描述生物系统中细胞活化的连贯建模程序

IF 0.3 Q4 MATHEMATICS
M. Scianna, A. Colombi
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引用次数: 2

摘要

生物系统通常由不同的细胞表型组成,具有特定的生物学特性和行为。特别是,细胞能够在内部或外部刺激下经历表型转变(即激活或分化)。为了考虑到这些现象,我们在这里提出了一个建模框架,在这个框架中,细胞集合可以根据它们的生物决定因素来集体描述(即,通过分布的质量密度)或单独描述(即,作为一组点/浓缩颗粒)。一套合适的规则包括引入细胞形状函数,然后定义了一个连贯的过程来模拟细胞激活机制,这意味着两种数学表示之间的切换。通过包括细胞迁移动力学和复制/凋亡过程,以及影响系统进化的选定扩散化学物质的动力学,描述细胞转变的理论环境得到了丰富。值得注意的是,我们的方法在所有类型的单元表示中提供了相同建模框架的一致性,因为它适合处理单个单元参数(即,单元尺寸和交互半径)到集体单元描述的经常模棱两可的转换。生物学相关的数值实现也被提出:特别是,它们处理细胞菌落内的表型转变和肿瘤球体的生长。这些现象构成的生物系统特别适合于评估所提出的模型的优点,并分析相关参数和赋予细胞形状功能的特定形式对细胞动力学的作用。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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.
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来源期刊
CiteScore
1.30
自引率
0.00%
发文量
3
审稿时长
16 weeks
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.
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