J. Stefan Institute, 1000 Ljubljana, Slovenia.
Proc Natl Acad Sci U S A. 2011 Sep 20;108(38):15727-32. doi: 10.1073/pnas.1107889108. Epub 2011 Sep 6.
We introduce a measure for energetic efficiency of biological cilia acting individually or collectively and numerically determine the optimal beating patterns according to this criterion. Maximizing the efficiency of a single cilium leads to curly, often symmetric, and somewhat counterintuitive patterns. However, when looking at a densely ciliated surface, the optimal patterns become remarkably similar to what is observed in microorganisms like Paramecium. The optimal beating pattern then consists of a fast effective stroke and a slow sweeping recovery stroke. Metachronal coordination is essential for efficient pumping and the highest efficiency is achieved with antiplectic waves. Efficiency also increases with an increasing density of cilia up to the point where crowding becomes a problem. We finally relate the pumping efficiency of cilia to the swimming efficiency of a spherical microorganism and show that the experimentally estimated efficiency of Paramecium is surprisingly close to the theoretically possible optimum.
我们提出了一种衡量单个或集体生物纤毛能量效率的方法，并根据这一标准数值确定了最优的拍打模式。最大化单个纤毛的效率会导致卷曲的、通常是对称的、有些反直觉的模式。然而，当观察到密集的纤毛表面时，最佳的模式变得与草履虫等微生物中观察到的非常相似。最优的拍打模式由一个快速有效的冲击和一个缓慢的扫动恢复冲程组成。同步协调对于有效的泵送是至关重要的，而最高的效率是通过反冲波实现的。效率也随着纤毛密度的增加而增加，直到拥挤成为一个问题。我们最后将纤毛的泵送效率与球形微生物的游动效率联系起来，并表明实验估计的草履虫效率惊人地接近理论上可能的最优值。
