Environmental influence on the pattern formation of collectively moving cells

研究领域：数学生物学这篇论文将致力于推导，研究和分析集体运动粒子的模型，如精子或其他细胞。我们将假设粒子可以自我推进，并且它们与复杂的异质环境相互作用。集体动力学研究当大量的行为体，如动物、人、微生物、晶体等，相互影响。一个特别关注的焦点是大规模秩序或模式的出现。著名的例子包括晶体中的全局排列、人的车道形成、细菌中的波和聚集、鱼群中的研磨或鸟类中的群集。我们考虑环境对动力学起重要作用的系统。一个例子是细胞，如成纤维细胞或入侵的癌细胞，通过由纤维和其他成分组成的组织移动。另一个例子是精子细胞通过女性生殖道移动并与目前的粘液相互作用。我们将假设环境被运动改变，反之亦然。在数学上，我们将从细胞和纤维的个体模型开始。这将形成基础，以获得平均场和宏观方程的密度和方向的细胞和纤维。我们将研究适当的缩放限制。我们将模拟基于个体的模型和连续模型，并比较行为。此外，我们将使用线性稳定性分析等工具来深入了解系统。如果可能的话，我们会将模型预测与细胞轨迹或精子数据等数据进行比较。

Research Area: Mathematical BiologyThe thesis will be devoted to deriving, studying and analysing models of collectively moving particles, such as sperm or other cells. We will assume that the particles can self-propel and that they interact with a complex, heterogeneous environment. Collective dynamics studies what happens when a large number of agents, such as animals, people, micro-organisms, crystals, etc., interact with each other. A particular focus is the emergence of large scale order or patterns. Famous examples include global alignment in crystals, lane formation for people, waves and aggregation in bacteria, milling in schools of fish or swarming in birds.We consider systems where the environment plays an important role for the dynamics. One example are cells, such as fibroblasts or invading cancer cells, moving through a tissue made up of fibres and other components. Another example are sperm cell moving through the female reproductive tract and interacting with the present mucus. We will assume the environment is modified by the movement and vice versa.Mathematically we will start with an individual based model for the cells and the fibres. This will form the basis to derive mean-field and macroscopic equations for the densities and directions of the cells and the fibres. We will examine appropriate scaling limits. We will simulate both the individual-based and continuum models and compare the behaviour. Additionally we will use tools such as linear stability analysis to gain insight into the system. If possible we will compare the model prediction with data such as cell tracks or sperm data.