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Frontiers of Mathematics in China

ISSN 1673-3452

ISSN 1673-3576(Online)

CN 11-5739/O1

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Front. Math. China    2023, Vol. 18 Issue (2) : 75-94    https://doi.org/10.3868/S140-DDD-023-0011-X
SURVEY　ARTICLE
Multiscale mathematical models for biological systems
Xiaoqiang SUN1(), Jiguang BAO2,3
1. School of Mathematics, Sun Yat-sen University, Guangzhou 510275, China
2. School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China
3. Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, China
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Abstract

Life activities are extremely complex phenomena in nature. From molecular signaling regulation to multi-cellular tissue formation and so on, the biological system consists of multiple temporal, spatial and functional scales. Multiscale mathematical models have extensive applications in life science research due to their capacity of appropriately simulating the complex multiscale biological systems. Many mathematical methods, including deterministic methods, stochastic methods as well as discrete or rule-based methods, have been widely used for modeling biological systems. However, the models at single scale are not sufficient to simulate complex biological systems. Therefore, in this paper we give a survey of two multiscale modeling approaches for biological systems. One approach is continuous stochastic method that couples ordinary differential equations and stochastic differential equations; Another approach is hybrid continuous-discrete method that couples agent-based model with partial differential equations. We then introduce the applications of these multiscale modeling approaches in systems biology and look ahead to the future research.
Keywords Multi-scale model      partial differential equations      agent-based model      systems biology     
Corresponding Author(s): Xiaoqiang SUN   
About author:

Peng Lei and Charity Ngina Mwangi contributed equally to this work.
Online First Date: 23 October 2023    Issue Date: 13 November 2023
 Cite this article:   
Xiaoqiang SUN,Jiguang BAO. Multiscale mathematical models for biological systems[J]. Front. Math. China, 2023, 18(2): 75-94.
 URL:  
https://academic.hep.com.cn/fmc/EN/10.3868/S140-DDD-023-0011-X
https://academic.hep.com.cn/fmc/EN/Y2023/V18/I2/75
Fig.1  Illustration of rules of migration of tip endothelial cells.
Fig.2  Flowchart of computational algorithm for multiscale PDE-Agent model.
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