{"title":"论一类迈克尔斯-门顿网络的稳定性","authors":"","doi":"10.1016/j.automatica.2024.111837","DOIUrl":null,"url":null,"abstract":"<div><p>We present a study of a class of closed Michaelis–Menten network models, which includes models of two categories of biochemical networks previously studied in the literature namely, processive and mixed mechanism phosphorylation futile cycle networks. The main focus of our study is on the uniqueness and stability of equilibrium points of this class of models. Firstly, we demonstrate that the total species concentration is a conserved quantity in models of this class. Next, we prove the existence of a unique positive equilibrium point in the set of points that correspond to a given total species concentration, using the intermediate value property of continuous functions. Finally, we demonstrate the asymptotic stability of this equilibrium point with respect to all initial conditions in the positive orthant that correspond to the same total species concentration as the equilibrium point, by constructing an appropriate Lyapunov function.</p></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":null,"pages":null},"PeriodicalIF":4.8000,"publicationDate":"2024-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the stability of a class of Michaelis–Menten networks\",\"authors\":\"\",\"doi\":\"10.1016/j.automatica.2024.111837\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We present a study of a class of closed Michaelis–Menten network models, which includes models of two categories of biochemical networks previously studied in the literature namely, processive and mixed mechanism phosphorylation futile cycle networks. The main focus of our study is on the uniqueness and stability of equilibrium points of this class of models. Firstly, we demonstrate that the total species concentration is a conserved quantity in models of this class. Next, we prove the existence of a unique positive equilibrium point in the set of points that correspond to a given total species concentration, using the intermediate value property of continuous functions. Finally, we demonstrate the asymptotic stability of this equilibrium point with respect to all initial conditions in the positive orthant that correspond to the same total species concentration as the equilibrium point, by constructing an appropriate Lyapunov function.</p></div>\",\"PeriodicalId\":55413,\"journal\":{\"name\":\"Automatica\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.8000,\"publicationDate\":\"2024-08-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Automatica\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0005109824003315\",\"RegionNum\":2,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"AUTOMATION & CONTROL SYSTEMS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Automatica","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0005109824003315","RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
On the stability of a class of Michaelis–Menten networks
We present a study of a class of closed Michaelis–Menten network models, which includes models of two categories of biochemical networks previously studied in the literature namely, processive and mixed mechanism phosphorylation futile cycle networks. The main focus of our study is on the uniqueness and stability of equilibrium points of this class of models. Firstly, we demonstrate that the total species concentration is a conserved quantity in models of this class. Next, we prove the existence of a unique positive equilibrium point in the set of points that correspond to a given total species concentration, using the intermediate value property of continuous functions. Finally, we demonstrate the asymptotic stability of this equilibrium point with respect to all initial conditions in the positive orthant that correspond to the same total species concentration as the equilibrium point, by constructing an appropriate Lyapunov function.
期刊介绍:
Automatica is a leading archival publication in the field of systems and control. The field encompasses today a broad set of areas and topics, and is thriving not only within itself but also in terms of its impact on other fields, such as communications, computers, biology, energy and economics. Since its inception in 1963, Automatica has kept abreast with the evolution of the field over the years, and has emerged as a leading publication driving the trends in the field.
After being founded in 1963, Automatica became a journal of the International Federation of Automatic Control (IFAC) in 1969. It features a characteristic blend of theoretical and applied papers of archival, lasting value, reporting cutting edge research results by authors across the globe. It features articles in distinct categories, including regular, brief and survey papers, technical communiqués, correspondence items, as well as reviews on published books of interest to the readership. It occasionally publishes special issues on emerging new topics or established mature topics of interest to a broad audience.
Automatica solicits original high-quality contributions in all the categories listed above, and in all areas of systems and control interpreted in a broad sense and evolving constantly. They may be submitted directly to a subject editor or to the Editor-in-Chief if not sure about the subject area. Editorial procedures in place assure careful, fair, and prompt handling of all submitted articles. Accepted papers appear in the journal in the shortest time feasible given production time constraints.