Blebs are cell protrusions generated by local membrane–cortex detachments followed by expansion of the plasma membrane. Blebs are formed by some migrating cells, e.g. primordial germ cells of the zebrafish. While blebs occur randomly at each part of the membrane in unpolarized cells, a polarization process guarantees the occurrence of blebs at a preferential site and thereby facilitates migration toward a specified direction. Little is known about the factors involved in the controlled and directed bleb generation, yet recent studies revealed the influence of an intracellular flow and the stabilizing role of the membrane–cortex linker molecule Ezrin. Based on this information, we develop and analyse a coupled bulk-surface model describing a potential cellular mechanism by which a bleb could be induced at a controlled site. The model rests upon intracellular Darcy flow and a diffusion–advection–reaction system, describing the temporal evolution from a homogeneous to a strongly anisotropic Ezrin distribution. We prove the well-posedness of the mathematical model and show that simulations qualitatively correspond to experimental observations, suggesting that indeed the interaction of an intracellular flow with membrane proteins can be the cause of the Ezrin redistribution accompanying bleb formation.

中文翻译：

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斑马鱼原始生殖细胞泡调节的数学模型

泡是由局部膜-皮质脱离随后质膜扩张产生的细胞突起。水泡是由一些迁移细胞形成的，例如斑马鱼的原始生殖细胞。虽然气泡随机出现在未极化细胞的膜的每个部分，但极化过程可确保在优先位置出现气泡，从而促进向特定方向的迁移。人们对受控和定向泡生成所涉及的因素知之甚少，但最近的研究揭示了细胞内流动的影响和膜-皮质连接分子 Ezrin 的稳定作用。基于这些信息，我们开发并分析了一个耦合的体积表面模型，该模型描述了一种潜在的细胞机制，通过该机制可以在受控位置诱导水泡。该模型基于细胞内达西流和扩散-平流-反应系统，描述了从均匀到强各向异性 Ezrin 分布的时间演变。我们证明了数学模型的适定性，并表明模拟定性地对应于实验观察，表明细胞内流动与膜蛋白的相互作用确实可能是 Ezrin 重新分布伴随气泡形成的原因。