Cell polarization is a multiphysics problem resulting from coupling protein pathways and cell morphological evolution. The most common example is asexual reproduction in budding yeast through Cdc42 and septin signals. However, how the interaction between the Cdc42-septin systems and the mechanical deformation of the cell surface is not well understood. To explore the interaction, we build a three-dimensional mechanochemical coupling framework to investigate the Cdc42-septin systems and elucidate how morphogenesis at the cell scale enhances the robustness of cell polarization in budding yeast. We utilize the viscous active shell model to describe the moving boundary of the cell surface, and the mechanochemical coupling is achieved through the introduction of cell surface mean curvature and active contraction-growth effects. With a normal effect of septin, numerical results demonstrate the budding processes with different transition shapes of budding profiles. On the other hand, the mechanochemical coupling problem with a weak effect of septin drives the emergence of wrinkles on the cell surface. We also apply linear perturbation analysis of the cell surface deformation to show how cell shape evolution is subjected to active contraction-growth effects. Our results show that a 3D coupled mechanochemical model can reproduce the budding morphology in yeast. Such a model provides a more comprehensive portrait of cell polarity and can be used to characterize both wild-type and mutant phenotypes such as septin mutants.

中文翻译：

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芽殖酵母细胞极化形态发生的机械化学模型

细胞极化是由蛋白质途径和细胞形态进化耦合产生的多物理问题。最常见的例子是芽殖酵母通过 Cdc42 和 septin 信号进行无性繁殖。然而，Cdc42-septin 系统与细胞表面机械变形之间的相互作用尚不清楚。为了探索这种相互作用，我们构建了一个三维机械化学耦合框架来研究 Cdc42-septin 系统，并阐明细胞尺度的形态发生如何增强芽殖酵母中细胞极化的鲁棒性。我们利用粘性活性壳模型来描述细胞表面的运动边界，并通过引入细胞表面平均曲率和主动收缩生长效应来实现力化学耦合。在septin的正常作用下，数值结果显示出芽过程具有不同的出芽轮廓过渡形状。另一方面，septin作用较弱的机械化学耦合问题导致细胞表面出现皱纹。我们还应用细胞表面变形的线性扰动分析来显示细胞形状演化如何受到主动收缩-生长效应的影响。我们的结果表明，3D 耦合机械化学模型可以重现酵母的出芽形态。这样的模型提供了细胞极性的更全面的描述，并且可用于表征野生型和突变体表型，例如septin突变体。