Cell polarization requires redistribution of specific proteins to the nascent front and back of a eukaryotic cell. Among these proteins are Rac and Rho, members of the small GTPase family that regulate the actin cytoskeleton. Rac promotes actin assembly and protrusion of the front edge, whereas Rho activates myosin-driven contraction at the back. Mathematical models of cell polarization at many levels of detail have appeared. One of the simplest based on “wave-pinning” consists of a pair of reaction–diffusion equations for a single GTPase. Mathematical analysis of wave-pinning so far is largely restricted to static domains in one spatial dimension. Here, we extend the analysis to cells that change in size, showing that both shrinking and growing cells can lose polarity. We further consider the feedback between mechanical tension, GTPase activation, and cell deformation in both static, growing, shrinking, and moving cells. Special cases (spatially uniform cell chemistry, the absence or presence of mechanical feedback) are analyzed, and the full model is explored by simulations in 1D. We find a variety of novel behaviors, including “dilution-induced” oscillations of Rac activity and cell size, as well as gain or loss of polarization and motility in the model cell.

中文翻译：

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单细胞中的细胞大小、机械张力和 GTPase 信号传导

细胞极化需要将特定蛋白质重新分配到真核细胞的新生前部和后部。这些蛋白质中有 Rac 和 Rho，它们是调节肌动蛋白细胞骨架的小 GTPase 家族的成员。Rac 促进肌动蛋白组装和前缘突出，而 Rho 激活后部肌球蛋白驱动的收缩。在许多细节层次上的细胞极化的数学模型已经出现。一个最简单的基于“波钉扎”的方法由一对单个 GTPase 的反应扩散方程组成。迄今为止，波钉扎的数学分析主要限于一个空间维度的静态域。在这里，我们将分析扩展到大小发生变化的细胞，表明收缩和生长的细胞都会失去极性。我们进一步考虑了机械张力、GTPase 激活之间的反馈，以及静态、生长、收缩和移动细胞中的细胞变形。分析了特殊情况（空间均匀的细胞化学、机械反馈的缺失或存在），并通过 1D 模拟探索完整模型。我们发现了各种新的行为，包括“稀释诱导”的 Rac 活性和细胞大小的振荡，以及模型细胞中极化和运动的获得或损失。