Flagella of eukaryotic cells are transient long cylindrical protrusions. The proteins needed to form and maintain flagella are synthesized in the cell body and transported to the distal tips. What `rulers' or `timers' a specific type of cells use to strike a balance between the outward and inward transport of materials so as to maintain a particular length of its flagella in the steady state is one of the open questions in cellular self-organization. Even more curious is how the two flagella of biflagellates, like Chlamydomonas Reinhardtii, communicate through their base to coordinate their lengths. In this paper we develop a stochastic model for flagellar length control based on a time-of-flight (ToF) mechanism. This ToF mechanism decides whether or not structural proteins are to be loaded onto an intraflagellar transport (IFT) train just before it begins its motorized journey from the base to the tip of the flagellum. Because of the ongoing turnover, the structural proteins released from the flagellar tip are transported back to the cell body also by IFT trains. We represent the traffic of IFT trains as a totally asymmetric simple exclusion process (TASEP). The ToF mechanism for each flagellum, together with the TASEP-based description of the IFT trains, combined with a scenario of sharing of a common pool of flagellar structural proteins in biflagellates, can account for all key features of experimentally known phenomena. These include ciliogenesis, resorption, deflagellation as well as regeneration after selective amputation of one of the two flagella. We also show that the experimental observations of Ishikawa and Marshall are consistent with the ToF mechanism of length control if the effects of the mutual exclusion of the IFT trains captured by the TASEP are taken into account. Moreover, we make new predictions on the flagellar length fluctuations and the role of the common pool.

中文翻译：

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双鞭毛真核生物的鞭毛长度控制：飞行时间、共享池、火车交通和合作现象

真核细胞的鞭毛是短暂的长圆柱形突起。形成和维持鞭毛所需的蛋白质在细胞体中合成并运输到远端。特定类型的细胞使用什么“统治者”或“计时器”来在物质的向外和向内运输之间取得平衡，以保持其鞭毛的特定长度处于稳定状态，这是细胞自学研究中的一个悬而未决的问题。组织。更奇怪的是双鞭毛虫的两个鞭毛，如莱茵衣藻，如何通过它们的基部交流以协调它们的长度。在本文中，我们开发了一种基于飞行时间 (ToF) 机制的鞭毛长度控制随机模型。这种 ToF 机制决定了结构蛋白是否要在鞭毛内运输 (IFT) 列车开始从基部到鞭毛尖端的机动旅程之前装载到该列车上。由于持续的周转，从鞭毛尖端释放的结构蛋白也通过 IFT 列车运输回细胞体。我们将 IFT 列车的流量表示为完全不对称的简单排除过程 (TASEP)。每个鞭毛的 ToF 机制，以及基于 TASEP 的 IFT 序列描述，结合共享双鞭毛藻中鞭毛结构蛋白公共池的场景，可以解释实验已知现象的所有关键特征。这些包括纤毛发生、再吸收、脱鞭毛以及选择性截肢两根鞭毛之一后的再生。我们还表明，如果考虑到 TASEP 捕获的 IFT 列车的互斥效应，Ishikawa 和 Marshall 的实验观察结果与长度控制的 ToF 机制是一致的。此外，我们对鞭毛长度波动和公共池的作用做出了新的预测。