{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:51:47Z","timestamp":1760143907350,"version":"build-2065373602"},"reference-count":37,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2024,3,6]],"date-time":"2024-03-06T00:00:00Z","timestamp":1709683200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["12261028","11961018","12201110","ZDYF2021SHFZ231","120RC451","2019RC168","Qhys2023-117","Qhys2022-182","Qhys2022-183"],"award-info":[{"award-number":["12261028","11961018","12201110","ZDYF2021SHFZ231","120RC451","2019RC168","Qhys2023-117","Qhys2022-182","Qhys2022-183"]}]},{"name":"Hainan Province Science and Technology Special Fund","award":["12261028","11961018","12201110","ZDYF2021SHFZ231","120RC451","2019RC168","Qhys2023-117","Qhys2022-182","Qhys2022-183"],"award-info":[{"award-number":["12261028","11961018","12201110","ZDYF2021SHFZ231","120RC451","2019RC168","Qhys2023-117","Qhys2022-182","Qhys2022-183"]}]},{"name":"Natural Science Foundation of Hainan Province","award":["12261028","11961018","12201110","ZDYF2021SHFZ231","120RC451","2019RC168","Qhys2023-117","Qhys2022-182","Qhys2022-183"],"award-info":[{"award-number":["12261028","11961018","12201110","ZDYF2021SHFZ231","120RC451","2019RC168","Qhys2023-117","Qhys2022-182","Qhys2022-183"]}]},{"name":"Hainan Province Innovative Scientific Research Project for Graduate Students","award":["12261028","11961018","12201110","ZDYF2021SHFZ231","120RC451","2019RC168","Qhys2023-117","Qhys2022-182","Qhys2022-183"],"award-info":[{"award-number":["12261028","11961018","12201110","ZDYF2021SHFZ231","120RC451","2019RC168","Qhys2023-117","Qhys2022-182","Qhys2022-183"]}]},{"name":"Academician Shi Jianming Station of Hainan Province","award":["12261028","11961018","12201110","ZDYF2021SHFZ231","120RC451","2019RC168","Qhys2023-117","Qhys2022-182","Qhys2022-183"],"award-info":[{"award-number":["12261028","11961018","12201110","ZDYF2021SHFZ231","120RC451","2019RC168","Qhys2023-117","Qhys2022-182","Qhys2022-183"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Gene expression comprises many asymmetric and complex processes. Transcriptional details revealed by the whole genome indicate that genes resort to transcriptional bursting and accumulate molecular memory. However, it is still unclear how the interplay of transcriptional bursting and memory regulates robustness and expression noise. Here, we consider a model of multiple coupled processes of protein polymerization to focus on decoding the effect of molecular memory. Using non-Markovian transformation technology, we first define the memory index to measure the correlation window of expression to decipher the mechanism of regulation. The results indicate that memory from synthesis can amplify expression noise, while memory originating from polymerization can reduce the lower bound of the noise of gene products; that is, the memory from different sources plays distinct regulatory roles to induce non-symmetry. Moreover, it is counterintuitive that the dual regulation from memory and bursting expression can directly suppress system noise, violating the principle that transcriptional bursting enhances noise. Our results not only provide a theoretical framework for investigating the function of memory but also imply that expression noise is not part of a half-power relationship with, nor mediated by, memory.<\/jats:p>","DOI":"10.3390\/sym16030315","type":"journal-article","created":{"date-parts":[[2024,3,6]],"date-time":"2024-03-06T08:43:14Z","timestamp":1709714594000},"page":"315","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Molecular-Memory-Induced Counter-Intuitive Noise Attenuator in Protein Polymerization"],"prefix":"10.3390","volume":"16","author":[{"given":"Xiaojun","family":"Bai","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Hainan University, Haikou 570228, China"},{"name":"Key Laboratory of Engineering Modeling and Statistical Computation of Hainan Province, Hainan University, Haikou 570228, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sizhe","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Hainan University, Haikou 570228, China"},{"name":"The School of Mathematics, Tianjin University, Tianjin 300072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xin","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Hainan University, Haikou 570228, China"},{"name":"Key Laboratory of Engineering Modeling and Statistical Computation of Hainan Province, Hainan University, Haikou 570228, China"},{"name":"School of Cyberspace Security, Hainan University, Haikou 570228, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4451-8883","authenticated-orcid":false,"given":"Haohua","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Hainan University, Haikou 570228, China"},{"name":"Key Laboratory of Engineering Modeling and Statistical Computation of Hainan Province, Hainan University, Haikou 570228, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,3,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"112261","DOI":"10.1016\/j.chaos.2022.112261","article-title":"Stochastic analysis of a complex gene-expression model","volume":"160","author":"Chen","year":"2022","journal-title":"Chaos Solitons Fractals"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2060","DOI":"10.1093\/bioinformatics\/btq328","article-title":"CplexA: A Mathematica package to study macromolecular-assembly control of gene expression","volume":"26","author":"Vilar","year":"2010","journal-title":"Bioinformatics"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"657","DOI":"10.1016\/j.bbagrm.2012.03.004","article-title":"Complex dynamics of transcription regulation","volume":"1819","author":"Stavreva","year":"2012","journal-title":"Biochim. 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