Mathematical Sciences: Studies in Pattern Formation and CellMovement

该项目是为理论和计算研究 图案形成和细胞运动，目的是（i） 阐明可以产生所观察到的 一系列的冷凝导致肱骨，桡骨和 尺骨和发育中的脊椎动物四肢的趾，（ii） 开发非相互作用细胞的微观模型， 动力学依赖于外部浓度场， 对这些场表现出各种行为反应，（iii） 发展人口水平的连续描述 这些细胞的行为，以及（iv）开发运动模型 密集的细胞聚集体。 首席研究员计划分析一个模型， 模式形成，包括细胞运动的随机 运动和趋化性，生产和扩散的 趋化性物种，和两种类型的细胞， 可相互转换的 一个主要目标是了解这些 过程相互作用产生空间模式。 分析和 数值计算将用于界定参数 模式可以在初始均匀的 组织，数值连续技术将用于 确定稳定模式如何依赖于参数。 的 其他进程的影响和各专门区域的作用 将在此背景下研究肢体。

This project is for theoretical and computational studies of pattern formation and cell movement with the aims of (i) elucidating the types of mechanisms that can produce the observed sequence of condensations leading to the humerus, the radius and ulna, and the digits in developing vertebrate limbs, (ii) developing microscopic models for non-interacting cells whose dynamics depend on external concentration fields and which exhibit various behavioral responses to these fields, (iii) developing continuum descriptions for the population-level behavior of such cells, and (iv) developing models for the motion of cells in dense aggregates. The principal investigator plans to analyze a model for pattern formation that incorporates cell movement by random motion and chemotaxis, the production and diffusion of the chemotatic species, and two types of cells that are interconvertible. A major objective is to understand how these processes interact to produce spatial patterns. Analysis and numerical computations will serve to delimit the parameter values for which pattern can develop in an initially-homogeneous tissue, and numerical continuation techniques will be used to determine how the stable patterns depend on parameters. The effects of other processes and the role of specialized regions of the limb will be investigated in this context.