Cell polarity is an important cellular process that cells use for various cellular functions such as asymmetric division, cell migration, and directionality determination. In asymmetric cell division, a mother cell creates multiple polarities of various proteins simultaneously within her membrane and cytosol to generate two different daughter cells. The formation of multiple polarities in asymmetric cell division has been found to be controlled via the regulatory system by upstream polarity of the membrane to downstream polarity of the cytosol, which is involved in not only polarity establishment but also polarity positioning. However, the mechanism for polarity positioning remains unclear. In this study, we found a general mechanism and mathematical structure for the multiple streams of polarities to determine their relative position via conceptional models based on the biological example of the asymmetric cell division process of C. elegans embryo. Using conceptional modeling and model reductions, we show that the positional relation of polarities is determined by a contrasting role of regulation by upstream polarity proteins on the transition process of diffusion dynamics of downstream proteins. We analytically prove that our findings hold under the general mathematical conditions, suggesting that the mechanism of relative position between upstream and downstream dynamics could be understood without depending on a specific type of bio-chemical reaction, and it could be the universal mechanism in multiple streams of polarity dynamics of the cell.

中文翻译：

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向缓慢或快速扩散的过渡为电池中的同相或反相极性提供了一般属性。

细胞极性是细胞用于各种细胞功能（例如不对称分裂，细胞迁移和方向性确定）的重要细胞过程。在不对称细胞分裂中，母细胞同时在其膜和细胞质内产生多种极性的多种蛋白质，从而生成两个不同的子细胞。已经发现不对称细胞分裂中的多个极性的形成是通过调节系统通过膜的上游极性至胞质溶胶的下游极性来控制的，其不仅涉及极性的建立而且还涉及极性的定位。但是，极性定位的机制仍然不清楚。在这个研究中，我们基于秀丽隐杆线虫胚胎非对称细胞分裂过程的生物学实例，通过概念模型发现了多种极性流的通用机制和数学结构。使用概念建模和模型简化，我们表明极性的位置关系是由上游极性蛋白在下游蛋白扩散动力学过渡过程中的调控作用所决定的。我们通过分析证明，我们的发现在一般数学条件下成立，这表明可以理解上游和下游动力学之间相对位置的机制，而无需依赖特定类型的生化反应，并且它可能是多种流中的通用机制电池的极性动力学。