{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,2]],"date-time":"2026-01-02T17:07:26Z","timestamp":1767373646756},"reference-count":36,"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>Developing methods for understanding the connectivity of signalling pathways is a major challenge in biological research. For this purpose, mathematical models are routinely developed based on experimental observations, which also allow the prediction of the system behaviour under different experimental conditions. Often, however, the same experimental data can be represented by several competing network models.<\/jats:p>\n          <\/jats:sec>\n          <jats:sec>\n            <jats:title>Results<\/jats:title>\n            <jats:p>In this paper, we developed a novel mathematical model\/experiment design cycle to help determine the probable network connectivity by iteratively invalidating models corresponding to competing signalling pathways. To do this, we systematically design experiments <jats:italic>in silico<\/jats:italic> that discriminate best between models of the competing signalling pathways. The method determines the inputs and parameter perturbations that will differentiate best between model outputs, corresponding to what can be measured\/observed experimentally. We applied our method to the unknown connectivities in the chemotaxis pathway of the bacterium <jats:italic>Rhodobacter sphaeroides<\/jats:italic>. We first developed several models of <jats:italic>R. sphaeroides<\/jats:italic> chemotaxis corresponding to different signalling networks, all of which are biologically plausible. Parameters in these models were fitted so that they all represented wild type data equally well. The models were then compared to current mutant data and some were invalidated. To discriminate between the remaining models we used ideas from control systems theory to determine efficiently <jats:italic>in silico<\/jats:italic> an input profile that would result in the biggest difference in model outputs. However, when we applied this input to the models, we found it to be insufficient for discrimination <jats:italic>in silico<\/jats:italic>. Thus, to achieve better discrimination, we determined the best change in initial conditions (total protein concentrations) as well as the best change in the input profile. The designed experiments were then performed on live cells and the resulting data used to invalidate all but one of the remaining candidate models.<\/jats:p>\n          <\/jats:sec>\n          <jats:sec>\n            <jats:title>Conclusion<\/jats:title>\n            <jats:p>We successfully applied our method to chemotaxis in <jats:italic>R. sphaeroides<\/jats:italic> and the results from the experiments designed using this methodology allowed us to invalidate all but one of the proposed network models. The methodology we present is general and can be applied to a range of other biological networks.<\/jats:p>\n          <\/jats:sec>","DOI":"10.1186\/1752-0509-3-105","type":"journal-article","created":{"date-parts":[[2009,10,31]],"date-time":"2009-10-31T19:20:43Z","timestamp":1257016843000},"update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["A model invalidation-based approach for elucidating biological signalling pathways, applied to the chemotaxis pathway in R. sphaeroides"],"prefix":"10.1186","volume":"3","author":[{"given":"Mark AJ","family":"Roberts","sequence":"first","affiliation":[]},{"given":"Elias","family":"August","sequence":"additional","affiliation":[]},{"given":"Abdullah","family":"Hamadeh","sequence":"additional","affiliation":[]},{"given":"Philip K","family":"Maini","sequence":"additional","affiliation":[]},{"given":"Patrick E","family":"McSharry","sequence":"additional","affiliation":[]},{"given":"Judith P","family":"Armitage","sequence":"additional","affiliation":[]},{"given":"Antonis","family":"Papachristodoulou","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2009,10,31]]},"reference":[{"key":"373_CR1","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":"373_CR2","doi-asserted-by":"publisher","first-page":"E49","DOI":"10.1371\/journal.pbio.0020049","volume":"2","author":"CV Rao","year":"2004","unstructured":"Rao CV, Kirby JR, Arkin AP: Design and diversity in bacterial chemotaxis: a comparative study in Escherichia coli and Bacillus subtilis. PLoS Biol. 2004, 2: E49- 10.1371\/journal.pbio.0020049","journal-title":"PLoS Biol"},{"key":"373_CR3","doi-asserted-by":"publisher","first-page":"1147","DOI":"10.1038\/81125","volume":"18","author":"B Palsson","year":"2000","unstructured":"Palsson B: The challenges of in silico biology. Nat Biotech. 2000, 18: 1147-1150. 10.1038\/81125.","journal-title":"Nat Biotech"},{"key":"373_CR4","doi-asserted-by":"publisher","first-page":"923","DOI":"10.1111\/j.1742-4658.2008.06843.x","volume":"276","author":"K Clemens","year":"2009","unstructured":"Clemens K, Jens T: Systems biology: experimental design. FEBS Journal. 2009, 276: 923-942. 10.1111\/j.1742-4658.2008.06843.x","journal-title":"FEBS Journal"},{"key":"373_CR5","doi-asserted-by":"publisher","first-page":"886","DOI":"10.1111\/j.1742-4658.2008.06844.x","volume":"276","author":"A Maksat","year":"2009","unstructured":"Maksat A, Yves F-N, Jaap AK, Joke GB: Systems biology: parameter estimation for biochemical models. FEBS Journal. 2009, 276: 886-902. 10.1111\/j.1742-4658.2008.06844.x","journal-title":"FEBS Journal"},{"key":"373_CR6","doi-asserted-by":"crossref","DOI":"10.1201\/9781420011432","volume-title":"An introduction to systems biology: design principles of biological circuits","author":"U Alon","year":"2006","unstructured":"Alon U: An introduction to systems biology: design principles of biological circuits. 2006, Boca Raton, Fla; London: Chapman & Hall\/CRC"},{"key":"373_CR7","doi-asserted-by":"publisher","first-page":"132","DOI":"10.1186\/1471-2105-10-132","volume":"10","author":"J Anderson","year":"2009","unstructured":"Anderson J, Papachristodoulou A: On validation and invalidation of biological models. BMC Bioinformatics. 2009, 10: 132- 10.1186\/1471-2105-10-132","journal-title":"BMC Bioinformatics"},{"key":"373_CR8","doi-asserted-by":"publisher","first-page":"1773","DOI":"10.1101\/gr.1226004","volume":"14","author":"A Kremling","year":"2004","unstructured":"Kremling A, Fischer S, Gadkar K, Doyle FJ, Sauter T, Bullinger E, Allg\u00f6wer F, Gilles ED: A benchmark for methods in reverse engineering and model discrimination: Problem formulation and solutions. Genome Res. 2004, 14: 1773-1785. 10.1101\/gr.1226004","journal-title":"Genome Res"},{"key":"373_CR9","doi-asserted-by":"publisher","first-page":"e30","DOI":"10.1371\/journal.pcbi.0040030","volume":"4","author":"JF Apgar","year":"2008","unstructured":"Apgar JF, Toettcher JE, Endy D, White FM, Tidor B: Stimulus design for model selection and validation in cell signaling. PLoS Comput Biol. 2008, 4: e30- 10.1371\/journal.pcbi.0040030","journal-title":"PLoS Comput Biol"},{"key":"373_CR10","doi-asserted-by":"publisher","first-page":"1379","DOI":"10.1021\/ie0203025","volume":"42","author":"BH Chen","year":"2003","unstructured":"Chen BH, Asprey SP: On the design of optimally informative dynamic experiments for model discrimination in multiresponse nonlinear situations. Ind Eng Chem Res. 2003, 42: 1379-1390. 10.1021\/ie0203025.","journal-title":"Ind Eng Chem Res"},{"key":"373_CR11","doi-asserted-by":"publisher","first-page":"717","DOI":"10.1177\/0037549703040937","volume":"79","author":"D Faller","year":"2003","unstructured":"Faller D, Klingmuller U, Timmer J: Simulation Methods for Optimal Experimental Design in Systems Biology. SIMULATION. 2003, 79: 717-725. 10.1177\/0037549703040937.","journal-title":"SIMULATION"},{"key":"373_CR12","doi-asserted-by":"publisher","first-page":"9","DOI":"10.1002\/bies.20343","volume":"28","author":"M Baker","year":"2006","unstructured":"Baker M, Wolanin P, Stock JB: Signal transduction in bacterial chemotaxis. Bioessays. 2006, 28: 9-22. 10.1002\/bies.20343","journal-title":"Bioessays"},{"key":"373_CR13","doi-asserted-by":"publisher","first-page":"1024","DOI":"10.1038\/nrm1524","volume":"5","author":"GH Wadhams","year":"2004","unstructured":"Wadhams GH, Armitage JP: Making sense of it all: Bacterial chemotaxis. Nat Rev Mol Cell Biol. 2004, 5: 1024-1037. 10.1038\/nrm1524","journal-title":"Nat Rev Mol Cell Biol"},{"key":"373_CR14","doi-asserted-by":"publisher","first-page":"2327","DOI":"10.1021\/bi972330a","volume":"37","author":"V Sourjik","year":"1998","unstructured":"Sourjik V, Schmitt R: Phosphotransfer between CheA, CheY1, and CheY2 in the chemotaxis signal transduction chain of Rhizobium meliloti. Biochemistry. 1998, 37: 2327-2335. 10.1021\/bi972330a","journal-title":"Biochemistry"},{"key":"373_CR15","doi-asserted-by":"publisher","first-page":"763","DOI":"10.1046\/j.1365-2958.2003.03716.x","volume":"50","author":"GH Wadhams","year":"2003","unstructured":"Wadhams GH, Warren AV, Martin AC, Armitage JP: Targeting of two signal transduction pathways to different regions of the bacterial cell. Mol Microbiol. 2003, 50: 763-770. 10.1046\/j.1365-2958.2003.03716.x","journal-title":"Mol Microbiol"},{"key":"373_CR16","doi-asserted-by":"publisher","first-page":"35","DOI":"10.1016\/S0022-2836(02)01031-8","volume":"324","author":"SL Porter","year":"2002","unstructured":"Porter SL, Armitage JP: Phosphotransfer in Rhodobacter sphaeroides Chemotaxis. J Mol Biol. 2002, 324: 35-45. 10.1016\/S0022-2836(02)01031-8","journal-title":"J Mol Biol"},{"key":"373_CR17","doi-asserted-by":"publisher","first-page":"251","DOI":"10.1016\/j.tim.2008.02.006","volume":"16","author":"SL Porter","year":"2008","unstructured":"Porter SL, Wadhams GH, Armitage JP: Rhodobacter sphaeroides: complexity in chemotactic signalling. Trends Microbiol. 2008, 16: 251-260. 10.1016\/j.tim.2008.02.006","journal-title":"Trends Microbiol"},{"key":"373_CR18","volume-title":"Applied optimal control: optimization, estimation, and control. Revised printing edn","author":"AE Bryson","year":"1975","unstructured":"Bryson AE, Ho Y-C: Applied optimal control: optimization, estimation, and control. Revised printing edn. 1975, New York; London: Hemisphere"},{"key":"373_CR19","volume-title":"Feedback control theory","author":"JC Doyle","year":"1992","unstructured":"Doyle JC, Francis BA, Tannenbaum A: Feedback control theory. 1992, New York Toronto: Macmillan Pub. Co: Collier Macmillan Canada; Maxwell Macmillan International"},{"key":"373_CR20","volume-title":"Feedback control of dynamic systems","author":"GF Franklin","year":"2005","unstructured":"Franklin GF, Powell JD, Emami-Naeini A: Feedback control of dynamic systems. 2005, Upper Saddle River, NJ: Pearson Prentice Hall, 5","edition":"5"},{"key":"373_CR21","doi-asserted-by":"publisher","first-page":"32694","DOI":"10.1074\/jbc.M606016200","volume":"281","author":"SL Porter","year":"2006","unstructured":"Porter SL, Wadhams GH, Martin AC, Byles ED, Lancaster DE, Armitage JP: The CheYs of Rhodobacter sphaeroides. J Biol Chem. 2006, 281: 32694-32704. 10.1074\/jbc.M606016200","journal-title":"J Biol Chem"},{"key":"373_CR22","doi-asserted-by":"publisher","first-page":"5172","DOI":"10.1128\/JB.186.15.5172-5177.2004","volume":"186","author":"A Ferre","year":"2004","unstructured":"Ferre A, de la Mora J, Ballado T, Camarena L, Dreyfus G: Biochemical study of multiple CheY response regulators of the chemotactic pathway of Rhodobacter sphaeroides. J Bacteriol. 2004, 186: 5172-5177. 10.1128\/JB.186.15.5172-5177.2004","journal-title":"J Bacteriol"},{"key":"373_CR23","doi-asserted-by":"publisher","first-page":"875","DOI":"10.1089\/cmb.2008.0211","volume":"16","author":"E August","year":"2009","unstructured":"August E, Papachristodoulou A: A new computational tool for establishing model parameter identifiability. J Comput Biol. 2009, 16: 875-885. 10.1089\/cmb.2008.0211","journal-title":"J Comput Biol"},{"key":"373_CR24","doi-asserted-by":"publisher","first-page":"778","DOI":"10.1099\/00221287-22-3-778","volume":"22","author":"WR Sistrom","year":"1960","unstructured":"Sistrom WR: A requirement for sodium in the growth of Rhodopseudomonas spheroides. J Gen Microbiol. 1960, 22: 778-785.","journal-title":"J Gen Microbiol"},{"key":"373_CR25","doi-asserted-by":"publisher","first-page":"6613","DOI":"10.1128\/AEM.01587-09","volume":"75","author":"AC Ind","year":"2009","unstructured":"Ind AC, Porter SL, Brown MT, Byles ED, de Beyer JA, Godfrey SA, Armitage JP: Inducible-Expression Plasmid for Rhodobacter sphaeroides and Paracoccus denitrificans. Appl Environ Microbiol. 2009, 75: 6613-6615. 10.1128\/AEM.01587-09","journal-title":"Appl Environ Microbiol"},{"key":"373_CR26","doi-asserted-by":"publisher","first-page":"4667","DOI":"10.1128\/JB.185.16.4667-4671.2003","volume":"185","author":"AC Martin","year":"2003","unstructured":"Martin AC, Nair U, Armitage JP, Maddock JR: Polar Localization of CheA2 in Rhodobacter sphaeroides Requires Specific Che Homologs. J Bacteriol. 2003, 185: 4667-4671. 10.1128\/JB.185.16.4667-4671.2003","journal-title":"J Bacteriol"},{"key":"373_CR27","doi-asserted-by":"publisher","first-page":"168","DOI":"10.1038\/16483","volume":"397","author":"U Alon","year":"1999","unstructured":"Alon U, Surette MG, Barkai N, Leibler S: Robustness in bacterial chemotaxis. Nature. 1999, 397: 168-171. 10.1038\/16483","journal-title":"Nature"},{"key":"373_CR28","volume-title":"DPhil Thesis","author":"M Gould","year":"2006","unstructured":"Gould M: Chemotaxis gene expression in Rhodobacter sphaeroides WS8N. DPhil Thesis. 2006, University of Oxford"},{"key":"373_CR29","volume-title":"D Phil Thesis","author":"M Brown","year":"2009","unstructured":"Brown M: Control of the Unidirectional Motor in Rhodobacter sphaeroides. D Phil Thesis. 2009, University of Oxford"},{"key":"373_CR30","doi-asserted-by":"publisher","first-page":"42","DOI":"10.1016\/0005-2728(85)90080-5","volume":"806","author":"JP Armitage","year":"1985","unstructured":"Armitage JP, Evans MCW: Control of the protonmotive force in Rhodopseudomonas sphaeroides in the light and dark and its effect on the initiation of flagellar rotation. Biochim Biophys Acta. 1985, 806: 42-55. 10.1016\/0005-2728(85)90080-5.","journal-title":"Biochim Biophys Acta"},{"key":"373_CR31","doi-asserted-by":"publisher","first-page":"54573","DOI":"10.1074\/jbc.M408855200","volume":"279","author":"SL Porter","year":"2004","unstructured":"Porter SL, Armitage JP: Chemotaxis in Rhodobacter sphaeroides requires an atypical histidine protein kinase. J Biol Chem. 2004, 279: 54573-54580. 10.1074\/jbc.M408855200","journal-title":"J Biol Chem"},{"key":"373_CR32","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1186\/1752-0509-3-25","volume":"3","author":"E August","year":"2009","unstructured":"August E, Papachristodoulou A: Efficient, sparse biological network determination. BMC Syst Biol. 2009, 3: 25- 10.1186\/1752-0509-3-25","journal-title":"BMC Syst Biol"},{"key":"373_CR33","volume-title":"Robust and optimal control","author":"K Zhou","year":"1996","unstructured":"Zhou K, Doyle JC, Glover K: Robust and optimal control. 1996, Prentice-Hall, Inc"},{"key":"373_CR34","first-page":"473","volume":"53","author":"RE Sockett","year":"1990","unstructured":"Sockett RE, Foster JCA, Armitage JP: Molecular biology of the Rhodobacter sphaeroides flagellum. FEMS Symp. 1990, 53: 473-479.","journal-title":"FEMS Symp"},{"key":"373_CR35","doi-asserted-by":"publisher","first-page":"4601","DOI":"10.1093\/emboj\/19.17.4601","volume":"19","author":"DS Shah","year":"2000","unstructured":"Shah DS, Porter SL, Martin AC, Hamblin PA, Armitage JP: Fine tuning bacterial chemotaxis: analysis of Rhodobacter sphaeroides behaviour under aerobic and anaerobic conditions by mutation of the major chemotaxis operons and cheY genes. EMBO J. 2000, 19: 4601-4613. 10.1093\/emboj\/19.17.4601","journal-title":"EMBO J"},{"key":"373_CR36","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1016\/0378-1119(92)90263-O","volume":"118","author":"RJ Penfold","year":"1992","unstructured":"Penfold RJ, Pemberton JM: An improved suicide vector for construction of chromosomal insertion mutations in bacteria. Gene. 1992, 118: 145-146. 10.1016\/0378-1119(92)90263-O","journal-title":"Gene"}],"container-title":["BMC Systems Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/1752-0509-3-105.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,9,1]],"date-time":"2021-09-01T03:25:25Z","timestamp":1630466725000},"score":1,"resource":{"primary":{"URL":"https:\/\/bmcsystbiol.biomedcentral.com\/articles\/10.1186\/1752-0509-3-105"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,10,31]]},"references-count":36,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2009,12]]}},"alternative-id":["373"],"URL":"https:\/\/doi.org\/10.1186\/1752-0509-3-105","relation":{},"ISSN":["1752-0509"],"issn-type":[{"value":"1752-0509","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,10,31]]},"assertion":[{"value":"2 June 2009","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"31 October 2009","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"31 October 2009","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"105"}}