Multiscale mathematical models for biological systems

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.

Graphical abstract

Keywords

Multi-scale model / partial differential equations / agent-based model / systems biology

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 62273364, 11871070 & 11371060) and the Guangdong Basic and Applied Basic Research Foundation (2020B1515020047).

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