趋化群体运动中的建模分析和计算

doi:10.12288/szjs.s2021-0737

趋化运动是细菌寻找食物、逃离有害物质的核心机制. 对于多细胞生物来说, 趋化运动对其发育和健康更是至关重要. 随着对趋化运动越来越多生物细节的理解, 其数学模型也越来越完备和复杂. 本文以大肠杆菌的趋化运动为例, 回顾了三个不同尺度的模型：上个世纪70年代提出的Keller-Segel模型, 80年代末提出的的速度跳跃模型以及本世纪初提出的含信号通路的动理学方程模型. 我们回顾近30年来这些模型提出的背景、建模思想、分析得到的关于解行为特性的一些主要结论, 以及相关数值算法, 并探讨不同尺度模型之间的联系和区别.

关键词： 趋化运动, 群体运动, Keller-Segel方程, 速度跳跃模型, 动理学方程, 含信号通路的动理学方程

Chemotaxis is the central mechanism for bacteria to find food and flee from poisons. In multicellular organisms, chemotaxis is critical for the development and health. Along with the understanding of more biological details of chemotaxis, the mathematical models become more complete and complex. We review three models for E.coli chemotaxis at different scales: the Keller-Segel model proposed in the 70’s last century, the velocity jump model given in the 90s and the pathway-based kinetic model proposed at the beginning of this century. We review the biological background of the proposed models, the modeling ideas, some main analytical results about the features of their solutions, the numerical methods and discuss about the connections and differences between models at different scales.

Key words: Chemotaxis, population level movement, Keller-Segel equation, velocity jump model, kinetic equation, Pathway-based kinetic equation

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摘要

趋化群体运动中的建模分析和计算

MODELING, ANALYSIS AND COMPUTATIONAL METHODS IN POPULATION LEVEL CHEMOTAXIS

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