We propose a model for cell polarization as a response to an external signal which results in a system of PDEs for different variants of a protein on the cell surface and interior respectively. We study stationary states of this model in certain parameter regimes in which several reaction rates on the membrane as well as the diffusion coefficient within the cell are large. It turns out that in suitable scaling limits steady states converge to solutions of some obstacle type problems. For these limiting problems we prove the onset of polarization if the total mass of protein is sufficiently small. For some variants we can even characterize precisely the critical mass for which polarization occurs.

中文翻译：

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用于细胞极化的体表面反应扩散系统

我们提出了一个细胞极化模型，作为对外部信号的响应，该模型分别导致细胞表面和内部蛋白质不同变体的 PDE 系统。我们在某些参数范围内研究该模型的稳态，其中膜上的几个反应速率以及细胞内的扩散系数很大。事实证明，在合适的缩放限制下，稳态收敛到一些障碍类型问题的解决方案。对于这些限制性问题，如果蛋白质的总质量足够小，我们证明了极化的开始。对于某些变体，我们甚至可以精确表征发生极化的临界质量。