Flagellated and Ciliated Microswimmers

真核生物的微游泳者通常用纤毛推进自己，纤毛状的结构像鞭子一样推动流体平行于细胞表面，或者鞭毛状的细丝状结构像蛇一样运动。事实上，真核生物的纤毛和鞭毛本质上具有相同的底层结构和活性蛋白质机制。从单细胞衣藻到多细胞团藻，许多长度尺度的微游泳者使用两到几千根纤毛在液体中游泳。对于有鞭毛的微游泳者来说，精子是一个典型的例子。在之前的资助期内，我们从理论上和数值上（“在计算机上”）研究了精子细胞在结构化、之字形微流体通道的强约束下的动力学，以及精子被拴在表面上的鞭毛跳动的动力学。精子在微通道中绕角游动的偏转角度与实验结果吻合较好。此外，模拟还揭示了拍型的重要作用。对栓住精子的节奏模式的分析揭示了二次谐波频率的重要贡献，这对转向很重要。对于多纤毛微游泳者，我们发现了一个复杂的动力学行为，它受身体周围流场和纤毛排列的影响。在接下来的资助期内，我们计划在理论和数值上研究复杂几何形状和不同节拍模式下的精子运动。特别是，我们将探讨二次谐波频率和拍幅在三维、化学梯度和受限几何中产生的运动的后果。此外，我们计划模拟多纤毛微型游泳者，类似于藻。最近的实验和初步模拟结果表明，纤毛的机械锚定对超时协调有很强的依赖性。重要的是，多纤毛微游泳者的游泳特性似乎强烈依赖于其元时间协调。我们将模拟具有不同类型的纤毛锚定的多纤毛微游泳者，以及控制和自组织的超时间协调。关键问题是游泳的方向和持久性，以及几个这样的微型游泳者的配对相互作用和集体行为。

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.