论文标题
散装地面波钉模型的数值研究
Numerical investigations of the bulk-surface wave pinning model
论文作者
论文摘要
散装表面波钉模型是用于研究细胞极化的反应扩散系统。它是由表面反应扩散方程组成的，与具有非线性边界条件的散装扩散方程耦合。随着表面成分形成特定模式，细胞极化会产生。由于蛋白质在细胞内部的扩散速度要比膜上快得多，因此在文献中，蛋白质通常被认为在空间上是均匀的。 {\ re，可以将模型还原为单个表面方程}。但是，{\ re在实际应用程序中}在空间非均匀的散装组件中可能是要考虑的重要玩家。在本文中，我们通过数值计算研究了整体成分的作用，更具体地说，是不同的大量扩散率如何影响极化响应。我们发现，批量分量确实是{\ re确定表面极化响应}的关键因素。此外，对于某些几何形状，是散装组分的空间异质性触发了极化响应，这在还原模型中可能是不可能的。 在研究迁移细胞模型时，了解极化如何取决于大量扩散率可能至关重要。
The bulk-surface wave pinning model is a reaction-diffusion system for studying cell polarisation. It is constituted by a surface reaction-diffusion equation, coupled to a bulk diffusion equation with a non-linear boundary condition. Cell polarisation arises as the surface component develops specific patterns. Since proteins diffuse much faster in the cell interior than on the membrane, in the literature, the bulk component is often assumed to be spatially homogeneous. {\re Therefore, the model can be reduced to a single surface equation}. However, {\re in real applications} a spatially non-uniform bulk component might be an important player to take into account. In this paper, we study, through numerical computations, the role of the bulk component and, more specifically, how different bulk diffusion rates might affect the polarisation response. We find that the bulk component is indeed a key factor in {\re determining the surface polarisation response}. Moreover, for certain geometries, it is the spatial heterogeneity of the bulk component that triggers the polarisation response, which might not be possible in a reduced model. Understanding how polarisation depends on bulk diffusivity might be crucial when studying models of migrating cells, which are naturally subject to domain deformation.
