Mathematical Sciences: Mathematical Models in Cell and Development Biology

该项目涉及各种研究， 生物学中细胞和发育过程的模型。主要 本研究的目的是解释发育中细胞的模式形成 人口作为机械化学现象，可以随后 公式化为数学模型， 方程和有限差分方程。在这类早期的工作中， 研究者依赖于线性稳定性分析。他现在 建议使用非线性反应扩散型模型，并计划 使用计算和模拟。我们将讨论的问题 包括以下步骤： 1.上皮细胞的机械化学机制是什么？ 在胚胎发生过程中折叠 2.间充质细胞聚集的空间模式 建立？ 3.细胞运动背后的机械化学机制是什么？ 4.软体动物的壳和蝴蝶翅膀上的图案是如何形成的 下来了？ 该项目福尔斯属于一般广泛的数学建模领域， 生物现象，因此具有跨学科性质。的 本研究使用的工具包括实验室实验、数学 分析和计算。调查员是一位公认的受人尊敬的 资深研究员，有着出色的业绩记录。

This project involves various studies on developing analytical models for cellular and developmental processes in biology. The main goal of this research is to explain pattern formation in developing cell populations as mechanical-chemical phenomena that can subsequently be formulated as mathematical models involving partial differential equations and finite difference equations. In earlier work of this type the investigator relied on the linear stability analysis. He now proposes to use nonlinear reaction-diffusion type models, and plans to use computation and simulation. The questions that will be addressed include: 1. What are the mechanochemical mechanisms underlying epithelial folding during embryogenesis? 2. How are spatial patterns of mesenchymal cell aggregation established? 3. What is the mechanochemical mechanism underlying cell motion? 4. How are the patterns on mollusk shells and butterfly wings laid down? The project falls in the general broad area of mathematical modeling of biological phenomena and as such is of interdisciplinary nature. The tools used is this research include laboratory experiments, mathematical analysis and computing. The investigator is a well established respected senior researcher with an outstanding track record.