{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:39:15Z","timestamp":1760060355495,"version":"build-2065373602"},"reference-count":39,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2025,8,23]],"date-time":"2025-08-23T00:00:00Z","timestamp":1755907200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62203064"],"award-info":[{"award-number":["62203064"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In biochemical reaction control loops, the fast response and accuracy of the system are often at odds with stability. Especially when the system faces external changes in different situations, the control system needs to be more robust. To address this problem, a novel ultrasensitive quasi-fuzzy proportional integral (QFPI) molecular controller using a covalent modification cycle is designed. The quasi-fuzzy control performance is achieved through a symmetric dual-rail covalent modification cycle structure. It can effectively suppress the impact of external changes on the controlled process and overcome the limitation of finite-time regulation caused by substrate consumption. At the same time, the time performance of the controller is significantly improved by utilizing the fast response characteristics of the ultrasensitive response. Subsequently, a single-rail optimization of the chemical reaction network (CRN) of the QFPI controller is performed to design a modified ultrasensitive quasi-fuzzy PI (M-QFPI) molecular controller. The M-QFPI controller not only significantly reduces the number of chemical reactions required to implement the controller, but also effectively improves the temporal performance and robustness of the controller. Finally, the effectiveness of the ultrasensitive quasi-fuzzy PI molecular controller for the control of the phosphorylation reaction process is verified. The results show that the ultrasensitive quasi-fuzzy PI control strategy provides an effective solution for the co-optimization of response speed, robustness and stability.<\/jats:p>","DOI":"10.3390\/sym17091376","type":"journal-article","created":{"date-parts":[[2025,8,25]],"date-time":"2025-08-25T00:09:32Z","timestamp":1756080572000},"page":"1376","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Symmetric Ultrasensitive Quasi-Fuzzy Molecular Controller"],"prefix":"10.3390","volume":"17","author":[{"given":"Yunfeng","family":"Liu","sequence":"first","affiliation":[{"name":"College of Information Science and Technology, Bohai University, Jinzhou 121000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Liang","family":"Pang","sequence":"additional","affiliation":[{"name":"College of Information Engineering, Liaoning Vocational University of Technology, Jinzhou 121000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bowen","family":"Fan","sequence":"additional","affiliation":[{"name":"College of Information Science and Technology, Bohai University, Jinzhou 121000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jingwang","family":"Yao","sequence":"additional","affiliation":[{"name":"College of Information Engineering, Liaoning Vocational University of Technology, Jinzhou 121000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,8,23]]},"reference":[{"key":"ref_1","first-page":"0380","article-title":"Control theory meets synthetic biology","volume":"12","author":"Dy","year":"2016","journal-title":"J. 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