Hydrodynamic forces shape eukaryotic microswimmers

Eukaryotic swimming cells encompass spermatozoa, algae and protozoa that use flagella or cilia for locomotion in aqueous environments. Their flexible appendages induce propulsive forces which are balanced by the viscous drag on the cells, thus leading to a directed swimming motion. We use our recently built database of cell motility (BOSO-Micro) and perform exploratory data analysis to address two questions of hydrodynamic optimality. We first examine the morphology of flexible flagella undergoing waving deformations and show that their amplitude-to-wavelength ratio is close to the one predicted theoretically to optimise the propulsion of active filaments. We then analyse ciliates, which achieve propulsion by the collective beating of short active cilia covering their surface. We show that the aspect ratios of ciliate cell bodies are close to the aspect ratio of an axisymmetric cell body predicted to minimise the viscous drag. Both results strongly suggest a crucial role played by hydrodynamic constraints, in particular viscous drag, in shaping eukaryotic swimming cells.