Department of Finemechanics, Tohoku University, Sendai, Miyagi 9808579, Japan;
Department of Finemechanics, Tohoku University, Sendai, Miyagi 9808579, Japan.
Proc Natl Acad Sci U S A. 2020 Dec 1;117(48):30201-30207. doi: 10.1073/pnas.2011146117. Epub 2020 Nov 16.
Planktonic microorganisms are ubiquitous in water, and their population dynamics are essential for forecasting the behavior of global aquatic ecosystems. Their population dynamics are strongly affected by these organisms' motility, which is generated by their hair-like organelles, called cilia or flagella. However, because of the complexity of ciliary dynamics, the precise role of ciliary flow in microbial life remains unclear. Here, we have used ciliary hydrodynamics to show that ciliates acquire the optimal propulsion efficiency. We found that ciliary flow highly resists an organism's propulsion and that the swimming velocity rapidly decreases with body size, proportional to the power of minus two. Accordingly, the propulsion efficiency decreases as the cube of body length. By increasing the number of cilia, however, efficiency can be significantly improved, up to 100-fold. We found that there exists an optimal number density of cilia, which provides the maximum propulsion efficiency for all ciliates. The propulsion efficiency in this case decreases inversely proportionally to body length. Our estimated optimal density of cilia corresponds to those of actual microorganisms, including species of ciliates and microalgae, which suggests that now-existing motile ciliates and microalgae have survived by acquiring the optimal propulsion efficiency. These conclusions are helpful for better understanding the ecology of microorganisms, such as the energetic costs and benefits of multicellularity in Volvocaceae, as well as for the optimal design of artificial microswimmers.
浮游微生物在水中无处不在，它们的种群动态对于预测全球水生生态系统的行为至关重要。它们的种群动态受到这些生物的运动性的强烈影响，这些运动性是由它们的毛发状细胞器（称为纤毛或鞭毛）产生的。然而，由于纤毛动力学的复杂性，纤毛流在微生物生命中的精确作用仍然不清楚。在这里，我们利用纤毛水动力学来展示纤毛虫获得了最佳的推进效率。我们发现纤毛流强烈阻碍了生物体的推进，并且游泳速度随体型迅速减小，与功率的负二次方成正比。因此，推进效率随体长的立方减小。然而，通过增加纤毛的数量，可以显著提高效率，最高可达 100 倍。我们发现存在一个最佳的纤毛数量密度，它为所有纤毛虫提供了最大的推进效率。在这种情况下，推进效率与体长成反比。我们估计的最佳纤毛密度与实际微生物的密度相对应，包括纤毛虫和微藻的物种，这表明现有的游动纤毛虫和微藻已经通过获得最佳的推进效率而存活下来。这些结论有助于更好地理解微生物的生态学，例如 Volvocaceae 中的多细胞生物的能量成本和收益，以及人工微游泳者的最佳设计。
