{"title":"描述生物系统中细胞活化的连贯建模程序","authors":"M. Scianna, A. Colombi","doi":"10.1515/caim-2017-0001","DOIUrl":null,"url":null,"abstract":"Abstract Biological systems are typically formed by different cell phenotypes, characterized by specific biological properties and behaviors. In particular, cells are able to undergo phenotypic transitions (i.e., activation or differentiation) upon internal or external stimuli. In order to take these phenomena into account, we here propose a modelling framework in which cell ensembles can be described collectively (i.e., through a distributed mass density) or individually (i.e., as a group of pointwise/concentrated particles) according to their biological determinants. A set of suitable rules involving the introduction of a cell shape function then defines a coherent procedure to model cell activation mechanisms, which imply a switch between the two mathematical representations. The theoretical environment describing cell transition is then enriched by including cell migratory dynamics and duplication/apoptotic processes, as well as the kinetics of selected diffusing chemicals inuencing the system evolution. Remarkably, our approach provides consistency of the same modeling framework across all types of cell representation, as it is suitable to cope with the often ambiguous translation of individual cell arguments (i.e., cell dimensions and interaction radii) into collective cell descriptions. Biologically relevant numerical realizations are also presented: in particular, they deal with phenotypic transitions within cell colonies and with the growth of a tumor spheroid. These phenomena constitute biological systems particularly suitable to assess the advantages of the proposed model and to analyze the role on cell dynamics both of relevant parameters and of the specific form given to the cell shape function.","PeriodicalId":37903,"journal":{"name":"Communications in Applied and Industrial Mathematics","volume":"8 1","pages":"1 - 22"},"PeriodicalIF":0.3000,"publicationDate":"2017-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"A coherent modeling procedure to describe cell activation in biological systems\",\"authors\":\"M. Scianna, A. Colombi\",\"doi\":\"10.1515/caim-2017-0001\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract Biological systems are typically formed by different cell phenotypes, characterized by specific biological properties and behaviors. In particular, cells are able to undergo phenotypic transitions (i.e., activation or differentiation) upon internal or external stimuli. In order to take these phenomena into account, we here propose a modelling framework in which cell ensembles can be described collectively (i.e., through a distributed mass density) or individually (i.e., as a group of pointwise/concentrated particles) according to their biological determinants. A set of suitable rules involving the introduction of a cell shape function then defines a coherent procedure to model cell activation mechanisms, which imply a switch between the two mathematical representations. The theoretical environment describing cell transition is then enriched by including cell migratory dynamics and duplication/apoptotic processes, as well as the kinetics of selected diffusing chemicals inuencing the system evolution. Remarkably, our approach provides consistency of the same modeling framework across all types of cell representation, as it is suitable to cope with the often ambiguous translation of individual cell arguments (i.e., cell dimensions and interaction radii) into collective cell descriptions. Biologically relevant numerical realizations are also presented: in particular, they deal with phenotypic transitions within cell colonies and with the growth of a tumor spheroid. These phenomena constitute biological systems particularly suitable to assess the advantages of the proposed model and to analyze the role on cell dynamics both of relevant parameters and of the specific form given to the cell shape function.\",\"PeriodicalId\":37903,\"journal\":{\"name\":\"Communications in Applied and Industrial Mathematics\",\"volume\":\"8 1\",\"pages\":\"1 - 22\"},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2017-03-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Communications in Applied and Industrial Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1515/caim-2017-0001\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Applied and Industrial Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/caim-2017-0001","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
A coherent modeling procedure to describe cell activation in biological systems
Abstract Biological systems are typically formed by different cell phenotypes, characterized by specific biological properties and behaviors. In particular, cells are able to undergo phenotypic transitions (i.e., activation or differentiation) upon internal or external stimuli. In order to take these phenomena into account, we here propose a modelling framework in which cell ensembles can be described collectively (i.e., through a distributed mass density) or individually (i.e., as a group of pointwise/concentrated particles) according to their biological determinants. A set of suitable rules involving the introduction of a cell shape function then defines a coherent procedure to model cell activation mechanisms, which imply a switch between the two mathematical representations. The theoretical environment describing cell transition is then enriched by including cell migratory dynamics and duplication/apoptotic processes, as well as the kinetics of selected diffusing chemicals inuencing the system evolution. Remarkably, our approach provides consistency of the same modeling framework across all types of cell representation, as it is suitable to cope with the often ambiguous translation of individual cell arguments (i.e., cell dimensions and interaction radii) into collective cell descriptions. Biologically relevant numerical realizations are also presented: in particular, they deal with phenotypic transitions within cell colonies and with the growth of a tumor spheroid. These phenomena constitute biological systems particularly suitable to assess the advantages of the proposed model and to analyze the role on cell dynamics both of relevant parameters and of the specific form given to the cell shape function.
期刊介绍:
Communications in Applied and Industrial Mathematics (CAIM) is one of the official journals of the Italian Society for Applied and Industrial Mathematics (SIMAI). Providing immediate open access to original, unpublished high quality contributions, CAIM is devoted to timely report on ongoing original research work, new interdisciplinary subjects, and new developments. The journal focuses on the applications of mathematics to the solution of problems in industry, technology, environment, cultural heritage, and natural sciences, with a special emphasis on new and interesting mathematical ideas relevant to these fields of application . Encouraging novel cross-disciplinary approaches to mathematical research, CAIM aims to provide an ideal platform for scientists who cooperate in different fields including pure and applied mathematics, computer science, engineering, physics, chemistry, biology, medicine and to link scientist with professionals active in industry, research centres, academia or in the public sector. Coverage includes research articles describing new analytical or numerical methods, descriptions of modelling approaches, simulations for more accurate predictions or experimental observations of complex phenomena, verification/validation of numerical and experimental methods; invited or submitted reviews and perspectives concerning mathematical techniques in relation to applications, and and fields in which new problems have arisen for which mathematical models and techniques are not yet available.