Flagellated and Ciliated Microswimmers

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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.