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Sequestration can be described as a mode of inactivation of a given protein by its binding to a second protein to form a new complex. In this complexed form, the original protein is prevented from performing its specific functions and is thus rendered inactive. We study a mathematical model of the mammalian circadian clock with a protein sequestration motif, which generates one of the negative feedback loops that guarantees periodic behaviour. First, the motif permits a time-scale separation, which can be used to simplify the model. We show that the simplified model admits a periodic orbit over a fairly large region of parameters. Second, we are able to show that the sequestration motif induces a phase response curve with a very specific form, implying that external perturbations can affect the system only in a narrow window of the periodic orbit. Finally, we compare our model with a classic Goodwin oscillator, to illustrate the dynamical and robustness properties induced by the protein sequestration motif.<\/jats:p>","DOI":"10.1098\/rsfs.2025.0008","type":"journal-article","created":{"date-parts":[[2025,8,22]],"date-time":"2025-08-22T07:05:13Z","timestamp":1755846313000},"update-policy":"https:\/\/doi.org\/10.1098\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Circadian clock model with sequestration repression motif: existence of periodic orbits and entrainment properties"],"prefix":"10.1098","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0009-0000-7865-8740","authenticated-orcid":true,"given":"Benjamin","family":"B\u00f6bel","sequence":"first","affiliation":[{"name":"Universit\u00e9 C\u00f4te d'Azur, Inria, CNRS, INRAE, Team Macbes","place":["Sophia Antipolis, France"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0647-9254","authenticated-orcid":true,"given":"Madalena","family":"Chaves","sequence":"additional","affiliation":[{"name":"Universit\u00e9 C\u00f4te d'Azur, Inria, CNRS, INRAE, Team Macbes","place":["Sophia Antipolis, France"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7156-7934","authenticated-orcid":true,"given":"Jean-Luc","family":"Gouz\u00e9","sequence":"additional","affiliation":[{"name":"Universit\u00e9 C\u00f4te d'Azur, Inria, CNRS, INRAE, Team Macbes","place":["Sophia Antipolis, France"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"175","published-online":{"date-parts":[[2025,8,22]]},"reference":[{"key":"e_1_3_8_2_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41580-019-0179-2"},{"key":"e_1_3_8_3_2","doi-asserted-by":"publisher","DOI":"10.1038\/nrg.2016.150"},{"key":"e_1_3_8_4_2","doi-asserted-by":"publisher","DOI":"10.1101\/sqb.2015.80.027490"},{"key":"e_1_3_8_5_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41583-018-0026-z"},{"key":"e_1_3_8_6_2","doi-asserted-by":"publisher","DOI":"10.1098\/rspb.1995.0153"},{"key":"e_1_3_8_7_2","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pcbi.1008459"},{"key":"e_1_3_8_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.csbj.2021.08.051"},{"key":"e_1_3_8_9_2","doi-asserted-by":"publisher","DOI":"10.1529\/biophysj.104.058388"},{"key":"e_1_3_8_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jtbi.2019.110015"},{"key":"e_1_3_8_11_2","volume-title":"Molecular biology of the cell","author":"Alberts B","year":"2022","unstructured":"Alberts B. 2022 Molecular biology of the cell, 7th edn. 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