{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T02:41:22Z","timestamp":1775788882510,"version":"3.50.1"},"reference-count":56,"publisher":"The Royal Society","issue":"211","license":[{"start":{"date-parts":[[2024,2,1]],"date-time":"2024-02-01T00:00:00Z","timestamp":1706745600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/royalsociety.org\/-\/media\/journals\/author\/Licence-to-Publish-20062019-final.pdf"},{"start":{"date-parts":[[2024,2,1]],"date-time":"2024-02-01T00:00:00Z","timestamp":1706745600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/royalsociety.org\/journals\/ethics-policies\/data-sharing-mining\/"}],"funder":[{"DOI":"10.13039\/501100024023","name":"Korea Institute for Advanced Study","doi-asserted-by":"crossref","award":["CG035003"],"award-info":[{"award-number":["CG035003"]}],"id":[{"id":"10.13039\/501100024023","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100024023","name":"Korea Institute for Advanced Study","doi-asserted-by":"crossref","award":["CG076501"],"award-info":[{"award-number":["CG076501"]}],"id":[{"id":"10.13039\/501100024023","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["royalsocietypublishing.org"],"crossmark-restriction":true},"short-container-title":["J. R. Soc. Interface."],"published-print":{"date-parts":[[2024,2]]},"abstract":"<jats:p>In many living organisms displaying circadian rhythms, the intake of energy often occurs in a periodic manner. Glycolysis is a prototypical biochemical reaction that exhibits a self-sustained oscillation under continuous injection of glucose. Here we study the effect of periodic injection of glucose on the glycolytic oscillation from a dynamical systems perspective. In particular, we employ Goldbeter\u2019s allosteric model of phosphofructokinase as a model system for glycolytic oscillations, and explore the effect of periodic substrate influx of varying frequencies and amplitudes by building the phase diagrams of Lyapunov exponents and oscillatory periods. When the frequency of driving is tuned around the harmonic and sub\/super-harmonic conditions of the natural frequency, the system is entrained to a frequency-locked state, forming an entrainment band that broadens with an increasing amplitude of driving. On the other hand, if the amplitude is substantial, the system may transition, albeit infrequent, to a chaotic state which defies prediction of dynamical behaviour. Our study offers in-depth understandings into the controllability of glycolytic oscillation as well as explaining physical underpinnings that enable the synchronous oscillations among a dense population of cells.<\/jats:p>","DOI":"10.1098\/rsif.2023.0588","type":"journal-article","created":{"date-parts":[[2024,2,13]],"date-time":"2024-02-13T19:05:15Z","timestamp":1707851115000},"update-policy":"https:\/\/doi.org\/10.1098\/crossmark-policy","source":"Crossref","is-referenced-by-count":2,"title":["Glycolytic oscillations under periodic drivings"],"prefix":"10.1098","volume":"21","author":[{"given":"Pureun","family":"Kim","sequence":"first","affiliation":[{"name":"Korea Institute for Advanced Study, Seoul 02455, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4844-7237","authenticated-orcid":true,"given":"Changbong","family":"Hyeon","sequence":"additional","affiliation":[{"name":"Korea Institute for Advanced Study, Seoul 02455, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"175","published-online":{"date-parts":[[2024,2,14]]},"reference":[{"key":"e_1_3_9_2_2","volume-title":"Molecular biology of the cell","author":"Alberts B","year":"2008","unstructured":"Alberts B, Johnson A, Lewis J, Raff M, Roberts K, Walter P. 2008 Molecular biology of the cell, 5th edn. New York, NY: Garland Science.","edition":"5"},{"key":"e_1_3_9_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/0006-3002(57)90141-5"},{"key":"e_1_3_9_4_2","doi-asserted-by":"publisher","DOI":"10.1146\/annurev.bi.40.070171.001321"},{"key":"e_1_3_9_5_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.72.10.3829"},{"key":"e_1_3_9_6_2","doi-asserted-by":"publisher","DOI":"10.1152\/ajpendo.1992.262.6.E800"},{"key":"e_1_3_9_7_2","doi-asserted-by":"publisher","DOI":"10.2337\/diab.46.9.1375"},{"key":"e_1_3_9_8_2","doi-asserted-by":"publisher","DOI":"10.1529\/biophysj.104.049262"},{"key":"e_1_3_9_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0006-3495(72)86164-2"},{"key":"e_1_3_9_10_2","doi-asserted-by":"publisher","DOI":"10.1038\/46329"},{"key":"e_1_3_9_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0006-3495(02)75377-0"},{"key":"e_1_3_9_12_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.78.5.2952"},{"key":"e_1_3_9_13_2","doi-asserted-by":"publisher","DOI":"10.1111\/j.1742-4658.2005.04639.x"},{"key":"e_1_3_9_14_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.70.11.3255"},{"key":"e_1_3_9_15_2","doi-asserted-by":"publisher","DOI":"10.1242\/jeb.81.1.7"},{"key":"e_1_3_9_16_2","doi-asserted-by":"publisher","DOI":"10.1146\/annurev.bi.40.070171.001321"},{"key":"e_1_3_9_17_2","volume-title":"Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering","author":"Strogatz SH","year":"2014","unstructured":"Strogatz SH. 2014 Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering. Boulder, CO: Westview Press."},{"key":"e_1_3_9_18_2","doi-asserted-by":"crossref","unstructured":"Pikovsky A Rosenblum M Kurths J. 2002 Synchronization: a universal concept in nonlinear science. Cambridge UK: Cambridge University Press.","DOI":"10.1017\/CBO9780511755743"},{"key":"e_1_3_9_19_2","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511803260"},{"key":"e_1_3_9_20_2","doi-asserted-by":"publisher","DOI":"10.1111\/j.1432-1033.1968.tb00175.x"},{"key":"e_1_3_9_21_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-2836(63)80091-1"},{"key":"e_1_3_9_22_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-2836(65)80285-6"},{"key":"e_1_3_9_23_2","doi-asserted-by":"publisher","DOI":"10.1146\/annurev-biophys-050511-102222"},{"key":"e_1_3_9_24_2","doi-asserted-by":"publisher","DOI":"10.1110\/ps.03259908"},{"key":"e_1_3_9_25_2","doi-asserted-by":"publisher","DOI":"10.1038\/nature13001"},{"key":"e_1_3_9_26_2","doi-asserted-by":"publisher","DOI":"10.1021\/acs.chemrev.8b00760"},{"key":"e_1_3_9_27_2","doi-asserted-by":"publisher","DOI":"10.1021\/acs.jpcb.1c01325"},{"key":"e_1_3_9_28_2","doi-asserted-by":"publisher","DOI":"10.1021\/ja0425942"},{"key":"e_1_3_9_29_2","doi-asserted-by":"publisher","DOI":"10.1021\/bi9711184"},{"key":"e_1_3_9_30_2","doi-asserted-by":"publisher","DOI":"10.1016\/0022-2836(68)90051-X"},{"key":"e_1_3_9_31_2","doi-asserted-by":"publisher","DOI":"10.1111\/j.1432-1033.1978.tb12765.x"},{"key":"e_1_3_9_32_2","doi-asserted-by":"publisher","DOI":"10.1021\/bi00173a044"},{"key":"e_1_3_9_33_2","doi-asserted-by":"publisher","DOI":"10.1063\/5.0043671"},{"key":"e_1_3_9_34_2","first-page":"213","article-title":"Small denominators, I: mappings of the circumference into itself","volume":"46","author":"Arnold VI","year":"1965","unstructured":"Arnold VI. 1965 Small denominators, I: mappings of the circumference into itself. AMS Trans. Series 2 46, 213. (doi:10.1007\/BF00275153)","journal-title":"AMS Trans. Series 2"},{"key":"e_1_3_9_35_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.50.1637"},{"key":"e_1_3_9_36_2","doi-asserted-by":"publisher","DOI":"10.1063\/1.881047"},{"key":"e_1_3_9_37_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cels.2021.03.003"},{"key":"e_1_3_9_38_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.physd.2008.12.012"},{"key":"e_1_3_9_39_2","doi-asserted-by":"publisher","DOI":"10.1006\/jtbi.1995.0087"},{"key":"e_1_3_9_40_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0301-4622(96)02195-3"},{"key":"e_1_3_9_41_2","doi-asserted-by":"publisher","DOI":"10.1126\/science.1200705"},{"key":"e_1_3_9_42_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.79.22.6917"},{"key":"e_1_3_9_43_2","doi-asserted-by":"publisher","DOI":"10.1016\/0301-0082(87)90023-2"},{"key":"e_1_3_9_44_2","doi-asserted-by":"publisher","DOI":"10.1113\/JP285015"},{"key":"e_1_3_9_45_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ceca.2021.102469"},{"key":"e_1_3_9_46_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.bpj.2009.02.026"},{"key":"e_1_3_9_47_2","doi-asserted-by":"publisher","DOI":"10.1111\/j.1432-1033.1996.00238.x"},{"key":"e_1_3_9_48_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0006-3495(00)76667-7"},{"key":"e_1_3_9_49_2","doi-asserted-by":"publisher","DOI":"10.1111\/j.1574-6976.2006.00034.x"},{"key":"e_1_3_9_50_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41598-020-76242-8"},{"key":"e_1_3_9_51_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.0706089104"},{"key":"e_1_3_9_52_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.97.042209"},{"key":"e_1_3_9_53_2","doi-asserted-by":"publisher","DOI":"10.1038\/srep29584"},{"key":"e_1_3_9_54_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.febslet.2006.11.068"},{"key":"e_1_3_9_55_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00294-021-01214-y"},{"key":"e_1_3_9_56_2","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511628870"},{"key":"e_1_3_9_57_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02128237"}],"container-title":["Journal of The Royal Society Interface"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/royalsocietypublishing.org\/doi\/pdf\/10.1098\/rsif.2023.0588","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/royalsocietypublishing.org\/doi\/full-xml\/10.1098\/rsif.2023.0588","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/royalsocietypublishing.org\/doi\/pdf\/10.1098\/rsif.2023.0588","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,20]],"date-time":"2024-02-20T04:31:05Z","timestamp":1708403465000},"score":1,"resource":{"primary":{"URL":"https:\/\/royalsocietypublishing.org\/doi\/10.1098\/rsif.2023.0588"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,2]]},"references-count":56,"journal-issue":{"issue":"211","published-print":{"date-parts":[[2024,2]]}},"alternative-id":["10.1098\/rsif.2023.0588"],"URL":"https:\/\/doi.org\/10.1098\/rsif.2023.0588","relation":{"has-preprint":[{"id-type":"doi","id":"10.1101\/2023.10.08.561464","asserted-by":"object"}]},"ISSN":["1742-5662"],"issn-type":[{"value":"1742-5662","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,2]]},"assertion":[{"value":"2023-10-09","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2024-01-17","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2024-02-14","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"20230588"}}