2009","journal-title":"PLoS Comput Biol"},{"key":"ref37","doi-asserted-by":"crossref","first-page":"2670","DOI":"10.1093\/bioinformatics\/btp415","article-title":"Statistical lower bounds on protein copy number from fluorescence expression images.","volume":"25","author":"L Zamparo","year":"2009","journal-title":"Bioinformatics"},{"key":"ref38","doi-asserted-by":"crossref","first-page":"5998","DOI":"10.1093\/emboj\/17.20.5998","article-title":"Cooperative DNA-binding by Bicoid provides a mechanism for threshold-dependent gene activation in the Drosophila embryo.","volume":"17","author":"DS Burz","year":"1998","journal-title":"EMBO J"},{"key":"ref39","doi-asserted-by":"crossref","first-page":"1195","DOI":"10.1242\/dev.122.4.1195","article-title":"The <italic>Drosophila<\/italic> morphogenetic protein Bicoid binds DNA cooperatively.","volume":"122","author":"XG Ma","year":"1996","journal-title":"Development"},{"key":"ref40","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1006\/jmbi.2000.4287","article-title":"Isolation of mutations that disrupt cooperative DNA binding by the <italic>Drosophila<\/italic> Bicoid protein.","volume":"305","author":"DS Burz","year":"2001","journal-title":"J Mol Biol"},{"key":"ref41","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1016\/j.cell.2007.05.026","article-title":"Stability and nuclear dynamics of the bicoid morphogen gradient.","volume":"130","author":"T Gregor","year":"2007","journal-title":"Cell"},{"key":"ref42","doi-asserted-by":"crossref","first-page":"e1000049","DOI":"10.1371\/journal.pbio.1000049","article-title":"Canalization of gene expression in the <italic>Drosophila<\/italic> blastoderm by gap gene cross regulation.","volume":"7","author":"Manu","year":"2009","journal-title":"PLoS Biol"},{"key":"ref43","doi-asserted-by":"crossref","first-page":"041917","DOI":"10.1103\/PhysRevE.77.041917","article-title":"Exact probabilistic solution of spatial-dependent stochastics and associated spatial potential landscape for the bicoid protein.","volume":"77","author":"D Lepzelter","year":"2008","journal-title":"Phys Rev E"},{"key":"ref44","doi-asserted-by":"crossref","first-page":"623","DOI":"10.1016\/j.ydbio.2007.09.058","article-title":"Modeling the bicoid gradient: diffusion and reversible nuclear trapping of a stable protein.","volume":"312","author":"M Coppey","year":"2007","journal-title":"Dev Biol"},{"key":"ref45","doi-asserted-by":"crossref","first-page":"915","DOI":"10.1016\/j.cub.2008.05.034","article-title":"Nuclear trapping shapes the terminal gradient in the <italic>Drosophila<\/italic> embryo.","volume":"18","author":"M Coppey","year":"2008","journal-title":"Curr Biol"},{"key":"ref46","doi-asserted-by":"crossref","first-page":"605","DOI":"10.1242\/dev.031195","article-title":"Formation of the <italic>bicoid<\/italic> morphogen gradient: an mRNA gradient dictates the protein gradient.","volume":"136","author":"AV Spirov","year":"2009","journal-title":"Development"},{"key":"ref47","article-title":"Statistical mechanics","author":"DA McQuarrie","year":"1976"},{"key":"ref48","article-title":"A modern course in statistical physics","author":"LE Reichl","year":"1980"},{"key":"ref49","article-title":"Handbook of stochastic methods. 3rd ed","author":"CW Gardiner","year":"2004"},{"key":"ref50","doi-asserted-by":"crossref","first-page":"9371","DOI":"10.1073\/pnas.1533293100","article-title":"Transcriptional regulatory cascades in development: Initial rates, not steady state, determine network kinetics.","volume":"100","author":"H Bolouri","year":"2003","journal-title":"Proc Nat Acad Sci USA"},{"key":"ref51","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1038\/ng869","article-title":"Regulation of noise in the expression of a single gene.","volume":"31","author":"EM Ozbudak","year":"2002","journal-title":"Nat Genet"},{"key":"ref52","doi-asserted-by":"crossref","first-page":"1142","DOI":"10.1126\/science.1178962","article-title":"Noise can induce bimodality in positive transcriptional feedback loops without bistability.","volume":"327","author":"T-L To","year":"2010","journal-title":"Science"},{"key":"ref53","doi-asserted-by":"crossref","first-page":"6305","DOI":"10.1073\/pnas.0701614104","article-title":"Discovering transcriptional regulatory regions in <italic>Drosophila<\/italic> by a nonalignment method for phylogenetic footprinting.","volume":"104","author":"A Sosinsky","year":"2007","journal-title":"Proc Nat Acad Sci USA"},{"key":"ref54","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1093\/oxfordjournals.molbev.a026107","article-title":"High sequence turnover in the regulatory regions of the developmental gene <italic>hunchback<\/italic> in insects.","volume":"16","author":"JM Hancock","year":"1999","journal-title":"Mol Biol Evol"},{"key":"ref55","doi-asserted-by":"crossref","first-page":"397","DOI":"10.1046\/j.1525-142X.2001.01043.x","article-title":"Rapid restructuring of <italic>bicoid<\/italic>-dependent <italic>hunchback<\/italic> promoters within and between Dipteran species: implications for molecular coevolution.","volume":"3","author":"AP McGregor","year":"2001","journal-title":"Evol and Dev"},{"key":"ref56","doi-asserted-by":"crossref","first-page":"846","DOI":"10.1126\/science.1099247","article-title":"Multiplex detection of RNA expression in <italic>Drosophila<\/italic> embryos.","volume":"305","author":"D Kosman","year":"2004","journal-title":"Science"},{"key":"ref57","doi-asserted-by":"crossref","first-page":"18403","DOI":"10.1073\/pnas.0509483102","article-title":"Diffusion and scaling during early embryonic pattern formation.","volume":"102","author":"T Gregor","year":"2005","journal-title":"Proc Nat Acad Sci USA"},{"key":"ref58","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1016\/j.devcel.2006.06.006","article-title":"Localization of <italic>bicoid<\/italic> mRNA in late oocytes is maintained by continual active transport.","volume":"11","author":"TT Weil","year":"2006","journal-title":"Dev Cell"},{"key":"ref59","doi-asserted-by":"crossref","first-page":"1055","DOI":"10.1016\/j.cub.2008.06.046","article-title":"Changes in <italic>bicoid<\/italic> mRNA anchoring highlight conserved mechanisms during the oocyte-to-embryo transition.","volume":"18","author":"TT Weil","year":"2008","journal-title":"Curr Biol"},{"key":"ref60","doi-asserted-by":"crossref","first-page":"471","DOI":"10.1126\/science.1173976","article-title":"Synchronous and stochastic patterns of gene activation in the <italic>Drosophila<\/italic> embryo.","volume":"325","author":"A Boettiger","year":"2009","journal-title":"Science"},{"key":"ref61","doi-asserted-by":"crossref","first-page":"849","DOI":"10.1038\/nature02189","article-title":"A self-organizing system of repressor gradients establishes segmental complexity in Drosophila.","volume":"426","author":"D Clyde","year":"2003","journal-title":"Nature"},{"key":"ref62","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1006\/dbio.2001.0355","article-title":"Thoracic patterning by the <italic>Drosophila<\/italic> gap gene <italic>hunchback<\/italic>.","volume":"237","author":"XL Wu","year":"2001","journal-title":"Dev Biol"},{"key":"ref63","doi-asserted-by":"crossref","first-page":"868","DOI":"10.1016\/j.cub.2008.05.050","article-title":"Precise registration of gene expression boundaries by a repressive morphogen in <italic>Drosophila<\/italic>.","volume":"18","author":"D Yu","year":"2008","journal-title":"Curr Biol"},{"key":"ref64","doi-asserted-by":"crossref","first-page":"230","DOI":"10.1049\/sb:20045021","article-title":"Spontaneous separation of bi-stable biochemical systems in spatial domains of opposite phases.","volume":"2","author":"J Elf","year":"2004","journal-title":"Syst Biol"},{"key":"ref65","doi-asserted-by":"crossref","first-page":"374","DOI":"10.1007\/s00427-005-0484-y","article-title":"A high- throughput method for quantifying gene expression data from early <italic>Drosophila<\/italic> embryos.","volume":"215","author":"H Janssens","year":"2005","journal-title":"Dev Genes Evol"},{"key":"ref66","article-title":"Shape Classification and Analysis: Theory and Practice, 2<sup>nd<\/sup> Ed","author":"LdF Costa","year":"2009"},{"key":"ref67","doi-asserted-by":"crossref","first-page":"320","DOI":"10.1007\/s00427-005-0472-2","article-title":"Removal of background signal from in situ data on the expression of segmentation genes in Drosophila.","volume":"215","author":"E Myasnikova","year":"2005","journal-title":"Dev Genes Evol"},{"key":"ref68","doi-asserted-by":"crossref","first-page":"824","DOI":"10.1155\/S1110865703302069","article-title":"Evolutionary techniques for image processing a large dataset of early <italic>Drosophila<\/italic> gene expression.","volume":"no. 8","author":"AV Spirov","year":"2003","journal-title":"EURASIP J on Appl Signal Processing 2003"},{"key":"ref69","doi-asserted-by":"crossref","DOI":"10.1201\/9781420035841","article-title":"Analysis of time series structure: SSA and related techniques","author":"N Golyandina","year":"2001"},{"key":"ref70","doi-asserted-by":"crossref","first-page":"825758","DOI":"10.1155\/2008\/825758","article-title":"Singular spectrum analysis of gene expression profiles of early <italic>Drosophila<\/italic> embryo: exponential-in-distance patterns.","volume":"2008","author":"T Alexandrov","year":"2008","journal-title":"Res Lett Signal Processing"},{"key":"ref71","doi-asserted-by":"crossref","first-page":"10761","DOI":"10.1002\/pamm.200810761","article-title":"Dependence of accuracy of ESPRIT estimates on signal eigenvalues: the case of a noisy sum of two real exponentials.","volume":"8","author":"T Alexandrov","year":"2009","journal-title":"Proc Appl Math Mech"},{"key":"ref72","first-page":"450","article-title":"2D-extension of Singular Spectrum Analysis: algorithm and elements of theory.","author":"N Golyandina","year":"2010"}],"container-title":["PLoS Computational Biology"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/dx.plos.org\/10.1371\/journal.pcbi.1001069","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,3,2]],"date-time":"2025-03-02T10:33:19Z","timestamp":1740911599000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1001069"}},"subtitle":[],"editor":[{"given":"Weixiong","family":"Zhang","sequence":"first","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2011,2,3]]},"references-count":72,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2011,2,3]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pcbi.1001069","relation":{},"ISSN":["1553-7358"],"issn-type":[{"value":"1553-7358","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,2,3]]}}}