Flagellated and Ciliated Microswimmers

真核生物微泳者通常通过纤毛(毛发状结构)或鞭毛(细丝状结构)推进自己，纤毛呈鞭状运动，推动液体平行于细胞表面，鞭毛呈丝状结构，呈蛇状运动。事实上，真核生物纤毛和鞭毛具有基本相同的底层结构和活性蛋白机制。从单细胞衣藻到多细胞Volvox，许多长度鳞片的微型游泳者使用两到数千根纤毛在液体中游泳。对于有鞭毛的微游泳者来说，精子就是一个典型的例子。在之前的资助期间，我们已经从理论和数值上研究了精子细胞在有结构的、锯齿形的微流体通道的强烈限制下的动力学，以及拴在表面上的精子鞭毛节拍的动力学。精子在微通道中游过拐角的偏转角与实验结果吻合较好。此外，仿真还揭示了节拍模式的重要作用。对系系精子节拍模式的分析表明，二次谐波频率对控制精子很重要。对于多纤毛微体游泳者，我们发现了一种复杂的动力学行为，它受到身体周围的流场和纤毛排列的影响。在接下来的资助期间，我们计划对精子在复杂几何形状和不同节拍模式下的运动进行理论和数值研究。特别是，我们将探索二次谐波频率和拍幅对所产生的运动在三维、化学梯度和受限几何中的影响。此外，我们计划模拟多纤毛微型游泳者，类似于Volvox藻类。最近的实验和初步模拟结果表明，纤毛的机械锚定强烈依赖于亚时配位。重要的是，多纤毛微体游泳者的游泳性能似乎强烈地依赖于它的亚配位。我们将模拟具有不同类型纤毛锚定的多纤毛微游泳者，并具有受控和自组织的超时协调。关键问题是游泳的方向和持久性，但也是几个这样的微泳者的配对互动和集体行为。

Eukaryotic microswimmers often propel themselves with cilia, hair-like structures that perform a whip-like motion to propel fluid parallel to the cell surface, or with flagella, filament-like structures that display a snake-like motion. In fact, eukaryotic cilia and flagella have essentially the same underlying structure and active protein machinery. From unicellular Chlamydomonas to multicellular Volvox, microswimmers of many length scales use two to thousands of cilia to swim through the fluid. For flagellated microswimmers, sperm is a paradigmatic example.In the previous grant period, we have studied theoretically and numerically (“in silico'') the dynamics of sperm cells in strong confinement of structured, zigzag-shaped, microfluidic channels, as well as the dynamics of the flagellar beat of sperm tethered to a surface. The deflection angle of sperm swimming around corners in microchannels agrees well with experimental results. Furthermore, the simulations reveal an important role of the beat pattern. The analysis of the beat pattern of tethered sperm reveals a significant contribution of a second-harmonic frequency, which turns out to be important for steering. For multi-ciliated microswimmers, we find a complex dynamical behavior which is affected by the flow field around the body, and the cilia arrangement. In the next grant period, we plan to study theoretically and numerically the sperm motion in complex geometries and with different beat patterns. In particular, we will explore the consequences of a second harmonic frequency and the beat amplitude for the resulting motion in three dimensions, in chemical gradients, and in confined geometries.Furthermore, we plan to simulate multi-ciliated microswimmers, similar to Volvox algae. Recent experiments and preliminary simulation results indicate a strong dependence of metachronal coordination on mechanical anchoring of the cilia. Importantly, the swimming properties of a multi-ciliated microswimmer seem to strongly depend on its metachronal coordination. We will simulate multi-ciliated microswimmers with different types of cilia anchoring, and with both controlled and self-organized metachronal coordination. Key questions are the direction and persistence of swimming, but also pair- interactions and collective behavior of several such microswimmers.