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Shape, shear, search and strife; mathematical models of bacteria

形状、剪切、搜索和冲突；

基本信息

批准号：
2440854
负责人：
金额：
--
依托单位：
University of Liverpool
依托单位国家：
英国
项目类别：
Studentship
财政年份：
2020
资助国家：
英国
起止时间：
2020 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=studentship-2440854
关键词：
Shape shear search strife mathematical

项目摘要

Biological pattern formation is one of the most intriguing phenomena in nature. Simplestexamples of such patterns are represented by travelling waves and stationary periodic patternswhich occur during various biological processes including morphogenesis and populationdynamics. Formation of these patterns in populations of motile microorganisms such asDictyostelium discoideum and E. coli have been shown in several experimental studies.Conditions for formation of various types of patterns are commonly addressed in mathematicalstudies of dynamical systems containing diffusion and advection terms. In project,we show spatio-temporal patterns formed by growing populations of chemotactically activebacteria. First, we show formation of travelling wavefronts and Turing patterns in a one-speciespopulation. We show that Turing patterns form when bacteria produce chemical which is astrong attractant. We then move on to a system of two interacting bacterial populations, one ofwhich produces a chemotactic agent for another. Our analysis and numerical simulations showthat in this case Turing patterns form when the chemical acts as a repellent. Study of conditionsfor formation of Turing patterns is done using linear stability analysis while their characteristics(amplitude and wavelength) are found using Fourier series. Analytical results are also supportedby means of numerical simulations.

生物模式的形成是自然界最有趣的现象之一。这种模式的最简单的例子是行波和固定的周期性模式，它们发生在各种生物过程中，包括形态发生和种群动力学。在一些实验研究中，这些模式在活动微生物群体中形成，如盘状盘基架菌和大肠杆菌。各种型态形成的条件通常在包含扩散和平流项的动力系统的数学研究中讨论。在项目中，我们展示了由不断增长的趋化活性细菌群体形成的时空模式。首先，我们展示了在一个物种种群中行波前和图灵模式的形成。我们表明，当细菌产生一种强引诱剂的化学物质时，就会形成图灵模式。然后我们转向两个相互作用的细菌种群的系统，其中一个为另一个产生趋化剂。我们的分析和数值模拟表明，在这种情况下，当化学物质作为驱虫剂时，就会形成图灵图案。用线性稳定性分析来研究图灵图的形成条件，用傅立叶级数来确定图灵图的特征（振幅和波长）。数值模拟结果也支持了分析结果。