{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,11]],"date-time":"2026-01-11T01:58:50Z","timestamp":1768096730649,"version":"3.49.0"},"reference-count":96,"publisher":"Springer Science and Business Media LLC","issue":"1","content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["BMC Syst Biol"],"published-print":{"date-parts":[[2009,12]]},"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:sec>\n            <jats:title>Background<\/jats:title>\n            <jats:p>Inverse modelling of gene regulatory networks (GRNs) capable of simulating continuous spatio-temporal biological processes requires accurate data and a good description of the system. If quantitative relations between genes cannot be extracted from direct measurements, an efficient method to estimate the unknown parameters is mandatory. A model that has been proposed to simulate spatio-temporal gene expression patterns is the connectionist model. This method describes the quantitative dynamics of a regulatory network in space. The model parameters are estimated by means of model-fitting algorithms. The gene interactions are identified without making any prior assumptions concerning the network connectivity. As a result, the inverse modelling might lead to multiple circuits showing the same quantitative behaviour and it is not possible to identify one optimal circuit. Consequently, it is important to address the quality of the circuits in terms of model robustness.<\/jats:p>\n          <\/jats:sec>\n          <jats:sec>\n            <jats:title>Results<\/jats:title>\n            <jats:p>Here we investigate the sensitivity and robustness of circuits obtained from reverse engineering a model capable of simulating measured gene expression patterns. As a case study we use the early gap gene segmentation mechanism in <jats:italic>Drosophila melanogaster<\/jats:italic>. We consider the limitations of the connectionist model used to describe GRN Inferred from spatio-temporal gene expression. We address the problem of circuit discrimination, where the selection criterion within the optimization technique is based of the least square minimization on the error between data and simulated results.<\/jats:p>\n          <\/jats:sec>\n          <jats:sec>\n            <jats:title>Conclusion<\/jats:title>\n            <jats:p>Parameter sensitivity analysis allows one to discriminate between circuits having significant parameter and qualitative differences but exhibiting the same quantitative pattern. Furthermore, we show that using a stochastic model derived from a deterministic solution, one can introduce fluctuations within the model to analyze the circuits' robustness. Ultimately, we show that there is a close relation between circuit sensitivity and robustness to fluctuation, and that circuit robustness is rather modular than global. The current study shows that reverse engineering of GRNs should not only focus on estimating parameters by minimizing the difference between observation and simulation but also on other model properties. Our study suggests that multi-objective optimization based on robustness and sensitivity analysis has to be considered.<\/jats:p>\n          <\/jats:sec>","DOI":"10.1186\/1752-0509-3-94","type":"journal-article","created":{"date-parts":[[2009,9,21]],"date-time":"2009-09-21T12:27:24Z","timestamp":1253536044000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":21,"title":["Inferring Drosophila gap gene regulatory network: a parameter sensitivity and perturbation analysis"],"prefix":"10.1186","volume":"3","author":[{"given":"Yves","family":"Fomekong-Nanfack","sequence":"first","affiliation":[]},{"given":"Marten","family":"Postma","sequence":"additional","affiliation":[]},{"given":"Jaap A","family":"Kaandorp","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2009,9,21]]},"reference":[{"key":"362_CR1","volume-title":"The regulatory genome - Gene regulatory networks in development and evolution","author":"E Davidson","year":"2006","unstructured":"Davidson E: The regulatory genome - Gene regulatory networks in development and evolution. 2006, London: Academic Press"},{"key":"362_CR2","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s00294-002-0285-z","volume":"41","author":"H Kitano","year":"2002","unstructured":"Kitano H: Looking beyond the details: a rise in system-oriented approaches in genetics and molecular biology. Curr Genet. 2002, 41: 1-10. 10.1007\/s00294-002-0285-z","journal-title":"Curr Genet"},{"key":"362_CR3","doi-asserted-by":"publisher","first-page":"1466","DOI":"10.1126\/science.1067407","volume":"296","author":"CC Guet","year":"2002","unstructured":"Guet CC, Elowitz MB, Hsing W, Leibler S: Combinatorial Synthesis of Genetic Networks. Science. 2002, 296: 1466-1470. 10.1126\/science.1067407","journal-title":"Science"},{"issue":"8","key":"362_CR4","doi-asserted-by":"publisher","first-page":"1867","DOI":"10.1016\/j.febslet.2005.02.007","volume":"579","author":"GC Julien Gagneur","year":"2005","unstructured":"Julien Gagneur GC: From molecular networks to qualitative cell behavior. FEBS letters. 2005, 579 (8): 1867-1871. 10.1016\/j.febslet.2005.02.007","journal-title":"FEBS letters"},{"issue":"Suppl 1","key":"362_CR5","doi-asserted-by":"publisher","first-page":"i19","DOI":"10.1093\/bioinformatics\/bti1048","volume":"21","author":"G Batt","year":"2005","unstructured":"Batt G, Ropers D, de Jong H, Geiselmann J, Mateescu R, Page M, Schneider D: Validation of qualitative models of genetic regulatory networks by model checking: analysis of the nutritional stress response in Escherichia coli. Bioinformatics. 2005, 21 (Suppl 1): i19-28. 10.1093\/bioinformatics\/bti1048","journal-title":"Bioinformatics"},{"issue":"3","key":"362_CR6","doi-asserted-by":"publisher","first-page":"289","DOI":"10.1016\/j.devcel.2006.08.006","volume":"11","author":"GT Reeves","year":"2006","unstructured":"Reeves GT, Muratov CB, Schupbach T, Shvartsman SY: Quantitative models of developmental pattern formation. Dev Cell. 2006, 11 (3): 289-300. 10.1016\/j.devcel.2006.08.006","journal-title":"Dev Cell"},{"key":"362_CR7","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1089\/10665270252833208","volume":"9","author":"H de Jong","year":"2002","unstructured":"de Jong H: Modeling and Simulation of Genetic Regulatory Systems: A Literature Review. J Comput Biol. 2002, 9: 67-103. 10.1089\/10665270252833208","journal-title":"J Comput Biol"},{"key":"362_CR8","volume-title":"PhD thesis","author":"P D'haeseleer","year":"2000","unstructured":"D'haeseleer P: Reconstructing Gene Network from Large Scale. PhD thesis. 2000, University of New Mexico"},{"issue":"11","key":"362_CR9","doi-asserted-by":"publisher","first-page":"2467","DOI":"10.1101\/gr.1262503","volume":"13","author":"CG Moles","year":"2003","unstructured":"Moles CG, Mendes P, Banga JR: Parameter Estimation in Biochemical Pathways: A Comparison of Global Optimization Methods. Genome Res. 2003, 13 (11): 2467-2474. 10.1101\/gr.1262503","journal-title":"Genome Res"},{"issue":"4","key":"362_CR10","doi-asserted-by":"publisher","first-page":"886","DOI":"10.1111\/j.1742-4658.2008.06844.x","volume":"276","author":"M Ashyraliyev","year":"2008","unstructured":"Ashyraliyev M, Fomekong-Nanfack Y, Kaandorp JA, Blom J: Systems biology: parameter estimation for biochemical models. FEBS Journal. 2008, 276 (4): 886-902. 10.1111\/j.1742-4658.2008.06844.x.","journal-title":"FEBS Journal"},{"issue":"6","key":"362_CR11","doi-asserted-by":"publisher","first-page":"e562","DOI":"10.1371\/journal.pone.0000562","volume":"2","author":"A Krishnan","year":"2007","unstructured":"Krishnan A, Giuliani A, Tomita M: Indeterminacy of Reverse Engineering of Gene Regulatory Networks: The Curse of Gene Elasticity. PLoS ONE. 2007, 2 (6): e562- 10.1371\/journal.pone.0000562","journal-title":"PLoS ONE"},{"issue":"10","key":"362_CR12","doi-asserted-by":"publisher","first-page":"1871","DOI":"10.1371\/journal.pcbi.0030189","volume":"3","author":"RN Gutenkunst","year":"2007","unstructured":"Gutenkunst RN, Waterfall JJ, Casey FP, Brown KS, Myers CR, Sethna JP: Universally sloppy parameter sensitivities in systems biology models. PLoS Comput Biol. 2007, 3 (10): 1871-1878. 10.1371\/journal.pcbi.0030189","journal-title":"PLoS Comput Biol"},{"issue":"11","key":"362_CR13","doi-asserted-by":"publisher","first-page":"813","DOI":"10.1038\/nrm2030","volume":"7","author":"K Jaqaman","year":"2006","unstructured":"Jaqaman K, Danuser G: Linking data to models: data regression. Nat Rev Mol Cell Biol. 2006, 7 (11): 813-819. 10.1038\/nrm2030","journal-title":"Nat Rev Mol Cell Biol"},{"key":"362_CR14","doi-asserted-by":"publisher","first-page":"951","DOI":"10.1109\/9.284871","volume":"39","author":"K Poolla","year":"1994","unstructured":"Poolla K, Khargonekar P, Tikku A, Krause J, Nagpal K: A Time-Domain Approach to Model Validation. IEEE Trans Automat Contr. 1994, 39: 951-959. 10.1109\/9.284871.","journal-title":"IEEE Trans Automat Contr"},{"key":"362_CR15","doi-asserted-by":"publisher","first-page":"2538","DOI":"10.1073\/pnas.012582499","volume":"99","author":"J Carlson","year":"2002","unstructured":"Carlson J, Doyle J: Complexity and robustness. Proc Natl Acad Sci. 2002, 99: 2538-2545. 10.1073\/pnas.012582499","journal-title":"Proc Natl Acad Sci"},{"key":"362_CR16","doi-asserted-by":"publisher","first-page":"137","DOI":"10.1038\/msb4100179","volume":"3","author":"H Kitano","year":"2007","unstructured":"Kitano H: Towards a theory of biological robustness. Mol Syst Biol. 2007, 3: 137- 10.1038\/msb4100179","journal-title":"Mol Syst Biol"},{"key":"362_CR17","doi-asserted-by":"publisher","first-page":"12","DOI":"10.1002\/cplx.10077","volume":"8","author":"E Jen","year":"2003","unstructured":"Jen E: Stable or robust? What's the difference?. Complexity. 2003, 8: 12-18. 10.1002\/cplx.10077.","journal-title":"Complexity"},{"key":"362_CR18","doi-asserted-by":"publisher","first-page":"91","DOI":"10.1098\/rspb.2007.1137","volume":"275","author":"A Wagner","year":"2008","unstructured":"Wagner A: Robustness and evolvability: a paradox resolved. Proc R Soc Lond B Biol Sci. 2008, 275: 91-100. 10.1098\/rspb.2007.1137.","journal-title":"Proc R Soc Lond B Biol Sci"},{"key":"362_CR19","doi-asserted-by":"publisher","first-page":"13210","DOI":"10.1073\/pnas.0401463101","volume":"101","author":"J Stelling","year":"2004","unstructured":"Stelling J, Gilles E, Doyle F: Robustness properties of circadian clock architectures. Proc Natl Acad Sci USA. 2004, 101: 13210-13215. 10.1073\/pnas.0401463101","journal-title":"Proc Natl Acad Sci USA"},{"issue":"6","key":"362_CR20","doi-asserted-by":"publisher","first-page":"675","DOI":"10.1016\/j.cell.2004.09.008","volume":"118","author":"J Stelling","year":"2004","unstructured":"Stelling J, Sauer U, Szallasi Z, Doyle FJ, Doyle J: Robustness of Cellular Functions. Cell. 2004, 118 (6): 675-685. 10.1016\/j.cell.2004.09.008","journal-title":"Cell"},{"key":"362_CR21","doi-asserted-by":"publisher","first-page":"8614","DOI":"10.1073\/pnas.151588598","volume":"98","author":"M Thattai","year":"2001","unstructured":"Thattai M, van Oudenaarden A: Intrinsic noise in gene regulatory networks. Proc Natl Acad Sci. 2001, 98: 8614-8619. 10.1073\/pnas.151588598","journal-title":"Proc Natl Acad Sci"},{"key":"362_CR22","doi-asserted-by":"publisher","first-page":"633","DOI":"10.1038\/nature01546","volume":"422","author":"W Blake","year":"2003","unstructured":"Blake W, Kaern M, Cantor C, Collins J: Noise in eukaryotic gene expression. Nature. 2003, 422: 633-637. 10.1038\/nature01546","journal-title":"Nature"},{"key":"362_CR23","volume-title":"Genome Research","author":"E Daniel","year":"2003","unstructured":"Daniel E, Zak GEG, Schwaber JS, Francis J, Doyle I: Importance of Input Perturbations and Stochastic Gene Expression in the Reverse Engineering of Genetic Regulatory Networks: Insights From an Identifiability Analysis of an In Silico Network. Genome Research. 2003"},{"issue":"Suppl 1","key":"362_CR24","doi-asserted-by":"publisher","first-page":"S21","DOI":"10.1186\/1471-2164-9-S1-S21","volume":"9","author":"Y Jin","year":"2008","unstructured":"Jin Y, Lindsey M: Stability analysis of genetic regulatory network with additive noises. BMC Genomics. 2008, 9 (Suppl 1): S21- 10.1186\/1471-2164-9-S1-S21","journal-title":"BMC Genomics"},{"key":"362_CR25","doi-asserted-by":"publisher","first-page":"231","DOI":"10.1038\/nature01258","volume":"420","author":"CV Rao","year":"2002","unstructured":"Rao CV, Wolf DM, Arkin AP: Control, exploitation and tolerance of intracellular noise. Nature. 2002, 420: 231-237. 10.1038\/nature01258","journal-title":"Nature"},{"key":"362_CR26","doi-asserted-by":"publisher","first-page":"913","DOI":"10.1038\/43199","volume":"387","author":"N Barkai","year":"1997","unstructured":"Barkai N, Leibler S: Robustness in simple biochemical networks. Nature. 1997, 387: 913-917. 10.1038\/43199","journal-title":"Nature"},{"key":"362_CR27","doi-asserted-by":"publisher","first-page":"188","DOI":"10.1038\/35018085","volume":"406","author":"EMM George von Dassow","year":"2000","unstructured":"George von Dassow EMM, Eli Meir , Odell GM: The segment polarity network is a robust developmental module. Nature. 2000, 406: 188-192. 10.1038\/35018085","journal-title":"Nature"},{"key":"362_CR28","doi-asserted-by":"publisher","first-page":"122","DOI":"10.1006\/dbio.2002.0664","volume":"246","author":"J Kastner","year":"2002","unstructured":"Kastner J, Solomon J, Fraser S: Modeling a Hox gene network in silico using a stochastic simulation algorithm. Developmental Biology. 2002, 246: 122-131. 10.1006\/dbio.2002.0664","journal-title":"Developmental Biology"},{"issue":"6098","key":"362_CR29","doi-asserted-by":"publisher","first-page":"668","DOI":"10.1038\/324668a0","volume":"324","author":"H Jackle","year":"1986","unstructured":"Jackle H, Tautz D, Schuh R, Seifert E, Lehmann R: Cross-regulatory interactions among the gap genes of Drosophila. Nature. 1986, 324 (6098): 668-670. 10.1038\/324668a0.","journal-title":"Nature"},{"key":"362_CR30","doi-asserted-by":"publisher","first-page":"57","DOI":"10.1016\/0012-1606(90)90053-L","volume":"140","author":"J Reinitz","year":"1990","unstructured":"Reinitz J, Levine M: Control of the initiation of homeotic gene expression by the gap genes giant and tailless in Drosophila. Dev Biol. 1990, 140: 57-72. 10.1016\/0012-1606(90)90053-L","journal-title":"Dev Biol"},{"key":"362_CR31","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1242\/dev.114.1.99","volume":"114","author":"M Capovilla","year":"1992","unstructured":"Capovilla M, Eldon ED, Pirrotta V: The giant gene of Drosophila encodes a b-ZIP DNA-binding protein that regulates the expression of other segmentation gap genes. Development. 1992, 114: 99-112.","journal-title":"Development"},{"key":"362_CR32","doi-asserted-by":"publisher","first-page":"849","DOI":"10.1038\/nature02189","volume":"426","author":"C DE","year":"2003","unstructured":"DE C, MSG C, X W, A P, D P: A self-organizing system of repressor gradients establishes segmental complexity in Drosophila. Nature. 2003, 426: 849-853. 10.1038\/nature02189","journal-title":"Nature"},{"key":"362_CR33","volume-title":"Molecular Biology of the Cell, Garland","author":"B Alberts","year":"2002","unstructured":"Alberts B, Johnson A, Lewis J, Raff M, Roberts K, Walter P: Molecular Biology of the Cell, Garland. 2002, Fourth","edition":"Fourth"},{"issue":"11","key":"362_CR34","doi-asserted-by":"publisher","first-page":"478","DOI":"10.1016\/0168-9525(96)10044-5","volume":"12","author":"HJ Rolando Rivera-Pomar","year":"1996","unstructured":"Rolando Rivera-Pomar HJ: From gradients to stripes in Drosophila embryogenesis: filling in the gaps. Trends in Genetics. 1996, 12 (11): 478-483. 10.1016\/0168-9525(96)10044-5","journal-title":"Trends in Genetics"},{"key":"362_CR35","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1242\/dev.101.1.1","volume":"101","author":"M Akam","year":"1987","unstructured":"Akam M: The molecular basis for metameric pattern in the Drosophila embryo. Development. 1987, 101: 1-22.","journal-title":"Development"},{"issue":"6185","key":"362_CR36","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1038\/335025a0","volume":"335","author":"PW Ingham","year":"1988","unstructured":"Ingham PW: The molecular genetics of embryonic pattern formation in Drosophila. Nature. 1988, 335 (6185): 25-34. 10.1038\/335025a0","journal-title":"Nature"},{"issue":"2","key":"362_CR37","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1016\/0092-8674(92)90466-P","volume":"68","author":"D St Johnston","year":"1992","unstructured":"St Johnston D, Nusslein-Volhard C: The origin of pattern and polarity in the Drosophila embryo. Cell. 1992, 68 (2): 201-219. 10.1016\/0092-8674(92)90466-P","journal-title":"Cell"},{"key":"362_CR38","doi-asserted-by":"publisher","first-page":"114","DOI":"10.1006\/jtbi.2001.2335","volume":"211","author":"L S\u00e1nchez","year":"2001","unstructured":"S\u00e1nchez L, Thieffry D: A logical analysis of the gap gene system. Theor Biol. 2001, 211: 114-141. 10.1006\/jtbi.2001.2335.","journal-title":"Theor Biol"},{"issue":"4","key":"362_CR39","doi-asserted-by":"publisher","first-page":"429","DOI":"10.1016\/S0022-5193(05)80391-1","volume":"152","author":"E Mjolsness","year":"1991","unstructured":"Mjolsness E, Sharp DH, Reinitz J: A connectionist model of development. J Theor Biol. 1991, 152 (4): 429-453. 10.1016\/S0022-5193(05)80391-1","journal-title":"J Theor Biol"},{"issue":"1-2","key":"362_CR40","doi-asserted-by":"publisher","first-page":"133","DOI":"10.1016\/0925-4773(94)00310-J","volume":"49","author":"J Reinitz","year":"1995","unstructured":"Reinitz J, Sharp DH: Mechanism of eve stripe formation. Mech Dev. 1995, 49 (1-2): 133-158. 10.1016\/0925-4773(94)00310-J","journal-title":"Mech Dev"},{"issue":"1-2","key":"362_CR41","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1016\/S0303-2647(98)00014-8","volume":"47","author":"DH Sharp","year":"1998","unstructured":"Sharp DH, Reinitz J: Prediction of mutant expression patterns using gene circuits. Biosystems. 1998, 47 (1-2): 79-90. 10.1016\/S0303-2647(98)00014-8","journal-title":"Biosystems"},{"issue":"6997","key":"362_CR42","doi-asserted-by":"publisher","first-page":"368","DOI":"10.1038\/nature02678","volume":"430","author":"J Jaeger","year":"2004","unstructured":"Jaeger J, Surkova S, Blagov M, Janssens H, Kosman D, Kozlov KN, Myasnikova E, Vanario-Alonso CE, Samsonova M, Sharp DH, Reinitz J: Dynamic control of positional information in the early Drosophila embryo. Nature. 2004, 430 (6997): 368-371. 10.1038\/nature02678","journal-title":"Nature"},{"issue":"5","key":"362_CR43","doi-asserted-by":"publisher","first-page":"e51","DOI":"10.1371\/journal.pcbi.0020051","volume":"2","author":"TJ Perkins","year":"2006","unstructured":"Perkins TJ, Jaeger J, Reinitz J, Glass L: Reverse engineering the gap gene network of Drosophila melanogaster. PLoS Comput Biol. 2006, 2 (5): e51- 10.1371\/journal.pcbi.0020051","journal-title":"PLoS Comput Biol"},{"issue":"10","key":"362_CR44","doi-asserted-by":"publisher","first-page":"1159","DOI":"10.1038\/ng1886","volume":"38","author":"H Janssens","year":"2006","unstructured":"Janssens H, Hou S, Jaeger J, Kim AR, Myasnikova E, Sharp D, Reinitz J: Quantitative and predictive model of transcriptional control of the Drosophila melanogaster even skipped gene. Nat Genet. 2006, 38 (10): 1159-1165. 10.1038\/ng1886","journal-title":"Nat Genet"},{"issue":"4","key":"362_CR45","doi-asserted-by":"publisher","first-page":"1721","DOI":"10.1534\/genetics.104.027334","volume":"167","author":"J Jaeger","year":"2004","unstructured":"Jaeger J, Blagov M, Kosman D, Kozlov KN, Myasnikova E, Surkova S, Vanario-Alonso CE, Samsonova M, Sharp DH, Reinitz J: Dynamical analysis of regulatory interactions in the gap gene system of Drosophila melanogaster. Genetics. 2004, 167 (4): 1721-1737. 10.1534\/genetics.104.027334","journal-title":"Genetics"},{"key":"362_CR46","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1093\/bioinformatics\/17.1.3","volume":"17","author":"E Myasnikova","year":"2001","unstructured":"Myasnikova E, Samsonova A, Kozlov K, Samsonova M, Reinitz J: Registration of the expression patterns of Drosophila segmentation genes by two independent methods. Bioinformatics. 2001, 17: 3-12. 10.1093\/bioinformatics\/17.1.3","journal-title":"Bioinformatics"},{"issue":"14","key":"362_CR47","doi-asserted-by":"publisher","first-page":"2212","DOI":"10.1093\/bioinformatics\/bth222","volume":"20","author":"E Poustelnikova","year":"2004","unstructured":"Poustelnikova E, Pisarev A, Blagov M, Samsonova M, Reinitz J: A database for management of gene expression data in situ. Bioinformatics. 2004, 20 (14): 2212-2221. 10.1093\/bioinformatics\/bth222","journal-title":"Bioinformatics"},{"issue":"2","key":"362_CR48","doi-asserted-by":"publisher","first-page":"646","DOI":"10.1006\/jcph.1998.6134","volume":"148","author":"KW Chu","year":"1999","unstructured":"Chu KW, Deng Y, Reinitz J: Parallel simulated annealing by mixing of states. J Comput Phys. 1999, 148 (2): 646-662. 10.1006\/jcph.1998.6134.","journal-title":"J Comput Phys"},{"key":"362_CR49","volume-title":"Tech Rep 8816","author":"J Lam","year":"1988","unstructured":"Lam J, Delosme JM: An Efficient Simulated Annealing Schedule: Derivation. Tech Rep 8816. 1988, Electrical Engineering Department, Yale, New Haven, CT"},{"key":"362_CR50","volume-title":"Tech Rep 8817","author":"J Lam","year":"1988","unstructured":"Lam J, Delosme JM: An Efficient Simulated Annealing Schedule: Implementation and Evaluation. Tech Rep 8817. 1988, Electrical Engineering Department, New Haven, CT"},{"issue":"24","key":"362_CR51","doi-asserted-by":"publisher","first-page":"3356","DOI":"10.1093\/bioinformatics\/btm433","volume":"23","author":"Y Fomekong-Nanfack","year":"2007","unstructured":"Fomekong-Nanfack Y, Kaandorp JA, Blom J: Efficient parameter estimation for spatio-temporal models of pattern formation: case study of Drosophila melanogaster. Bioinformatics. 2007, 23 (24): 3356-3363. 10.1093\/bioinformatics\/btm433","journal-title":"Bioinformatics"},{"key":"362_CR52","doi-asserted-by":"crossref","unstructured":"Ashyraliyev M, Jaeger J, Blom JG: Parameter estimation and determinability analysis applied to Drosophila gap gene circuits. BMC Systems Biology. 2008, 2 (83):","DOI":"10.1186\/1752-0509-2-83"},{"key":"362_CR53","doi-asserted-by":"publisher","first-page":"135","DOI":"10.1006\/jtbi.1993.1112","volume":"163","author":"BC Goodwin","year":"1993","unstructured":"Goodwin BC, Kauffman S, Murray JD: Is Morphogenesis an Intrinsically Robust Process?. Journal of Theoretical Biology. 1993, 163: 135-144. 10.1006\/jtbi.1993.1112","journal-title":"Journal of Theoretical Biology"},{"issue":"10","key":"362_CR54","doi-asserted-by":"publisher","first-page":"5699","DOI":"10.1073\/pnas.091485998","volume":"98","author":"RB Azevedo","year":"2001","unstructured":"Azevedo RB, Leroi AM: A power law for cells. Proc Natl Acad Sci USA. 2001, 98 (10): 5699-5704. 10.1073\/pnas.091485998","journal-title":"Proc Natl Acad Sci USA"},{"key":"362_CR55","doi-asserted-by":"publisher","first-page":"52","DOI":"10.1186\/1752-0509-1-52","volume":"1","author":"YF Wu","year":"2007","unstructured":"Wu YF, Myasnikova E, Reinitz J: Master equation simulation analysis of immunostained Bicoid morphogen gradient. BMC Syst Biol. 2007, 1: 52- 10.1186\/1752-0509-1-52","journal-title":"BMC Syst Biol"},{"issue":"22","key":"362_CR56","doi-asserted-by":"publisher","first-page":"2340","DOI":"10.1021\/j100540a008","volume":"81","author":"DT Gillespie","year":"1977","unstructured":"Gillespie DT: Exact stochastic simulation of coupled chemical reactions. Journal of Physical Chemistry. 1977, 81 (22): 2340-2361. 10.1021\/j100540a008.","journal-title":"Journal of Physical Chemistry"},{"issue":"6161","key":"362_CR57","doi-asserted-by":"publisher","first-page":"281","DOI":"10.1038\/332281a0","volume":"332","author":"D Tautz","year":"1988","unstructured":"Tautz D: Regulation of the Drosophila segmentation gene hunchback by two maternal morphogenetic centres. Nature. 1988, 332 (6161): 281-284. 10.1038\/332281a0","journal-title":"Nature"},{"issue":"2","key":"362_CR58","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1242\/dev.111.2.367","volume":"111","author":"E Eldon","year":"1991","unstructured":"Eldon E, Pirrotta V: Interactions of the Drosophila gap gene giant with maternal and zygotic pattern-forming genes. Development. 1991, 111 (2): 367-378.","journal-title":"Development"},{"key":"362_CR59","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1016\/S0070-2153(07)81002-7","volume":"81","author":"D Umulis","year":"2008","unstructured":"Umulis D, O'Connor MB, Othmer HG: Robustness of embryonic spatial patterning in Drosophila melanogaster. Curr Top Dev Biol. 2008, 81: 65-111. full_text","journal-title":"Curr Top Dev Biol"},{"issue":"2","key":"362_CR60","doi-asserted-by":"publisher","first-page":"209","DOI":"10.1029\/2000WR900291","volume":"37","author":"N Sun","year":"2001","unstructured":"Sun N, Sun NZ, Elimelech M, Ryan JN: Sensitivity analysis and parameter identifiability for colloid transport in geochemically heterogeneous porous media. Water Resources Research. 2001, 37 (2): 209-222. 10.1029\/2000WR900291.","journal-title":"Water Resources Research"},{"issue":"6","key":"362_CR61","doi-asserted-by":"publisher","first-page":"955","DOI":"10.1023\/A:1013215108374","volume":"35","author":"EM Myasnikova","year":"2001","unstructured":"Myasnikova EM, Samsonova AA, Samsonova MG, Reinitz J: Spatial registration of in situ gene expression data. Molecular Biology. 2001, 35 (6): 955-960. 10.1023\/A:1013215108374.","journal-title":"Molecular Biology"},{"issue":"3","key":"362_CR62","doi-asserted-by":"publisher","first-page":"205","DOI":"10.1016\/0925-4773(91)90019-3","volume":"35","author":"G Bronner","year":"1991","unstructured":"Bronner G, Jackle H: Control and function of terminal gap gene activity in the posterior pole region of the Drosophila embryo. Mech Dev. 1991, 35 (3): 205-211. 10.1016\/0925-4773(91)90019-3","journal-title":"Mech Dev"},{"issue":"2","key":"362_CR63","doi-asserted-by":"publisher","first-page":"271","DOI":"10.1016\/S0092-8674(00)80566-8","volume":"96","author":"JC Dunlap","year":"1999","unstructured":"Dunlap JC: Molecular Bases for Circadian Clocks. Cell. 1999, 96 (2): 271-290. 10.1016\/S0092-8674(00)80566-8","journal-title":"Cell"},{"issue":"3","key":"362_CR64","doi-asserted-by":"publisher","first-page":"309","DOI":"10.1016\/j.devcel.2005.08.006","volume":"9","author":"FR Cross","year":"2005","unstructured":"Cross FR, Siggia ED: Shake It, Don't Break It: Positive Feedback and the Evolution of Oscillator Design. Developmental Cell. 2005, 9 (3): 309-310. 10.1016\/j.devcel.2005.08.006","journal-title":"Developmental Cell"},{"issue":"2","key":"362_CR65","doi-asserted-by":"publisher","first-page":"342","DOI":"10.1016\/j.jtbi.2005.11.034","volume":"241","author":"F Alves","year":"2006","unstructured":"Alves F, Dilao R: Modeling segmental patterning in Drosophila: Maternal and gap genes. J Theor Biol. 2006, 241 (2): 342-359. 10.1016\/j.jtbi.2005.11.034","journal-title":"J Theor Biol"},{"issue":"2","key":"362_CR66","doi-asserted-by":"publisher","first-page":"164","DOI":"10.1134\/S0006350908020085","volume":"53","author":"V Gursky","year":"2008","unstructured":"Gursky V, Kozlov K, Samsonov A, Reinitz J: Model with asymptotically stable dynamics for Drosophila gap gene network. Biophysics. 2008, 53 (2): 164-176. 10.1134\/S0006350908020085.","journal-title":"Biophysics"},{"issue":"2","key":"362_CR67","doi-asserted-by":"publisher","first-page":"54","DOI":"10.1038\/scientificamerican0896-54","volume":"275","author":"C Nusslein-Volhard","year":"1996","unstructured":"Nusslein-Volhard C: Gradients that organize embryo development. Sci Am. 1996, 275 (2): 54-55.","journal-title":"Sci Am"},{"issue":"51","key":"362_CR68","doi-asserted-by":"publisher","first-page":"18403","DOI":"10.1073\/pnas.0509483102","volume":"102","author":"T Gregor","year":"2005","unstructured":"Gregor T, Bialek W, de Ruyter van Steveninck RR, Tank DW, Wieschaus EF: Diffusion and scaling during early embryonic pattern formation. Proc Natl Acad Sci USA. 2005, 102 (51): 18403-18407. 10.1073\/pnas.0509483102","journal-title":"Proc Natl Acad Sci USA"},{"issue":"4","key":"362_CR69","doi-asserted-by":"publisher","first-page":"2195","DOI":"10.1529\/biophysj.104.044131","volume":"87","author":"XJ Feng","year":"2004","unstructured":"Feng XJ, Hooshangi S, Chen D, Li G, Weiss R, Rabitz H: Optimizing genetic circuits by global sensitivity analysis. Biophys J. 2004, 87 (4): 2195-2202. 10.1529\/biophysj.104.044131","journal-title":"Biophys J"},{"issue":"4954","key":"362_CR70","doi-asserted-by":"publisher","first-page":"495","DOI":"10.1126\/science.2158673","volume":"248","author":"D Weigel","year":"1990","unstructured":"Weigel D, Jurgens G, Klingler M, Jackle H: Two gap genes mediate maternal terminal pattern information in Drosophila. Science. 1990, 248 (4954): 495-498. 10.1126\/science.2158673","journal-title":"Science"},{"key":"362_CR71","doi-asserted-by":"publisher","first-page":"832","DOI":"10.1109\/JPROC.2006.871776","volume":"94","author":"H El-Samad","year":"2006","unstructured":"El-Samad H, Prajna SAP, Doyle J, Khammash M: Advanced methods and algorithms for biological networks analysis. Proc IEEE. 2006, 94: 832-853. 10.1109\/JPROC.2006.871776.","journal-title":"Proc IEEE"},{"key":"362_CR72","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1016\/j.automatica.2005.08.007","volume":"42","author":"S Prajna","year":"2006","unstructured":"Prajna S: Barrier certificates for nonlinear model validation. Automatica. 2006, 42: 117-126. 10.1016\/j.automatica.2005.08.007.","journal-title":"Automatica"},{"issue":"9","key":"362_CR73","doi-asserted-by":"publisher","first-page":"3196","DOI":"10.1529\/biophysj.106.083485","volume":"91","author":"J Tomshine","year":"2006","unstructured":"Tomshine J, Kaznessis YN: Optimization of a stochastically simulated gene network model via simulated annealing. Biophys J. 2006, 91 (9): 3196-3205. 10.1529\/biophysj.106.083485","journal-title":"Biophys J"},{"key":"362_CR74","unstructured":"Fomekong-Nanfack Y, Postma M, Kaandorp JA: Inferring Drosophila gap gene regulatory network: pattern analysis of simulated gene expression profiles and stability analysis. [To appear in BMC System Biology]."},{"issue":"2-3","key":"362_CR75","doi-asserted-by":"publisher","first-page":"248","DOI":"10.1016\/j.biosystems.2005.06.016","volume":"83","author":"M Rodriguez-Fernandez","year":"2006","unstructured":"Rodriguez-Fernandez M, Mendes P, Banga JR: A hybrid approach for efficient and robust parameter estimation in biochemical pathways. Biosystems. 2006, 83 (2-3): 248-265. 10.1016\/j.biosystems.2005.06.016","journal-title":"Biosystems"},{"issue":"2","key":"362_CR76","doi-asserted-by":"publisher","first-page":"122","DOI":"10.1038\/nrg2509","volume":"10","author":"DJ Wilkinson","year":"2009","unstructured":"Wilkinson DJ: Stochastic modelling for quantitative description of heterogeneous biological systems. Nat Rev Genet. 2009, 10 (2): 122-133. 10.1038\/nrg2509","journal-title":"Nat Rev Genet"},{"key":"362_CR77","doi-asserted-by":"crossref","unstructured":"Manu , Surkova S, Spirov AV, Gursky VV, Janssens H, Kim AR, Radulescu O, Vanario-Alonso CE, Sharp DH, Samsonova M, Reinitz J: Canalization of Gene Expression in the Drosophila Blastoderm by Gap Gene Cross Regulation. PLoS Biology. 2009, 7 (3):","DOI":"10.1371\/journal.pbio.1000049"},{"issue":"3","key":"362_CR78","doi-asserted-by":"publisher","first-page":"e64","DOI":"10.1371\/journal.pbio.0030064","volume":"3","author":"M Isalan","year":"2005","unstructured":"Isalan M, Lemerle C, Serrano L: Engineering gene networks to emulate Drosophila embryonic pattern formation. PLoS Biol. 2005, 3 (3): e64- 10.1371\/journal.pbio.0030064","journal-title":"PLoS Biol"},{"issue":"2","key":"362_CR79","doi-asserted-by":"publisher","first-page":"279","DOI":"10.1109\/TCBB.2007.070203","volume":"4","author":"J Handl","year":"2007","unstructured":"Handl J, Kell DB, Knowles J: Multiobjective optimization in bioinformatics and computational biology. IEEE\/ACM Trans Comput Biol Bioinform. 2007, 4 (2): 279-292. 10.1109\/TCBB.2007.070203","journal-title":"IEEE\/ACM Trans Comput Biol Bioinform"},{"key":"362_CR80","volume-title":"Multi-Objective Optimization using EvolutionaryAlgorithms","author":"K Deb","year":"2001","unstructured":"Deb K: Multi-Objective Optimization using EvolutionaryAlgorithms. 2001, Wiley"},{"key":"362_CR81","volume-title":"Multiobjective Optimization, Principles and Case Studies","author":"Y Colette","year":"2003","unstructured":"Colette Y, Siarry P: Multiobjective Optimization, Principles and Case Studies. 2003, Springer"},{"key":"362_CR82","first-page":"502","volume-title":"Fourth Int Conf on Genetic Algorithms ICGA'4","author":"G Syswerda","year":"1991","unstructured":"Syswerda G, Palmucci J: The application of genetic algorithms to resource scheduling. Fourth Int Conf on Genetic Algorithms ICGA'4. Edited by: Belew R, Booker L. 1991, 502-508. San Mateo, California.: Morgan Kaufmann Pub"},{"key":"362_CR83","first-page":"291","volume-title":"Parallel Problem Solving from Nature PPSN'2, LNCS","author":"W Jakob","year":"1992","unstructured":"Jakob W, Gorges-Schleuter M, Blume C: Application of genetic algorithms to task planning and learning. Parallel Problem Solving from Nature PPSN'2, LNCS. Edited by: Manner R, Manderick B. 1992, 291-300. Amsterdam. North-Holland"},{"key":"362_CR84","first-page":"597","volume-title":"Fifth Int. Conf. on Genetic Algorithms","author":"G Jones","year":"1993","unstructured":"Jones G, Brown R, Clark D, Willett P, Glen R: Searching databases of twodimensional and three-dimensional chemical structures using genetic algorithms. Fifth Int. Conf. on Genetic Algorithms. Edited by: Forrest S. 1993, 597-602. San Mateo, California.: Morgan Kaufmann"},{"key":"362_CR85","volume-title":"Genetic Algorithms in Search, Optimization, and Machine Learning","author":"DE Goldberg","year":"1989","unstructured":"Goldberg DE: Genetic Algorithms in Search, Optimization, and Machine Learning. 1989, Addison-Wesley Professional"},{"key":"362_CR86","first-page":"231","volume-title":"Soft Computing in Engineering Design and Manufacturing","author":"P Bentley","year":"1997","unstructured":"Bentley P, Wakefield J: Soft Computing in Engineering Design and Manufacturing. 1997, 231-240. chap. Finding acceptable Pareto-optimal solutions using multiobjective genetic algorithms"},{"key":"362_CR87","first-page":"2084","volume-title":"IEEE Proceedings of the 2004 congress on evolutionary computation: CEC 2004","author":"K Praveen","year":"2004","unstructured":"Praveen K, Sanjoy D, Stephen W, L RJ: A multi-objective GA-simplex hybrid approach for gene regulatory network models. IEEE Proceedings of the 2004 congress on evolutionary computation: CEC 2004. 2004, 2084-2090."},{"issue":"8","key":"362_CR88","doi-asserted-by":"publisher","first-page":"1085","DOI":"10.1093\/bioinformatics\/btn075","volume":"24","author":"PK Liu","year":"2008","unstructured":"Liu PK, Wang FS: Inference of biochemical network models in S-system using multiobjective optimization approach. Bioinformatics. 2008, 24 (8): 1085-1092. 10.1093\/bioinformatics\/btn075","journal-title":"Bioinformatics"},{"key":"362_CR89","first-page":"198","volume-title":"Parallel Problem Solving from Nature - Proceedings of 1st Workshop, (PPSN 1), Volume 496 of Lecture Notes in Computer Science","author":"R Lohmann","year":"1991","unstructured":"Lohmann R: Application of Evolution Strategy in Parallel Populations. Parallel Problem Solving from Nature - Proceedings of 1st Workshop, (PPSN 1), Volume 496 of Lecture Notes in Computer Science. Edited by: Schwefel HP, M\u00e4anner R. 1991, 198-208. Berlin, Germany: Springer-Verlag"},{"key":"362_CR90","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1242\/jcs.61.1.31","volume":"61","author":"VE Foe","year":"1983","unstructured":"Foe VE, Alberts BM: Studies of nuclear and cytoplasmic behaviour during the five mitotic cycles that precede gastrulation in Drosophila embryogenesis. J Cell Sci. 1983, 61: 31-70.","journal-title":"J Cell Sci"},{"issue":"2","key":"362_CR91","doi-asserted-by":"publisher","first-page":"233","DOI":"10.1109\/TSMCC.2004.841906","volume":"35","author":"TP Runarsson","year":"2005","unstructured":"Runarsson TP, Yao X: Search biases in constrained evolutionary optimization. IEEE Transactions on Systems, Man, and Cybernetics, Part C. 2005, 35 (2): 233-243. 10.1109\/TSMCC.2004.841906.","journal-title":"IEEE Transactions on Systems, Man, and Cybernetics, Part C"},{"key":"362_CR92","volume-title":"Tech Rep WM-CS-2005-01","author":"RM Lewis","year":"2005","unstructured":"Lewis RM, Shepherd A, Torczon V: Implementing generating set search methods for linearly constrained minimization. Tech Rep WM-CS-2005-01. 2005, [Revised July 2006], Department of Computer Science, College of William & Mary"},{"key":"362_CR93","doi-asserted-by":"publisher","first-page":"66","DOI":"10.1038\/scientificamerican0792-66","volume":"267","author":"JH Holland","year":"1992","unstructured":"Holland JH: Genetic Algorithms. Sci Am. 1992, 267: 66-72.","journal-title":"Sci Am"},{"issue":"9","key":"362_CR94","doi-asserted-by":"publisher","first-page":"1876","DOI":"10.1021\/jp993732q","volume":"104","author":"M Gibson","year":"2000","unstructured":"Gibson M, Bruck J: Efficient Exact Stochastic Simulation of Chemical Systems with Many Species and Many Channels. Journal of Physical Chemistry A. 2000, 104 (9): 1876-1889. 10.1021\/jp993732q.","journal-title":"Journal of Physical Chemistry A"},{"key":"362_CR95","doi-asserted-by":"publisher","first-page":"290","DOI":"10.1007\/s004270050184","volume":"208","author":"D Kosman","year":"1998","unstructured":"Kosman D, Small S, Reinitz J: Rapid preparation of a panel of polyclonal antibodies to Drosophila segmentation proteins. Dev Genes Evol. 1998, 208: 290-294. 10.1007\/s004270050184","journal-title":"Dev Genes Evol"},{"key":"362_CR96","first-page":"195","volume-title":"Proceedings of the Seventh International Conference on Intelligent Systems for Molecular Biology","author":"E Myasnikova","year":"1999","unstructured":"Myasnikova E, Kosman D, Reinitz J, Samsonova M: Spatio-Temporal Registration of the Expression Patterns of Drosophila Segmentation Genes. Proceedings of the Seventh International Conference on Intelligent Systems for Molecular Biology. 1999, 195-201. AAAI Press"}],"container-title":["BMC Systems Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/1752-0509-3-94.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,9,1]],"date-time":"2021-09-01T03:19:35Z","timestamp":1630466375000},"score":1,"resource":{"primary":{"URL":"https:\/\/bmcsystbiol.biomedcentral.com\/articles\/10.1186\/1752-0509-3-94"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,9,21]]},"references-count":96,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2009,12]]}},"alternative-id":["362"],"URL":"https:\/\/doi.org\/10.1186\/1752-0509-3-94","relation":{},"ISSN":["1752-0509"],"issn-type":[{"value":"1752-0509","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,9,21]]},"assertion":[{"value":"22 January 2009","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 September 2009","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 September 2009","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"94"}}