{"title":"A spatial measure-valued model for chemical reaction networks in heterogeneous systems","authors":"Lea Popovic, Amandine Veber","doi":"10.1214/22-aap1904","DOIUrl":null,"url":null,"abstract":"We propose a novel measure valued process which models the behaviour of chemical reaction networks in spatially heterogeneous systems. It models reaction dynamics between different molecular species and continuous movement of molecules in space. Reactions rates at a spatial location are proportional to the mass of different species present locally and to a location specific chemical rate, which may be a function of the local or global species mass as well. We obtain asymptotic limits for the process, with appropriate rescaling depending on the abundance of different molecular types. In particular, when the mass of some species in the scaling limit is discrete while the mass of the others is continuous, we obtain a new type of spatial random evolution process. This process can be shown, in some situations, to correspond to a measure-valued piecewise deterministic Markov process in which the discrete mass of the process evolves stochastically, and the continuous mass evolves in a deterministic way between consecutive jump times of the discrete part.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1214/22-aap1904","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 3
Abstract
We propose a novel measure valued process which models the behaviour of chemical reaction networks in spatially heterogeneous systems. It models reaction dynamics between different molecular species and continuous movement of molecules in space. Reactions rates at a spatial location are proportional to the mass of different species present locally and to a location specific chemical rate, which may be a function of the local or global species mass as well. We obtain asymptotic limits for the process, with appropriate rescaling depending on the abundance of different molecular types. In particular, when the mass of some species in the scaling limit is discrete while the mass of the others is continuous, we obtain a new type of spatial random evolution process. This process can be shown, in some situations, to correspond to a measure-valued piecewise deterministic Markov process in which the discrete mass of the process evolves stochastically, and the continuous mass evolves in a deterministic way between consecutive jump times of the discrete part.
期刊介绍:
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.