Aerospace & Mechanical Engineering, University of Southern California, Los Angeles, CA 90089, USA.
Mathematics, University of Michigan, Ann Arbor, MI 48109, USA.
J R Soc Interface. 2021 Jan;18(174):20200660. doi: 10.1098/rsif.2020.0660. Epub 2021 Jan 13.
Beating flagella exhibit a variety of synchronization modes. This synchrony has long been attributed to hydrodynamic coupling between the flagella. However, recent work with flagellated algae indicates that a mechanism internal to the cell, through the contractile fibres connecting the flagella basal bodies, must be at play to actively modulate flagellar synchrony. Exactly how basal coupling mediates flagellar coordination remains unclear. Here, we examine the role of basal coupling in the synchronization of the model biflagellate using a series of mathematical models of decreasing levels of complexity. We report that basal coupling is sufficient to achieve inphase, antiphase and bistable synchrony, even in the absence of hydrodynamic coupling and flagellar compliance. These modes can be reached by modulating the activity level of the individual flagella or the strength of the basal coupling. We observe a slip mode when allowing for differential flagellar activity, just as in experiments with live cells. We introduce a dimensionless ratio of flagellar activity to basal coupling that is predictive of the mode of synchrony. This ratio allows us to query biological parameters which are not yet directly measurable experimentally. Our work shows a concrete route for cells to actively control the synchronization of their flagella.
鞭毛表现出多种同步模式。这种同步性长期以来归因于鞭毛之间的水动力耦合。然而，最近对鞭毛藻类的研究表明，细胞内的一种机制，通过连接鞭毛基体的收缩纤维，必须发挥作用以主动调节鞭毛的同步性。基底连接如何介导鞭毛协调仍然不清楚。在这里，我们使用一系列简化程度不同的数学模型来研究模型双鞭毛中基底连接的作用。我们报告说，即使没有水动力耦合和鞭毛顺应性，基底连接也足以实现同相、反相和双稳态同步。这些模式可以通过调节单个鞭毛的活性水平或基底连接的强度来实现。当允许存在不同的鞭毛活性时，我们观察到滑动模式，就像在活细胞实验中一样。我们引入了一个无量纲的鞭毛活性与基底连接的比值，它可以预测同步模式。这个比值使我们能够查询生物参数，这些参数目前还不能通过实验直接测量。我们的工作为细胞主动控制其鞭毛的同步性提供了具体途径。
