Tanasijević Ivan, Lauga Eric
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, United Kingdom.
Phys Rev E. 2021 Feb;103(2-1):022403. doi: 10.1103/PhysRevE.103.022403.
Cellular appendages conferring motility, such as flagella and cilia, are known to synchronise their periodic beats. The origin of synchronization is a combination of long-range hydrodynamic interactions with physical mechanisms allowing the phases of these biological oscillators to evolve. Two of such mechanisms have been identified by previous work, the elastic compliance of the periodic orbit or oscillations driven by phase-dependent biological forcing, both of which can lead generically to stable phase locking. In order to help uncover the physical mechanism for hydrodynamic synchronization most essential overall in biology, we theoretically investigate in this paper the effect of strong confinement on the effectiveness of hydrodynamic synchronization. Following past work, we use minimal models of cilia where appendages are modeled as rigid spheres forced to move along circular trajectories near a rigid surface. Strong confinement is modeled by adding a second nearby surface, parallel to the first one, where the distance between the surfaces is much smaller than the typical distance between the cilia, which results in a qualitative change in the nature of hydrodynamic interactions. We calculate separately the impact of hydrodynamic confinement on the synchronization dynamics of the elastic compliance and the force modulation mechanisms and compare our results to the usual case with a single surface. Applying our results to the biologically relevant situation of nodal cilia, we show that force modulation is a mechanism that leads to phase-locked states under strong confinement that are very similar to those without confinement as a difference with the elastic compliance mechanism. Our results point therefore to the robustness of force modulation for synchronization, an important feature for biological dynamics that therefore suggests it could be the most essential physical mechanism overall in arrays of nodal cilia. We further examine the distinct biologically relevant situation of primary cilia and show in that case that the difference in robustness of the mechanisms is not as pronounced but still favors the force modulation.
已知赋予细胞运动能力的附属结构，如鞭毛和纤毛，会使其周期性搏动同步。同步的起源是长程流体动力学相互作用与使这些生物振荡器相位得以演化的物理机制的结合。先前的研究已经确定了其中两种机制，即周期轨道的弹性柔顺性或由相位依赖的生物驱动力驱动的振荡，这两种机制通常都能导致稳定的锁相。为了帮助揭示生物学中整体上最为关键的流体动力学同步的物理机制，我们在本文中从理论上研究了强约束对流体动力学同步有效性的影响。按照以往的研究，我们使用纤毛的最小模型，其中附属结构被建模为在刚性表面附近沿圆形轨迹运动的刚性球体。通过添加第二个与第一个平行的附近表面来模拟强约束，两个表面之间的距离远小于纤毛之间的典型距离，这导致流体动力学相互作用的性质发生了质的变化。我们分别计算了流体动力学约束对弹性柔顺性和力调制机制同步动力学的影响，并将我们的结果与单表面的通常情况进行比较。将我们的结果应用于节点纤毛的生物学相关情况，我们表明力调制是一种在强约束下导致锁相状态的机制，这些状态与无约束时的状态非常相似，这与弹性柔顺性机制不同。因此，我们的结果表明力调制对于同步具有稳健性，这是生物动力学的一个重要特征，因此表明它可能是节点纤毛阵列中整体上最为关键的物理机制。我们进一步研究了初级纤毛独特的生物学相关情况，并表明在这种情况下，机制稳健性的差异不那么明显，但仍然有利于力调制。
