{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,13]],"date-time":"2026-05-13T22:21:44Z","timestamp":1778710904906,"version":"3.51.4"},"reference-count":45,"publisher":"Oxford University Press (OUP)","issue":"14","license":[{"start":{"date-parts":[[2016,10,2]],"date-time":"2016-10-02T00:00:00Z","timestamp":1475366400000},"content-version":"vor","delay-in-days":2700,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc\/2.0\/uk\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2009,7,15]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Motivation: Synthetic biology is to engineer artificial biological systems to investigate natural biological phenomena and for a variety of applications. However, the development of synthetic gene networks is still difficult and most newly created gene networks are non-functioning due to uncertain initial conditions and disturbances of extra-cellular environments on the host cell. At present, how to design a robust synthetic gene network to work properly under these uncertain factors is the most important topic of synthetic biology.<\/jats:p>\n               <jats:p>Results: A robust regulation design is proposed for a stochastic synthetic gene network to achieve the prescribed steady states under these uncertain factors from the minimax regulation perspective. This minimax regulation design problem can be transformed to an equivalent stochastic game problem. Since it is not easy to solve the robust regulation design problem of synthetic gene networks by non-linear stochastic game method directly, the Takagi\u2013Sugeno (T\u2013S) fuzzy model is proposed to approximate the non-linear synthetic gene network via the linear matrix inequality (LMI) technique through the Robust Control Toolbox in Matlab. Finally, an in silico example is given to illustrate the design procedure and to confirm the efficiency and efficacy of the proposed robust gene design method.<\/jats:p>\n               <jats:p>Availability: \u00a0http:\/\/www.ee.nthu.edu.tw\/bschen\/SyntheticBioDesign_supplement.pdf<\/jats:p>\n               <jats:p>Contact: \u00a0bschen@ee.nthu.edu.tw<\/jats:p>\n               <jats:p>Supplementary information: \u00a0Supplementary data are available at Bioinformatics online.<\/jats:p>","DOI":"10.1093\/bioinformatics\/btp310","type":"journal-article","created":{"date-parts":[[2009,5,13]],"date-time":"2009-05-13T01:39:59Z","timestamp":1242178799000},"page":"1822-1830","source":"Crossref","is-referenced-by-count":37,"title":["Robust synthetic biology design: stochastic game theory approach"],"prefix":"10.1093","volume":"25","author":[{"given":"Bor-Sen","family":"Chen","sequence":"first","affiliation":[{"name":"1 Laboratory of Control and Systems Biology, Department of Electrical Engineering, National Tsing Hua University, Hsinchu, 30013 and 2 Department of Biological Science and Technology, National Chiao Tung University, Hsinchu, 30068, Taiwan, R.O.C."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chia-Hung","family":"Chang","sequence":"additional","affiliation":[{"name":"1 Laboratory of Control and Systems Biology, Department of Electrical Engineering, National Tsing Hua University, Hsinchu, 30013 and 2 Department of Biological Science and Technology, National Chiao Tung University, Hsinchu, 30068, Taiwan, R.O.C."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hsiao-Ching","family":"Lee","sequence":"additional","affiliation":[{"name":"1 Laboratory of Control and Systems Biology, Department of Electrical Engineering, National Tsing Hua University, Hsinchu, 30013 and 2 Department of Biological Science and Technology, National Chiao Tung University, Hsinchu, 30068, Taiwan, R.O.C."}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2009,5,12]]},"reference":[{"key":"2023013112051532100_B1","doi-asserted-by":"crossref","first-page":"1866","DOI":"10.1126\/science.1089072","article-title":"Biological networks: the tinkerer as an engineer","volume":"301","author":"Alon","year":"2003","journal-title":"Science"},{"key":"2023013112051532100_B2","volume-title":"An Introduction to Systems Biology: Design Principles of Biological Circuits","author":"Alon","year":"2007"},{"key":"2023013112051532100_B3","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/msb4100073","article-title":"Synthetic biology: new engineering rules for an emerging discipline","volume":"2","author":"Andrianantoandro","year":"2006","journal-title":"Mol. Syst. Biol."},{"key":"2023013112051532100_B4","doi-asserted-by":"crossref","first-page":"771","DOI":"10.1038\/nbt0708-771","article-title":"Setting the standard in synthetic biology","volume":"26","author":"Arkin","year":"2008","journal-title":"Nat. Biotechnol."},{"key":"2023013112051532100_B5","volume-title":"Robust Control Toolbox User's Guide","author":"Balas","year":"2008"},{"key":"2023013112051532100_B6","article-title":"Dynamic Noncooperative Game Theory","volume-title":"Society for Industrial and Applied Mathematics","author":"Basar","year":"1999","edition":"2"},{"key":"2023013112051532100_B7","doi-asserted-by":"crossref","first-page":"2415","DOI":"10.1093\/bioinformatics\/btm362","article-title":"Robustness analysis and tuning of synthetic gene networks","volume":"23","author":"Batt","year":"2007","journal-title":"Bioinformatics"},{"key":"2023013112051532100_B8","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611970777","article-title":"Linear Matrix Inequalities in System and Control Theory","volume-title":"Society for Industrial Mathematics","author":"Boyd","year":"1994"},{"key":"2023013112051532100_B9","doi-asserted-by":"crossref","first-page":"787","DOI":"10.1038\/nbt1413","article-title":"Refinement and standardization of synthetic biological parts and devices","volume":"26","author":"Canton","year":"2008","journal-title":"Nat. Biotechnol."},{"key":"2023013112051532100_B10","doi-asserted-by":"crossref","first-page":"114","DOI":"10.1109\/TBCAS.2008.926728","article-title":"Robust engineered circuit design principles for stochastic biochemical networks with parameter uncertainties and disturbances","volume":"2","author":"Chen","year":"2008","journal-title":"IEEE Trans. Biomed. Circuits Syst."},{"key":"2023013112051532100_B11","doi-asserted-by":"crossref","first-page":"342","DOI":"10.1016\/j.mbs.2007.11.002","article-title":"Robust filtering circuit design for stochastic gene networks under intrinsic and extrinsic molecular noises","volume":"211","author":"Chen","year":"2008","journal-title":"Math. Biosci."},{"key":"2023013112051532100_B12","doi-asserted-by":"crossref","first-page":"571","DOI":"10.1109\/91.797980","article-title":"Robustness design of nonlinear dynamic systems via fuzzy linear control","volume":"7","author":"Chen","year":"1999","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"2023013112051532100_B13","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1109\/91.855915","article-title":"Mixed H2\/H\u221e fuzzy output feedback control design for nonlinear dynamic systems: an LMI approach","volume":"8","author":"Chen","year":"2000","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"2023013112051532100_B14","doi-asserted-by":"crossref","first-page":"222","DOI":"10.1109\/91.995123","article-title":"Fuzzy differential games for nonlinear stochastic systems: suboptimal approach","volume":"10","author":"Chen","year":"2002","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"2023013112051532100_B15","doi-asserted-by":"crossref","first-page":"824","DOI":"10.1016\/j.jtbi.2008.04.024","article-title":"Robust model matching control of immune systems under environmental disturbances: dynamic game approach","volume":"253","author":"Chen","year":"2008","journal-title":"J. Theor. Biol."},{"key":"2023013112051532100_B16","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1109\/TSMCB.2007.906975","article-title":"Robust H\u221e stabilization design in gene networks under stochastic molecular noises: Fuzzy-interpolation approach","volume":"38","author":"Chen","year":"2008","journal-title":"IEEE Trans. Syst. Man Cybern. B"},{"key":"2023013112051532100_B17","doi-asserted-by":"crossref","first-page":"2005.0032","DOI":"10.1038\/msb4100007","article-title":"From systems biology to synthetic biology","volume":"1","author":"Church","year":"2005","journal-title":"Mol. Syst. Biol."},{"key":"2023013112051532100_B18","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1089\/10665270252833208","article-title":"Modeling and simulation of genetic regulatory systems: a literature review","volume":"9","author":"de Jong","year":"2002","journal-title":"J. Comput. Biol."},{"key":"2023013112051532100_B19","doi-asserted-by":"crossref","first-page":"449","DOI":"10.1038\/nature04342","article-title":"Foundations for engineering biology","volume":"438","author":"Endy","year":"2005","journal-title":"Nature"},{"key":"2023013112051532100_B20","doi-asserted-by":"crossref","first-page":"158","DOI":"10.1126\/science.303.5655.158","article-title":"Synthetic biology: microbes made to order","volume":"303","author":"Ferber","year":"2004","journal-title":"Science"},{"key":"2023013112051532100_B21","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1101\/gr.5776007","article-title":"Synthetic biology projects in vitro","volume":"17","author":"Forster","year":"2007","journal-title":"Genome Res."},{"key":"2023013112051532100_B22","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1038\/35002131","article-title":"Construction of a genetic toggle switch in Escherichia coli","volume":"403","author":"Gardner","year":"2000","journal-title":"Nature"},{"key":"2023013112051532100_B23","doi-asserted-by":"crossref","first-page":"198","DOI":"10.1016\/j.mib.2004.02.002","article-title":"Robust control in bacterial regulatory circuits","volume":"7","author":"Goulian","year":"2004","journal-title":"Curr. Opin. Microbiol."},{"key":"2023013112051532100_B24","doi-asserted-by":"crossref","first-page":"224","DOI":"10.1038\/nature01257","article-title":"Engineered gene circuits","volume":"420","author":"Hasty","year":"2002","journal-title":"Nature"},{"key":"2023013112051532100_B25","doi-asserted-by":"crossref","first-page":"2790","DOI":"10.1093\/bioinformatics\/btl469","article-title":"Synthetic biology - putting engineering into biology","volume":"22","author":"Heinemann","year":"2006","journal-title":"Bioinformatics"},{"key":"2023013112051532100_B26","doi-asserted-by":"crossref","first-page":"3581","DOI":"10.1073\/pnas.0408507102","article-title":"Ultrasensitivity and noise propagation in a synthetic transcriptional cascade","volume":"102","author":"Hooshangi","year":"2005","journal-title":"Proc. Natl Acad. Sci. USA"},{"key":"2023013112051532100_B27","doi-asserted-by":"crossref","first-page":"676","DOI":"10.1109\/TFUZZ.2004.834811","article-title":"A novel Takagi-Sugeno-based robust adaptive fuzzy sliding-mode controller","volume":"12","author":"Hwang","year":"2004","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"2023013112051532100_B28","doi-asserted-by":"crossref","first-page":"545","DOI":"10.1038\/nbt1208","article-title":"RNA synthetic biology","volume":"24","author":"Isaacs","year":"2006","journal-title":"Nat. Biotechnol."},{"key":"2023013112051532100_B29","doi-asserted-by":"crossref","first-page":"940","DOI":"10.1016\/j.ces.2005.06.033","article-title":"Multi-scale models for gene network engineering","volume":"61","author":"Kaznessis","year":"2006","journal-title":"Chem. Eng. Sci.e"},{"key":"2023013112051532100_B30","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1186\/1752-0509-1-47","article-title":"Models for synthetic biology","volume":"1","author":"Kaznessis","year":"2007","journal-title":"BMC Syst. Biol."},{"key":"2023013112051532100_B31","doi-asserted-by":"crossref","first-page":"1662","DOI":"10.1126\/science.1069492","article-title":"Systems biology: a brief overview","volume":"295","author":"Kitano","year":"2002","journal-title":"Science"},{"key":"2023013112051532100_B32","doi-asserted-by":"crossref","first-page":"826","DOI":"10.1038\/nrg1471","article-title":"Biological robustness","volume":"5","author":"Kitano","year":"2004","journal-title":"Nat. Rev. Genet."},{"key":"2023013112051532100_B33","doi-asserted-by":"crossref","first-page":"8414","DOI":"10.1073\/pnas.0402940101","article-title":"Programmable cells: interfacing natural and engineered gene networks","volume":"101","author":"Kobayashi","year":"2004","journal-title":"Proc. Natl Acad. Sci."},{"key":"2023013112051532100_B34","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1186\/1471-2105-8-12","article-title":"Efficient classification of complete parameter regions based on semidefinite programming","volume":"8","author":"Kuepfer","year":"2007","journal-title":"BMC Bioinformatics"},{"key":"2023013112051532100_B35","doi-asserted-by":"crossref","first-page":"491","DOI":"10.1109\/TFUZZ.2004.832526","article-title":"Fuzzy target tracking control of autonomous mobile robots by using infrared sensors","volume":"12","author":"Li","year":"2004","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"2023013112051532100_B36","doi-asserted-by":"crossref","first-page":"539","DOI":"10.1109\/91.940967","article-title":"LMI-based fuzzy chaotic synchronization and communications","volume":"9","author":"Lian","year":"2001","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"2023013112051532100_B37","doi-asserted-by":"crossref","first-page":"1107","DOI":"10.1016\/j.jmb.2006.03.064","article-title":"Regulatory dynamics of synthetic gene networks with positive feedback","volume":"359","author":"Maeda","year":"2006","journal-title":"J. Mol. Biol."},{"key":"2023013112051532100_B38","doi-asserted-by":"crossref","first-page":"735","DOI":"10.1007\/s00253-006-0664-3","article-title":"The promise of synthetic biology","volume":"73","author":"Pleiss","year":"2006","journal-title":"Appl. Microbiol. Biotechnol."},{"key":"2023013112051532100_B39","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1088\/1478-3975\/3\/4\/007","article-title":"Computer-aided design of modular protein devices: Boolean AND gene activation","volume":"3","author":"Salis","year":"2006","journal-title":"Phys. Biol."},{"key":"2023013112051532100_B40","doi-asserted-by":"crossref","DOI":"10.7551\/mitpress\/9780262195485.001.0001","volume-title":"System Modeling in Cellular Biology: From Concepts to Nuts and Bolts","author":"Szallasi","year":"2006"},{"key":"2023013112051532100_B41","doi-asserted-by":"crossref","first-page":"116","DOI":"10.1109\/TSMC.1985.6313399","article-title":"Fuzzy identification of systems and its applications to modeling and control","volume":"15","author":"Takagi","year":"1985","journal-title":"IEEE Trans.Syst. Man Cybern."},{"key":"2023013112051532100_B42","first-page":"25","article-title":"The promise and perils of synthetic biology","volume":"12","author":"Tucker","year":"2006","journal-title":"New Atlantis"},{"key":"2023013112051532100_B43","doi-asserted-by":"crossref","first-page":"571","DOI":"10.1146\/annurev.biochem.69.1.571","article-title":"Mechanisms and control of mRNA decapping in Saccharomyces cerevisiae","volume":"69","author":"Tucker","year":"2000","journal-title":"Ann. Rev. Biochem."},{"key":"2023013112051532100_B44","doi-asserted-by":"crossref","first-page":"1973","DOI":"10.1137\/S0363012903423727","article-title":"State feedback H\u221e control for a class of nonlinear stochastic systems","volume":"44","author":"Zhang","year":"2006","journal-title":"SIAM J. Control Optim."},{"key":"2023013112051532100_B45","doi-asserted-by":"crossref","first-page":"589","DOI":"10.1109\/TSP.2004.840724","article-title":"Robust H\u221e filtering for nonlinear stochastic systems","volume":"53","author":"Zhang","year":"2005","journal-title":"IEEE Trans. Signal Process."}],"container-title":["Bioinformatics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/bioinformatics\/article-pdf\/25\/14\/1822\/48992930\/bioinformatics_25_14_1822.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/bioinformatics\/article-pdf\/25\/14\/1822\/48992930\/bioinformatics_25_14_1822.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,1,31]],"date-time":"2023-01-31T21:21:55Z","timestamp":1675200115000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/bioinformatics\/article\/25\/14\/1822\/224771"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,5,12]]},"references-count":45,"journal-issue":{"issue":"14","published-print":{"date-parts":[[2009,7,15]]}},"URL":"https:\/\/doi.org\/10.1093\/bioinformatics\/btp310","relation":{},"ISSN":["1367-4811","1367-4803"],"issn-type":[{"value":"1367-4811","type":"electronic"},{"value":"1367-4803","type":"print"}],"subject":[],"published-other":{"date-parts":[[2009,7,15]]},"published":{"date-parts":[[2009,5,12]]}}}