The biomechanical role of extra-axonemal structures in shaping the flagellar beat of Euglena

Giancarlo Cicconofri; Giovanni Noselli; Antonio DeSimone

Interestingly, the lack of symmetry of the spinning lasso beat produces swimming trajectories with rotations coupled with translations [25] . In turn, cell body rotations have a role in phototaxis (see Discussion and Outlook Section and [12] ). In the light of these observations, our analysis shows that the beat of the euglenid flagellum can be seen as an example of a biological function arising from the competition between antagonistic structural components. It is not dissimilar from the body-flagellum interaction in Trypanosoma, which generates 3d motility. But the principle is much more general in biology and many other examples can be found across kingdoms and species and at widely different scales. For instance in plants, a mechanism of seed dispersal arises from the mechanical competition between the two valves of the seed pods, see, e.g., [3] for Bauhinia variegata and [15] for Cardamine hirsuta. Contraction by antagonistic muscles is key for animal movement and, in particular, for the functioning of hydrostatic skeletons (used from wormlike invertebrates to arms and tentacles of cephalopods, to the trunk of elephants, see [16] ). A similar principle of antagonistic contraction along perpendicularly oriented families of fibers is at work at the sub-cellualr level, for example in the antagonistic motor protein dynamics in contractile ring structures important in cell division and development (see, e.g., [8] ). At the same sub-cellular scale, competing elastic forces arising from lipid-protein interactions are often crucial in determining the stability of complex shapes of the cellular membrane [31] , and in the case of the overall structure of the coronavirus envelope [29] .