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U.S.A."],"published-print":{"date-parts":[[2026,6,9]]},"abstract":"<jats:p>Turing patterns are a cornerstone of biological self-organization, yet their emergence typically requires finely tuned parameters occupying narrow regions of high-dimensional space. This poses a fundamental challenge: how can evolving biological systems reliably find and exploit such rare conditions? In this work, we propose that common biochemical limit cycles, such as those arising from genetic feedback loops, can act as natural explorers of Turing space. By coupling a reaction\u2013diffusion system to an orbit that modulates some of its parameters, we show that the system can dynamically sweep through Turing-permissive regimes and generate transient spatial patterns. We use an entropy-based measure in Fourier space to quantify pattern formation and demonstrate how cycles enhance the detectability and robustness of Turing islands. We further explore how coupling to positional gradients increases reproducibility, suggesting a route from oscillatory dynamics to stable developmental programs. Our results highlight a powerful mechanism by which nature might bootstrap complex spatial structure from simple temporal motifs.<\/jats:p>","DOI":"10.1073\/pnas.2536690123","type":"journal-article","created":{"date-parts":[[2026,6,4]],"date-time":"2026-06-04T15:54:47Z","timestamp":1780588487000},"update-policy":"https:\/\/doi.org\/10.1073\/pnas.cm10313","source":"Crossref","is-referenced-by-count":1,"title":["How nature discovers rare Turing islands: Exploration by common limit cycles"],"prefix":"10.1073","volume":"123","author":[{"ORCID":"https:\/\/orcid.org\/0009-0005-4774-1978","authenticated-orcid":false,"given":"Seyoon","family":"Kim","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/041kmwe10","id-type":"ROR","asserted-by":"publisher"}],"name":"Department of Life Sciences & Centre for Integrative Systems Biology and Bioinformatics, Imperial College London","place":["London, United Kingdom"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0001-8455-8903","authenticated-orcid":false,"given":"Antonio","family":"Matas-Gil","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/041kmwe10","id-type":"ROR","asserted-by":"publisher"}],"name":"Department of Life Sciences & Centre for Integrative Systems Biology and Bioinformatics, Imperial College London","place":["London, United Kingdom"]},{"id":[{"id":"https:\/\/ror.org\/02jx3x895","id-type":"ROR","asserted-by":"publisher"}],"name":"Division of Infection and Immunity & Institute for the Physics of Living Systems, University College London","place":["London, United Kingdom"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1379-659X","authenticated-orcid":false,"given":"Robert G.","family":"Endres","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/041kmwe10","id-type":"ROR","asserted-by":"publisher"}],"name":"Department of Life Sciences & Centre for Integrative Systems Biology and Bioinformatics, Imperial College London","place":["London, United Kingdom"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"341","published-online":{"date-parts":[[2026,6,4]]},"reference":[{"key":"e_1_3_4_1_2","doi-asserted-by":"publisher","DOI":"10.1098\/rstb.1952.0012"},{"key":"e_1_3_4_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.xcrp.2025.103056"},{"key":"e_1_3_4_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cels.2019.07.007"},{"key":"e_1_3_4_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/0092-8674(88)90183-3"},{"key":"e_1_3_4_5_2","doi-asserted-by":"publisher","DOI":"10.1126\/science.1252960"},{"key":"e_1_3_4_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-5193(69)80016-0"},{"key":"e_1_3_4_7_2","doi-asserted-by":"publisher","DOI":"10.1038\/35002125"},{"key":"e_1_3_4_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cels.2024.11.002"},{"key":"e_1_3_4_9_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF00289234"},{"key":"e_1_3_4_10_2","doi-asserted-by":"publisher","DOI":"10.7554\/eLife.14022"},{"key":"e_1_3_4_11_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11538-018-0535-y"},{"key":"e_1_3_4_12_2","doi-asserted-by":"crossref","unstructured":"M. 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